Designing edge currents using mesoscopic patterning in chiral d-wave superconductors

Abstract

Chiral superconductors are topological as characterized by a finite Chern number and chiral edge modes. Direct fingerprints of chiral superconductivity are thus often taken to be spontaneous edge currents with associated magnetic signatures. However, a number of recent theoretical studies have shown that the total edge current along semi-infinite edges is greatly reduced or even vanishes in many scenarios for all pairing symmetries except chiral $p$-wave, thus impeding experimental detection. We demonstrate how mesoscopic finite-sized samples can be designed to give rise to a shape- and size-dependent strong enhancement of the chiral edge currents and their generated orbital magnetic moment and magnetic fields. In particular, we find that low rotational symmetry systems, such as pentagons and hexagons, give rise to the largest currents, while circular disks also generate large currents but in the opposite direction. We estimate the resulting magnetic fields to be as large as $0.01-0.5$ mT, with a magnetic moment approaching ${\mu }_B/2$ per Cooper pair (Bohr magneton ${\mu }_B$). The current and magnetic signatures diverge with shrinking system sizes, eventually cut off by finite-size suppression of chiral superconductivity. We extract the full phase diagram as a function of temperature and system size for different geometries, including competing superconducting orders. In geometries strongly suppressing only one of the $d$-wave components, we find an additional heat capacity jump, as large as $10\%$ of the bulk normal-superconducting transition, marking the transition between a chiral and a nodal $d$-wave state. This further acts as an indirect signature of chiral superconductivity. Our results are relevant for system sizes on the order of tens to hundreds of coherence lengths, and highlight mesoscopic patterning as a viable route to experimentally identify chiral $d$-wave superconductivity.

arXiv comment20 pages, 12 figures

References in corpus (129)

