Weyl semimetals are three-dimensional topological states of matter, in a sense that they host paired monopoles and antimonopoles of Berry curvature in momentum space, leading to the chiral anomaly. The chiral anomaly has long been believed to give a positive magnetoconductivity or negative magnetoresistivity in strong and parallel fields. However, several recent experiments on both Weyl and Dirac topological semimetals show a negative magnetoconductivity in high fields. Here, we study the magnetoconductivity of Weyl and Dirac semimetals in the presence of shortrange scattering potentials. In a strong magnetic field applied along the direction that connects two Weyl nodes, we find that the conductivity along the field direction is determined by the Fermi velocity, instead of by the Landau degeneracy. We identify three scenarios in which the high-field magnetoconductivity is negative. Our findings show that the high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly and will be helpful for interpreting the inconsistency in the recent experiments and earlier theories.

Fast radio bursts (FRBs) are radio bursts characterized by millisecond durations, high Galactic latitude positions, and high dispersion measures. Very recently, the cosmological origin of FRB 150418 has been confirmed by Keane et al. (2016), and FRBs are now strong competitors as cosmological probes. The simple sharp feature of the FRB signal is ideal for them to probe some of the fundamental laws of physics. Here we show that by analyzing the delay time between different frequencies, the FRB data can place stringent upper limits on the rest mass of the photon. For FRB 150418 at z = 0.492, one can potentially reach m γ ≤ 5.2 × 10 −47 g, which is 10 20 times smaller than the rest mass of electron, and is about 10 3 times smaller than that obtained using other astrophysical sources with the same method.

Searching for the signature of the violation of chiral charge conservation in solids has inspired a growing passion on the magneto-transport in topological semimetals. One of the open questions is how the conductivity depends on magnetic fields in a semimetal phase when the Fermi energy crosses the Weyl nodes. Here, we study both the longitudinal and transverse magnetoconductivity of a topological Weyl semimetal near the Weyl nodes with the help of a two-node model that includes all the topological semimetal properties. In the semimetal phase, the Fermi energy crosses only the 0th Landau bands in magnetic fields. For a finite potential range of impurities, it is found that both the longitudinal and transverse magnetoconductivity are positive and linear at the Weyl nodes, leading to an anisotropic and negative magnetoresistivity. The longitudinal magnetoconductivity depends on the potential range of impurities. The longitudinal conductivity remains finite at zero field, even though the density of states vanishes at the Weyl nodes. This work establishes a relation between the linear magnetoconductivity and the intrinsic topological Weyl semimetal phase. I. INTRODUCTIONSearching for the violation of chiral charge conservation in solids started with Nielsen and Ninomiya's proposal in 1983 [1], in which the chiral charge is not conserved in a 1D system of two bands with opposite chirality. To simulate the 1D chiral bands, they proposed to use the lowest Landau bands of a 3D semimetal, and expected that the longitudinal magnetoconductance becomes extremely strong. Recently, thanks to the discovery of a number of realistic materials of topological semimetals [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], there is a growing passion on their electronic transport [22][23][24][25][26][27][28][29][30] and signatures of the chiral anomaly [31][32][33][34][35].Earlier theories on the longitudinal magnetoconductivity arrived at various results [36][37][38][39][40][41][42][43]. In the semiclassical limit, where the Landau levels are not well formed, a positive B 2 magnetoconductivity was predicted [36,37], and is under intensive experimental investigation recently [44][45][46][47][48][49][50][51]. In the semiclassical approaches, the Fermi energy should overwhelm the relaxation rate, not exactly at the Weyl nodes. The B 2 magnetoconductivity is also obtained by modeling the disorder as long-range charged impurities in the quantum limit [41]. In the scenario similar to that proposed by Nielsen and Ninomiya, different results have been obtained so far, depending on models and treatments [37][38][39][40][41]. Literally, a semimetal must have a Fermi energy crossing the Weyl nodes. Nevertheless, little attention is paid to the magnetoconduction in the exact semimetal phase. More importantly, the Weyl nodes always appear in pairs. The intrinsic connection of the Weyl nodes and the inter-node scattering are two factors to affect the transport properties because the chiral anomaly occurs between two Weyl node...

