Berry phase theory of planar Hall effect in Topological Insulators

Negative longitudinal magnetoresistance, in the presence of an external magnetic field parallel to the direction of an applied current, has recently been experimentally verified in Weyl semimetals and topological insulators in the bulk conduction limit. The appearance of negative longitudinal magnetoresistance in topological semimetals is understood as an effect of chiral anomaly, whereas it is not well-defined in topological insulators. Another intriguing phenomenon, planar Hall effect - appearance of a transverse voltage in the plane of applied co-planar electric and magnetic fields not perfectly aligned to each other, a configuration in which the conventional Hall effect vanishes, has recently been suggested to exist in Weyl semimetals. In this paper we present a quasi-classical theory of planar Hall effect of a three-dimensional topological insulator in the bulk conduction limit. Starting from Boltzmann transport equations we derive the expressions for planar Hall conductivity and longitudinal magnetoconductivity in topological insulators and show the important roles played by the orbital magnetic moment for the appearance of planar Hall effect. Our theoretical results predict specific experimental signatures for topological insulators that can be directly checked in experiments.Comment: 18 pages, 3 figure

Mirror anomaly and anomalous Hall effect in type-I Dirac semimetals

In addition to the well known chiral anomaly, Dirac semimetals have been argued to exhibit mirror anomaly, close analogue to the parity anomaly of ($2+1$)-dimensional massive Dirac fermions. The observable response of such anomaly is manifested in a singular step-like anomalous Hall response across the mirror-symmetric plane in the presence of a magnetic field. Although this result seems to be valid in type-II Dirac semimetals (strictly speaking, in the linearized theory), we find that type-I Dirac semimetals do not possess such an anomaly in anomalous Hall response even at the level of the linearized theory. In particular, we show that the anomalous Hall response continuously approaches zero as one approaches the mirror symmetric angle in a type-I Dirac semimetal as opposed to the singular Hall response in a type-II Dirac semimetal. Moreover, we show that, under certain condition, the anomalous Hall response may vanish in a linearized type-I Dirac semimetal, even in the presence of time reversal symmetry breaking.Comment: 6 pages, 5 figure

Bulk band inversion and surface Dirac cones in LaSb and LaBi : Prediction of a new topological heterostructure

We perform \textit{ab initio} investigations of the bulk and surface band structures of LaSb and LaBi and resolve the existing disagreements about the topological property of LaSb, considering LaBi as a reference. We examine the bulk band structure for band inversion, along with the stability of surface Dirac cones (if any) to time-reversal-preserving perturbations, as a strong diagnostic test for determining the topological character of LaSb, LaBi and LaSb-LaBi multilayer. A detailed \textit{ab initio} investigation of a multilayer consisting of alternating unit cells of LaSb and LaBi shows the presence of band inversion in the bulk and a massless Dirac cone on the (001) surface, which remains stable under the influence of time-reversal-preserving perturbations, thus confirming the topologically non-trivial nature of the multilayer in which the electronic properties can be tailored as per requirement. A detailed $\mathbb{Z}_2$ invariant calculation is performed to arrive at a holistic conclusion

Experimental and materials considerations for the topological superconducting state in electron and hole doped semiconductors: searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures

In proximity to an s-wave superconductor, a one- or two-dimensional, electron- or hole-doped semiconductor with a sizable spin-orbit coupling and a Zeeman splitting can support a topological superconducting (TS) state. The semiconductor TS state has Majorana fermions as localized zero-energy excitations at order parameter defects such as vortices and sample edges. Here we examine the effects of quenched disorder from the semiconductor surface on the stability of the TS state in both electron- and hole-doped semiconductors. By considering the interplay of broken time reversal symmetry (due to Zeeman splitting) and disorder we derive an expression for the disorder suppression of the superconducting quasiparticle gap in the TS state. We conclude that the effects of disorder can be minimized by increasing the ratio of the spin-orbit energy with the Zeeman splitting. By giving explicit numbers we show that a stable TS state is possible in both electron- and hole-doped semiconductors for experimentally realistic values of parameters. We discuss possible suitable semiconductor materials which should be the leading candidates for the Majorana search in solid state systems.Comment: 11 pages, 2 figures: v3 published versio

Floating phase in a dissipative Josephson junction array

We consider dissipative quantum phase transitions in Josephson junction arrays and show that the disordered phase in this extended system can be viewed as an unusual floating phase in which the states of local $(0+1)$-dimensional elements (single Josephson junctions) can slide past each other despite arbitrary range spatial couplings among them. The unusual character of the metal-superconductor quantum critical point can be tested by measurements of the current voltage characteristic. This may be the simplest and most natural example of a floating phase.Comment: 4 pages, RevTex4. The revised version contains higher order renormalization group equations and the corresponding phase diagra