• Topological Insulators
• Topological insulators and superconductors
• Non-Abelian Anyons and Topological Quantum Computation
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Periodic table for topological insulators and superconductors
• Search for Majorana fermions in superconductors
• Topological superconductors: a review
• Direct imaging of the coexistence of ferromagnetism and superconductivity at the LaAlO3/SrTiO3 interface
• Chiral superconductivity from repulsive interactions in doped graphene
• Spontaneously polarized half-gapped superconductivity
• Spin-polarized supercurrents for spintronics: a review of current progress
• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Quasiclassical Green's function approach to mesoscopic superconductivity
• Topological Superconductivity in Twisted Multilayer Graphene
• Scanning nano-SQUID with single electron spin sensitivity
• Vortex phase diagram for mesoscopic superconducting disks
• Chiral Superconductors
• Chiral SDW and d + id superconductivity in the magic-angle twisted bilayer-graphene
• Observation of half-height magnetization steps in Sr2RuO4
• Chiral P-Wave Order in Sr_2RuO_4
• Quasiparticle States near the Surface and the Domain Wall in a p_x\pm i p_y-Wave Superconductor
• Andreev bound states in high-$T_c$ superconducting junctions
• Edge modes, edge currents, and gauge invariance in $p_x+i{p}_y$ superfluids and superconductors
• Resonating valence bonds and mean-field d-wave superconductivity in graphite
• Bulk-edge correspondence for two-dimensional topological insulators
• Experimental Evidence for Giant Vortex States in a Mesoscopic Superconducting Disk
• Strong Correlations and d+id Superconductivity in Twisted Bilayer Graphene
• Upper limit on spontaneous supercurrents in Sr${}_2$RuO${}_4$
• Distribution functions in non-equilibrium theory of superconductivity and Andreev spectroscopy in unconventional superconductors
• Chiral d-wave superconductivity in doped graphene
• Exotic Superconducting Properties in the Electron-Hole Compensated Heavy Fermion `Semimetal' URu2Si2
• Evidence for Time-Reversal-Symmetry-Broken Superconductivity in Locally Noncentrosymmetric SrPtAs
• Unconventional Superconductivity in UTe2
• On edge states in superconductor with time inversion symmetry breaking
• Limits on Superconductivity-Related Magnetization in Sr${}_2$RuO${}_4$ and PrOs${}_4$Sb${}_{12}$ from Scanning SQUID Microscopy
• Chiral $d$-wave Superconductivity in SrPtAs
• Pairing symmetry of interacting fermions on twisted bilayer graphene superlattice
• Spontaneous Hall effect in chiral p-wave superconductor
• Correlations and electronic order in a two-orbital honeycomb lattice model for twisted bilayer graphene
• High-temperature topological superconductivity in twisted double layer copper oxides
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Direct Observation of Vortex Shells and Magic Numbers in Mesoscopic Superconducting Disks
• Surface States, Edge Currents and the Angular Momentum of Chiral p-wave Superfluids
• Scanning SQUID susceptometers with sub-micron spatial resolution
• Stabilizing Even-Parity Chiral Superconductivity in Sr${}_2$RuO${}_4$
• Thermodynamic properties of thin films of superfluid 3He-A
• Unconventional topological superconductivity and phase diagram for an effective two-orbital model as applied to twisted bilayer graphene
• Time-Reversal-Symmetry-Breaking Superconductivity in Epitaxial Bismuth/Nickel Bilayers
• The scattering problem in non-equilibrium quasiclassical theory of metals and superconductors: general boundary conditions and applications
• Nanoscale imaging of equilibrium quantum Hall edge currents and of the magnetic monopole response in graphene
• Edge properties of the chiral d-wave superconducting state in doped graphene
• Anisotropic chiral d+id superconductivity in NaxCoO2 yH2O
• Pairing symmetry and spontaneous vortex-antivortex lattice in superconducting twisted-bilayer graphene: Bogoliubov-de Gennes approach
• Resonance from antiferromagnetic spin fluctuations for superconductivity in UTe${}_2$
• Vanishing edge currents in non-$p$-wave topological chiral superconductors
• Orbital Angular Momentum and Spectral Flow in Two Dimensional Chiral Superfluids
• Anomalous normal fluid response in a chiral superconductor UTe2
• Topological chiral superconductivity with spontaneous vortices and supercurrent in twisted bilayer graphene
• Non-topological nature of the edge current in a chiral p-wave superconductor
• Observation of Half-Quantum Flux in Unconventional Superconductor $\beta$-Bi${}_2$Pd
• Current inversion at the edges of a chiral $\mathbf{p}$-wave superconductor
• Mass flows and angular momentum density for $p_x+i{p}_y$ paired fermions in a harmonic trap
• Membrane-based nanocalorimeter for high-resolution measurements of low-temperature specific heat
• Broken translational and time-reversal symmetry in superconducting films
• Evidence for a Spatially-Modulated Superfluid Phase of ${}^3$He under Confinement
• Evidence for chiral superconductivity on a silicon surface
• Stabilized Pair Density Wave via Nanoscale Confinement of Superfluid ${}^3$He
