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Register a new userCuprate superconductors as viewed through a striped lens
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J. M. Tranquada
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Understanding the electron pairing in hole-doped cuprate superconductors has been a challenge, in particular because the normal state from which it evolves is unprecedented. Now, after three and a half decades of research, involving a wide range of experimental characterizations, it is possible to delineate a clear and consistent cuprate story. It starts with doping holes into a charge-transfer insulator, resulting in in-gap states. These states exhibit a pseudogap resulting from the competition between antiferromagnetic superexchange $J$ between nearest-neighbor Cu atoms (a real-space interaction) and the kinetic energy of the doped holes, which, in the absence of interactions, would lead to extended Bloch-wave states whose occupancy is characterized in reciprocal space. To develop some degree of coherence on cooling, the spin and charge correlations must self-organize in a cooperative fashion. A specific example of resulting emergent order is that of spin and charge stripes, as observed in La$_{2-x}$Ba$_x$CuO$_4$. While stripe order frustrates bulk superconductivity, it nevertheless develops pairing and superconducting order of an unusual character. The antiphase order of the spin stripes decouples them from the charge stripes, which can be viewed as hole-doped, two-leg, spin-$frac12$ ladders. To achieve superconducting order, the pair correlations in neighboring ladders must develop phase order. In the presence of spin stripe order, antiphase Josephson coupling can lead to pair-density-wave superconductivity. Alternatively, in-phase superconductivity requires that the spin stripes have an energy gap, which empirically limits the coherent superconducting gap. Hence, superconducting order in the cuprates involves a compromise between the pairing scale, which is maximized at $xsimfrac18$, and phase coherence, which is optimized at $xsim0.2$.
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The increased transmission, observed in the EXAFS region of their X-ray absorption spectra, as cuprate materials go through the superconducting transition temperature Tc is correlated with an increase in Abrikosov Vortex expulsion in zero magnetic field as the temperature T approaches Tc.
We study the properties of a quasi-one dimensional superconductor which consists of an alternating array of two inequivalent chains. This model is a simple charicature of a locally striped high temperature superconductor, and is more generally a theoretically controllable system in which the superconducting state emerges from a non-Fermi liquid normal state. Even in this limit, ``d-wave like order parameter symmetry is natural, but the superconducting state can either have a complete gap in the quasi-particle spectrum, or gapless ``nodal quasiparticles. We also find circumstances in which antiferromagnetic order (typically incommensurate) coexists with superconductivity.
Geometrical Berry phase is recognized as having profound implications for the properties of electronic systems. Over the last decade, Berry phase has been essential to our understanding of new materials, including graphene and topological insulators. The Berry phase can be accessed via its contribution to the phase mismatch in quantum oscillation experiments, where electrons accumulate a phase as they traverse closed cyclotron orbits in momentum space. The high-temperature cuprate superconductors are a class of materials where the Berry phase is thus far unknown despite the large body of existing quantum oscillations data. In this report we present a systematic Berry phase analysis of Shubnikov - de Haas measurements on the hole-doped cuprates YBa$_2$Cu$_3$O$_{y}$, YBa$_2$Cu$_4$O$_8$, HgBa$_2$CuO$_{4 + delta}$, and the electron-doped cuprate Nd$_{2-x}$Ce$_x$CuO$_4$. For the hole-doped materials, a trivial Berry phase of 0 mod $2pi$ is systematically observed whereas the electron-doped Nd$_{2-x}$Ce$_x$CuO$_4$ exhibits a significant non-zero Berry phase. These observations set constraints on the nature of the high-field normal state of the cuprates and points towards contrasting behaviour between hole-doped and electron-doped materials. We discuss this difference in light of recent developments related to charge density-wave and broken time-reversal symmetry states.
The origin of the exceptionally strong superconductivity of cuprates remains a subject of debate after more than two decades of investigation. Here we follow a new lead: The onset temperature for superconductivity scales with the strength of the anomalous normal-state scattering that makes the resistivity linear in temperature. The same correlation between linear resistivity and Tc is found in organic superconductors, for which pairing is known to come from fluctuations of a nearby antiferromagnetic phase, and in pnictide superconductors, for which an antiferromagnetic scenario is also likely. In the cuprates, the question is whether the pseudogap phase plays the corresponding role, with its fluctuations responsible for pairing and scattering. We review recent studies that shed light on this phase - its boundary, its quantum critical point, and its broken symmetries. The emerging picture is that of a phase with spin-density-wave order and fluctuations, in broad analogy with organic, pnictide, and heavy-fermion superconductors.
Hole-doped cuprate high temperature superconductors have ushered in the modern era of high temperature superconductivity (HTS) and have continued to be at center stage in the field. Extensive studies have been made, many compounds discovered, voluminous data compiled, numerous models proposed, many review articles written, and various prototype devices made and tested with better performance than their nonsuperconducting counterparts. The field is indeed vast. We have therefore decided to focus on the major cuprate materials systems that have laid the foundation of HTS science and technology and present several simple scaling laws that show the systematic and universal simplicity amid the complexity of these material systems, while referring readers interested in the HTS physics and devices to the review articles. Developments in the field are mostly presented in chronological order, sometimes with anecdotes, in an attempt to share some of the moments of excitement and despair in the history of HTS with readers, especially the younger ones.
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