Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects

Abstract

Chiral superconductors spontaneously break time-reversal symmetry and host topologically protected edge modes, supposedly generating chiral edge currents which are typically taken as a characteristic fingerprint of chiral superconductivity. However, recent studies have shown that the total edge current in two dimensions (2D) often vanishes for all chiral superconductors except for chiral $p$-wave, especially at low temperatures, thus severely impeding potential experimental verification and characterization of these superconductors. In this work, we use quasiclassical theory of superconductivity to study mesoscopic disc-schaped chiral $d$-wave superconductors. We find that mesoscopic finite-size effects cause a dramatic enhancement of the total charge current and orbital magnetic moment (OMM), even at low temperatures. We study how these quantities scale with temperature, spontaneous Meissner screening, and system radius $\mathcal{R}\in [5,200]{\xi }_0$ with superconducting coherence length ${\xi }_0$. We find a general $1/\mathcal{R}$ scaling in the total charge current and OMM for sufficiently large systems, but this breaks down in small systems, instead producing a local maximum at $\mathcal{R}\approx 10\text{–}20{\xi }_0$ due to mesoscopic finite-size effects. These effects also cause a spontaneous charge-current reversal opposite to the chirality below $\mathcal{R}<10{\xi }_0$. Our work highlights mesoscopic systems as a route to experimentally verify chiral $d$-wave superconductivity, measurable with magnetometry.

23 pages, 14 figures

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