Topological insulators are a unique class of materials characterized by a Dirac cone state of helical Dirac fermions in the middle of a bulk gap. When the thickness of a three-dimensional topological insulator is reduced, however, the interaction between opposing surface states opens a gap that removes the helical Dirac cone, converting the material back to a normal system of ordinary fermions....

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We discuss a non-Fermi liquid gapless metallic surface state of the topological band insulator. It has an odd number of gapless Dirac fermions coupled to a noncompact Uð1Þ gauge field. This can be viewed as a vortex dual to the conventional Dirac fermion surface state. This sur...

The Evans wave equation [1] of general relativity is expressed in spinor form, thus producing the Dirac equation in general relativity. The Dirac equation in special relativity is recovered in the limit of Euclidean or flat spacetime. By deriving the Dirac equation from the Evans equation it is demonstrated that the former originates in a novel metric compatibility condition, a geometrical cons...

We present a pilot-wave model for quantum field theory in which the Dirac sea is taken seriously. The model ascribes particle trajectories to all the fermions, including the fermions filling the Dirac sea. The model is deterministic and applies to the regime in which fermion-number is super-selected. This work is a further elaboration of work by Colin, in which a Dirac sea pilot-wave model is p...

We discuss the exact chiral symmetry and its spontaneous breakdown in lattice QCD with the Dirac operators satisfying the GinspargWilson relation. The axial vector current, which turns out to be related to the vector current simply by the insertion of the operator γ5(1−aD), is explicitly constructed in the case of the Neuberger-Dirac operator. We also consider an Euclidean proof of the Nambu-Go...

In this paper, we develop the theoretical foundations of discrete Dirac mechanics, that is, discrete mechanics of degenerate Lagrangian/Hamiltonian systems with constraints. We first construct discrete analogues of Tulczyjew’s triple and induced Dirac structures by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this framework provides ...

Abstract: We prove that for a Dirac operator, with no resonance at thresholds nor eigenvalue at thresholds, the propagator satisfies propagation and dispersive estimates. When this linear operator has only two simple eigenvalues sufficiently close to each other, we study an associated class of nonlinear Dirac equations which have stationary solutions. As an application of our decay estimates, w...

For the innovation of spintronic technologies, Dirac materials, in which low-energy excitation is described as relativistic Dirac fermions, are one of the most promising systems because of the fascinating magnetotransport associated with extremely high mobility. To incorporate Dirac fermions into spintronic applications, their quantum transport phenomena are desired to be manipulated to a large...

We study a class of Dirac semimetals that feature an eightfold-degenerate double Dirac point. We show that 7 of the 230 space groups can host such Dirac points and argue that they all generically display linear dispersion. We introduce an explicit tight-binding model for space groups 130 and 135. Space group 135 can host an intrinsic double Dirac semimetal with no additional states at the Fermi...

The spectrum of a Schrödinger operator with a perfect honeycomb lattice potential has special points, called Dirac points where the lowest two branches of the spectrum touch. Deformations can result in the merging and disappearance of the Dirac points and the originally intersecting dispersion relation branches separate. Corresponding to these deformations, nonlinear envelope equations are deri...