Doping-induced quantum spin Hall insulator to superconductor transition

TL;DR

This paper investigates the transition from a quantum spin Hall insulator to a superconductor induced by doping, revealing a complex interplay of topological and superconducting phases through large-scale quantum Monte Carlo simulations.

Contribution

It demonstrates that doping induces a transition from a quantum spin Hall state to a superconductor with a unified critical point, challenging mean-field predictions and revealing critical behavior.

Findings

Critical chemical potential for superconductivity and spin Hall order vanish simultaneously.

Fluctuation length scale diverges near the transition, indicating continuous or weakly first-order transition.

Doping versus chemical potential curve is nonlinear, implying a dynamical critical exponent z > 2.

Abstract

A unique property of a dynamically generated quantum spin Hall state are Goldstone modes that correspond to the long-wavelength fluctuations of the spin-orbit coupling order parameter whose topological Skyrmion excitations carry charge 2$e$. Within the model considered here, upon varying the chemical potential, we observe two transitions: An s-wave superconducting order parameter develops at a critical chemical potential $\mu_{c1}$, corresponding to the excitation gap of pairs of fermions, and at $\mu_{c2}$ the SO(3) order parameter of the quantum spin Hall state vanishes. Using negative-sign-free, large-scale quantum Monte Carlo simulations, we show that $\mu_{c1}=\mu_{c2}$ within our accuracy -- we can resolve dopings away from half filling down to $\delta = 0.0017$. The length scale associated with the fluctuations of the quantum spin Hall order parameter grows down to our lowest doping, suggesting either a continuous or a weakly first-order transition. Contrary to mean-field expectations, the doping versus chemical potential curve is not linear, indicating a dynamical critical exponent $z > 2$ if the transition is continuous.