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

Physical Review X (submitted), (2021)

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

Vasil Rokaj, Markus Penz, Michael A. Sentef, Michael Ruggenthaler, Angel Rubio

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. 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 σ xy =e 2 ν/h(1+η 2 ) by the light-matter coupling η . Most of the aforementioned phenomena should be experimentally accessible and corresponding implications are discussed.

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We would like to thank J. Faist for useful discussions. This work was supported by the European Research Council (ERC-2015-AdG694097), the Cluster of Excellence \Advanced Imaging of Matter" (AIM), Grupos Consolidados (IT1249-19), SFB925 \Light induced dynamics and control of correlated quantum systems", the Austrian Science Fund (J 4107-N27), and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via the Emmy Noether program (SE 2558/2). The Flatiron Institute is a division of the Simons Foundation.

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