Conflict thesis

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Conflict_thesis

The conflict thesis is a historiographical approach in the history of science that originated in the 19th century with John William Draper and Andrew Dickson White. It maintains that there is an intrinsic intellectual conflict between religion and science, and that it inevitably leads to hostility. The consensus among historians of science is that the thesis has long been discredited, which explains the rejection of the thesis by contemporary scholars. Into the 21st century, historians of science widely accept a complexity thesis.

Studies on scientists and the general public show that the conflict perspective is not prevalent.

Historical conflict thesis

Andrew Dickson White

 

John William Draper

Before the 19th century, no one had pitted "science" against "religion" or vice versa in writing. The relationship between religion and science became an actual formal topic of discourse in the 19th century. More specifically, it was around the mid-19th century that discussion of "science and religion" first emerged because before this time, the term science still included moral and metaphysical dimensions, was not inherently linked to the scientific method, and the term scientist did not emerge until 1834. The scientist John William Draper (1811–1882) and the writer Andrew Dickson White (1832–1918) were the most influential exponents of the conflict thesis between religion and science. Draper had been the speaker in the British Association meeting of 1860 which led to the famous confrontation between Bishop Samuel Wilberforce and Thomas Henry Huxley over Darwinism, and in America "the religious controversy over biological evolution reached its most critical stages in the late 1870s". In the early 1870s, the American science-popularizer Edward Livingston Youmans invited Draper to write a History of the Conflict Between Religion and Science (1874), a book replying to contemporary issues in Roman Catholicism, such as the doctrine of papal infallibility, and mostly criticizing what he claimed to be anti-intellectualism in the Catholic tradition, but also making criticisms of Islam and of Protestantism. Draper's preface summarises the conflict thesis:

The history of Science is not a mere record of isolated discoveries; it is a narrative of the conflict of two contending powers, the expansive force of the human intellect on one side, and the compression arising from traditionary faith and human interests on the other.

— John William Draper, History of the Conflict Religion, 1881

In 1874 White published his thesis in Popular Science Monthly and in book form as The Warfare of Science:

In all modern history, interference with science in the supposed interest of religion, no matter how conscientious such interference may have been, has resulted in the direst evils both to religion and to science—and invariably. And, on the other hand, all untrammeled scientific investigation, no matter how dangerous to religion some of its stages may have seemed, for the time, to be, has invariably resulted in the highest good of religion and of science.

— Andrew Dickson White, The Warfare of Science, 1876

Such thesis was not to be intended, as many successively did, as a statement of complete and necessary enmity between science and christianity at all times. On the contrary White asserted that numerous examples of support from christianity to science can be observed:

You will not understand me at all to say that religion has done nothing for science. It has done much for it. The work of Christianity has been mighty indeed. Through these two thousand years, despite the waste of its energies on all the things its Blessed Founder most earnestly condemned on fetich and subtlety and war and pomp it has undermined servitude, mitigated tyranny, given hope to the hopeless, comfort to the afflicted, light to the blind, bread to the starving, joy to the dying, and this work continues. And its work for science, too, has been great. It has fostered science often. Nay, it has nourished that feeling of self-sacrifice for human good, which has nerved some of the bravest men for these battles. Unfortunately, a devoted army of good men started centuries ago with the idea that independent scientific investigation is unsafe that theology must intervene to superintend its methods, and the Biblical record, as an historical compendium and scientific treatise, be taken as a standard to determine its results. So began this great modern war.

— Andrew Dickson White, The Warfare of Science, 1876

In 1896, White published A History of the Warfare of Science with Theology in Christendom, the culmination of over thirty years of research and publication on the subject, criticizing what he saw as restrictive, dogmatic forms of Christianity. In the introduction, White emphasized that he arrived at his position after the difficulties of assisting Ezra Cornell in establishing a university without any official religious affiliation.

The criticism of White is not entirely recent: historian of medicine James Joseph Walsh criticized White's perspective as anti-historical in The Popes and Science; the History of the Papal Relations to Science During the Middle Ages and Down to Our Own Time (1908), which he dedicated to Pope Pius X:

[T]he story of the supposed opposition of the Church and the Popes and the ecclesiastical authorities to science in any of its branches, is founded entirely on mistaken notions. Most of it is quite imaginary. Much of it is due to the exaggeration of the significance of the Galileo incident. Only those who know nothing about the history of medicine and of science continue to harbor it. That Dr. White's book, contradicted as it is so directly by all serious histories of medicine and of science, should have been read by so many thousands in this country, and should have been taken seriously by educated men, physicians, teachers, and even professors of science who want to know the history of their own sciences, only shows how easily even supposedly educated men may be led to follow their prejudices rather than their mental faculties, and emphasizes the fact that the tradition that there is no good that can possibly come out of the Nazareth of the times before the reformation, still dominates the intellects of many educated people who think that they are far from prejudice and have minds perfectly open to conviction.

— James Joseph Walsh, The Popes and Science; the History of the Papal Relations to Science During the Middle Ages and Down to Our Own Time, 1908

In God and Nature (1986), David Lindberg and Ronald Numbers report that "White's Warfare apparently did not sell as briskly as Draper's Conflict, but in the end it proved more influential, partly, it seems, because Draper's work was soon dated, and because White's impressive documentation gave the appearance of sound scholarship". During the 20th century, historians' acceptance of the conflict thesis declined until fully rejected in the 1970s. David B. Wilson notes:

Despite the growing number of scholarly modifications and rejections of the conflict model from the 1950s [...] in the 1970s leading historians of the nineteenth century still felt required to attack it. [...] Whatever the reason for the continued survival of the conflict thesis, two other books on the nineteenth century that were published in the 1970s hastened its final demise among historians of science [...] 1974 [...] Frank Turner [...] Between Science and Religion [...] Even more decisive was the penetrating critique "Historians and Historiography" [...] [by] James Moore [...] at the beginning of his Post-Darwinian Controversies (1979).

