Polaritonic Hofstadter Butterfly and Cavity-Control of the Quantized Hall Conductance

TL;DR

This paper extends the QED-Bloch theory to predict fractal polaritonic spectra and cavity-controlled modifications of the Hofstadter butterfly and quantum Hall conductance in 2D materials under strong magnetic fields.

Contribution

It introduces the QED-Bloch framework for analyzing periodic materials in magnetic fields coupled to quantized light, revealing new fractal spectra and cavity effects on Hall conductance.

Findings

Cavity coupling modifies the Hofstadter butterfly spectrum.

Quantum Hall conductance is altered by light-matter interaction.

Fractal polaritonic spectra emerge as a function of cavity strength.

Abstract

In a previous work [Phys. Rev. Lett. 123, 047202 (2019)] a translationally invariant framework called quantum-electrodynamical Bloch (QED-Bloch) theory was introduced for the description of periodic materials in homogeneous magnetic fields and strongly coupled to the quantized photon field in the optical limit. For such systems, we show that QED-Bloch theory predicts the existence of fractal polaritonic spectra as a function of the cavity coupling strength. In addition, for the energy spectrum as a function of the relative magnetic flux we find that a terahertz cavity can modify the standard Hofstadter butterfly. In the limit of no quantized photon field, QED-Bloch theory captures the well-known fractal spectrum of the Hofstadter butterfly and can be used for the description of 2D materials in strong magnetic fields, which are of great experimental interest. As a further application, we consider Landau levels under cavity confinement and show that the cavity alters the quantized Hall conductance and that the Hall plateaus are modified as $\sigma_{xy}=e^2\nu/h(1+\eta^2)$ by the light-matter coupling $\eta$. Most of the aforementioned phenomena should be experimentally accessible and corresponding implications are discussed.