The edge states in the quantum spin Hall effect are expected to be protected by time reversal symmetry. The experimental observation of the quantized conductance was reported in the InAs/GaSb quantum well [Du et al, arXiv:1306.1925], up to a large magnetic field, which raises a question on the robustness of the edge states in the quantum spin Hall effect under time reversal symmetry breaking. Here we present a theoretical calculation on topological invariants for the Benevig-Hughes-Zhang model in an external magnetic field, and find that the quantum spin Hall effect retains robust up to a large magnetic field. The critical value of the magnetic field breaking the quantum spin Hall effect is dominantly determined by the band gap at the Γ point instead of the indirect band gap between the conduction and valence bands. This illustrates that the quantum spin Hall effect could persist even under time reversal symmetry breaking.PACS numbers: 72.25. Dc,

Majorana fermions feature non-Abelian exchange statistics and promise fascinating applications in topological quantum computation. Recently, second-order topological superconductors (SOTSs) have been proposed to host Majorana fermions as localized quasiparticles with zero excitation energy, pointing out a new avenue to facilitate topological quantum computation. We provide a minimal model for SOTSs and systematically analyze the features of Majorana zero modes with analytical and numerical methods. We further construct the fundamental fusion principles of zero modes stemming from single or multiple SOTS islands. Finally, we propose concrete schemes in different setups formed by SOTSs, enabling us to exchange and fuse the zero modes for non-Abelian braiding and holonomic quantum gate operations.

Second-order topological superconductors (SOTSs) host localized Majorana fermions and provide a new platform for topological quantum computation. We propose a remarkable and feasible way to realize networks based on SOTSs which allow to nucleate and braid Majorana bound states (MBSs) in an all-electrical manner without fine-tuning. The proposed setups are scalable in a straightforward way and can accommodate any even number of MBSs. Moreover, the MBSs in the networks allow defining qubits whose states can be initialized and read out by measuring Josephson currents flowing between SOTS islands. Our proposal can be implemented in monolayers of FeTe1−xSex and inverted Hg(Cd)Te quantum wells in proximity to conventional superconductors.

The integer quantum Hall effect is a topological state of quantum matter in two dimensions, and has recently been observed in three-dimensional topological insulator thin films. Here we study the Landau levels and edge states of surface Dirac fermions in topological insulators under strong magnetic field. We examine the formation of the quantum plateaux of the Hall conductance and find two different patterns, in one pattern the filling number covers all integers while only odd integers in the other. We focus on the quantum plateau closest to zero energy and demonstrate the breakdown of the quantum spin Hall effect resulting from structure inversion asymmetry. The phase diagrams of the quantum Hall states are presented as functions of magnetic field, gate voltage and chemical potential. This work establishes an intuitive picture of the edge states to understand the integer quantum Hall effect for Dirac electrons in topological insulator thin films.

A conservative constraint on the rest mass of the photon can be estimated under the assumption that the frequency dependence of dispersion from astronomical sources is mainly contributed by the nonzero photon mass effect. Photon mass limits have been earlier set through the optical emissions of the Crab Nebula pulsar, but we prove that these limits can be significantly improved with the dispersion measure (DM) measurements of radio pulsars in the Large and Small Magellanic Clouds. The combination of DM measurements of pulsars and distances of the Magellanic Clouds provide a strict upper limit on the photon mass as low as m γ ≤ 2.0 × 10 −45 g, which is at least four orders of magnitude smaller than the constraint from the Crab Nebula pulsar. Although our limit is not as tight as the current best result (∼ 10 −47 g) from a fast radio burst (FRB 150418) at a cosmological distance, the cosmological origin of FRB 150418 remains under debate; and our limit can reach the same high precision of FRB 150418 when it has an extragalactic origin (∼ 10 −45 g).