(3+1) Massive Dirac Fermions with Ultracold Atoms in Optical Lattices

We propose the experimental realization of (3+1) relativistic Dirac fermions using ultracold atoms in a rotating optical lattice or, alternatively, in a synthetic magnetic field. This approach has the advantage to give mass to the Dirac fermions by coupling the ultracold atoms to a Bragg pulse. A dimensional crossover from (3+1) to (2+1) Dirac fermions can be obtained by varying the anisotropy of the lattice. We also discuss under which conditions the interatomic potentials give rise to relativistically invariant interactions among the Dirac fermions

Renormalization Group Approach to Stability of Two-dimensional Interacting Type-II Dirac Fermions

The type-II Weyl/Dirac fermions are a generalization of conventional or type-I Weyl/Dirac fermions, whose conic spectrum is tilted such that the Fermi surface becomes lines in two dimensions, and surface in three dimensions rather than discrete points of the conventional Weyl/Dirac fermions. The mass-independent renormalization group calculations show that the tilting parameter decreases monotonically with respect to the length scale, which leads to a transition from two dimensional type-II Weyl/Dirac fermions to the type-I ones. Because of the non-trivial Fermi surface, a photon gains a finite mass partially via the chiral anomaly, leading to the strong screening effect of the Weyl/Dirac fermions. Consequently, anisotropic type-II Dirac semimetals become stable against the Coulomb interaction. This work provides deep insight into the interplay between the geometry of Fermi surface and the Coulomb interaction.Comment: Final pulished versio

Non-Abelian statistics of vortices with non-Abelian Dirac fermions

We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core, to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities, and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, a genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined non-locally by Majorana fermions located at two spatially separated vortices.Comment: 32 pages, no figures, v3: published versio

First direct observation of Dirac fermions in graphite

Originating from relativistic quantum field theory, Dirac fermions have been recently applied to study various peculiar phenomena in condensed matter physics, including the novel quantum Hall effect in graphene, magnetic field driven metal-insulator-like transition in graphite, superfluid in 3He, and the exotic pseudogap phase of high temperature superconductors. Although Dirac fermions are proposed to play a key role in these systems, so far direct experimental evidence of Dirac fermions has been limited. Here we report the first direct observation of massless Dirac fermions with linear dispersion near the Brillouin zone (BZ) corner H in graphite, coexisting with quasiparticles with parabolic dispersion near another BZ corner K. In addition, we report a large electron pocket which we attribute to defect-induced localized states. Thus, graphite presents a novel system where massless Dirac fermions, quasiparticles with finite effective mass, and defect states all contribute to the low energy electronic dynamics.Comment: Nature Physics, in pres

Simulation and detection of Dirac fermions with cold atoms in an optical lattice

We propose an experimental scheme to simulate and observe relativistic Dirac fermions with cold atoms in a hexagonal optical lattice. By controlling the lattice anisotropy, one can realize both massive and massless Dirac fermions and observe the phase transition between them. Through explicit calculations, we show that both the Bragg spectroscopy and the atomic density profile in a trap can be used to demonstrate the Dirac fermions and the associated phase transition.Comment: 4 pages; Published versio

Two dimensional Dirac fermions and quantum magnetoresistance in CaMnBi2_2

We report two dimensional Dirac fermions and quantum magnetoresistance in single crystals of CaMnBi$_2$. The non-zero Berry's phase, small cyclotron resonant mass and first-principle band structure suggest the existence of the Dirac fermions in the Bi square nets. The in-plane transverse magnetoresistance exhibits a crossover at a critical field $B^*$ from semiclassical weak-field $B^2$ dependence to the high-field unsaturated linear magnetoresistance ($\sim 120$ in 9 T at 2 K) due to the quantum limit of the Dirac fermions. The temperature dependence of $B^*$ satisfies quadratic behavior, which is attributed to the splitting of linear energy dispersion in high field. Our results demonstrate the existence of two dimensional Dirac fermions in CaMnBi$_2$ with Bi square nets.Comment: 5 pages, 4 figure