Cavity Modification of the Quantum Hall Effects*

Cavity modification of materials is a novel research field motivated by the advances in strong light-matter interactions. In this talk we present how the strong coupling of Landau levels (in a two-dimensional electron gas) to the cavity field leads to the emergence of quasiparticles between the Landau levels and the photons, known as Landau polaritons [1]. The Landau polaritons have direct implications for the transport properties of the electron gas [3,4]. Further, we will present how our theory predicts that the cavity field can alter the fundamental quantization of the Hall conductance in the integer regime [4], as it has been also recently observed experimentally [3]. Connections of our theoretical prediction to these experiments will be discussed. Finally, in the case where the electron gas is replaced by a 2D periodic material we show that our theory predicts the emergence of polaritonic fractal energy spectra as a function of the cavity coupling strength [4]. The polaritonic fractal spectra are a polaritonic extension of the well-known Hofstadter butterfly [5]. 

[1] V. Rokaj, M. Penz, M. A. Sentef, M. Ruggenthaler, and A. Rubio, Phys. Rev. Lett. 123, 047202 (2019)

[2] G. L. Paravicini-Bagliani et al., Nat. Phys. 15, 186-190 (2019)

[3] F. Appugliese et al., Science 375 (6584), 1030-1034 (2022)

[4] V. Rokaj, M. Penz, M.A. Sentef, M. Ruggenthaler, A. Rubio, Phys. Rev. B 105, 205424 (2022)

[5] D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976)