María A. H. Vozmediano

Gauge fields in graphene

The physics of graphene is acting as a bridge between quantum field theory and condensed matter physics due to the special quality of the graphene quasiparticles behaving as massless two dimensional Dirac fermions. Moreover, the particular structure of the 2D crystal lattice sets the arena to study and unify concepts from elasticity, topology and cosmology. In this paper we analyze these connections combining a pedagogical, intuitive approach with a more rigorous formalism when required.

Geometrical and topological aspects of graphene and related materials

Graphene, a two-dimensional crystal made of carbon atoms, provides a new and unexpected bridge between low- and high-energy physics. The field has evolved very quickly and there are already a number of good reviews available in the literature. Graphene constitutes a condensed-matter realization of lower dimensional quantum field theory models that were proposed to confront important—still unresolved—puzzles in the area: chiral symmetry breaking and quark confinement. The new materials named topological insulators, closely related to graphene, are physical realizations of topological field theory. This article reviews some of these topics with the aim of bridging the gap and making these condensed-matter issues accessible to high-energy readers. The electronic interactions in the monolayer are analyzed with special emphasis on the recent experimental confirmation of some theoretical predictions. The issue of spontaneous chiral symmetry breaking in the model materials is also reviewed. Finally we give an extensive description of some recent topological properties of graphene that allow us to understand the main aspects of topological insulators.

Charge inhomogeneities due to smooth ripples in graphene sheets

We study the effect of the curved ripples observed in the free standing graphene samples on the electronic structure of the system. We model the ripples as smooth curved bumps and compute the Greens function of the Dirac fermions in the curved surface. Curved regions modify the Fermi velocity that becomes a function of the point on the graphene surface and induce energy dependent oscillations in the local density of states around the position of the bump. The corrections are estimated to be of a few percent of the flat density at the typical energies explored in local probes such as scanning tunnel microscopy that should be able to observe the predicted correlation of the morphology with the electronics. We discuss the connection of the present work with the recent observation of charge anisotropy in graphene and propose that it can be used as an experimental test of the curvature effects.

Novel effects of strains in graphene and other two dimensional materials

The analysis of the electronic properties of strained or lattice deformed graphene combines ideas from classical condensed matter physics, soft matter, and geometrical aspects of quantum field theory (QFT) in curved spaces. Recent theoretical and experimental work shows the influence of strains in many properties of graphene not considered before, such as electronic transport, spin–orbit coupling, the formation of Moire patterns and optics. There is also significant evidence of anharmonic effects, which can modify the structural properties of graphene. These phenomena are not restricted to graphene, and they are being intensively studied in other two dimensional materials, such as the transition metal dichalcogenides. We review here recent developments related to the role of strains in the structural and electronic properties of graphene and other two dimensional compounds.

Magnetic moments in the presence of topological defects in graphene

Instituto de Ciencia de Materiales de Madrid,CSIC, Cantoblanco, E-28049 Madrid, Spain.(Dated: June 21, 2008)We study the influence of pentagons, dislocations and other topological defects breaking thesublattice symmetry on the magnetic properties of a graphene lattice in a Hartree Fock mean fieldscheme. The ground state of the system with a number of vacancies or similar defects belonging tothe same sublattice is known to have total spin equal to the number of uncoordinated atoms in thelattice for any value of the Coulomb repulsion U according to the Lieb theorem. We show that thepresence of a single pentagonal ring in a large lattice is enough to alter this behavior and a criticalvalue of U is needed to get the polarized ground state. Glide dislocations made of a pentagon-heptagon pair induce more dramatic changes on the lattice and the critical value of U needed topolarize the ground state depends on the density and on the relative position of the defects. Wefound a region in parameter space where the polarized and unpolarized ground states coexist.

Space dependent Fermi velocity in strained graphene

We investigate some apparent discrepancies between two different models for curved graphene: the one based on tight-binding and elasticity theory, and the covariant approach based on quantum field theory in curved space. We demonstrate that strained or corrugated samples will have a space-dependent Fermi velocity in either approach that can affect the interpretation of local probe experiments in graphene. We also generalize the tight-binding approach to general inhomogeneous strain and find a gauge field proportional to the derivative of the strain tensor that has the same form as the one obtained in the covariant approach.

Dislocations and torsion in graphene and related systems

Abstract A continuum model to study the influence of dislocations on the electronic properties of condensed matter systems is described and analyzed. The model is based on a geometrical formalism that associates a density of dislocations with the torsion tensor and uses the technique of quantum field theory in curved space. When applied to two-dimensional systems with Dirac points like graphene we find that dislocations couple in the form of vector gauge fields similar to these arising from curvature or elastic strain. We also describe the ways to couple dislocations to normal metals with a Fermi surface.

Elastic Gauge Fields in Weyl Semimetals.

We show that, as happens in graphene, elastic deformations couple to the electronic degrees of freedom as pseudogauge fields in Weyl semimetals. We derive the form of the elastic gauge fields in a tight-binding model hosting Weyl nodes and see that this vector electron-phonon coupling is chiral, providing an example of axial gauge fields in three dimensions. As an example of the new response functions that arise associated with these elastic gauge fields, we derive a nonzero phonon Hall viscosity for the neutral system at zero temperature. The axial nature of the fields provides a test of the chiral anomaly in high energy with three axial vector couplings.

Gauge fields from strain in graphene

This research was supported in part by Spanish MECD Grants No. FIS2008-00124, No. FIS2011-23713, No. PIB2010BZ-00512, and No. FPA2009-10612, the Spanish Consolider-Ingenio 2010 Programme CPAN (CSD2007- 00042), and Basque Government Grant No. IT559-10. F.d.J. acknowledges support from the “Programa Nacional de Movilidad de Recursos Humanos” (Spanish MECD).

Generalized effective Hamiltonian for graphene under nonuniform strain

We use a symmetry approach to construct a systematic derivative expansion of the low-energy effective Hamiltonian modifying the continuum Dirac description of graphene in the presence of nonuniform elastic deformations. We extract all experimentally relevant terms and describe their physical significance. Among them there is a new gap-opening term that describes the Zeeman coupling of the elastic pseudomagnetic field and the pseudospin. We determine the value of the couplings using a generalized tight-binding model.