[Paper Review] Higher-order topological superconductivity from repulsive interactions in kagome and honeycomb systems

Tommy Li, Max Geier+2 more|arXiv (Cornell University)|Aug 24, 2021

Topological Materials and Phenomena4 citations

TL;DR

This paper proposes a mechanism for higher-order topological superconductivity in kagome and honeycomb lattices driven by repulsive electron-electron interactions, where Berry phase-induced interference converts repulsion into effective attraction near Dirac points. The resulting p+iτp superconducting state hosts gapped edge modes and robust Majorana corner states, confirmed via exact diagonalization and symmetry analysis, offering a microscopic explanation for unconventional superconductivity in AV₃Sb₃ materials.

ABSTRACT

We discuss a pairing mechanism in interacting two-dimensional multipartite lattices that intrinsically leads to a second order topological superconducting state with a spatially modulated gap. When the chemical potential is close to Dirac points, oppositely moving electrons on the Fermi surface undergo an interference phenomenon in which the Berry phase converts a repulsive electron-electron interaction into an effective attraction. The topology of the superconducting phase manifests as gapped edge modes in the quasiparticle spectrum and Majorana Kramers pairs at the corners. We present symmetry arguments which constrain the possible form of the electron-electron interactions in these systems and classify the possible superconducting phases which result. Exact diagonalization of the Bogoliubov-de Gennes Hamiltonian confirms the existence of gapped edge states and Majorana corner states, which strongly depend on the spatial structure of the gap. Possible applications to vanadium-based superconducting kagome metals AV$_3$Sb$_3$ (A=K,Rb,Cs) are discussed.

Motivation & Objective

• To identify a microscopic mechanism for higher-order topological superconductivity in two-dimensional multipartite lattices without requiring external proximity or fine-tuned parameters.
• To demonstrate that repulsive Coulomb interactions can induce effective pairing via Berry phase-mediated destructive interference near Dirac points.
• To classify possible superconducting phases arising from lattice-symmetry-consistent electron-electron interactions in kagome and honeycomb systems.
• To confirm the existence of topological edge and corner states through exact diagonalization of the Bogoliubov-de Gennes Hamiltonian.
• To propose a mechanism explaining unconventional superconductivity in vanadium-based kagome metals AV₃Sb₃ (A=K,Rb,Cs) with weak correlations.

Proposed method

• Constructs a generalized Hubbard model with spin- and orbital-symmetry-respecting interactions on kagome and honeycomb lattices, constrained by lattice point group symmetries.
• Derives effective pairing interactions using a weak-coupling approach, showing that Berry phase effects convert repulsive interactions into effective attraction for specific scattering channels near Dirac points.
• Derives the real-space pairing potential Δ(r,r′) as a spatially modulated function involving cosine and sine terms of the wavevector sum K·(r + r′), with phase shifts determined by sublattice structure.
• Performs exact diagonalization of the Bogoliubov-de Gennes Hamiltonian on finite-sized lattices with open boundaries to probe quasiparticle spectra and detect edge and corner modes.
• Simplifies the pairing potential by neglecting long-range correlations, retaining only the dominant short-range component Δ′cos( K·(r + r′) + φ) or sin( K·(r + r′) + φ) for analytical tractability.
• Establishes that the resulting superconducting state belongs to class BDI (time-reversal and chiral symmetry), ensuring topological protection of Majorana zero modes.

Experimental results

Research questions

• RQ1 Can repulsive electron-electron interactions in kagome and honeycomb lattices with Dirac points lead to higher-order topological superconductivity without requiring fine-tuning or external proximity effects?
• RQ2 How do Berry phase effects from the Fermi surface topology mediate an effective attraction between oppositely moving electrons, enabling Cooper pairing despite repulsive interactions?
• RQ3 What are the symmetry-allowed forms of electron-electron interactions in these lattices, and which lead to topologically non-trivial superconducting phases?
• RQ4 What is the spatial structure of the superconducting gap function, and how does it determine the existence of gapped edge modes and Majorana corner states?
• RQ5 Can this mechanism explain the emergence of unconventional superconductivity in AV₃Sb₃ materials, where correlations are weak but superconductivity is robust?

Key findings

• Repulsive interactions in kagome and honeycomb lattices can induce a second-order topological superconducting phase with a spatially modulated gap function, due to Berry phase-induced interference near Dirac points.
• The superconducting pairing potential takes the form Δ(r,r′) = Δ′Re{e^{i(K·(r+r′)+φ+π/2)}[φ₊₊(r)φ₊₋(r′) − φ₊₋(r)φ₊₊(r′)]}, leading to a p+iτp-like pairing state.
• Exact diagonalization confirms the presence of gapped edge modes and zero-energy Majorana corner states, which are robust under symmetry-preserving perturbations.
• For the honeycomb lattice, the pairing potential reduces to Δ(r,r′) = Δ′sin(K·(r + r′) + φ), while for the kagome lattice it becomes Δ(r,r′) = Δ′cos(K·(r + r′) + φ) with phase shifts between sublattices.
• The superconducting state belongs to class BDI, ensuring topological protection of Majorana corner modes due to time-reversal and chiral symmetries.
• The mechanism provides a plausible explanation for unconventional superconductivity in AV₃Sb₃ materials, where weak correlations and strong spin-orbit coupling coexist with topological superconducting order.