Intrinsic Second-Order Topological Superconductors with Tunable Majorana Zero Modes

TL;DR

This paper demonstrates that a specific two-dimensional Dirac semimetal can host a second-order topological superconductor with tunable Majorana zero modes, using mean-field theory to identify the pairing symmetry and boundary control.

Contribution

It reveals that nonsymmorphic Dirac semimetals can intrinsically host second-order topological superconductivity with controllable Majorana modes.

Findings

Even-parity $d_{x^{2}-y^{2}}$-wave pairing is favored.

The superconducting state hosts Majorana zero modes at boundaries.

Majorana modes can be manipulated via boundary sublattice terminations.

Abstract

Dirac semimetals, with their protected Dirac points, present an ideal platform for realizing intrinsic topological superconductivity. In this work, we investigate superconductivity in a two-dimensional, square-lattice nonsymmorphic Dirac semimetal. In the normal state near half-filling, the Fermi surface consists of two distinct pockets, each enclosing a Dirac point at a time-reversal invariant momentum ($\textbf{X}=(\pi,0)$ and $\textbf{Y}=(0,\pi)$). Considering an on-site repulsive and nearest-neighbor attractive interaction, we use self-consistent mean-field theory to determine the ground-state pairing symmetry. We find that an even-parity, spin-singlet $d_{x^{2}-y^{2}}$-wave pairing is favored as it gives rise to a fully gapped superconducting state. Since the pairing amplitude has opposite signs on the two Dirac Fermi pockets, the superconducting state is identified as a second-order topological superconductor. The hallmark of this topological phase is the emergence of Majorana zero modes at the system's boundaries. Notably, the positions of these Majorana modes are highly controllable and can be manipulated simply by tailoring the boundary sublattice terminations. Our results highlight the promise of nonsymmorphic Dirac semimetals for realizing and manipulating Majorana modes.