Magnetic penetration depth in topological superconductors: Effect of Majorana surface states and application for UTe2

Abstract

In this study, we examine how orbital degrees of freedom and Majorana surface states influence the magnetic penetration depth in the superconductor UTe2. Using a two-orbital model, we analyze pairing states belonging to the irreducible representations of the D2h crystal symmetry: Au, B1u, B2u, and B3u. For bulk nodal states such as B2u, we find that the penetration depth for screening currents along the antinodal direction and the cylindrical axis scales as T2, in strong contrast to the conventional T4 law. This behavior originates from quasiparticles near the point nodes contributing to the interorbital paramagnetic current. We further show that Majorana surface states can dominate the low-temperature response. The fully gapped Au state hosts Majorana cones, which produce a T3 dependence of the penetration depth when the ratio of penetration depth to coherence length (κ) is small. In contrast, the other pairing states exhibit Majorana Fermi arcs: The exponent is n=2 along the dispersive direction, while along the dispersionless direction it depends on whether the arcs terminate at end points. The exponent n=2 in the dispersive direction is robust, while it in the dispersionless direction relies on the presence or absence of the end points of the arcs and deviates from n=2 when end points are absent. Our results demonstrate that penetration-depth measurements provide a direct probe of Majorana surface states in low-κ superconductors. For larger κ, the surface contribution becomes negligible and the temperature dependence is governed by bulk quasiparticles.

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