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Manuscript Title: Computational implementation of the Kubo formula for the static conductance: application to two-dimensional quantum dots.
Authors: J.A. Verges
Program title: KUBO
Catalogue identifier: ADKI_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 118(1999)71
Programming language: Fortran.
Computer: Alphaserver 1200.
Operating system: UNIX 4.0D.
RAM: 7.0M words
Word size: 64
Keywords: Solid state physics, Transport properties, Conductance, Kubo formula, One-band two-dimensional, Tight-binding, Hamiltonian, Field magnetic, Random fluxes, Diagonal disorder.
Classification: 7.9.

Nature of problem:
Conductance evaluation plays a central role in the study of the physical properties of quantum dots [1]. The finite mesoscopic system under study is connected to infinite leads defining an infinitesimal voltage drop. Kubo formula is used for the conductance calculation once the Green function of the whole system is known. Dependence of the conductance on the number of conducting modes in the leads, size and shape of the dot, Fermi energy, presence of conventional diagonal disorder or random magnetic fluxes through the plaquettes and a uniform magnetic field through the sample can be considered as needed.

Solution method:
The calculation of the Green function of the system formed by the quantum dots and the leads is the main concern of the program [2]. Firstly, the selfenergy due to a semi-infinite ideal lead is calculated. Secondly, this selfenergy is used as the starting value for an iteration through the sample that takes into account its shape and local disorder and magnetic fluxes. Thirdly, the final selfenergy is matched via a two-slab Green function calculation with the selfenergy coming from the opposite sample side. Finally, Kubo formula is used for obtaining the system conductance from the current traversing the dot.

The more important restriction is the use of just a one-band tight-binding Hamiltonian. Other program characteristics, like the rectangular shape of the sample, the position of the leads near opposite sample corners, etc, can be easily changed.

Running time:
The calculation of the conductance at a fixed Fermi energy for ten random realizations of 100 x 100 disordered samples takes 225 seconds on a DECstation 3000 Model 400.

[1] For reviews of mesoscopic physics see C.W.J. Beenakker and H. van Houten, in Solid State Physics, edited by H. Ehrenreich and D. Turnbull (Academic Press, New York, 1991), Vol. 44, pp. 1-228; Mesoscopic Phenomena in Solids edited by B.L. Altshuler, P.A. Lee and R.A. Webb (North-Holland, New York, 1991).
[2] The following book by Datta gives a good account of both the basic concepts and the practical things that should be solved to get the conductance of a mesoscopic system, S. Datta, Electronic Transport in Mesoscopic Systems, (Cambridge University Press, Cambridge, 1995).