— David B. Wilson, The Historiography of Science and Religion, in Science & Religion: A Historical Introduction, 2002

In his course on science and religion, historian Lawrence Principe summarizes Draper's and White's works by saying:

While we can look today with astonishment upon the shoddy character of Draper and White's writings, their books have had enormous impact, and we can't deny that. Much of this is due to their great success in their creating a myth for science as a religion. Their myth of science as a religion is replete with battles, and martyrdoms, and saints, and creeds. And as we know, or should know, myths are often much more powerful than historical realities.

— Lawrence M. Principe, Science and Religion (2006), Lecture 2

In the coursebook, Principe writes:

No serious historians of science or of the science–religion issue today maintain the warfare thesis [...] The origins of the warfare thesis lie in the late 19th century, specifically in the work of two men – John William Draper and Andrew Dickson White. These men had specific political purposes in mind when arguing their case, and the historical foundations of their work are unreliable.

— Lawrence M. Principe, Science and Religion (2006)

Regarding the scholarship of Draper's work, Principe says:

How does he [John William Draper] support his contention of conflict? Well, unfortunately, with some of the worst historical writing you are ever likely to come across. Historical facts are confected, causes and chronologies twisted to the author's purpose. We find interpretations made merely by declaration. We find quotations violently taken out of context. And instances, quite a few of them where Draper claims a historical writer said something in fact 180 degrees away from what he actually claimed...Much of Draper's book is so ridiculous, so malodramatic, so rabid, it's hard for a knowledgeable person actually to read it without a wry smirk...Let's start with a simple and a notorious example: the idea that before Columbus people thought that the world was flat. Well, in fact, it is Draper and White, specifically, both of them, who bear most of the blame for popularizing this baseless view to the extent that nowadays, 80 percent of school teachers still foist this upon poor innocent school children. The fact is that of course the sphericity of the Earth was well established by the fifth century BC by the Greeks, and a good measure of its circumference made by the third century BC. And these facts were never forgotten in learned Western Culture.

— Lawrence M. Principe, Science and Religion (2006), Lecture 2

Principe's summary comment on Draper's work at the end of his coursebook reads: "The book that started the conflict myth. Take a sense of humor and/or a stiff drink with this dated bit of melodrama."

However, according to historian of science and religion James C. Ungureanu, Draper and White actually hoped their narratives would preserve religious belief, not remove it. For them, science was ultimately a scapegoat for a much older argument that dated back to the Protestant Reformation, where progressive and liberal theologies had their conflict with traditional and orthodox theologies. This would place the notion of "conflict" within the history of theological ideas.

Modern views

Academic

Historians of science today have moved away from a conflict model, which is based mainly on two historical episodes (those involving Galileo and Darwin) in favor of a "complexity" model, because religious figures took positions on both sides of each dispute and there was no overall aim by any party involved in discrediting religion. Biologist Stephen Jay Gould said: "White's and Draper's accounts of the actual interaction between science and religion in Western history do not differ greatly. Both tell a tale of bright progress continually sparked by science. And both develop and use the same myths to support their narrative, the flat-earth legend prominently among them". In a summary of the historiography of the conflict thesis, Colin A. Russell, the former President of Christians in Science, said that "Draper takes such liberty with history, perpetuating legends as fact that he is rightly avoided today in serious historical study. The same is nearly as true of White, though his prominent apparatus of prolific footnotes may create a misleading impression of meticulous scholarship".

In Science & Religion, Gary Ferngren proposes a complex relationship between religion and science:

While some historians had always regarded the Draper-White thesis as oversimplifying and distorting a complex relationship, in the late twentieth century it underwent a more systematic reevaluation. The result is the growing recognition among historians of science that the relationship of religion and science has been much more positive than is sometimes thought. Although popular images of controversy continue to exemplify the supposed hostility of Christianity to new scientific theories, studies have shown that Christianity has often nurtured and encouraged scientific endeavour, while at other times the two have co-existed without either tension or attempts at harmonization. If Galileo and the Scopes trial come to mind as examples of conflict, they were the exceptions rather than the rule.

— Gary Ferngren (editor). Science & Religion: A Historical Introduction, 2002

A few modern historians of science (such as Peter Barker, Bernard R. Goldstein, and Crosbie Smith) proposed that scientific discoveries – such as Kepler's laws of planetary motion in the 17th century, and the reformulation of physics in terms of energy, in the 19th century – were driven by religion. Religious organizations and clerics figure prominently in the broad histories of science, until the professionalization of the scientific enterprise, in the 19th century, led to tensions between scholars taking religious and secular approaches to nature. Even the prominent examples of religion's apparent conflict with science, the Galileo affair (1614) and the Scopes trial (1925), were not pure instances of conflict between science and religion, but included personal and political facts in the development of each conflict.

Galileo affair

Main article: Galileo affair

Galileo Before the Holy Office, a 19th-century painting by Joseph-Nicolas Robert-Fleury

The Galileo affair was a sequence of events that begin around 1610, culminating with the trial and house arrest of Galileo Galilei by the Roman Catholic Inquisition in 1633 for his support of heliocentrism. In 1610, Galileo published his Sidereus Nuncius (Starry Messenger), describing the surprising observations that he had made with the new telescope, namely the phases of Venus and the Galilean moons of Jupiter. With these observations he promoted the heliocentric theory of Nicolaus Copernicus (published in De revolutionibus orbium coelestium in 1543). Galileo's initial discoveries were met with opposition within the Catholic Church, and in 1616, the Inquisition declared heliocentrism to be formally heretical. Heliocentric books were banned and Galileo was ordered to refrain from holding, teaching or defending heliocentric ideas. Part of the verdict on Galileo read "[Heliocentrism] is foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture". Nonetheless, historians note that Galileo never did observe the earth's motion and lacked empirical proof at the time; and that he was placed under house arrest, not imprisoned by the Inquisition.

