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Chiral superconductors spontaneously break time-reversal symmetry and hosttopologically protected edge modes, supposedly generating chiral edge currentswhich are typically taken as a characteristic fingerprint of chiralsuperconductivity. However, recent studies have shown that the total edgecurrent in two dimensions (2D) often vanishes for all chiral superconductorsexcept for chiral $p$-wave, especially at low temperatures, thus severelyimpeding potential experimental verification and characterization of thesesuperconductors. In this work, we use quasiclassical theory ofsuperconductivity to study mesoscopic disc-schaped chiral $d$-wavesuperconductors. We find that mesoscopic finite-size effects cause a dramaticenhancement of the total charge current and orbital magnetic moment (OMM), evenat 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 sufficientlylarge systems, but this breaks down in small systems, instead producing a localmaximum at $\mathcal{R} \approx 10{\text{--}}20\xi_0$ due to mesoscopicfinite-size effects. These effects also cause a spontaneous charge-currentreversal opposite to the chirality below $\mathcal{R} < 10\xi_0$. Our workhighlights mesoscopic systems as a route to experimentally verify chiral$d$-wave superconductivity, measurable with magnetometry.

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