sign in sign up
<<
Home , State of matter

COMMENTARY

Fragile at high magnetic fields COMMENTARY Michael R. Normana,1

Ever since the discovery of superconductivity by Kamerlingh Onnes’ group in 1911, this phenomenon Normal State Vortex has continued to intrigue successive generations of

scientists. One of the most spectacular discoveries Vortex since 1911 was that of high- supercon- Vortex Lattice ductivity in a copper oxide (1). Tens of thousands of Magnetic Field papers have been written on these cuprate materials, Meissner yet 35 years later, they continue to surprise us. In Meissner Temperature Temperature PNAS, Hsu et al. (2) demonstrate that a fragile form of superconductivity persists in a cuprate up to the Fig. 1. Left: The phases of a type II superconductor in the – highest magnetic field they can muster. field temperature plane (3). In the Meissner state, the ’ magnetic field is expelled. Above this, the magnetic field The original superconductor discovered by Onnes penetrates as an array of quantized vortices (vortex group is of a class now known as type I superconduc- lattice). Above the upper critical field, the vortex cores tors. These superconductors expel a magnetic field, overlap and superconductivity disappears (normal state). with superconductivity surviving up to a critical field Right: In cuprates and other low-dimensional superconductors, the vortex state splits into a where the gain due to superconductivity glassy , separated by a line, above which equals that associated with the magnetic field. How- there is a liquid of vortices (4, 5). This liquid is separated ever, in 1957, Abrikosov (3) proposed another class of by a crossover line (dashed line) from the normal state. superconductors, now known as type II superconduc- The high field limit of this phase diagram is still debated and is the subject of the study by Hsu et al. (2). tors. In these superconductors (as illustrated in Fig. 1, Left), above a lower critical field, superconductivity survives in the form of a unique state of where liquid is separated from the normal state by just a the magnetic field penetrates as an array of quantized crossover line. Most theories (4, 5) focus on lower magnetic flux lines. Once the cores of these so- magnetic fields, where one can think in terms of ther- called vortices overlap, then superconductivity dis- mal fluctuations, with the vortex lattice melting much appears at a higher field known as the upper critical like a solid melts to form a liquid. However, in the field. Since superconductivity survives to much high-field, low-temperature regime, quantum effects higher magnetic fields, most practical applications come into play, making theoretical treatments more involve type II superconductors. This requires that difficult, but in turn opening up the possibility for more the vortices be pinned, as their motion leads to dis- surprises. sipation and thus a finite resistance. To proceed, we should mention that cuprates have Now, when high-temperature superconductivity a somewhat complicated phase diagram (6). The par- was discovered in 1986, there was a realization that ent phase is a magnetic . Upon introduction they differ in fundamental ways from conventional of carriers (typically by chemical doping), magnetism is type II superconductors. In particular, these materials suppressed and superconductivity emerges. This are highly two-dimensional in , and therefore superconductivity as a function of temperature and the vortex lattice is more fragile (Fig. 1, Right). At doping takes the form of a dome. The maximum of low , it takes the form of a glassy state this dome separates the lower doped region (known (4). Thermal fluctuations lead to depinning of the vor- as underdoped) from the higher doped region tices, with the glassy state melting to form a liquid of (known as overdoped). The underdoped side is the vortices that leads to dissipation. As such, this vortex more intriguing of the two, as it is characterized by a

aMaterials Science Division, Argonne National Laboratory, Lemont, IL 60439 Author contributions: M.R.N. wrote the paper. The author declares no competing interest. Published under the PNAS license.

See companion article, “Unconventional matter state hosts quantum oscillations in the underdoped high-Tc cuprates,” 10.1073/pnas.2021216118. 1Email: [email protected]. Published February 9, 2021.

