Seminars Archive

Breakdown of the topological protection in the integer Quantum Hall effect through vacuum field in metamaterial cavities

Jérôme Faist
Institute of Quantum Electronics, ETH Zurich

Abstract
When a collection of electronic excitations are strongly coupled to a single mode cavity, mixed light-matter excitations called polaritons are created. The situation is especially interesting when the strength of the light-matter coupling WR is such that the coupling energy becomes close to the one of the bare matter resonance w0. For this value of parameters, the system enters the so-called ultra-strong coupling regime, in which a number of very interesting physical effects were predicted caused by the counter-rotating and diamagnetic terms of the Hamiltonian. In a microcavity, the strength of the electric field caused by the vacuum fluctuations, to which the strength of the lightmatter coupling WR is proportional, scales inversely with the cavity volume. One very interesting feature of the circuitbased metamaterials is the fact that this volume can be scaled down to deep subwavelength values in all three dimension of space (1). Using metamaterial coupled to two-dimensional electron gases under a strong applied magnetic field, we have now explored to which extend this volume can be scaled down and reached a regime where the stability of the polariton is limited by diffraction into a continuum of plasmon modes (2). We have also used transport to probe the ultra-strong light-matter coupling (3), and show now that the latter can induce a breakdown of the integer quantum Hall effect (4). The phenomenon is explained in terms of cavity-assisted hopping, an antiresonant process where a an electron can scatter from one edge of the sample to the other by “borrowing” a photon from the cavity (5). Our experiments show the importance of “photonic disorder” or field gradients on the effect. Recently a proposal suggested that the value of the quantization voltage can be renormalized by the cavity (6), but later work demonstrated that such renormalization corresponds to a singular point in the parameter space (7). We have investigated this effect experimentally using a Wheatstone bridge geometry (8) and found the quantization to be held. 1. Scalari, G. et al. Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial. Science 335, 1323–1326 (2012). 2. Rajabali, S. et al. Polaritonic Nonlocality in Light Matter Interaction. Nat Photon 15, 690–695 (2021). 3. Paravicini-Bagliani, G. L. et al. Magneto-Transport Controlled by Landau Polariton States. Nat. Phys. 15, 186–190 (2019). 4. Appugliese, F. et al. Breakdown of topological protection by cavity vacuum fields in the integer quantum Hall effect. Science 375, 1030–1034 (2022). 5. Ciuti, C. Cavity-mediated electron hopping in disordered quantum Hall systems. Phys. Rev. B 104, 155307 (2021). 6. Rokaj, V., Penz, M., Sentef, M. A., Ruggenthaler, M. & Rubio, A. Polaritonic Hofstadter butterfly and cavity control of the quantized Hall conductance. Phys. Rev. B 105, 205424 (2022). 7. Rokaj, V. et al. On the Topological Protection of the Quantum Hall Effect in a Cavity. Preprint at https://doi.org/10.48550/arXiv.2305.10558 (2023). 8. Schopfer, F. & Poirier, W. Testing universality of the quantum Hall effect by means of the Wheatstone bridge. J. Appl. Phys. 102, 054903 (2007).