Unconventional superconductor

Unconventional superconductors are materials that display superconductivity which does not conform to either the conventional BCS theory or the Nikolay Bogolyubov's theory or its extensions.

Detailed history

The first unconventional singlet d-wave superconductor, CeCu₂Si₂, a type of heavy fermion metal, was discovered in 1978 by Frank Steglich.^[1] In the early eighties, many more unconventional, heavy fermion superconductors were discovered, including UBe₁₃,^[2] UPt₃ ^[3] and URu₂Si₂.^[4] In each of these materials, the anisotropic nature of the pairing is 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.^[5]

The first unconventional triplet superconductor, organic material (TMTSF)₂PF₆, was discovered by Denis Jerome and Klaus Bechgaard in 1979.^[6] Recent 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.^[7]

High-temperature singlet d-wave superconductivity was discovered by J.G. Bednorz and K.A. Müller in 1986, who 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 is well above the highest critical temperature known at the time (T_c = 23 K) and thus the new family of materials were 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. As early as 1987, superconductivity above 77 K, the boiling point of nitrogen, was achieved. This is 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. 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, in recent years other unconventional superconductors have been discovered. These include some that do not superconduct at high temperatures, such as the strontium ruthenate oxide compounds, but that, like the 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 display more unconventional features.

In 2008 a new class (layered oxypnictide superconductors), for example LaOFeAs, were discovered that do not include copper.^[8][9][10] An oxypnictide of samarium seems to have a T_c of about 43 K which is higher than predicted by BCS theory.^[11] Tests at up to 45 teslas^[12][13] suggest the upper critical field of LaFeAsO_0.89F_0.11 may be around 64 teslas. Some other iron-based superconductors do not contain oxygen.

History and progress

• April 1986 - The term high-temperature superconductor was first used to designate the new family of cuprate-perovskite ceramic materials discovered by Johannes Georg Bednorz and Karl Alexander Müller,^[14] for which they won the Nobel Prize in Physics the following year. Their discovery of the first high-temperature superconductor, LaBaCuO, with a transition temperature of 35 K, generated great excitement.
• LSCO (La_2-xSr_xCuO₂) discovered the same year.
• January 1987 - YBCO was discovered to have a T_c of 90 K.^[15]
• 1988 - BSCCO discovered with T_c up to 107 K,^[16] and TBCCO (T=thallium) discovered to have T_c of 125 K.

• 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,^[17] possibly 164 K under high pressure.^[18]
• Recently, other unconventional superconductors, not based on cuprate structure, have been discovered.^[19] Some have unusually high values of the critical temperature, T_c, and hence they are sometimes also called high-temperature superconductors.

After more than twenty years of intensive research the origin of high-temperature superconductivity is still not clear, but it seems that instead of electron-phonon attraction mechanisms, as in conventional superconductivity, one is dealing with genuine electronic mechanisms (e.g. by antiferromagnetic correlations), and instead of s-wave pairing, d-waves are substantial.

One goal of all this research is room-temperature superconductivity.^[20]

Examples

Examples of high-T_c cuprate superconductors include La_1.85Ba_0.15CuO₄, and YBCO (yttrium-barium-copper-oxide), which is famous as the first material to achieve superconductivity above the boiling point of liquid nitrogen.

Process

Perovskites are made by mixing oxides in stoichiometric quantities and then heating in a furnace at high temperatures in an oxygen-rich atmosphere.

Ongoing research

The question of how superconductivity arises in high-temperature superconductors is one of the major unsolved problems of theoretical condensed matter physics as of 2011. The mechanism that causes the electrons in these crystals to form pairs is not known.

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 mechanism

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.^[21] 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 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 was the interlayer coupling model, according to which a layered structure consisting of BCS-type (s symmetry) superconductor can enhance the superconductivity by itself.^[22] 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.

Thus, 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.

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 symmetry

There was a clever experimental design to overcome the muddy situation. An experiment based on flux quantization of a three-grain ring of YBa₂Cu₃O₇ (YBCO) was proposed to test the symmetry of the order parameter in the HTS. The symmetry of the order parameter could best be probed at the junction interface as the Cooper pairs tunnel across a Josephson junction or weak link.^[23] It was expected that only for a junction of d symmetry superconductors there could occur a half-integer flux, that is, a spontaneous magnetization. However, even if the junction experiment is the strongest method to determine the symmetry of the HTS order parameter, there have been ambiguous results of the junction experiments.

J. R. Kirtley and C. C. Tsuei thought that the ambiguous results came from the defect inside the HTS, so that they designed the experiment where both of clean limit (no defect) and dirty limit (maximum of defects) were simultaneously considered.^[24] In the experiment, the spontaneous magnetization was clearly observed in YBCO, which absolutely supported the d symmetry of the order parameter in YBCO. Because YBCO is orthorhombic, it might inherently have an admixture of s symmetry. So, by tuning their technique further, they found that there was an admixture of s symmetry in YBCO within about 3%.^[25] Also, they found that there was a pure d_x²-y² order parameter symmetry in the tetragonal Tl₂Ba₂CuO₆.^[26]

References

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10. New High-Temperature Superconductors Are Iron-based With Unusual Magnetic Properties
11. Samarium oxypnictide
12. High-temp superconductors pave way for 'supermagnets'
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