PNAS 2021 Vol. 118 No. 7 e2100372118 https://doi.org/10.1073/pnas.2100372118 | 1of3 Downloaded by guest on September 24, 2021 partial energy gap known as the pseudogap that persists to be due to reconstruction of the Fermi surface by a novel form of much higher temperatures than the superconducting phase. superconductivity called a pair density wave (12), where the su- What this pseudogap is has continued to be debated over the perconductivity is modulated in space by the same correlations years. However, within this phase, evidence for a charge den- that cause the charge density wave. Certainly, more studies need sity wave exists, which can also exist to a higher temperature to be done before we can elucidate the true nature of this high than the superconducting phase. Only in certain cuprates does field state. this charge density state exhibit long-range order. However, for the cuprate studied by Hsu et al. (2), although only short-range In PNAS, Hsu et al. demonstrate that a fragile order exists at low magnetic fields, long-range order is estab- form of superconductivity persists in a cuprate lished at around 15 tesla (7). up to the highest magnetic field they can muster. Most previous measurements of the cuprates have indicated that the upper critical field at zero temperature might be as low as Now, the above discussion might give the impression that the 20 to 25 tesla (8). This is thought to be due to competition of the results of Hsu et al. (2) are unique to underdoped cuprates. This is superconducting phase with this charge density wave one, with likely not correct. Even overdoped cuprates, which have a large superconductivity being suppressed once long-range charge or- unreconstructed Fermi surface, show an H–T phase diagram like der appears. These measurements are based on resistive or ther- the Right plot of Fig. 1 (13). In addition, this H–T phase diagram modynamic probes. Now enter Hsu et al. (2). Their claim is that has also been seen in noncuprates including organic supercon- this somewhat small upper critical field, when determined by the ductors (14) and bismuthates (15). As their upper critical fields are resistance, is due to using too large a measurement current. That lower than cuprates, they would likely provide a more ideal plat- is, the high field state is very fragile, and even a small current is form to study this fragile superconducting state, assuming that it sufficient to depin the vortices and cause dissipation, leading to also exists in these materials. the potentially erroneous conclusion that one has entered the Finally, as mentioned in several of these papers, the nearly normal state. However, very surprisingly, this low-temperature, vertical phase line of superconductivity in the field–temperature high field state they find persists to fields as high as this group plane at high fields and low temperatures might be a sign of could employ (2). Therefore, the upper field boundary of this reentrant superconductivity due to Landau level quantization phase, if it exists, is not known. (16). This is obviously related to the quantum oscillations, which So, what is the nature of this unique quantum state? First, it are also a result of Landau quantization. In a Landau level exhibits quantum oscillations that are indicative of the existence language, the suppression of the upper critical field with tem- of a Fermi surface (9). Unlike the oscillations seen for overdoped perature is due to terms which pair that are not diag- cuprates that indicate a large Fermi surface, these oscillations in- onal in the Landau level index (so-called off-diagonal terms). dicate that the Fermi surface has reconstructed to form a However, in the high field limit, where the number of Landau smaller surface. It is thought that the source of this reconstruction levels is much smaller, the diagonal terms can dominate, leading is the above-mentioned charge density wave phase. However, in principle to superconductivity that can persist to fields signif- as made very evident by Hsu et al. (2), these oscillations also exist icantly higher than the semiclassical upper critical field (16). in the presence of superconductivity. In fact, the authors find Whether the observed phenomenon in the study by Hsu et al. that the amplitude of the oscillations do not differ between the (2) is due to this, or slightly less radical suggestions like super- vortex solid phase and the vortex liquid phase. Although quantum conducting inhomogeneity (17) or fragility due to the presence oscillations are known to exist in type II superconductors (10), of competing density wave order (18), remains to be seen. Cer- these oscillations in cuprates are surprisingly robust given the tainly, with the measurements of Hsu et al. (2), we have entered a very large superconducting energy gap associated with the regime of ultra–high-field superconductivity. Its implications re- high-temperature superconducting state. This leads to the dis- main to be determined. It will certainly be fun elucidating what tinct possibility that the superconducting gap is suppressed they are. on the small Fermi surfaces being observed by the quantum oscillations. However, more intriguing possibilities have been Acknowledgments suggested by Hsu et al. (2). In particular, this author and Davis This was supported by the Materials Sciences and Engineering Division, (11), along with others, have proposed that the oscillations might Basic Energy Sciences, Office of Science, US Department of Energy.

