Alberto Cortijo

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.

Electronic properties of curved graphene sheets

A model is proposed to study the electronic structure of slightly curved graphene sheets with an arbitrary number of pentagon-heptagon pairs and Stone-Wales defects based on a cosmological analogy. The disorder induced by curvature produces characteristic patterns in the local density of states that can be observed in scanning tunnel and transmission electron microscopy.

Tunable Casimir repulsion with three dimensional topological insulators

In this Letter, we show that switching between repulsive and attractive Casimir forces by means of external tunable parameters could be realized with two topological insulator plates. We find two regimes where a repulsive (attractive) force is found at small (large) distances between the plates, canceling out at a critical distance. For a frequency range where the effective electromagnetic action is valid, this distance appears at length scales corresponding to 1 - ϵ(ω) ∼ (2/π)αθ.

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.

Aharonov-Bohm interferences from local deformations in graphene

Mechanical deformations in graphene have been shown to be associated with ‘fictitious’ magnetic fields. Theoretical work now suggests that these fields can give rise to an analogue of the Aharonov–Bohm effect, a phenomenon that might be used to sensitively detect small deformations of the graphene sheet.

Condensed matter realization of the axial magnetic effect

The axial magnetic effect, i.e., the generation of an energy current parallel to an axial magnetic field coupling with opposite signs to left- and right-handed fermions is a non-dissipative transport phenomenon intimately related to the gravitational contribution to the axial anomaly. An axial magnetic field is naturally realized in condensed matter in the so called Weyl semi-metals. We show that the edge states of a Weyl semimetal at finite temperature possess a temperature dependent angular momentum in the direction of the vector potential intrinsic to the system. Such a condensed matter realization provides a plausible context for the experimental confirmation of the elusive gravitational anomaly.

Effect of finite temperature and uniaxial anisotropy on the Casimir effect with three-dimensional topological insulators

In this work we study the Casimir effect with three-dimensional topological insulators including the effects of temperature and uniaxial anisotropy. We find that the reported repulsive behavior and the equilibrium point are robust features of the system, and are favored by low temperatures and the enhancement of the optical response parallel to the optical axis. The dependence of the equilibrium point with temperature and with the topological magnetoelectric polarizability characteristic of three-dimensional topological insulators is also discussed. PACS numbers: