Quadrupole spin polarization as signature of second-order topological superconductors

TL;DR

This paper proposes that quadrupole spin polarization at edges is a key signature of second-order topological superconductors, offering a new experimental detection method beyond zero-bias conductance peaks.

Contribution

It introduces the concept of quadrupole spin polarization as a novel signature for identifying second-order topological superconductors, supported by analytical, numerical, and simulation results.

Findings

Quadrupole spin polarization appears at edges of topological superconductors.

This polarization disappears at the topological phase transition.

Spin-polarized scanning tunneling microscopy can detect this feature.

Abstract

We study theoretically second-order topological superconductors characterized by the presence of pairs of zero-energy Majorana corner states. We uncover a quadrupole spin polarization at the system edges that provides a striking signature to identify topological phases, thereby complementing standard approaches based on zero-bias conductance peaks due to Majorana corner states. We consider two different classes of second-order topological superconductors with broken time-reversal symmetry and show that both classes are characterized by a quadrupolar structure of the spin polarization that disappears as the system passes through the topological phase transition. This feature can be accessed experimentally using spin-polarized scanning tunneling microscopes. We study different models hosting second-order topological phases, both analytically and numerically, and using Keldysh techniques we provide numerical simulations of the spin-polarized currents probed by scanning tips.