Unified topological phase diagram of quantum Hall and superconducting vortex-lattice states

TL;DR

This paper maps the complex topological phase diagram of a 2D electron gas under magnetic field and superconducting vortices, revealing numerous topological phases and the critical role of Landau-level mixing.

Contribution

It provides a comprehensive theory for the topological phases in a quantum Hall-superconductor hybrid system, accounting for arbitrary parameter ratios and Landau-level effects.

Findings

Landau-level mixing splits quantum Hall transition lines into multiple transitions with larger Chern number jumps.

Weak pairing can lead to either trivial or topological superconductivity depending on Landau level tuning.

The phase diagram features a rich variety of topological superconducting phases with chiral edge modes.

Abstract

We present the global topological phase diagram of a two-dimensional electron gas placed in a quantizing magnetic field and proximitized by a superconducting vortex lattice. Our theory allows for arbitrary ratios of the pairing amplitude, magnetic field, and chemical potential. By analyzing the Bogoliubov--de Gennes Hamiltonian, we show that the resulting phase diagram is highly nontrivial, featuring a plethora of topological superconducting phases with chiral edge modes of quasiparticles. Landau-level mixing plays an essential role in our theory: even in the weak-pairing limit, it generically splits the integer quantum Hall transition lines into a sequence of transitions with larger Chern number jumps of both signs protected by the symmetries of the superconducting vortex lattice. Interestingly, we find that weak pairing induces trivial or topological superconductivity when chemical potential is tuned to a Landau level energy, depending on the Landau level index.