[Paper Review] Moir\'e surface states and enhanced superconductivity in topological insulators

Taige Wang, Noah F. Q. Yuan+1 more|arXiv (Cornell University)|Oct 19, 2020

Topological Materials and Phenomena52 references50 citations

TL;DR

This paper proposes that moiré superlattices on topological insulator surfaces host high-order van Hove singularities (VHS) with power-law divergent density of states (DOS), leading to strongly enhanced superconductivity via electron-phonon coupling. Unlike conventional systems, the topological surface states prevent band gaps, and the divergent DOS at high-order VHS enables a power-law enhancement of the superconducting critical temperature Tc, which is robust against perturbations and distinct from exponential Tc enhancements in ordinary metals.

ABSTRACT

Recently, moir\'e superlattices have been found on the surface of topological insulators (TI) due to the rotational misalignment of topmost layers. In this work, we study the effects of moir\'e superlattices on the topological surface states using a continuum model of Dirac electrons moving in a periodic potential. Unlike twisted bilayer graphene, moir\'e surface states cannot host isolated bands due to their topological nature. Instead, we find (high-order) van Hove singularities (VHS) in the moir\'e band structure that give rise to divergent density of states (DOS) and enhance interaction effects. Due to spin-momentum locking in moir\'e surface states, possible interaction channels are limited. In the presence of phonon mediated attraction, superconductivity is strongly enhanced by the power-law divergent DOS at high-order VHS. The transition temperature $T_c$ exhibits a power-law dependence on the retarded electron-phonon interaction strength $\lambda^*$. This enhancement is found to be robust under various perturbations from the high-order VHS.

Motivation & Objective

• To understand the electronic structure of moiré superlattices on topological insulator surfaces, where time-reversal symmetry preserves gapless Dirac cones.
• To investigate the emergence of high-order van Hove singularities (VHS) in the moiré band structure due to topological constraints.
• To analyze how power-law divergent density of states at high-order VHS enhances electron-phonon mediated superconductivity.
• To determine the robustness of superconducting enhancement under perturbations away from high-order VHS.
• To provide a theoretical framework for experimentally observing enhanced superconductivity in moiré topological insulator heterostructures.

Proposed method

• Modeling topological surface states as massless Dirac fermions in a periodic scalar potential using a continuum effective Hamiltonian.
• Using a C3-symmetric periodic potential with reciprocal vectors Gj to simulate moiré superlattices in topological insulators.
• Identifying high-order VHS through momentum-space critical points where both velocity and Hessian determinant vanish, leading to power-law DOS divergence.
• Solving the BCS gap equation within the Anderson-Morel approximation to compute the superconducting critical temperature Tc.
• Incorporating both electron-phonon attraction and Coulomb repulsion, with retardation effects reducing effective Coulomb repulsion.
• Performing numerical band structure calculations to locate VHS and Fermi surface nesting at varying potential strengths and twisted angles.

Experimental results

Research questions

• RQ1 Can high-order van Hove singularities emerge in moiré surface states of topological insulators due to their topological constraints?
• RQ2 How does the power-law divergent density of states at high-order VHS affect electron-phonon superconductivity?
• RQ3 What is the functional form of the superconducting critical temperature Tc in the presence of high-order VHS, and how does it compare to conventional systems?
• RQ4 Is the superconducting enhancement robust under deviations from the high-order VHS condition?
• RQ5 Can moiré superlattices in topological insulators provide a platform for enhanced, tunable superconductivity?

Key findings

• High-order van Hove singularities emerge at the K-point in the moiré Brillouin zone when the potential strength is tuned to U = 1.36vF /L, where three Fermi surfaces intersect.
• The density of states exhibits a power-law divergence N(ξ) ∝ |ξ|ν with −1 < ν < 0 near high-order VHS, leading to a strongly enhanced interaction-driven response.
• The superconducting critical temperature Tc follows a power-law dependence on the retarded electron-phonon coupling strength λ∗, Tc ∝ λ∗^α, which is parametrically enhanced compared to the exponentially small Tc in ordinary metals.
• The enhancement of Tc is robust under perturbations such as deviations from the magic angle or small potential fluctuations, due to the absence of band gaps and large electron velocities away from VHS.
• Retardation effects reduce the effective Coulomb repulsion, further favoring superconductivity in the presence of divergent DOS.
• The model predicts a tunable platform for enhanced superconductivity via twist angle control, with a predicted magic angle θc ≈ 0.74° for U = 1.36vF /L.