Transport through nanostructures
Wavepackets are well suited to model the transport of electrons through potentials given i.e. in semiconductor devices [18,19,24]. Our main emphasis is to include potentials due to gates, donor layer atoms, and contacts directly in the evaluation of the conductivity. By working in position space, we can make accurate models of the spatial electron flow through a device [18,19]. The current is experimentally accessible by sophisticated imaging methods, like Scanning Probe Microscopy.
Beyond linear response theories
For a detailed comparison with experimental data, it is necessary to consider the details of the measurement setup in the calculation. Our work on interferences and phase-jumps in Aharonov-Bohm interferometers [26] is a good example of our device simulation with non-zero voltage differences and finite currents.
Quantum Hall effect
The quantum Hall effect occurs in devices harboring a two-dimensional electron gas at low temperatures in the presence of a magnetic field, through which a current flows.
The coupling of the appearance of the quantum Hall effect to the transport of a current through the device (via the Hall voltage across the sample) raises interesting questions:
- Is there a Quantum Hall effect without a current?
- How to include the current (and Hall voltage) in a (non-linear) transport theory?
- Is there a Quantum Hall effect in a clean sample (without disorder)?
- Exist half-filled Landau levels without incorporating interactions?
Our approach works by quantizing the system based on the mean-field potential obtained from the classical, fully Coulomb-interacting system [25]. The potential distribution, which we obtain from our classical calculation, has been observed under conditions of the quantized Hall effect. Our microscopic calculation traces the emergence of the Hall potential back to interactions and the current injecting contact regions and thus highlights the importance of interactions and the choice of boundary conditions for the classical and integer quantized Hall effects.
Based on the mean-field potential, we calculate the Green function of an non-interacting Fermi gas in the magnetic field AND the potential. The main results are surprising:
- The electric (Hall) field leads to a broadening of Landau levels and finally at high currents to a breakdown of the quantized conductivity. The predicted behavior is in precise agreement with an empirical breakdown law observed in experiments [6,13].
- A splitting of higher Landau levels is induced by a homogeneous electric field. This leads to additional plateaus at non-integer multiples of the conductivity quantum (we predict fractions at 5/2, 7/2, not 9/2, 11/2, and again at 13/2, 15/2). The splitting and broadening is dependent on the level index [6,15].
- There is a natural transition of the quantum Hall effect to the classical
Hall effect at
- High temperatures.
- High currents.
- High Landau levels.
All these results are obtained within a simple, yet consistent approach which incorporates the Hall field directly in the expressions for the conductivity. A semiclassical interpretation of th quantum mechanical Green function is given in [9].
References
| [26] | Phase shifts and phase pi-jumps in four-terminal waveguide Aharonov-Bohm interferometers | ||
| C. Kreisbeck, T. Kramer, S. Buchholz, S. Fischer, U. Kunze, D. Reuter, A. Wieck | |||
| Phys. Rev. B, 82, 165329 (2010) | article | arxiv | |
| [25] | Self-consistent calculation of electric potentials in Hall devices | ||
| T. Kramer, V. Krueckl, E. Heller, and R. Parrott | |||
| Phys. Rev. B, 81, 205306 (2010) | article | arxiv | |
| [24] | Wave packet approach to transport in mesoscopic systems | ||
| T. Kramer, C. Kreisbeck, and V. Krueckl | |||
| Physica Scripta, 82, 038101 (2010) | article | arxiv | |
| [23] | Theory of the quantum Hall effect in finite graphene devices | ||
| T. Kramer, C. Kreisbeck, V. Krueckl, E. Heller, R. Parrott, and C.-T. Liang | |||
| Phys. Rev. B, 81, 081410(R) (2010) | article | arxiv | |
| [19] | An efficient and accurate method to obtain the energy-dependent Green function for general potentials | ||
| T. Kramer, E. Heller, and R. Parrott | |||
| J. Phys.: Conference Series, 99 012010 (2008) [Open Access] | article | arxiv | |
| [18] | Imaging Magnetic Focusing of Coherent Electron Waves | ||
| K. Aidala, R. Parrott, T. Kramer, R. Westervelt, E. Heller, M. Hanson, and A. Gossard | |||
| Nature Physics, 3 , 464-468 (2007) | article | arxiv | |
| [15] | Landau level broadening without disorder, non-integer plateaus without interactions – an alternative model of the quantum Hall effect | ||
| T. Kramer | |||
| Revista Mexicana de Física S, 52, 49-55, (2006) | article | arxiv | |
| [13] | A heuristic quantum theory of the integer quantum Hall effect | ||
| T. Kramer | |||
| International Journal of Modern Physics B, 20, 1243-1260, (2006) | article | arxiv | |
| [9] | Electron drift orbits in crossed electromagnetic fields and the quantum Hall effect | ||
| T. Kramer | |||
| Group theoretical methods in physics. Institute of Physics Conference Series Number 185., Edited by G.S. Pogosyan, L.E. Vicent and K.B. Wolf, Cocoyoc, Mexico, pp. 353-358, (2004) | book | arxiv | |
| [8] | Propagation in crossed magnetic and electric fields: The quantum source approach | ||
| T. Kramer and C. Bracher | |||
| Symmetries in Science XI, Edited by B. Gruber, G. Marmo, and N. Yoshinaga, Kluwer, Dordrecht, (2004) | book | arxiv | |
| [6] | Electron propagation in crossed magnetic and electric fields | ||
| T. Kramer, C. Bracher, and M. Kleber | |||
| J. Opt. B: Quantum Semiclass. Opt., 6, 21-27, (2004) | article | arxiv | |