Magnetic response of Majorana Kramers pairs with an order-two symmetry

TL;DR

This paper explores how Majorana Kramers pairs in topological superconductors exhibit anisotropic magnetic responses influenced by symmetries, classifies these responses based on topological invariants, and applies the theory to UCoGe.

Contribution

It provides a systematic method to determine surface magnetic responses of Majorana Kramers pairs considering order-two symmetries and classifies responses into four types based on topological invariants.

Findings

Magnetic responses are classified into four types based on topological invariants.

Surface magnetic responses depend on Fermi-surface topology and Cooper pair symmetry.

Application to UCoGe reveals biaxially anisotropic magnetic response.

Abstract

We study an intrinsic relation between the topology of bulk electronic states and magnetic responses of Majorana Kramers pairs, Kramers pairs of Majorana fermions, on a surface of time-reversal-invariant topological superconductors. Majorana Kramers pairs respond to an applied magnetic field anisotropically due to the interplay between time-reversal and crystal symmetries. In this paper, we propose a systematic procedure to determine such surface magnetic responses in systems with an order-two symmetry. From the analysis of topological invariants associated with an order-two symmetry, it is found that magnetic responses are classified into four types, which are attributed to different topological invariants and exhibit distinguishable, characteristic magnetic responses. For a Kramers pair of Majorana fermions protected by $\mathbb{Z}_2$ topological invariants, we clarify that types of magnetic responses are determined only from Fermi--surface topology and symmetry of Cooper pairs. Finally, we apply our theory to the topological nonsymmorphic crystalline superconducting state in UCoGe, which exhibits a biaxially anisotropic magnetic response.