Breaking time-reversal and translational symmetry at edges of $d$-wave superconductors: microscopic theory and comparison with quasiclassical theory

Abstract

We report results of a microscopic calculation of a second-order phase transition into a state breaking time-reversal and translational invariance along pair-breaking edges of $d$-wave superconductors. By solving a tight-binding model through exact diagonalization with the Bogoliubov-de~Gennes method, we find that such a state with current loops having a diameter of a few coherence lengths is energetically favorable below $T^{\ast }$ between 10%-20% of $T_{\mathrm{c}}$ of bulk superconductivity, depending on model parameters. This extends our previous studies of such a phase crystal within the quasiclassical theory of superconductivity, and shows that the instability is not qualitatively different when including a more realistic band structure and the fast oscillations on the scale of the Fermi wavelength. Effects of size quantization and Friedel oscillations are not detrimental. We also report on a comparison with quasiclassical theory with the Fermi surfaces extracted from the tight-binding models used in the microscopic calculation. There are quantitative differences in for instance the value of $T^{\ast }$ between the different models, but we can explain the predicted transition temperature within each model as due to the different spectral weights of zero-energy Andreev bound states and the resulting gain in free energy by breaking time-reversal and translational invariance below $T^{\ast }$.

arXiv comment15 pages and 9 figures

References in corpus (49)

• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Tunneling into Current-Carrying Surface States of High T${}_c$ Superconductors
• Pronounced drop of ${}^{17}$O NMR Knight shift in superconducting state of Sr${}_2$RuO${}_4$
• Topology of Andreev Bound States with Flat Dispersion
• Andreev bound states in high-$T_c$ superconducting junctions
• Distribution functions in non-equilibrium theory of superconductivity and Andreev spectroscopy in unconventional superconductors
• Quasiparticles in the vortex lattice of unconventional superconductors: Bloch waves or Landau levels?
• Reduction of the ${}^{17}$O Knight shift in the Superconducting State and the Heat-up Effect by NMR Pulses on Sr${}_2$RuO${}_4$
• A knitting algorithm for calculating Green functions in quantum systems
• Chebyshev-BdG: an efficient numerical approach to inhomogeneous superconductivity
• A proposal for reconciling diverse experiments on the superconducting state in Sr2RuO4
• Quasiparticles and Vortices in Unconventional Superconductors
• The Effect of Surfaces on the Tunneling Density of States of an Anisotropically Paired Superconductor
• Impurity scattering and localization in $d$-wave superconductors
• Free Energy of an Inhomogeneous Superconductor: a Wave Function Approach
• Low-Temperature Magnetic Penetration Depth in d-Wave Superconductors: Zero-Energy Bound State and Impurity Effects
• Relation of Extended Van Hove Singularities to High-Temperature Superconductivity within Strong-Coupling Theory
• Superconducting order parameter of Sr${}_2$RuO${}_4$: a microscopic perspective
• Paramagnetic instability of small topological superconductors
• Theory of Local Density of States of d-Wave Superconducting State Near the Surfaces of the t-J Model
• Paramagnetic instability at normal-metal - superconductor interfaces
• Spontaneously broken time-reversal symmetry in high-temperature superconductors
• Broken translational and time-reversal symmetry in superconducting films
• Experimental test for subdominant superconducting phases with complex order parameters in cuprate grain boundary junctions
• Edge-Ferromagnetism from Majorana Flat-Bands: Application to Split Tunneling-Conductance Peaks in the High-Tc Cuprates
• Observation of Caroli-de Gennes-Matricon Vortex States in YBa${}_2$Cu${}_3$O${}_{7-\delta }$
• Time-reversal symmetry breaking at Josephson tunnel junctions of purely d-wave superconductors
• Boundary states with elevated critical temperatures in Bardeen-Cooper-Schrieffer superconductors
• Instabilities at [110] Surfaces of d_{x^2-y^2} Superconductors
• Self-consistent interface properties of d and s-wave superconductors
• Unconventional vortex states in nanoscale superconductors due to shape-induced resonances in the inhomogeneous Cooper-pair condensate
• The Anderson prescription for surfaces and impurities
• Vortex states in nanoscale superconducting squares: the influence of quantum confinement
• Spontaneously broken translational symmetry at edges of high-temperature superconductors: thermodynamics in magnetic field
• Index theoretic characterization of d-wave superconductors in the vortex state
• Search for broken time-reversal symmetry near the surface of YBCO films using Beta-NMR
• Model evidence of a superconducting state with a full energy gap in small cuprate islands
• Quasiclassical expressions for the free energy of superconducting systems
• A Self-Consistent Microscopic Theory of Surface Superconductivity
• Andreev Bound States in Superconducting Films and Confined Superfluid He-3
• Phase Crystals
• Field-induced reentrant superconductivity in thin films of nodal superconductor
• Fermi surface effect on spontaneous breaking of time-reversal symmetry in unconventional superconducting films
• Spectral footprints of impurity scattering in graphene nanoribbons
• Spontaneous symmetry-breaking at surfaces of $d$-wave superconductors: influence of geometry and surface ruggedness
• Time-reversal symmetry breaking and gapped surface states due to spontaneous emergence of new order in $d$-wave nanoislands
• Emergence of $d\pm ip$-wave superconducting state at the edge of $d$-wave superconductors mediated by Andreev-bound-state-driven ferromagnetic fluctuations
• Emergence of strongly correlated electronic states driven by the Andreev bound state in d-wave superconductors
• Spontaneous generation of fractional vortex-antivortex pairs at single edges of high-Tc superconductors

Cited by in corpus (11)

• Spontaneous time-reversal symmetry breaking by disorder in superconductors
• Quasiclassical theory of charge transport across mesoscopic normal metal-superconducting heterostructures with current conservation
• Disorder-robust phase crystal in high-temperature superconductors stabilized by strong correlations
• Robust and tunable coreless vortices and fractional vortices in chiral $d$-wave superconductors
• SuperConga: an open-source framework for mesoscopic superconductivity
• A finite element method for the quasiclassical theory of superconductivity
• Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects
• Sparse modeling approach for quasiclassical theory of superconductivity
• Impurity strength-temperature phase diagram with phase crystals and competing time-reversal symmetry breaking states in nodal $d$-wave superconductors
• Designing edge currents using mesoscopic patterning in chiral d-wave superconductors
• Strengthened correlations near [110] edges of $d$-wave superconductors in the t-J model with the Gutzwiller approximation