Intrinsic Angular Momentum and Intrinsic Magnetic Moment of Chiral Superconductor on Two-Dimensional Square Lattice

TL;DR

This paper investigates the intrinsic magnetic moment and angular momentum in chiral superconductors on a 2D square lattice, highlighting conditions under which these properties are observable, especially in multi-band systems like Sr$_2$RuO$_4$.

Contribution

It provides a detailed analysis of IMM and IAM in chiral superconductors, emphasizing the effects of surface currents and multi-band structures on their observability.

Findings

IMM and IAM are on the order of μ_B N and ħ N, respectively.

Surface currents can cancel these effects in single-band models.

Multi-band systems can allow IAM observation despite surface current cancellations.

Abstract

The intrinsic magnetic moment (IMM) and intrinsic angular momentum (IAM) of a chiral superconductor with $p$-wave symmetry on a two-dimensional square lattice are discussed on the basis of the Bogoliubov-de Gennes equation. The the IMM and IAM are shown to be on the order of $\mu_{\rm B}N$ and $\hbar N$, respectively, $N$ being the total number of particles, without an extra factor $(T_{\rm c}/T_{\rm F})^{\gamma}$ ($\gamma=1,2$), and parallel to the pair angular momentum. They arise from the current in the surface layer with a width on the order of the coherence length $\xi_{0}$, the size of Cooper pairs. However, in a single-band model, they are considerably canceled by the contribution from the Meissner surface current in a layer with the width of the penetration depth $\lambda$, making it difficult to observe them experimentally. In the case of multi-band metals with both electron-like and hole-like bands, however, considerable cancellation still occurs for the IMM but not for the IAM, making it possible to observe the IAM selectively because the effect of the Meissner current becomes less important. As an example of a multi-band metal, the case of the spin-triplet chiral superconductor Sr$_2$RuO$_4$ is discussed and experiments for observing the IAM are proposed.