Quantum Electrodynamical Bloch Theory with Homogeneous Magnetic Fields

Physical Review Letters 123, 047202 (2019)

Quantum Electrodynamical Bloch Theory with Homogeneous Magnetic Fields

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

We propose a solution to the problem of Bloch electrons in a homogeneous magnetic field by including the quantum fluctuations of the photon field. A generalized quantum electrodynamical (QED)-Bloch theory from first principles is presented. In the limit of vanishing quantum fluctuations, we recover the standard results of solid-state physics: the fractal spectrum of the Hofstadter butterfly. As a further application, we show how the well-known Landau physics is modified by the photon field and that Landau polaritons emerge. This shows that our QED-Bloch theory does not only allow us to capture the physics of solid-state systems in homogeneous magnetic fields but also novel features that appear at the interface of condensed matter physics and quantum optics.

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We would like to thank M. Altarelli, J. Faist, H. Huebener, A. Imamoglu, J. Kaye, and A. Millis for insightful discussions. M. P. acknowledges support by the Erwin Schrödinger Fellowship No. J 4107-N27 of the FWF (Austrian Science Fund). M. A. S. acknowledges financial support by the DFG through the Emmy Noether programme (No. SE 2558/2-1). A. R. acknowledges financial support by the European Research Council (No. ERC-2015-AdG-694097). The Flatiron Institute is a division of the Simons Foundation.

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