Abstract
We present a numerical method which allows to efficiently calculate quantum transport through phase-coherent scattering structures, so-called “quantum billiards”. Our approach consists of an extension of the commonly used Recursive Green’s Function Method (RGM), which proceeds by a discretization of the scattering geometry on a lattice with nearest-neighbour coupling. We show that the efficiency of the RGM can be enhanced considerably by choosing symmetry-adapted grids reflecting the shape of the billiard. Combining modules with different grid structure to assemble the entire scattering geometry allows to treat the quantum scattering problem of a large class of systems very efficiently. We will illustrate the computational challenges involved in the calculations and present results that have been obtained with our method.
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References
Aigner, F., Rotter, S., Burgdörfer, J.: Shot noise in the chaotic-to-regular crossover regime. Phys. Rev. Lett. 94, 216801 (2005)
Baranger, H.U., DiVincenzo, D.P., Jalabert, R.A., Stone, A.D.: Classical and quantum ballistic-transport anomalies in microjunctions. Phys. Rev. B 44, 10637 (1991)
Feist, J., Bäcker, A., Ketzmerick, R., Rotter, S., Huckestein, B., Burgdörfer, J. (to be published)
Ferry, D.K., Goodnick, S.M.: Transport in Nanostructures. Cambridge University Press, Cambridge (1997)
Libisch, F., Rotter, S., Burgdörfer, J., Kormńyos, A., Cserti, J.: Bound states in Andreev billiards with soft walls. Phys. Rev. B 72, 075304 (2005)
Mamaluy, D., Sabathil, M., Vogl, P.: Efficient method for the calculation of ballistic quantum transport. J. Appl. Phys. 93, 4628 (2003)
Marcus, C.M., Rimberg, A.J., Westervelt, R.M., Hopkins, P.F., Gossard, A.C.: Conductance fluctuations and chaotic scattering in ballistic microstructures. Phys. Rev. Lett. 69, 506 (1992)
Rotter, S., Tang, J.-Z., Wirtz, L., Trost, J., Burgdörfer, J.: Modular recursive Green’s function method for ballistic quantum transport. Phys. Rev. B 62, 1950 (2000)
Rotter, S., Weingartner, B., Rohringer, N., Burgdörfer, J.: Ballistic quantum transport at high energies and high magnetic fields. Phys. Rev. B 68, 165302 (2003)
Skjånes, J., Hauge, E.H., Schön, G.: Magnetotransport in a two-dimensional tight-binding model. Phys. Rev. B 50, 8636 (1994)
Sols, F., Macucci, M., Ravaioli, U., Hess, K.: Theory for a quantum modulated transistor. J. Appl. Phys. 66, 3892 (1989)
Stöckmann, H.-J.: Quantum Chaos. Cambridge University Press, Cambridge (1999)
Weingartner, B., Rotter, S., Burgdörfer, J.: Simulation of electron transport through a quantum dot with soft walls. Phys. Rev. B 72, 115342 (2005)
Yang, X., Ishio, H., Burgdörfer, J.: Statistics of magnetoconductance in ballistic cavities. Phys. Rev. B 52, 8219 (1995)
Zozoulenko, I.V., Maaø, F.A., Hauge, E.H.: Coherent magnetotransport in confined arrays of antidots. Phys. Rev. B 53, 7975 (1996)
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Rotter, S., Weingartner, B., Libisch, F., Aigner, F., Feist, J., Burgdörfer, J. (2006). A Modular Method for the Efficient Calculation of Ballistic Transport Through Quantum Billiards. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2005. Lecture Notes in Computer Science, vol 3743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11666806_67
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DOI: https://doi.org/10.1007/11666806_67
Publisher Name: Springer, Berlin, Heidelberg
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