A solvable model of Landau quantization breakdown
arXiv:1809.02487 · doi:10.1140/epjb/e2019-100107-7
Abstract
Physics of two-dimensional electron gases under perpendicular magnetic field often displays three distinct stages when increasing the field amplitude: a low field regime with classical magnetotransport, followed at intermediate field by a Shubnikov-de Haas phase where the transport coefficients present quantum oscillations, and, ultimately, the emergence at high field of the quantum Hall effect with perfect quantization of the Hall resistance. A rigorous demonstration of this general paradigm is still limited by the difficulty in solving models of quantum Hall bars with macroscopic lateral dimensions and smooth disorder. We propose here the exact solution of a simple model exhibiting similarly two sharp transitions that are triggered by the competition of cyclotron motion and potential-induced drift. As a function of increasing magnetic field, one observes indeed three distinct phases showing respectively fully broken, partially smeared, or perfect Landau level quantization. This model is based on a non-rotationally invariant, inverted two-dimensional harmonic potential, from which a full quantum solution is obtained using 4D phase space quantization. The developed formalism unifies all three possible regimes under a single analytical theory, as well as arbitrary quadratic potentials, for all magnetic field values.
v3: this version is a slightly improved version of the final publication (a few typos in Section 3 and Appendix A have been corrected). This final publication is available at Springer via http://dx.doi.org/10.1140/epjb/e2019-100107-7
References in corpus (12)
- The Quantum Hall Transition in Real Space: From Localized to Extended States
- Robust Nodal Structure of Landau Level Wave Functions Revealed by Fourier Transform Scanning Tunneling Spectroscopy
- High magnetic field theory for the local density of states in graphene with smooth arbitrary potential landscapes
- Quantum transport properties of two-dimensional electron gases under high magnetic fields
- Microscopics of disordered two-dimensional electron gases under high magnetic fields: Equilibrium properties and dissipation in the hydrodynamic regime
- Magnetotransport of electrons in quantum Hall systems
- Local density of states in disordered two-dimensional electron gases at high magnetic field
- Electron quantum dynamics in closed and open potentials at high magnetic fields: Quantization and lifetime effects unified by semicoherent states
- Classical percolation fingerprints in the high-temperature regime of the integer quantum Hall effect
- Tomographic Probability Representation for States of Charge moving in Varying Field
- Nonlocal correlations of the local density of states in disordered quantum Hall systems
- Tomographic probability representation in the problem of transitions between the Landau levels