215 research outputs found
Four-terminal resistances in mesoscopic networks of metallic wires: Weak localisation and correlations
We consider the electronic transport in multi-terminal mesoscopic networks of
weakly disordered metallic wires. After a brief description of the classical
transport, we analyze the weak localisation (WL) correction to the
four-terminal resistances, which involves an integration of the Cooperon over
the wires with proper weights. We provide an interpretation of these weights in
terms of classical transport properties. We illustrate the formalism on
examples and show that weak localisation to four-terminal conductances may
become large in some situations. In a second part, we study the correlations of
four-terminal resistances and show that integration of Diffuson and Cooperon
inside the network involves the same weights as the WL. The formulae are
applied to multiconnected wire geometries.Comment: 20 pages, contribution to a special issue in Physica E "Frontiers in
quantum electronic transport - in memory of Markus B\"uttiker
Topological phase transitions in the 1D multichannel Dirac equation with random mass and a random matrix model
We establish the connection between a multichannel disordered model --the 1D
Dirac equation with matricial random mass-- and a random matrix
model corresponding to a deformation of the Laguerre ensemble. This allows us
to derive exact determinantal representations for the density of states and
identify its low energy () behaviour
. The vanishing of the exponent
for specific values of the averaged mass over disorder ratio
corresponds to phase transitions of topological nature characterised by the
change of a quantum number (Witten index) which is deduced straightforwardly in
the matrix model.Comment: 7+4 pages, 9+1 pdf figures ; v2: paper reorganised, discussion of
non-isotropic case adde
Non-linear conductance in mesoscopic weakly disordered wires -- Interaction and magnetic field asymmetry
We study the non-linear conductance in coherent quasi-1D weakly disordered metallic wires. The analysis
is based on the calculation of two fundamental correlators (correlations of
conductance's functional derivatives and correlations of injectivities), which
are obtained explicitly by using diagrammatic techniques. In a coherent wire of
length , we obtain (and
), where is the Thouless
energy and the diffusion constant; the small dimensionless factor results
from screening, i.e. cannot be obtained within a simple theory for
non-interacting electrons. Electronic interactions are also responsible for an
asymmetry under magnetic field reversal: the antisymmetric part of the
non-linear conductance (at high magnetic field) being much smaller than the
symmetric one, , where
is the dimensionless (linear) conductance of the wire. Weakly coherent regimes
are also studied: for , where is the phase
coherence length, we get
, and
(at
high magnetic field). When thermal fluctuations are important, where , we obtain
(the result is
dominated by the effect of screening) and
. All the
precise dimensionless prefactors are obtained. Crossovers towards the zero
magnetic field regime are also analysed.Comment: RevTeX, 39 pages, 38 pdf figures ; v2: Sections II, VII, VIII & IX
reorganised, refs added ; v3: Table I updated, Appendices B & C extended, to
appear in Phys. Rev.
Local Friedel sum rule on graphs
We consider graphs made of one-dimensional wires connected at vertices and on
which may live a scalar potential. We are interested in a scattering situation
where the graph is connected to infinite leads. We investigate relations
between the scattering matrix and the continuous part of the local density of
states, the injectivities, emissivities and partial local density of states.
Those latter quantities can be obtained by attaching an extra lead at the point
of interest and by investigating the transport in the limit of zero
transmission into the additional lead. In addition to the continuous part
related to the scattering states, the spectrum of graphs may present a discrete
part related to states that remain uncoupled to the external leads. The theory
is illustrated with the help of a few simple examples.Comment: 25 pages, LaTeX, 8 figure
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