5 research outputs found
Resistivity of a Metal between the Boltzmann Transport Regime and the Anderson Transition
We study the transport properties of a finite three dimensional disordered
conductor, for both weak and strong scattering on impurities, employing the
real-space Green function technique and related Landauer-type formula. The
dirty metal is described by a nearest neighbor tight-binding Hamiltonian with a
single s-orbital per site and random on-site potential (Anderson model). We
compute exactly the zero-temperature conductance of a finite size sample placed
between two semi-infinite disorder-free leads. The resistivity is found from
the coefficient of linear scaling of the disorder averaged resistance with
sample length. This ``quantum'' resistivity is compared to the semiclassical
Boltzmann expression computed in both Born approximation and multiple
scattering approximation.Comment: 5 pages, 3 embedded EPS figure
A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade
We provide a framework for analyzing the problem of interacting electrons in
a ballistic quantum dot with chaotic boundary conditions within an energy
(the Thouless energy) of the Fermi energy. Within this window we show that the
interactions can be characterized by Landau Fermi liquid parameters. When ,
the dimensionless conductance of the dot, is large, we find that the disordered
interacting problem can be solved in a saddle-point approximation which becomes
exact as (as in a large-N theory). The infinite theory shows a
transition to a strong-coupling phase characterized by the same order parameter
as in the Pomeranchuk transition in clean systems (a spontaneous
interaction-induced Fermi surface distortion), but smeared and pinned by
disorder. At finite , the two phases and critical point evolve into three
regimes in the plane -- weak- and strong-coupling regimes separated
by crossover lines from a quantum-critical regime controlled by the quantum
critical point. In the strong-coupling and quantum-critical regions, the
quasiparticle acquires a width of the same order as the level spacing
within a few 's of the Fermi energy due to coupling to collective
excitations. In the strong coupling regime if is odd, the dot will (if
isolated) cross over from the orthogonal to unitary ensemble for an
exponentially small external flux, or will (if strongly coupled to leads) break
time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we
are treating charge-channel instabilities in spinful systems, leaving
spin-channel instabilities for future work. No substantive results are
change