The affair is an example commonly used by advocates of the conflict thesis. Maurice Finocchiaro writes that the affair epitomizes the common view of "the conflict between enlightened science and obscurantist religion," and that this view promotes "the myth that alleges the incompatibility between science and religion." Finocchiaro writes, "I believe that such a thesis is erroneous, misleading, and simplistic," and refers to John Draper, Andrew White, Voltaire, Einstein, Bertrand Russell, and Karl Popper as writers or icons who have promoted it. Finocchiaro notes that the situation was complex and objections to the Copernican system included arguments that were philosophical and scientific, as well as theological.

Pope Urban VIII had been an admirer and supporter of Galileo, and there is evidence he did not believe the Inquisition's declaration rendered heliocentrism a heresy. Urban may have rather viewed heliocentrism as a potentially dangerous or rash doctrine that nevertheless had utility in astronomical calculations. In 1632, Galileo published his Dialogue Concerning the Two Chief World Systems, which implicitly defended heliocentrism, and was popular. Pope Urban VIII had asked that his own views on the matter be included in Galileo's book, and were voiced by a character named "Simplicio", who was a simpleton. This angered the Pope and weakened Galileo's position politically. Responding to mounting controversy over theology, astronomy and philosophy, the Roman Inquisition tried Galileo in 1633 and found him "vehemently suspect of heresy", sentencing him to house arrest. Galileo's Dialogue was banned and he was ordered to "abjure, curse and detest" heliocentric ideas. Galileo was kept under house arrest until his death in 1642.

Index Librorum Prohibitorum

Main article: Index Librorum Prohibitorum

In 1559, Pope Paul IV promulgated the Pauline Index which is also known as Index Librorum Prohibitorum. While it has been described by some as "the turning-point for the freedom of enquiry in the Catholic world", the effects of the Index were actually minimal and it was largely ignored. After less than a year, it was replaced by the Tridentine Index which relaxed aspects of the Pauline Index that had been criticized and had prevented its acceptance. It is inaccurate to describe the Index as being an enduring and definitive statement of Catholic censorship. It contained a list of "heretical" or "amoral" publications that were forbidden for Catholics to read or print and included not just heretics but anti-clerical authors and Protestant Christians.

Scientists and public perceptions

The conflict thesis is still held to be true in whole or in part by some scientists, including the theoretical physicist and cosmologist Stephen Hawking, who said "There is a fundamental difference between religion, which is based on authority, [and] science, which is based on observation and reason. Science will win because it works." Others, such as Steven Weinberg, grant that it is possible for science and religion to be compatible since some prominent scientists are also religious, but he sees some significant tensions that potentially weaken religious beliefs overall.

However, global studies on actual beliefs held by scientists show that most scientists do not subscribe to conflict perspective (only about 1⁄3 or less hold this view) and instead most believe that the relation is independence or collaboration between science and religion. As such, "the conflict perspective on science and religion is an invention of the West".

A study done on scientists from 21 American universities showed that most did not perceive conflict between science and religion either. In the study, the strength of religiosity in the home in which a scientist was raised, current religious attendance, peers' attitudes toward religion, all had an impact on whether or not scientists saw religion and science as in conflict. Scientists who had grown up with a religion and retained that identity or had identified as spiritual or had religious attendance tended to perceive less or no conflict. However, those not attending religious services were more likely to adopt a conflict paradigm. Additionally, scientists were more likely to reject conflict thesis if their peers held positive views of religion.

Science historian Ronald Numbers suggests though the conflict theory lingers in the popular mind due to few sets of controversies such as creation–evolution, stem cells, and birth control, he notes that the history of science reflects no intrinsic and inevitable conflict between religion and science. Many religious groups have made statements regarding the compatibility of religion and science, urging, for example, "school board members to preserve the integrity of the science curriculum by affirming the teaching of the theory of evolution as a core component of human knowledge. We ask that science remain science and that religion remain religion, two very different, but complementary, forms of truth." The Magis Center for Reason and Faith was founded specifically to apply science in support of belief in a deity and the Christian religion. Some scholars such as Brian Stanley and Denis Alexander propose that mass media are partly responsible for popularizing conflict theory, most notably the myth that prior to Columbus, people believed the Earth was flat. David C. Lindberg and Numbers point out that "there was scarcely a Christian scholar of the Middle Ages who did not acknowledge Earth's sphericity and even know its approximate circumference". Numbers gives the following as mistakes arising from conflict theory that have gained widespread currency: "the Church prohibited autopsies and dissections during the Middle Ages", "the rise of Christianity killed off ancient science", and "the medieval Christian church suppressed the growth of the natural sciences". Some Christian writers, notably Reijer Hooykaas and Stanley Jaki, have argued that Christianity was important, if not essential, for the rise of modern science. Lindberg and Numbers, however, believe this overstates the case for such a connection.

Research on perceptions of science among the American public concludes that most religious groups see no general epistemological conflict with science, and that they have no differences with nonreligious groups in propensity to seek out scientific knowledge, although there are often epistemic or moral conflicts when scientists make counterclaims to religious tenets. The Pew Center made similar findings and also noted that the majority of Americans (80–90 percent) strongly support scientific research, agree that science makes society and individual's lives better, and 8 in 10 Americans would be happy if their children were to become scientists. Even strict creationists tend to express very favorable views towards science. A study of US college students concluded that the majority of undergraduates in both the natural and social sciences do not see conflict between science and religion. Another finding in the study was that it is more likely for students to move from a conflict perspective to an independence or collaboration perspective than vice versa.

