PROGRAM SUMMARY
Title of program:
KUBO
Catalogue identifier:
ADKI
Ref. in CPC:
118(1999)71
Distribution format: uuencoded compressed tar file
Operating system: UNIX 4.0D
High speed store required:
7.0MK words
Number of bits in a word:
64
Number of lines in distributed program, including test data, etc:
676
Programming language used: Fortran
Computer: Alphaserver 1200
Nature of physical 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.
Method of solution
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.
Restrictions on the complexity of the program
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.
Typical 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.
References
[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).