81 research outputs found
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
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
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
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
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