Some scientific topics like evolution are often seen as a "point of friction" even though there is widespread acceptance of evolution across all 20 countries with diverse religious backgrounds in one study. Age, rather than religion, correlates better on attitudes on relating to biotechnology.

Evolution strategy

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Evolution_strategy

In computer science, an evolution strategy (ES) is an optimization technique based on ideas of evolution. It belongs to the general class of evolutionary computation or artificial evolution methodologies.

History

The 'evolution strategy' optimization technique was created in the early 1960s and developed further in the 1970s and later by Ingo Rechenberg, Hans-Paul Schwefel and their co-workers.

Methods

Evolution strategies use natural problem-dependent representations, so problem space and search space are identical. In common with evolutionary algorithms, the operators are applied in a loop. An iteration of the loop is called a generation. The sequence of generations is continued until a termination criterion is met.

The special feature of the ES is the self-adaptation of mutation step sizes and the coevolution associated with it. The ES is briefly presented using the standard form, pointing out that there are many variants. The real-valued chromosome contains, in addition to the ${\displaystyle n}$ decision variables, ${\displaystyle n^{\prime }}$ mutation step sizes ${\displaystyle {\sigma }_j}$, where: ${\displaystyle 1\le j\le n^{\prime }\le n}$. Often one mutation step size is used for all decision variables or each has its own step size. Mate selection to produce ${\displaystyle \lambda }$ offspring is random, i.e. independent of fitness. First, new mutation step sizes are generated per mating by intermediate recombination of the parental ${\displaystyle {\sigma }_j}$ with subsequent mutation as follows:

${\displaystyle {\sigma }_j^{\prime }={\sigma }_j\cdot e^{(\mathcal{N}(0,1)-{\mathcal{N}}_j(0,1))}}$

where ${\displaystyle \mathcal{N}(0,1)}$ is a normally distributed random variable with mean ${\displaystyle 0}$ and standard deviation ${\displaystyle 1}$. ${\displaystyle \mathcal{N}(0,1)}$ applies to all ${\displaystyle {\sigma }_j^{\prime }}$, while ${\displaystyle {\mathcal{N}}_j(0,1)}$ is newly determined for each ${\displaystyle {\sigma }_j^{\prime }}$. Next, discrete recombination of the decision variables is followed by a mutation using the new mutation step sizes as standard deviations of the normal distribution. The new decision variables ${\displaystyle x_j^{\prime }}$ are calculated as follows:

${\displaystyle x_j^{\prime }=x_j+{\mathcal{N}}_j(0,{\sigma }_j^{\prime })}$

This results in an evolutionary search on two levels: First, at the problem level itself and second, at the mutation step size level. In this way, it can be ensured that the ES searches for its target in ever finer steps. However, there is also the danger of being able to skip larger invalid areas in the search space only with difficulty.

The ES knows two variants of best selection for the generation of the next parent population: In the ${\displaystyle (\mu ,\lambda )}$-ES, only the ${\displaystyle \mu }$ best offspring are used, whereas in the elitist ${\displaystyle (\mu +\lambda )}$-ES, the ${\displaystyle \mu }$ best are selected from parents and children.

Bäck and Schwefel recommend that the value of ${\displaystyle \lambda }$ should be seven times the population size ${\displaystyle \mu }$, whereby ${\displaystyle \mu }$ must not be chosen too small because of the strong selection pressure. Suitable values for ${\displaystyle \mu }$ are application-dependent and must be determined experimentally.

Individual step sizes for each coordinate, or correlations between coordinates, which are essentially defined by an underlying covariance matrix, are controlled in practice either by self-adaptation or by covariance matrix adaptation (CMA-ES). When the mutation step is drawn from a multivariate normal distribution using an evolving covariance matrix, it has been hypothesized that this adapted matrix approximates the inverse Hessian of the search landscape. This hypothesis has been proven for a static model relying on a quadratic approximation.

The selection of the next generation in evolution strategies is deterministic and only based on the fitness rankings, not on the actual fitness values. The resulting algorithm is therefore invariant with respect to monotonic transformations of the objective function. The simplest evolution strategy operates on a population of size two: the current point (parent) and the result of its mutation. Only if the mutant's fitness is at least as good as the parent one, it becomes the parent of the next generation. Otherwise the mutant is disregarded. This is a ${\displaystyle \mathit{(}\mathit{1}\mathit{+}\mathit{1}\mathit{)}}$-ES. More generally, ${\displaystyle \lambda }$ mutants can be generated and compete with the parent, called ${\displaystyle \mathit{(}\mathit{1}\mathit{+}\lambda \mathit{)}}$-ES. In ${\displaystyle (1,\lambda )}$-ES the best mutant becomes the parent of the next generation while the current parent is always disregarded. For some of these variants, proofs of linear convergence (in a stochastic sense) have been derived on unimodal objective functions.

Unconventional superconductor

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Unconventional_superconductor

Unconventional superconductors are materials that display superconductivity which is not explained by the usual BCS theory or its extension, the Eliashberg theory. The pairing in unconventional superconductors may originate from some other mechanism than the electron–phonon interaction. Alternatively, a superconductor is unconventional if the superconducting order parameter transforms according to a non-trivial irreducible representation of the point group or space group of the system. Per definition, superconductors that break additional symmetries to U (1) symmetry are known as unconventional superconductors.

History

The superconducting properties of CeCu₂Si₂, a type of heavy fermion material, were reported in 1979 by Frank Steglich. For a long time it was believed that CeCu₂Si₂ was a singlet d-wave superconductor, but since the mid-2010s, this notion has been strongly contested. In the early eighties, many more unconventional, heavy fermion superconductors were discovered, including UBe₁₃, UPt₃ and URu₂Si₂. In each of these materials, the anisotropic nature of the pairing was implicated by the power-law dependence of the nuclear magnetic resonance (NMR) relaxation rate and specific heat capacity on temperature. The presence of nodes in the superconducting gap of UPt₃ was confirmed in 1986 from the polarization dependence of the ultrasound attenuation.

