368 research outputs found
Thermodynamics and Transport in Mesoscopic Disordered Networks
We describe the effects of phase coherence on transport and thermodynamic
properties of a disordered conducting network. In analogy with
weak-localization correction, we calculate the phase coherence contribution to
the magnetic response of mesoscopic metallic isolated networks. It is related
to the return probability for a diffusive particle on the corresponding
network. By solving the diffusion equation on various types of networks,
including a ring with arms, an infinite square network or a chain of connected
rings, we deduce the magnetic response. As it is the case for transport
properties --weak-localization corrections or universal conductance
fluctuations-- the magnetic response can be written in term of a single
function S called spectral function which is related to the spatial average of
the return probability on the network. We have found that the magnetization of
an ensemble of CONNECTED rings is of the same order of magnitude as if the
rings were disconnected.Comment: Proceedings of Minerva Workshop on Mesoscopics, Fractals and Neural
Networks, Eilat, March 1997, 13 pages, RevTeX, 2 figure
Artificial graphenes: Dirac matter beyond condensed matter
After the discovery of graphene and its many fascinating properties, there
has been a growing interest for the study of "artificial graphenes". These are
totally different and novel systems which bear exciting similarities with
graphene. Among them are lattices of ultracold atoms, microwave or photonic
lattices, "molecular graphene" or new compounds like phosphorene. The advantage
of these structures is that they serve as new playgrounds for measuring and
testing physical phenomena which may not be reachable in graphene, in
particular: the possibility of controlling the existence of Dirac points (or
Dirac cones) existing in the electronic spectrum of graphene, of performing
interference experiments in reciprocal space, of probing geometrical properties
of the wave functions, of manipulating edge states, etc. These cones, which
describe the band structure in the vicinity of the two connected energy bands,
are characterized by a topological "charge". They can be moved in reciprocal
space by appropriate modification of external parameters (pressure, twist,
sliding, stress, etc.). They can be manipulated, created or suppressed under
the condition that the total topological charge be conserved. In this short
review, I discuss several aspects of the scenarios of merging or emergence of
Dirac points as well as the experimental investigations of these scenarios in
condensed matter and beyond.Comment: 16 pages, 26 figures. To appear in Comptes-rendus de l'Acad\'emie des
Sciences, Franc
Persistent Currents for Interacting Electrons: a Simple Hartree-Fock Picture
The average persistent current of diffusive electrons in the Hartree-Fock
approximation is derived in a simple non-diagrammatic picture. The Fourier
expansion directly reflects the winding number decomposition of the diffusive
motion around the ring. One recovers the results of Ambegaokar and Eckern, and
Schmid. Moreover one finds an expression for which is valid beyond the
diffusive regime.Comment: 7 pages, latex, no figure
Mesoscopic Charge Density Wave in a Magnetic Flux
The stability of a Charge Density Wave (CDW) in a one-dimensional ring
pierced by a Aharonov-Bohm flux is studied in a mean-field picture. It is found
that the stability depends on the parity of the number of electrons. When
the size of the ring becomes as small as the coherence length , the CDW
gap increases for even and decreases for odd . Then when is even,
the CDW gap decreases with flux but it increases when is odd. The variation
of the BCS ratio with size and flux is also calculated. We derive the harmonics
expansion of the persistent current in a presence of a finite gap.Comment: Latex, 7 pages, 10 figure
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