https://doi.org/10.1140/epjb/e2002-00351-2
Structure of quantum disordered wave functions: weak localization, far tails, and mesoscopic transport
1
Department of Physics, Georgetown University, Washington, DC 20057-0995, USA
2
Department of Physics, Virginia Commonwealth University, Richmond, VA 23284, USA
Corresponding author: a bnikolic@physics.georgetown.edu
Received:
19
August
2002
Published online:
19
November
2002
We report on the comprehensive numerical study of the fluctuation
and correlation properties of wave functions in three-dimensional
mesoscopic diffusive conductors. Several large sets of nanoscale
samples with finite metallic conductance, modeled by an Anderson
model with different strengths of diagonal box disorder, have
been generated in order to investigate both small and large
deviations (as well as the connection between them) of the
distribution function of eigenstate amplitudes from the universal
prediction of random matrix theory. We find that small, weak
localization-type, deviations contain both diffusive
contributions (determined by the bulk and boundary conditions
dependent terms) and ballistic ones which are generated by
electron dynamics below the length scale set by the mean free
path . By relating the extracted parameters of the
functional form of nonperturbative deviations (“far tails”) to
the exactly calculated transport properties of mesoscopic
conductors, we compare our findings based on the full solution of
the Schrödinger equation to different approximative analytical
treatments. We find that statistics in the far tail can be
explained by the exp-log-cube asymptotics (convincingly refuting
the log-normal alternative), but with parameters whose dependence
on
is linear and, therefore, expected to be dominated by
ballistic effects. It is demonstrated that both small deviations
and far tails depend explicitly on the sample size—the
remaining puzzle then is the evolution of the far tail parameters
with the size of the conductor since short-scale physics is
supposedly insensitive to the sample boundaries.
PACS: 73.21.-b – Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems / 73.20.Fz – Weak or Anderson localization / 73.23.-b – Electronic transport in mesoscopic systems / 05.45.Mt – Quantum chaos; semiclassical methods
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002