• Suppression of Spontaneous Supercurrents in a Chiral p-Wave Superconductor
• Edge Channels of Broken-Symmetry Quantum Hall States in Graphene probed by Atomic Force Microscopy
• Spin-fluctuation-induced pairing in twisted bilayer graphene
• Effects of Strong Magnetic Fields on Pairing Fluctuations in High Temperature Superconductors
• High-temperature Majorana zero modes
• Spontaneous edge current in a small chiral superconductor with a rough surface
• Scanning SQUID Microscope Study of Vortex Polygons and Shells in Weak Pinning Disks of an Amorphous Superconducting Film
• Boundary states with elevated critical temperatures in Bardeen-Cooper-Schrieffer superconductors
• Inverse proximity effect and influence of disorder on triplet supercurrents in strongly spin-polarized ferromagnets
• Unconventional vortex states in nanoscale superconductors due to shape-induced resonances in the inhomogeneous Cooper-pair condensate
• Quantum Phase Diagram and Spontaneously Emergent Topological Chiral Superconductivity in Doped Triangular-Lattice Mott Insulators
• Chiral Majorana Modes via Proximity to a Twisted Cuprate Bilayer
• Chiral singlet superconductivity in the weakly correlated metal LaPt3P
• Spatially Modulated Superfluid State in Two-Dimensional ${}^4$He Films
• Orbital momentum of chiral superfluids and spectral asymmetry of edge states
• Niobium in clean limit: an intrinsic type-I superconductor
• Broken symmetries in URu2Si2
• Vortex states in nanoscale superconducting squares: the influence of quantum confinement
• Microscopic derivation of superconductor-insulator boundary conditions for Ginzburg-Landau theory revisited. Enhanced superconductivity at boundaries with and without magnetic field
• Spontaneous surface flux pattern in chiral p-wave superconductors - revisited
• Cryogen-free variable temperature scanning SQUID microscope
• Quasiclassical expressions for the free energy of superconducting systems
• Edge current and orbital angular momentum of chiral superfluids revisited
• Local density of states at polygonal boundaries of d-wave superconductors
• Andreev Bound States in Superconducting Films and Confined Superfluid He-3
• Spontaneous Edge Current in Higher Chirality Superconductors
• ${}^3$He Universe 2020
• Quasiclassical theory of charge transport across mesoscopic normal metal-superconducting heterostructures with current conservation
• Possibility of chiral $d$-wave state in the hexagonal pnictide superconductor SrPtAs
• Boundary Superconductivity in the BCS Model
• Ground state angular momentum, spectral asymmetry, and topology in chiral superfluids and superconductors
• Local observation of linear-$T$ superfluid density and anomalous vortex dynamics in URu${}_2$Si${}_2$
• High-temperature Majorana corner modes in a $d+i{d}^{\prime }$ superconductor heterostructure: Application to twisted bilayer cuprate superconductors
• Destruction of surface states of ($d_{zx}+i{d}_{yz}$)-wave superconductor by surface roughness: application to Sr${}_2$RuO${}_4$
• Coreless vortices as direct signature of chiral $d$-wave superconductivity
• Surface magnetism in a chiral d-wave superconductor with hexagonal symmetry
• Breaking time-reversal and translational symmetry at edges of $d$-wave superconductors: microscopic theory and comparison with quasiclassical theory
• Triangular pair density wave in confined superfluid ${}^3$He
• Spontaneous helical order of a chiral p-wave superfluid confined in nano-scale channels
• Changing the type of superconductivity by magnetic and potential scattering
• Surface-dominated finite size effects in nanoconfined superfluid helium
• Robust and tunable coreless vortices and fractional vortices in chiral $d$-wave superconductors
• Half-Quantum Vortices in Nematic and Chiral Phases of ${}^3$He
• Limiting mechanism for critical current in topologically frustrated Josephson junctions
• Josephson effects in twisted nodal superconductors
• Thermopower and thermophase in a $d$-wave superconductor
• Non-thermodynamic nature of the orbital angular momentum in neutral fermionic superfluids
• Anisotropic criteria for the type of superconductivity
• Weyl Fermions and Broken Symmetry Phases of Laterally Confined ${}^3$He Films
• SuperConga: an open-source framework for mesoscopic superconductivity
• Robustness of chiral surface current and subdominant $s$-wave Cooper pairs
• Tuning topological superconductivity within the $t$-$J$-$U$ model of twisted bilayer cuprates
• Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects
• Directly Detecting the Edge Current in a $p_x+i{p}_y$ Topological Superfluid
• Phenomenology of the chiral $d$-wave state in the hexagonal pnictide superconductor SrPtAs
• Vortex bound states of charge and magnetic fluctuations-induced topological superconductors in heterostructures
• Superfluid phase transition of nanoscale-confined helium-3
• BCS Critical Temperature on Half-Spaces
• Magnetic edge fields in UTe${}_2$ near zero background fields
• Enhanced Superconductivity at a Corner for the Linear BCS Equation
• Impurity strength-temperature phase diagram with phase crystals and competing time-reversal symmetry breaking states in nodal $d$-wave superconductors