3D quantum Hall effect of Fermi arcs in topological semimetals

The quantum Hall effect is usually observed in 2D systems. We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. Via a "wormhole" tunneling assisted by the Weyl nodes, the Fermi arcs at opposite surfaces can form a complete Fermi loop and support the quantum Hall effect. The edge states of the Fermi arcs show a unique 3D distribution, giving an example of (d-2)-dimensional boundary states. This is distinctly different from the surface-state quantum Hall effect from a single surface of topological insulator. As the Fermi energy sweeps through the Weyl nodes, the sheet Hall conductivity evolves from the 1/B dependence to quantized plateaus at the Weyl nodes. This behavior can be realized by tuning gate voltages in a slab of topological semimetal, such as the TaAs family, Cd$_3$As$_2$, or Na$_3$Bi. This work will be instructive not only for searching transport signatures of the Fermi arcs but also for exploring novel electron gases in other topological phases of matter.Comment: 5 pages, 3 figure

Aqua­{4,4′-dibromo-6,6′-dimeth­oxy-2,2′-[ethane-1,2-diylbis(nitrilo­methyl­idyne)]diphenolato}copper(II)

The title complex, [Cu(C18H16Br2N2O4)(H2O)], lies on a crystallographic mirror plane with the CuII ion coordinated by two N atoms and two O atoms of a tetra­dentate Schiff base ligand and one O atom from a water ligand in a slightly distorted square-pyramidal environment. The mirror plane, which coincides with the Cu—Owater bond, imposes disorder of the atoms of the ethyl­ene group. In the crystal structure, inter­molecular O—H⋯O hydrogen bonds link complex mol­ecules into extended chains along [100]

Critical theories of phase transition between symmetry protected topological states and their relation to the gapless boundary theories

Symmetry protected topological states (SPTs) have the same symmetry and the phase transition between them are beyond Landau's symmetry breaking formalism. In this paper we study (1) the critical theory of phase transition between trivial and non-trivial SPTs, and (2) the relation between such critical theory and the gapless boundary theory of SPTs. Based on examples of SO(3) and SU(2) SPTs, we propose that under appropriate boundary condition the critical theory contains the delocalized version of the boundary excitations. In addition, we prove that the boundary theory is the critical theory spatially confined between two SPTs. We expect these conclusions to hold in general and, in particular, for discrete symmetry groups as well.Comment: 16 pages, 7 figure