The first unconventional triplet superconductor, organic material (TMTSF)₂PF₆, was discovered by Denis Jerome, Klaus Bechgaard and coworkers in 1980.^[10] Experimental works by Paul Chaikin's and Michael Naughton's groups as well as theoretical analysis of their data by Andrei Lebed have firmly confirmed unconventional nature of superconducting pairing in (TMTSF)₂X (X=PF₆, ClO₄, etc.) organic materials.

High-temperature singlet d-wave superconductivity was discovered by J.G. Bednorz and K.A. Müller in 1986, who also discovered that the lanthanum-based cuprate perovskite material LaBaCuO₄ develops superconductivity at a critical temperature (T_c) of approximately 35 K (-238 degrees Celsius). This was well above the highest critical temperature known at the time (T_c = 23 K), and thus the new family of materials was called high-temperature superconductors. Bednorz and Müller received the Nobel prize in Physics for this discovery in 1987. Since then, many other high-temperature superconductors have been synthesized.

LSCO (La_2−xSr_xCuO₄) was discovered the same year (1986). Soon after, in January 1987, yttrium barium copper oxide (YBCO) was discovered to have a T_c of 90 K, the first material to achieve superconductivity above the boiling point of liquid nitrogen (77 K). This was highly significant from the point of view of the technological applications of superconductivity because liquid nitrogen is far less expensive than liquid helium, which is required to cool conventional superconductors down to their critical temperature. In 1988 bismuth strontium calcium copper oxide (BSCCO) with T_c up to 107 K, and thallium barium calcium copper oxide (TBCCO) (T=thallium) with T_c of 125 K were discovered. The current record critical temperature is about T_c = 133 K (−140 °C) at standard pressure, and somewhat higher critical temperatures can be achieved at high pressure. Nevertheless, at present it is considered unlikely that cuprate perovskite materials will achieve room-temperature superconductivity.

On the other hand, other unconventional superconductors have been discovered. These include some that do not superconduct at high temperatures, such as strontium ruthenate Sr₂RuO₄, but that, like high-temperature superconductors, are unconventional in other ways. (For example, the origin of the attractive force leading to the formation of Cooper pairs may be different from the one postulated in BCS theory.) In addition to this, superconductors that have unusually high values of T_c but that are not cuprate perovskites have been discovered. Some of them may be extreme examples of conventional superconductors (this is suspected of magnesium diboride, MgB₂, with T_c = 39 K). Others could display more unconventional features.

In 2008 a new class that does not include copper (layered oxypnictide superconductors), for example LaOFeAs, was discovered. An oxypnictide of samarium seemed to have a T_c of about 43 K, which was higher than predicted by BCS theory. Tests at up to 45 T suggested the upper critical field of LaFeAsO_0.89F_0.11 to be around 64 T. Some other iron-based superconductors do not contain oxygen.

As of 2009, the highest-temperature superconductor (at ambient pressure) is mercury barium calcium copper oxide (HgBa₂Ca₂Cu₃O_x), at 138 K and is held by a cuprate-perovskite material, possibly 164 K under high pressure.

Other unconventional superconductors not based on cuprate structure have too been found. Some have unusually high values of the critical temperature, T_c, and hence they are sometimes also called high-temperature superconductors.

Graphene

In 2017, scanning tunneling microscopy and spectroscopy experiments on graphene proximitized to the electron-doped (non-chiral) d-wave superconductor Pr_2−xCe_xCuO₄ (PCCO) revealed evidence for an unconventional superconducting density of states induced in graphene. Publications in March 2018 provided evidence for unconventional superconducting properties of a graphene bilayer where one layer was offset by a "magic angle" of 1.1° relative to the other.

Ongoing research

While the mechanism responsible for conventional superconductivity is well described by the BCS theory, the mechanism for unconventional superconductivity is still unknown. After more than twenty years of intense research, the origin of high-temperature superconductivity is still not clear, being one of the major unsolved problems of theoretical condensed matter physics. It appears that unlike conventional superconductivity driven by electron-phonon attraction, genuine electronic mechanisms (such as antiferromagnetic correlations) are at play. Moreover, d-wave pairing, rather than s-wave, is significant.

One goal of much research is room-temperature superconductivity.

Despite intensive research and many promising leads, an explanation has so far eluded scientists. One reason for this is that the materials in question are generally very complex, multi-layered crystals (for example, BSCCO), making theoretical modeling difficult.

Possible mechanisms

The most controversial topic in condensed matter physics has been the mechanism for high-T_c superconductivity (HTS). There have been two representative theories on the HTS : (See also Resonating valence bond theory )

Weak-coupling theory

Firstly, it has been suggested that the HTS emerges by antiferromagnetic spin fluctuation in a doped system. According to this weak-coupling theory, the pairing wave function of the HTS should have a d_x²−y² symmetry. Thus, whether the symmetry of the pairing wave function is the d symmetry or not is essential to demonstrate on the mechanism of the HTS in respect of the spin fluctuation. That is, if the HTS order parameter (pairing wave function) does not have d symmetry, then a pairing mechanism related to spin fluctuation can be ruled out. The tunnel experiment (see below) seems to detect d symmetry in some HTS.

Interlayer coupling model

Secondly, there is the interlayer coupling model, according to which a layered structure consisting of BCS-type (s symmetry) superconductor can enhance the superconductivity by itself. By introducing an additional tunneling interaction between each layer, this model successfully explained the anisotropic symmetry of the order parameter in the HTS as well as the emergence of the HTS.

