Higher-order topological superconductivity in type-II time-reversal-symmetric Weyl semimetals with a hybrid pairing

TL;DR

This work investigates intrinsic superconductivity in a minimal type-II time-reversal-symmetric Weyl semimetal with two orbitals. Using a self-consistent mean-field approach, it finds a hybrid pairing of singlet $s$-wave and triplet $p$-wave that is organized by surface Fermi-arc configurations, yielding a distinct dichotomy: $s$-wave dominates on one surface while $p$-wave dominates on the other. The superconducting state is fully gapped and hosts second-order topological hinge states, confirmed by edge-band spectra, corner-state spectra, and windings of the quadrupole moment $q_{xz}(k_y)$ at $k_y= ext{±π/2}$. The results position type-II TRWSMs as intrinsic, tunable platforms for unconventional and topological superconductivity with potential for high-temperature realizations and hinge-state physics.

Abstract

We employed the self-consistent method on a two-orbital type-II time-reversal-symmetric Weyl semimetal, revealing a hybrid pairing of singlet $s$-wave and triplet $p$-wave. We present a detailed analysis of the normal-state electronic structure and the self-consistent results. Our findings indicate that the selection of hybrid pairings is governed by distinct surface Fermi-arc configurations: specifically, $s$-wave pairing dominates on the bottom surface, while $p$-wave pairing prevails on the top. Furthermore, the emergent superconducting state is a second-order topological superconductors with hinge states in the system. Our results identify type-II time-reversal-invariant Weyl semimetals as a promising intrinsic platform for realizing unconventional and topological superconductivity.

Figures (4)

• Figure 1: Normal-state electronic structures with partially opening boundary condition in the $z$ direction. Top row: energy spectra at the ${k_y} = \pi/2$ slice (a), and at the ${k_x} = \pi/2$ slice (b). Middle row: zero-energy spectral functions on the $z = 1$ surface (c) and on the $z = N_z$ surface (d). Bottom row: orbital-resolved LDOS curves on the $z = 1$, $z = N_z$ surfaces and in the bulk ($z = N_z/2$).
• Figure 2: Superconducting pairing and superconducting-state electronic structure with partially opening boundary condition in the $z$ direction. Top row: the layer-dependent superconducting order parameters obtained by the self-consistent method. Bottom row: orbital-resolved superconducting-state LDOS curves on the $z = 1$, $z = N_z$ surfaces, and in the bulk ($z = N_z/2$).
• Figure 3: Electronic structures with partially opening boundary condition in the $x$ and $z$ directions. In the left panel, (a) superconducting spectrum; (b) zoom-in of the region of the left edge bands. In the right panel, orbital dependent spectral functions at the four corners (c–f) and at the lateral edges (g–j).
• Figure 4: Quadrupole moment for each ${k_y}$-sliced layer.