Single Dirac Fermion Research Articles

Manipulation of the Dirac cones and the anomaly in the graphene related quantum Hall effect

The quantum Hall effect in graphene is regarded to be involving half-integer topological numbers associated with the massless Dirac particle, this is usually not apparent due to the doubling of the Dirac cones. Here we theoretically consider two classes of lattice models in which we manipulate the Dirac cones with either (a) two Dirac points that have mutually different energies, or (b) multiple Dirac cones having different Fermi velocities. We have shown, with an explicit calculation of the topological (Chern) number for case (a) and with an adiabatic argument for case (b) that the results are consistent with the picture that a single Dirac fermion contributes the half-odd integer series (… -3/2, -1/2, 1/2, 3/2, …) to the Hall conductivity when the Fermi energy traverses the Landau levels.

Single valley Dirac fermions in zero-gap HgTe quantum wells

Dirac fermions have been studied intensively in condensed matter physics in recent years. Many theoretical predictions critically depend on the number of valleys where the Dirac fermions are realized. In this work, we report the discovery of a two dimensional system with a single valley Dirac cone. We study the transport properties of HgTe quantum wells grown at the critical thickness separating between the topologically trivial and the quantum spin Hall phases. At high magnetic fields, the quantized Hall plateaus demonstrate the presence of a single valley Dirac point in this system. In addition, we clearly observe the linear dispersion of the zero mode spin levels. Also the conductivity at the Dirac point and its temperature dependence can be understood from single valley Dirac fermion physics.

Hexagonal Warping Effects in the Surface States of the Topological InsulatorBi2Te3

A single two-dimensional Dirac fermion state has been recently observed on the surface of the topological insulator Bi2Te3 by angle-resolved photoemission spectroscopy. We study the surface band structure using k x p theory and find an unconventional hexagonal warping term, which is the counterpart of cubic Dresselhaus spin-orbit coupling in rhombohedral structures. We show that this hexagonal warping term naturally explains the observed hexagonal snowflake Fermi surface. The strength of hexagonal warping is characterized by a single parameter, which is extracted from the size of the Fermi surface. We predict a number of testable signatures of hexagonal warping in spectroscopy experiments on Bi2Te3. We also explore the possibility of a spin-density wave due to strong nesting of the Fermi surface.

Nonperturbative volume reduction of large-NQCD with adjoint fermions

We use nonperturbative lattice techniques to study the volume-reduced ``Eguchi-Kawai'' version of four-dimensional large-$N$ QCD with a single adjoint Dirac fermion. We explore the phase diagram of this single-site theory in the space of quark mass and gauge coupling using Wilson fermions for a number of colors in the range $8\ensuremath{\le}N\ensuremath{\le}15$. Our evidence suggests that these values of $N$ are large enough to determine the nature of the phase diagram for $N\ensuremath{\rightarrow}\ensuremath{\infty}$. We identify the region in the parameter space where the $({Z}_{N}{)}^{4}$ center symmetry is intact. According to previous theoretical work using the orbifolding paradigm, and assuming that translation invariance is not spontaneously broken in the infinite-volume theory, in this region volume reduction holds: the single-site and infinite-volume theories become equivalent when $N\ensuremath{\rightarrow}\ensuremath{\infty}$. We find strong evidence that this region includes both light and heavy quarks (with masses that are at the cutoff scale), and our results are consistent with this region extending toward the continuum limit. We also compare the action density and the eigenvalue density of the overlap Dirac operator in the fundamental representation with those obtained in large-$N$ pure-gauge theory.

Probing Neutral Majorana Fermion Edge Modes with Charge Transport

We propose two experiments to probe the Majorana fermion edge states that occur at a junction between a superconductor and a magnet deposited on the surface of a topological insulator. Combining two Majorana fermions into a single Dirac fermion on a magnetic domain wall allows the neutral Majorana fermions to be probed with charge transport. We will discuss a novel interferometer for Majorana fermions, which probes their Z2 phase. This setup also allows the transmission of neutral Majorana fermions through a point contact to be measured. We introduce a point contact formed by a superconducting junction and show that its transmission can be controlled by the phase difference across the junction. We discuss the feasibility of these experiments using the recently discovered topological insulator Bi2Se3.

Chirality and fermion number in a knotted soliton background

We consider the coupling of a single Dirac fermion to the three component unit vector field which appears as an order parameter in the Faddeev model. Classically, the coupling is determined by requiring that it preserves a certain local frame independence. But quantum mechanically the separate left- and right-chiral fermion number currents suffer from a frame anomaly. We employ this anomaly to compute the fermion number of a knotted soliton. The result coincides with the self-linking number of the soliton. In particular, the anomaly structure of the fermions relates directly to the inherent chiral properties of the soliton. Our result suggests that interactions between fermions and knotted solitons can lead to phenomena akin the Callan–Rubakov effect.

On the induced transverse gauge invariant mass term

We derive a general expression for the gauge invariant mass (mG) for an Abelian gauge field, as induced by vacuum polarization, in 1 + 1 dimensions. From its relation to the chiral anomaly, we show that mG has to satisfy a certain dynamical quantization condition. This quantization can, on the other hand, be explicitly verified by using the exact general expression for the gauge invariant mass in terms of the fermion propagator. This result is applied to some explicit examples, exploring the possibility of having interesting physical situations where the value of mG departs from its canonical value of e2/π for a single massless Dirac fermion in 1 + 1 dimensions. We also study the possibility of generalizing the results to the (2 + 1)-dimensional case at finite temperature, showing that there are indeed situations where a finite and non-vanishing gauge invariant mass is induced.