Topological Imbert-Fedorov shift in Weyl semimetals

The Goos-H\"anchen (GH) shift and the Imbert-Fedorov (IF) shift are optical phenomena which describe the longitudinal and transverse lateral shifts at the reflection interface, respectively. Here, we report the GH and IF shifts in Weyl semimetals (WSMs) - a promising material harboring low energy Weyl fermions, a massless fermionic cousin of photons. Our results show that GH shift in WSMs is valley-independent which is analogous to that discovered in a 2D relativistic material - graphene. However, the IF shift has never been explored in non-optical systems, and here we show that it is valley-dependent. Furthermore, we find that the IF shift actually originates from the topological effect of the system. Experimentally, the topological IF shift can be utilized to characterize the Weyl semimetals, design valleytronic devices of high efficiency, and measure the Berry curvature

One-dimensional quantum channel in a graphene line defect

Using a tight-binding model, we study a line defect in graphene where a bulk energy gap is opened by sublattice symmetry breaking. It is found that sublattice symmetry breaking may induce many configurations that correspond to different band spectra. In particular, a gapless state is observed for a configuration which hold a mirror symmetry with respect to the line defect. We find that this gapless state originates from the line defect and is independent of the width of the graphene ribbon, the location of the line defect, and the potentials in the edges of the ribbon. In particular, the gapless state can be controlled by the gate voltage embedded below the line defect. Finally, this result is supported with conductance calculations. This study shows how a quantum channel could be constructed using a line defect, and how the quantum channel can be controlled by tuning the gate voltage embedded below the line defect.Comment: 8 pages, 10 figure

Disorder and metal-insulator transitions in Weyl semimetals

The Weyl semimetal (WSM) is a newly proposed quantum state of matter. It has Weyl nodes in bulk excitations and Fermi arcs surface states. We study the effects of disorder and localization in WSMs and find three exotic phase transitions. (I) Two Weyl nodes near the Brillouin zone boundary can be annihilated pairwise by disorder scattering, resulting in the opening of a topologically nontrivial gap and a transition from a WSM to a three-dimensional (3D) quantum anomalous Hall state. (II) When the two Weyl nodes are well separated in momentum space, the emergent bulk extended states can give rise to a direct transition from a WSM to a 3D diffusive anomalous Hall metal. (III) Two Weyl nodes can emerge near the zone center when an insulating gap closes with increasing disorder, enabling a direct transition from a normal band insulator to a WSM. We determine the phase diagram by numerically computing the localization length and the Hall conductivity, and propose that the exotic phase transitions can be realized on a photonic lattice.Comment: 7 pages with appendix, 6 figure

Disorder induced field effect transistor in bilayer and trilayer graphene

We propose use of disorder to produce a field effect transistor (FET) in biased bilayer and trilayer graphene. Modulation of the bias voltage can produce large variations in the conductance when the disorder's effects are confined to only one of the graphene layers. This effect is based on the bias voltage's ability to select which of the graphene layers carries current, and is not tied to the presence of a gap in the density of states. In particular, we demonstrate this effect in models of gapless ABA-stacked trilayer graphene, gapped ABC-stacked trilayer graphene, and gapped bilayer graphene.Comment: 21 pages, 7 figure