8 research outputs found
Universal conductivity and dimensional crossover in multi-layer graphene
We show, by exact Renormalization Group methods, that in multi-layer graphene
the dimensional crossover energy scale is decreased by the intra-layer
interaction, and that for temperatures and frequencies greater than such scale
the conductivity is close to the one of a stack of independent layers up to
small corrections
Lattice quantum electrodynamics for graphene
The effects of gauge interactions in graphene have been analyzed up to now in
terms of effective models of Dirac fermions. However, in several cases lattice
effects play an important role and need to be taken consistently into account.
In this paper we introduce and analyze a lattice gauge theory model for
graphene, which describes tight binding electrons hopping on the honeycomb
lattice and interacting with a three-dimensional quantum U(1) gauge field. We
perform an exact Renormalization Group analysis, which leads to a renormalized
expansion that is finite at all orders. The flow of the effective parameters is
controlled thanks to Ward Identities and a careful analysis of the discrete
lattice symmetry properties of the model. We show that the Fermi velocity
increases up to the speed of light and Lorentz invariance spontaneously emerges
in the infrared. The interaction produces critical exponents in the response
functions; this removes the degeneracy present in the non interacting case and
allow us to identify the dominant excitations. Finally we add mass terms to the
Hamiltonian and derive by a variational argument the correspondent gap
equations, which have an anomalous non-BCS form, due to the non trivial effects
of the interaction.Comment: 44 pages, 6 figure
Universality of conductivity in interacting graphene
The Hubbard model on the honeycomb lattice describes charge carriers in
graphene with short range interactions. While the interaction modifies several
physical quantities, like the value of the Fermi velocity or the wave function
renormalization, the a.c. conductivity has a universal value independent of the
microscopic details of the model: there are no interaction corrections,
provided that the interaction is weak enough and that the system is at half
filling. We give a rigorous proof of this fact, based on exact Ward Identities
and on constructive Renormalization Group methods
Anomalous behavior in an effective model of graphene with Coulomb interactions
We analyze by exact Renormalization Group (RG) methods the infrared
properties of an effective model of graphene, in which two-dimensional massless
Dirac fermions propagating with a velocity smaller than the speed of light
interact with a three-dimensional quantum electromagnetic field. The fermionic
correlation functions are written as series in the running coupling constants,
with finite coefficients that admit explicit bounds at all orders. The
implementation of Ward Identities in the RG scheme implies that the effective
charges tend to a line of fixed points. At small momenta, the quasi-particle
weight tends to zero and the effective Fermi velocity tends to a finite value.
These limits are approached with a power law behavior characterized by
non-universal critical exponents.Comment: 42 pages, 7 figures; minor corrections, one appendix added (Appendix
A). To appear in Ann. Henri Poincar
Universality of charge transport in weakly interacting fermionic systems
We review two rigorous results on the transport properties of weakly interacting fermionic systems on 2d lattices, in the linear response regime. First, we discuss the universality of the longitudinal conductivity for interacting graphene. Then, we focus on the transverse conductivity of general weakly interacting gapped fermionic systems, and we establish its universality. This last result proves the stability of the integer quantum Hall effect against weak interactions. The proofs are based on combinations of fermionic cluster expansion techniques, renormalization group and lattice Ward identities
Universal Edge Transport in Interacting Hall Systems
We study the edge transport properties of 2d interacting Hall systems, displaying single-mode chiral edge currents. For this class of many-body lattice models, including for instance the interacting Haldane model, we prove the quantization of the edge charge conductance and the bulk-edge correspondence. Instead, the edge Drude weight and the edge susceptibility are interaction-dependent; nevertheless, they satisfy exact universal scaling relations, in agreement with the chiral Luttinger liquid theory. Moreover, charge and spin excitations differ in their velocities, giving rise to the spin-charge separation phenomenon. The analysis is based on exact renormalization group methods, and on a combination of lattice and emergent Ward identities. The invariance of the emergent chiral anomaly under the renormalization group flow plays a crucial role in the proof
Universality of the Hall Conductivity in Interacting Electron Systems
We prove the quantization of the Hall conductivity for general weakly interacting gapped fermionic systems on two-dimensional periodic lattices. The proof is based on fermionic cluster expansion techniques combined with lattice Ward identities, and on a reconstruction theorem that allows us to compute the Kubo conductivity as the analytic continuation of its imaginary time counterpart