In order to solve this unsettled problem, there have been numerous experiments such as photoelectron spectroscopy, NMR, specific heat measurement, etc. Unfortunately, the results were ambiguous, where some reports supported the d symmetry for the HTS but others supported the s symmetry. This muddy situation possibly originated from the indirect nature of the experimental evidence, as well as experimental issues such as sample quality, impurity scattering, twinning, etc.

Superexchange

Promising experimental results from various researchers in September 2022, including Weijiong Chen, J.C. Séamus Davis and H. Eisiaki revealed that superexchange of electrons is possibly the most probable reason for high-temperature superconductivity.

Previous studies on the symmetry of the HTS order parameter

The symmetry of the HTS order parameter has been studied in nuclear magnetic resonance measurements and, more recently, by angle-resolved photoemission and measurements of the microwave penetration depth in a HTS crystal. NMR measurements probe the local magnetic field around an atom and hence reflect the susceptibility of the material. They have been of special interest for the HTS materials because many researchers have wondered whether spin correlations might play a role in the mechanism of the HTS.

NMR measurements of the resonance frequency on YBCO indicated that electrons in the copper oxide superconductors are paired in spin-singlet states. This indication came from the behavior of the Knight shift, the frequency shift that occurs when the internal field is different from the applied field: In a normal metal, the magnetic moments of the conduction electrons in the neighborhood of the ion being probed align with the applied field and create a larger internal field. As these metals go superconducting, electrons with oppositely directed spins couple to form singlet states. In the anisotropic HTS, perhaps NMR measurements have found that the relaxation rate for copper depends on the direction of the applied static magnetic field, with the rate being higher when the static field is parallel to one of the axes in the copper oxide plane. While this observation by some group supported the d symmetry of the HTS, other groups could not observe it.

Also, by measuring the penetration depth, the symmetry of the HTS order parameter can be studied. The microwave penetration depth is determined by the superfluid density responsible for screening the external field. In the s wave BCS theory, because pairs can be thermally excited across the gap Δ, the change in superfluid density per unit change in temperature goes as exponential behavior, exp(-Δ/k_BT). In that case, the penetration depth also varies exponentially with temperature T. If there are nodes in the energy gap as in the d symmetry HTS, electron pair can more easily be broken, the superfluid density should have a stronger temperature dependence, and the penetration depth is expected to increase as a power of T at low temperatures. If the symmetry is specially d_x²-y² then the penetration depth should vary linearly with T at low temperatures. This technique is increasingly being used to study superconductors and is limited in application largely by the quality of available single crystals.

Photoemission spectroscopy also could provide information on the HTS symmetry. By scattering photons off electrons in the crystal, one can sample the energy spectra of the electrons. Because the technique is sensitive to the angle of the emitted electrons one can determine the spectrum for different wave vectors on the Fermi surface. However, within the resolution of the angle-resolved photoemission spectroscopy (ARPES), researchers could not tell whether the gap goes to zero or just gets very small. Also, ARPES are sensitive only to the magnitude and not to the sign of the gap, so it could not tell if the gap goes negative at some point. This means that ARPES cannot determine whether the HTS order parameter has the d symmetry or not.

Junction experiment supporting the d-wave symmetry

There was a clever experimental design to overcome the muddy situation. An experiment based on pair tunneling and flux quantization in a three-grain ring of YBa₂Cu₃O₇ (YBCO) was designed to test the symmetry of the order parameter in YBCO.  Such a ring consists of three YBCO crystals with specific orientations consistent with the d-wave pairing symmetry to give rise to a spontaneously generated half-integer quantum vortex at the tricrystal meeting point. Furthermore, the possibility that junction interfaces can be in the clean limit (no defects) or with maximum zig-zag disorder was taken into account in this tricrystal experiment. A proposal of studying vortices with half magnetic flux quanta in heavy-fermion superconductors in three polycrystalline configurations was reported in 1987 by V. B. Geshkenbein, A. Larkin and A. Barone in 1987.

In the first tricrystal pairing symmetry experiment, the spontaneous magnetization of half flux quantum was clearly observed in YBCO, which convincingly supported the d-wave symmetry of the order parameter in YBCO. Because YBCO is orthorhombic, it might inherently have an admixture of s-wave symmetry. So, by tuning their technique further, it was found that there was an admixture of s-wave symmetry in YBCO within about 3%. Also, it was demonstrated by Tsuei, Kirtley et al. that there was a pure d_x²-y² order parameter symmetry in the tetragonal Tl₂Ba₂CuO₆.

History of superconductivity

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/History_of_superconductivity

The number of patent families (in red) and non-patent publications (in blue) about superconductivity by year. Also shown as black vertical lines are the main breakthroughs in the field.

Superconductivity is the phenomenon of certain materials exhibiting zero electrical resistance and the expulsion of magnetic fields below a characteristic temperature. The history of superconductivity began with Dutch physicist Heike Kamerlingh Onnes's discovery of superconductivity in mercury in 1911. Since then, many other superconducting materials have been discovered and the theory of superconductivity has been developed. These subjects remain active areas of study in the field of condensed matter physics.

The study of superconductivity has a fascinating history, with several breakthroughs having dramatically accelerated publication and patenting activity in this field, as shown in the figure on the right and described in details below. Throughout its 100+ year history the number of non-patent publications per year about superconductivity has been a factor of 10 larger than the number of patent families, which is characteristic of a technology, that has not achieved a substantial commercial success (see Technological applications of superconductivity).

With the help of the Van der Waals' equation of state, the critical-point parameters of gases could be accurately predicted from thermodynamic measurements made at much higher temperatures. Heike Kamerlingh Onnes was influenced by the work of Van der Waals.

