Effective theory of lattice electrons strongly coupled to quantum electromagnetic fields

TL;DR

This paper develops a high-frequency effective theory for lattice electrons strongly coupled to quantum electromagnetic fields, revealing tunable electronic band topology, emergent quasi-one-dimensional physics, and unconventional superconductivity in cavity-coupled systems.

Contribution

It introduces a nonperturbative high-frequency expansion for effective models of strongly coupled light-matter systems with arbitrary photon dispersion.

Findings

Cavity tuning can modify electronic band dispersion and topology.

Emergence of quasi-one-dimensional physics in 2D lattices due to anisotropic band renormalization.

Induction of topologically nontrivial quantum Hall states via cavity symmetry breaking.

Abstract

Recent experiments have revealed the tantalizing possibility of fabricating lattice electronic systems strongly coupled to quantum fluctuations of electromagnetic fields, e.g., by means of geometry confinement from a cavity or artificial gauge fields in quantum simulators. In this work, we develop a high-frequency expansion to construct the effective models for lattice electrons strongly coupled to a continuum of off-resonant photon modes with arbitrary dispersion. The theory is nonperturbative in the light-matter coupling strength, and is therefore particularly suitable for the ultrastrong light-matter coupling regime. Using the effective models, we demonstrate how the dispersion and topology of the electronic energy bands can be tuned by the cavity. In particular, quasi-one-dimensional physics can emerge in a two-dimensional square lattice due to a spatially anisotropic band renormalization, and a topologically nontrivial anomalous quantum Hall state can be induced in a honeycomb lattice when the cavity setup breaks time-reversal symmetry. We also demonstrate that the photon-mediated interaction induces an unconventional superconducting paired phase distinct from the pair-density-wave state discussed in models with truncated light-matter coupling. Finally, we study a realistic setup of a Fabry-P\'{e}rot cavity. Our work provides a systematic framework to explore the emergent phenomena due to strong light-matter coupling and points out new directions of engineering orders and topological states in solids.