[Paper Review] Higher-order topological superconductivity: possible realization in Fermi gases and Sr$_2$RuO$_4$

Zhigang Wu, Zhongbo Yan+1 more|arXiv (Cornell University)|Nov 3, 2018

Cold Atom Physics and Bose-Einstein Condensates4 citations

TL;DR

This paper proposes a platform for realizing second-order topological superconductivity in bilayer spin-polarized Fermi gases with intralayer chiral p-wave pairing and tunable interlayer s- or d-wave pairing. It demonstrates that Majorana zero modes emerge not only at corners but also at terminations of 1D defects like domain walls, with the topological phase controllable via interlayer coupling and pairing tuning.

ABSTRACT

We propose to realize second-order topological superconductivity in bilayer spin-polarized Fermi gas superfluids. We focus on systems with intralayer chiral $p$-wave pairing and with tunable interlayer hopping and interlayer interactions. Under appropriate circumstances, an interlayer even-parity $s$- or $d$-wave pairing may coexist with the intralayer $p$-wave. Our model supports localized Majorana zero modes not only at the corners of the system geometry, but also at the terminations of certain one-dimensional defects, such as lattice line defects and superfluid domain walls. We show how such topological phases and the Majorana zero modes therein can be manipulated in a multitude of ways by tuning the interlayer pairing and hopping. Generalized to spinful systems, we further propose that the putative $p$-wave superconductor Sr$_{2}$RuO$_{4}$, when subject to uniaxial strains, may also realize the desired topological phase.

Motivation & Objective

• To propose a novel platform for realizing higher-order topological superconductivity (HOTSC) in ultracold Fermi gases with tunable interlayer coupling and pairing.
• To demonstrate that Majorana zero modes (MZMs) can emerge at corners and at the ends of 1D topological defects such as superfluid domain walls and line defects.
• To show that the topological phase can be dynamically tuned by controlling interlayer hopping and pairing symmetry, enabling experimental manipulation of MZMs.
• To extend the proposal to realistic materials by suggesting that strained Sr2RuO4 may host mixed-parity pairing, enabling HOTSC in a pristine material system.
• To provide experimental signatures—such as zero-bias peaks in local density of states (LDOS)—to detect the topological phase and distinguish it from trivial or conventional superconducting states.

Proposed method

• Construct a bilayer spin-polarized Fermi gas model with intralayer chiral p-wave pairing and interlayer even-parity (s- or d-wave) pairing, allowing for tunable interlayer hopping and interactions.
• Use a single-band tight-binding Hamiltonian to model the system, incorporating both intralayer and interlayer pairing terms, with parameters adjustable to access different topological phases.
• Analyze the system's topological invariant and edge modes using numerical diagonalization and compute the local density of states (LDOS) to detect zero-bias peaks indicative of MZMs.
• Investigate the effects of uniaxial strain on Sr2RuO4 by modeling the transition from helical p-wave to even-parity pairing, suggesting a mixed-parity phase at intermediate strains.
• Examine the role of interlayer coupling in layered systems, showing that MZMs remain robust at zero energy under weak interlayer hopping and become weakly dispersive under interlayer pairing.
• Use symmetry considerations and band structure analysis to argue that the mixed-parity phase is stable and detectable via LDOS measurements at corners and edges.

Experimental results

Research questions

• RQ1 Can second-order topological superconductivity be realized in a bilayer Fermi gas with tunable interlayer coupling and pairing?
• RQ2 Where do Majorana zero modes localize in such a system—only at corners, or also at the ends of 1D defects like domain walls?
• RQ3 How can the topological phase be experimentally tuned and probed using interlayer parameters?
• RQ4 Can the putative p-wave superconductor Sr2RuO4 be driven into a higher-order topological superconducting phase via uniaxial strain?
• RQ5 What experimental signatures, such as LDOS features, can distinguish the mixed-parity HOTSC phase from conventional superconducting states?

Key findings

• The bilayer Fermi gas model supports a second-order topological superconducting phase with Majorana zero modes localized at system corners and at terminations of 1D defects such as superfluid domain walls.
• The system exhibits tunable topological phases via control of interlayer hopping and pairing strength, enabling dynamic manipulation of MZMs.
• In the mixed-parity phase with |Δd| > |Δs|, a prominent zero-bias peak appears at corners in the local density of states (LDOS), while edge modes are gapped, providing a distinguishing signature.
• The LDOS at edges shows a depletion near zero bias due to the gapping of helical edge modes by even-parity pairing, further distinguishing the HOTSC phase.
• Under uniaxial strain, Sr2RuO4 may host a mixed-parity superconducting state with coexisting p-wave and even-parity (s- or d-wave) pairing, enabling a realization of HOTSC in a real material.
• The interlayer coupling in Sr2RuO4 preserves zero-energy MZMs when interlayer hopping is weak, and induces only slight dispersion when interlayer pairing is present, maintaining topological robustness.