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arXiv:1401.3138 · Journal of the Physical Society of Japan

Flux Phase as Possible Time-Reversal Symmetry Breaking Surface States of High-TC Cuprate Superconductors

Kazuhiro Kuboki

Published Apr 7, 2014• 7 citations
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Abstract

At a (110) surface of a $d_{x^2-y-2}$-wave superconductor, superconducting order is strongly suppressed. In such a situation, ordered states that are forbidden in the bulk may arise. This problem is studied for high-$T_C$ cuprate superconductors by treating the $t-J$ model with extended transfer integrals using the Bogoliubov de Gennes method. It is found that a flux phase with staggered currents along the surface, or an antiferromagnetic state can occur near the surface. Stability of the emergent surface states is different from system to system depending on the shapes of their Fermi surfaces. Possible relation to the experiments on the Kerr effect that suggest time-reversal symmetry breaking is discussed.

DOI
10.7566/jpsj.83.054703

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At a (110) surface of a dx2−y−2d_{x^2-y-2}dx2−y−2​-wave superconductor, superconducting order is strongly suppressed. In such a situation, ordered states that are forbidden in the bulk may arise. This problem is studied for high-TCT_CTC​ cuprate superconductors by treating the t−Jt-Jt−J model with extended transfer integrals using the Bogoliubov de Gennes method. It is found that a flux phase with staggered currents along the surface, or an antiferromagnetic state can occur near the surface. Stability of the emergent surface states is different from system to system depending on the shapes of their Fermi surfaces. Possible relation to the experiments on the Kerr effect that suggest time-reversal symmetry breaking is discussed.
In order to study the time-reversal symmetry (T{\cal T}T) breaking near a (110) surface of a high-TCT_CTC​ cuprate YBCO, we consider the flux phase in a bilayer t−Jt-Jt−J model. Although the stable solution in the bulk is the dx2−y−2d_{x^2-y-2}dx2−y−2​-wave superconducting (SC) state, free energy of the flux phase is close to it, and thus the flux phase may occur when the SC order is disturbed by inhomogeneity, e.g., surface or impurity. It is found that, depending on the doping rate, the flux phase in which spontaneous magnetic fields in two layers have opposite signs may be stabilized. This may lead to a surface state with local T{\cal T}T violation but without local magnetic field.
Due to nontrivial orbital pairing symmetry, surfaces and interfaces of high-Tc superconductors sup- port states which violate time-reversal (T -) symmetry. Such naturally degenerate states, useful as work- ing states of a qubit, are standard for atomic or molecular-size qubit prototypes (e.g. based on nuclear spins), but exceptional for mesoscopic qubits. (In particular, they hold promise of a better scalability.) In these lectures I review the physics of T -breaking on surfaces and interfaces of high-Tc superconductors; then describe existing proposals for high-Tc based qubits and the current state of experiments; Finally, I discuss the decoherence sources in the system, open questions, and future research directions.
We study the stability of the time-reversal symmetry breaking staggered-flux phase of a single band Hubbard model, within the variational cluster approach. For intermediate and small values of the interaction UUU, we find metastable solutions for the staggered-flux phase, with a maximum current per bond at $U\ensuremath{\approx}3.2$. However, allowing for antiferromagnetic and superconducting long-range order it turns out that in the region at and close to half filling the antiferromagnetic phase is the most favorable energetically. The effect of nearest-neighbor interaction is also considered. Our results show that a negative nearest-neighbor interaction and finite doping favors the stability of the staggered-flux phase. We also present preliminary results for the three-band Hubbard model obtained with a restricted set of variational parameters. For this case, no spontaneous time-reversal symmetry breaking phase is found in our calculations.
It has recently been realized that the gap nodes of multiband superconductors that break time-reversal symmetry generically take the form of Fermi surfaces of Bogoliubov quasiparticles. However, these Fermi surfaces lead to a nonzero density of states (DOS) at the Fermi energy, which typically disfavors such superconducting states. It has thus not been clear whether they can be stable for reasonable pairing interactions or are in practice preempted by time-reversal-symmetric states with vanishing DOS. In this Letter, we show within BCS theory applied to a paradigmatic model that the time-reversal-symmetry-breaking states are indeed stabilized over broad parameter ranges at weak coupling. Moreover, we introduce a fast method that involves solving the inverse BCS gap equation, does not require iteration, does not suffer from convergence problems, and can handle metastable solutions.
Spatial dependencies of the pair potential and the local density of states near the surfaces of dx2−y2d_{x^{2}-y^{2}}dx2−y2​-wave superconductors are studied theoretically. The calculation is based on the t-J model within a mean-field theory with Gutzwiller approximation. Various types of surface geometries are considered. Similar to our result in the extended Hubbard model, it is found that the formation of zero-energy states strongly depends on the surface geometry. In addition to this feature, the zero-energy states give peak splitting for the (110) surfaces when the super-exchange interaction JJJ is large. This is due to the induced s-wave component near the surface. The present result explains the microscopic origin of the spontaneous time- reversal symmetry breaking at the surfaces of high-TcT_{c}Tc​ superconductors.
We analyze a mean-field model of electrons on a square lattice with two types of interaction: forward scattering favoring a ddd-wave Pomeranchuk instability and a BCS pairing interaction driving ddd-wave superconductivity. By tuning the interaction parameters a rich variety of phase diagrams is obtained. If the BCS interaction is not too strong, Fermi surface symmetry breaking is stabilized around van Hove filling, and coexists with superconductivity at low temperatures. For pure forward scattering Fermi surface symmetry breaking occurs typically via a first order transition at low temperatures. The presence of superconductivity reduces the first order character of this transition and, if strong enough, can turn it into a continuous one. This gives rise to a quantum critical point within the superconducting phase. The superconducting gap tends to suppress Fermi surface symmetry breaking. For a relatively strong BCS interaction, Fermi surface symmetry breaking can be limited to intermediate temperatures, or can be suppressed completely by pairing.