[Paper Review] Topological Superconductivity in an s-wave Superconductor and Its Implication to Iron-based Superconductors

Shengshan Qin, Chen Fang+2 more|arXiv (Cornell University)|Jun 8, 2021

Topological Materials and Phenomena4 citations

TL;DR

This paper demonstrates that s-wave superconductivity in centrosymmetric, nonsymmorphic lattices—specifically the P4/nmm space group of iron-based superconductors—can host second-order topological superconductivity protected by mirror symmetry. It identifies a sign-changed s-wave pairing state as a topological phase hosting 2Z degenerate Dirac cones on (10) edges and Z pairs of Majorana modes at (11)/(11̄) corners, providing a measurable signature to resolve the pairing symmetry debate in iron-based superconductors.

ABSTRACT

In the presence of both space and time reversal symmetries, an s-wave A1g superconducting state is usually topologically trivial. Here we demonstrate that an exception can take place in a type of nonsymmorphic lattice structures. We specify the demonstration in a system with a centrosymmetric space group P4/nmm, the symmetry group that governs iron-based superconductors, by showing the existence of a second-order topological state protected by a mirror symmetry. The topological superconductivity is featured by 2Z degenerate Dirac cones on the (1,0) edge, and Z pairs of Majorana modes at the intersection between the (1,1) and (1,-1) edges. The topological invariance and Fermi surface criterion for the topological state are provided. Moreover, we point out that the previously proposed s-wave state in iron-based superconductors, which features a sign-changed superconducting order parameter between two electron pockets, is such a topological state. Thus, these results not only open a new route to pursue topological superconductivity, but also establish a measurable quantity to settle one long-lasting debate on the pairing nature of iron-based superconductors.

Motivation & Objective

• To explore whether s-wave superconductivity in centrosymmetric, nonsymmorphic lattices can host nontrivial topology despite conventional expectations.
• To establish a topological invariant and Fermi surface criterion for second-order topological superconductivity in such systems.
• To identify the sign-changed s-wave pairing state in iron-based superconductors as a candidate for second-order topological superconductivity.
• To provide a measurable, experimentally accessible signature (edge Dirac cones and corner Majorana modes) to resolve the long-standing debate on pairing symmetry in iron-based superconductors.

Proposed method

• Analyzes the P4/nmm space group (characteristic of iron-based superconductors) to identify how nonsymmorphic symmetries—specifically glide mirror and screw rotation—enable topological states in s-wave superconductors.
• Constructs a second-order topological superconducting state in the A1g pairing channel with a 2Z winding number protected by mirror symmetry.
• Derives an effective Hamiltonian for edge modes showing a Dirac-like theory with a spatially varying mass term, leading to localized Majorana modes at corners.
• Applies a Fermi surface criterion based on the topology of the Fermi surface and the symmetry of the superconducting order parameter to identify topological phases.
• Uses a tight-binding model with five d-orbitals and spin-orbit coupling to simulate the normal state of monolayer FeSe, fitting parameters to experimental band structures.
• Implements a sign-changed s-wave pairing form Δ₀ + 2Δ₁(cos kₓ + cos kᵧ) to model the superconducting state and confirms topological features via numerical edge state calculations.

Experimental results

Research questions

• RQ1 Can s-wave superconductivity in centrosymmetric, nonsymmorphic lattices—such as those in iron-based superconductors—host nontrivial topological order?
• RQ2 What topological invariants and symmetry protections govern such topological superconducting states?
• RQ3 Does the previously proposed sign-changed s-wave pairing state in iron-based superconductors correspond to a second-order topological superconductor?
• RQ4 Can the topological nature of this pairing state be probed experimentally via edge and corner modes?

Key findings

• The s-wave superconducting state in the P4/nmm lattice exhibits second-order topological superconductivity due to mirror symmetry protection, despite time and space reversal symmetries.
• The system hosts 2Z degenerate Dirac cones on the (10) edge, where mirror symmetry is preserved, indicating a nontrivial topological invariant.
• At the intersection of (11) and (11̄) edges, Z pairs of Majorana modes are localized, arising from a domain wall in the effective mass term of the edge Hamiltonian.
• The Fermi surface criterion identifies topological superconductivity when the Fermi surface encloses regions with opposite signs of the superconducting order parameter, consistent with sign-changed s-wave pairing.
• The sign-changed s-wave pairing state in iron-based superconductors—previously proposed based on ARPES and tunneling data—is confirmed as a second-order topological superconductor with measurable edge and corner modes.
• Numerical simulations of monolayer FeSe confirm the presence of two degenerate Majorana cones on the (10) edge under the sign-changed s-wave pairing, validating the theoretical prediction.