1 J. G. Bednorz, K. A. Müller, Possible high Tc superconductivity in the Ba-La-Cu-O system. Z. Phys. B Condens. Matter 64, 189–193 (1986). 2 Y.-T. Hsu et al., Unconventional quantum vortex matter state hosts quantum oscillations in the underdoped high-Tc cuprates. Proc. Natl. Acad. Sci. U.S.A., 10.1073/pnas.2021216118 (2021). 3 A. A. Abrikosov, On the magnetic properties of superconductors of the second group. Sov. Phys. JETP 5, 1174–1182 (1957). 4 D. S. Fisher, M. P. A. Fisher, D. A. Huse, Thermal fluctuations, quenched disorder, phase transitions, and transport in type-II superconductors. Phys. Rev. B Condens. Matter 43, 130–159 (1991). 5 G. Blatter, M. V. Feigel’man, V. B. Geshkenbein, A. I. Larkin, V. M. Vinokur, Vortices in high-temperature superconductors. Rev. Mod. Phys. 66,1125–1388 (1994). 6 B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, J. Zaanen, From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015).

7 J. Chang et al., Magnetic field controlled charge density wave coupling in underdoped YBa2Cu3O6+x. Nat. Commun. 7, 11494 (2016). 8 C. Proust, L. Taillefer, The remarkable underlying ground states of cuprate superconductors. Annu. Rev. Condens. Matter Phys. 10, 409–429 (2019).

9 N. Doiron-Leyraud et al., Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor. Nature 447, 565–568 (2007). 10 T. J. B. M. Janssen et al., Quantitative investigation of the de Haas-van Alphen effect in the superconducting state. Phys. Rev. B Condens. Matter Mater. Phys. 57, 11698–11712 (1998). 11 M. R. Norman, J. C. S. Davis, Quantum oscillations in a biaxial pair density wave state. Proc. Natl. Acad. Sci. U.S.A. 115, 5389–5391 (2018).

2of3 | PNAS Norman https://doi.org/10.1073/pnas.2100372118 Fragile superconductivity at high magnetic fields Downloaded by guest on September 24, 2021 12 D. F. Agterberg et al., The of pair-density waves: Cuprate superconductors and beyond. Annu. Rev. Condens. Matter Phys. 11, 231–270 (2020).

13 A. P. Mackenzie et al., Resistive upper critical field of Tl2Ba2CuO6 at low temperatures and high magnetic fields. Phys. Rev. Lett. 71, 1238–1241 (1993). 14 T. Sasaki et al., Low-temperature vortex liquid states induced by quantum fluctuations in the quasi-two-dimensional organic superconductor κ-(BEDT-

TTF)2Cu(NCS)2. Phys. Rev. B Condens. Matter Mater. Phys. 66, 224513 (2002). 15 V. F. Gantmakher et al., Positive curvature in the temperature dependence of Hc2 in KxBa1-xBiO3. Phys. Rev. B Condens. Matter 54, 6133–6136 (1996). 16 M. Rasolt, Z. Tesanovic, Theoretical aspects of superconductivity in very high magnetic fields. Rev. Mod. Phys. 64, 709–754 (1992).

17 B. Spivak, F. Zhou, Mesoscopic effects in disordered superconductors near Hc2. Phys. Rev. Lett. 74, 2800–2803 (1995). 18 Y. Yu, S. A. Kivelson, Fragile superconductivity in the presence of weakly disordered charge density waves. Phys. Rev. B 99, 144513 (2019).

Norman PNAS | 3of3 Fragile superconductivity at high magnetic fields https://doi.org/10.1073/pnas.2100372118 Downloaded by guest on September 24, 2021