In 1908, Heike Kamerlingh Onnes became the first to make liquid helium and this led directly to his 1911 discovery of superconductivity.

Heike Kamerlingh Onnes (right), the discoverer of superconductivity. Paul Ehrenfest, Hendrik Lorentz, Niels Bohr stand to his left.

Exploring ultra-cold phenomena (to 1908)

James Dewar initiated research into electrical resistance at low temperatures. Dewar and John Ambrose Fleming predicted that at absolute zero, pure metals would become perfect electromagnetic conductors (though, later, Dewar altered his opinion on the disappearance of resistance, believing that there would always be some resistance). Walther Hermann Nernst developed the third law of thermodynamics and stated that absolute zero was unattainable. Carl von Linde and William Hampson, both commercial researchers, nearly at the same time filed for patents on the Joule–Thomson effect for the liquefaction of gases. Linde's patent was the climax of 20 years of systematic investigation of established facts, using a regenerative counterflow method. Hampson's designs was also of a regenerative method. The combined process became known as the Hampson–Linde liquefaction process.

Onnes purchased a Linde machine for his research. On March 21, 1900, Nikola Tesla was granted a patent for the means for increasing the intensity of electrical oscillations by lowering the temperature, which was caused by lowered resistance. Within this patent it describes the increased intensity and duration of electric oscillations of a low temperature resonating circuit. It is believed that Tesla had intended that Linde's machine would be used to attain the cooling agents.

A milestone was achieved on July 10, 1908, when Heike Kamerlingh Onnes at Leiden University in the Netherlands produced, for the first time, liquified helium, which has a boiling point of 4.2 K (−269 °C) at atmospheric pressure.

Sudden and fundamental disappearance

Heike Kamerlingh Onnes and Jacob Clay reinvestigated Dewar's earlier experiments on the reduction of resistance at low temperatures. Onnes began the investigations with platinum and gold, replacing these later with mercury (a more readily refinable material). Onnes's research into the resistivity of solid mercury at cryogenic temperatures was accomplished by using liquid helium as a refrigerant. On April 8, 1911, 16:00 hours Onnes noted "Kwik nagenoeg nul", which translates as "[Resistance of] mercury almost zero." At the temperature of 4.19 K, he observed that the resistivity abruptly disappeared (the measuring device Onnes was using did not indicate any resistance). Onnes disclosed his research in 1911, in a paper titled "On the Sudden Rate at Which the Resistance of Mercury Disappears." Onnes stated in that paper that the "specific resistance" became thousands of times less in amount relative to the best conductor at ordinary temperature. Onnes later reversed the process and found that at 4.2 K, the resistance returned to the material. The next year, Onnes published more articles about the phenomenon. Initially, Onnes called the phenomenon "supraconductivity" (1913) and, only later, adopted the term "superconductivity." For his research, he was awarded the Nobel Prize in Physics in 1913.

Onnes conducted an experiment, in 1912, on the usability of superconductivity. Onnes introduced an electric current into a superconductive ring and removed the battery that generated it. Upon measuring the electric current, Onnes found that its intensity did not diminish with the time. The current persisted due to the superconductive state of the conductive medium.

In subsequent decades, superconductivity was found in several other materials; In 1913, lead at 7 K, in 1930's niobium at 10 K, and in 1941 niobium nitride at 16 K.

Enigmas and solutions (1933–1979)

The next important step in understanding superconductivity occurred in 1933, when Walther Meissner and Robert Ochsenfeld discovered that superconductors expelled applied magnetic fields, a phenomenon that has come to be known as the Meissner effect. In 1935, brothers Fritz London and Heinz London showed that the Meissner effect was a consequence of the minimization of the electromagnetic free energy carried by superconducting current.

In 1937, Lev Shubnikov discovered a new type of superconductors (later called type-II superconductors), that presented a mixed phase between ordinary and superconductive properties.

In 1950, the phenomenological Ginzburg–Landau theory of superconductivity was devised by Lev Landau and Vitaly Ginzburg. The Ginzburg–Landau theory, which combined Landau's theory of second-order phase transitions with a Schrödinger-like wave equation, had great success in explaining the macroscopic properties of superconductors. In particular, Alexei Abrikosov showed that Ginzburg–Landau theory predicts the division of superconductors into the two categories now referred to as type I and type II supeconductivity. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize in Physics for their work (Landau having died in 1968). Also in 1950, Emanuel Maxwell and, almost simultaneously, C.A. Reynolds et al. found that the critical temperature of a superconductor depends on the isotopic mass of the constituent element. This important discovery pointed to the electron-phonon interaction as the microscopic mechanism responsible for superconductivity.

On the experimental side, collaborations of Bernd T. Matthias in the 1950s with John Kenneth Hulm and Theodore H. Geballe, led to the discovery of hundreds of low temperature superconductors using a technique based on the Meissner effect. Due to his experience, he came up with Matthias' rules in 1954, a set of empirical guidelines on how to find these types of superconductors.

BCS theory

The complete microscopic theory of superconductivity was finally proposed in 1957 by John Bardeen, Leon N. Cooper, and Robert Schrieffer. This BCS theory explained the superconducting current as a superfluid of Cooper pairs, pairs of electrons interacting through the exchange of phonons. For this work, the authors were awarded the Nobel Prize in Physics in 1972. The BCS theory was set on a firmer footing in 1958, when Nikolay Bogolyubov showed that the BCS wavefunction, which had originally been derived from a variational argument, could be obtained using a canonical transformation of the electronic Hamiltonian. In 1959, Lev Gor'kov showed that the BCS theory reduced to the Ginzburg-Landau theory close to the critical temperature. Gor'kov was the first to derive the superconducting phase evolution equation ${\displaystyle 2eV=\hslash \frac{\mathrm{\partial }\varphi }{\mathrm{\partial }t}}$.

