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.

20 pages, 12 figures

References in corpus (39)

• Non-Abelian Anyons and Topological Quantum Computation
• Classification of topological insulators and superconductors in three spatial dimensions
• Observation of half-height magnetization steps in Sr2RuO4
• Chiral P-Wave Order in Sr_2RuO_4
• Exotic Superconducting Properties in the Electron-Hole Compensated Heavy Fermion `Semimetal' URu2Si2
• High-temperature topological superconductivity in twisted double layer copper oxides
• Surface States, Edge Currents and the Angular Momentum of Chiral p-wave Superfluids
• Thermodynamic properties of thin films of superfluid 3He-A
• Vanishing edge currents in non-$p$-wave topological chiral superconductors
• Orbital Angular Momentum and Spectral Flow in Two Dimensional Chiral Superfluids
• Non-topological nature of the edge current in a chiral p-wave superconductor
• 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 chiral superconductivity on a silicon surface
• Suppression of Spontaneous Supercurrents in a Chiral p-Wave Superconductor
• 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
• 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
• Possibility of chiral $d$-wave state in the hexagonal pnictide superconductor SrPtAs
• High-temperature Majorana corner modes in a $d+i{d}^{\prime }$ superconductor heterostructure: Application to twisted bilayer cuprate superconductors
• Surface magnetism in a chiral d-wave superconductor with hexagonal symmetry
• 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
• Robust and tunable coreless vortices and fractional vortices in chiral $d$-wave superconductors
• Limiting mechanism for critical current in topologically frustrated Josephson junctions
• Anisotropic criteria for the type of superconductivity
• Robustness of chiral surface current and subdominant $s$-wave Cooper pairs
• Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects
• Tuning topological superconductivity within the $t$-$J$-$U$ model of twisted bilayer cuprates
• Superfluid phase transition of nanoscale-confined helium-3
• BCS Critical Temperature on Half-Spaces
• Magnetic edge fields in UTe${}_2$ near zero background fields
• Impurity strength-temperature phase diagram with phase crystals and competing time-reversal symmetry breaking states in nodal $d$-wave superconductors
• Enhanced Superconductivity at a Corner for the Linear BCS Equation