Little–Parks effect

The Little–Parks effect was discovered in 1962 in experiments with empty and thin-walled superconducting cylinders subjected to a parallel magnetic field. The electrical resistance of such cylinders shows a periodic oscillation with the magnetic flux through the cylinder, the period being h/2e = 2.07×10⁻¹⁵ V·s. The explanation provided by William Little and Ronald Parks is that the resistance oscillation reflects a more fundamental phenomenon, i.e. periodic oscillation of the superconducting critical temperature (T_c). This is the temperature at which the sample becomes superconducting. The Little-Parks effect is a result of collective quantum behavior of superconducting electrons. It reflects the general fact that it is the fluxoid rather than the flux which is quantized in superconductors. The Little-Parks effect demonstrates that the vector potential couples to an observable physical quantity, namely the superconducting critical temperature.

Commercial activity

Main article: Technological applications of superconductivity

Soon after discovering superconductivity in 1911, Kamerlingh Onnes attempted to make an electromagnet with superconducting windings but found that relatively low magnetic fields destroyed superconductivity in the materials he investigated. Much later, in 1955, George Yntema succeeded in constructing a small 0.7-tesla iron-core electromagnet with superconducting niobium wire windings. Then, in 1961, J. E. Kunzler, E. Buehler, F. S. L. Hsu, and J. H. Wernick made the startling discovery that at 4.2 kelvins, a compound consisting of three parts niobium and one part tin was capable of supporting a current density of more than 100,000 amperes per square centimeter in a magnetic field of 8.8 teslas. Despite being brittle and difficult to fabricate, niobium-tin has since proved extremely useful in supermagnets generating magnetic fields as high as 20 teslas. In 1962, Ted Berlincourt and Richard Hake discovered that less brittle alloys of niobium and titanium are suitable for applications up to 10 teslas. Promptly thereafter, commercial production of niobium-titanium supermagnet wire commenced at Westinghouse Electric Corporation and at Wah Chang Corporation. Although niobium-titanium boasts less-impressive superconducting properties than those of niobium-tin, niobium-titanium has, nevertheless, become the most widely used “workhorse” supermagnet material, in large measure a consequence of its very high ductility and ease of fabrication. However, both niobium-tin and niobium-titanium find wide application in MRI medical imagers, bending and focusing magnets for enormous high-energy particle accelerators, and a host of other applications. Conectus, a European consortium for superconductivity, estimated that in 2014, global economic activity, for which superconductivity was indispensable, amounted to about five billion euros, with MRI systems accounting for about 80% of that total.

In 1962, Brian Josephson made the important theoretical prediction that a supercurrent can flow between two pieces of superconductor separated by a thin layer of insulator. This phenomenon, now called the Josephson effect, is exploited by superconducting devices such as SQUIDs. It is used in the most accurate available measurements of the magnetic flux quantum h/2e, and thus (coupled with the quantum Hall resistivity) for the Planck constant h. Josephson was awarded the Nobel Prize in Physics for this work in 1973.

In 1973 Nb
₃Ge found to have T_c of 23 K, which remained the highest ambient-pressure T_c until the discovery of the cuprate high-temperature superconductors in 1986 (see below).

Unconventional supercconductivity.

Main article: Unconventional superconductor

First unconventional superconductors

In 1979, two new classes of superconductors where discovered that could not be explained by BCS theory: heavy fermion superconductors and organic superconductors.

The first heavy fermion superconductor, CeCu₂Si₂, was discovered by Frank Steglich. Since then over 30 heavy fermion superconductors were found (in materials based on Ce, U), with a critical temperature up to 2.3 K (in CeCoIn₅).

Klaus Bechgaard and Denis Jérome synthesized the first organic superconductor (TMTSF)₂PF₆ (the corresponding material class was named after him later) with a transition temperature of T_C = 0.9 K, at an external pressure of 11 kbar.

High-temperature superconductors

Main article: High-temperature superconductors

Superconductor timeline

In 1986, J. Georg Bednorz and K. Alex Mueller discovered superconductivity in a lanthanum-based cuprate perovskite material, which had a transition temperature of 35 K (Nobel Prize in Physics, 1987) and was the first of the high-temperature superconductors. It was shortly found (by Ching-Wu Chu) that replacing the lanthanum with yttrium, i.e. making YBCO, raised the critical temperature to 92 K, which was important because liquid nitrogen could then be used as a refrigerant (at atmospheric pressure, the boiling point of nitrogen is 77 K). This is important commercially because liquid nitrogen can be produced cheaply on-site with no raw materials, and is not prone to some of the problems (solid air plugs, etc.) of helium in piping. Many other cuprate superconductors have since been discovered, and the theory of superconductivity in these materials is one of the major outstanding challenges of theoretical condensed-matter physics.

In March 2001, superconductivity of magnesium diboride (MgB
₂) was found with T_c = 39 K.

In 2008, the oxypnictide or iron-based superconductors were discovered, which led to a flurry of work in the hope that studying them would provide a theory of the cuprate superconductors.

In 2013, room-temperature superconductivity was attained in YBCO for picoseconds, using short pulses of infrared laser light to deform the material's crystal structure.

In 2017 it was suggested that undiscovered superhard materials (e.g. critically doped beta-titanium Au) might be a candidate for a new superconductor with Tc, substantially higher than HgBaCuO (138 K), possibly up to 233 K, which would be higher even than H₂S. A lot of research suggests that additionally nickel could replace copper in some perovskites, offering another route to room temperature. Li+ doped materials can also be used, i.e. the spinel battery material LiTi₂O_x and the lattice pressure can increase Tc to over 13.8 K. Also LiHx has been theorized to metallise at a substantially lower pressure than H and could be a candidate for a Type 1 superconductor.