Deconfined Criticality and Bosonization Duality in Easy-Plane Chern-Simons Two-Dimensional Antiferromagnets.

Two-dimensional quantum systems with competing orders can feature a deconfined quantum critical point, yielding a continuous phase transition that is incompatible with the Landau-Ginzburg-Wilson scenario, predicting instead a first-order phase transition. This is caused by the LGW order parameter breaking up into new elementary excitations at the critical point. Canonical candidates for deconfined quantum criticality are quantum antiferromagnets with competing magnetic orders, captured by the easy-plane CP^{1} model.

Fractional Angular Momentum at Topological Insulator Interfaces.

Recently, two fundamental topological properties of a magnetic vortex at the interface of a superconductor (SC) and a strong topological insulator (TI) have been established: The vortex carries both a Majorana zero mode relevant for topological quantum computation and, for a time-reversal invariant TI, a charge of e/4. This fractional charge is caused by the axion term in the electromagnetic Lagrangian of the TI. Here we determine the angular momentum J of the vortices, which in turn determines their mutual statistics.

Josephson Currents Induced by the Witten Effect.

We reveal the existence of a new type of topological Josephson effect involving type II superconductors and three-dimensional topological insulators as tunnel junctions. We predict that vortex lines induce a variant of the Witten effect that is the consequence of the axion electromagnetic response of the topological insulator: at the interface of the junction each flux quantum attains a fractional electrical charge of e/4. As a consequence, if an external magnetic field is applied perpendicular to the junction, the Witten effect induces an ac Josephson effect in the absence of any external voltage.

A high-temperature ferromagnetic topological insulating phase by proximity coupling.

Topological insulators are insulating materials that display conducting surface states protected by time-reversal symmetry, wherein electron spins are locked to their momentum. This unique property opens up new opportunities for creating next-generation electronic, spintronic and quantum computation devices. Introducing ferromagnetic order into a topological insulator system without compromising its distinctive quantum coherent features could lead to the realization of several predicted physical phenomena.

Fluctuation-induced magnetization dynamics and criticality at the interface of a topological insulator with a magnetically ordered layer.

We consider a theory for a two-dimensional interacting conduction electron system with strong spin-orbit coupling on the interface between a topological insulator and the magnetic (ferromagnetic or antiferromagnetic) layer. For the ferromagnetic case we derive the Landau-Lifshitz equation, which features a contribution proportional to a fluctuation-induced electric field obtained by computing the topological (Chern-Simons) contribution from the vacuum polarization. We also show that fermionic quantum fluctuations reduce the critical temperature T[over ˜](c) at the interface relative to the critical temperature T(c) of the bulk, so that in the interval T[over ˜](c)≤T View Article and Find Full Text PDF

Strong-coupling topological Josephson effect in quantum wires.

We investigate the Josephson effect for a setup with two lattice quantum wires featuring Majorana zero energy boundary modes at the tunnel junction. In the weak-coupling regime, the exact solution reproduces the perturbative result for the energy containing a contribution ∼ ± cos(ϕ/2) relative to the tunneling of paired Majorana fermions. As the tunnel amplitude g grows relative to the hopping amplitude w, the gap between the energy levels gradually diminishes until it closes completely at the critical value gc [Formula: see text].

Quantum electrodynamics in 2 + 1 dimensions, confinement, and the stability of U(1) spin liquids.

Compact quantum electrodynamics in 2 + 1 dimensions often arises as an effective theory for a Mott insulator, with the Dirac fermions representing the low-energy spinons. An important and controversial issue in this context is whether a deconfinement transition takes place. We perform a renormalization group analysis to show that deconfinement occurs when N > Nc = 36/pi3 approximately to 1.

Deconfinement transition in three-dimensional compact U(1) gauge theories coupled to matter fields.

It is shown that permanent confinement in three-dimensional compact U(1) gauge theory can be destroyed by matter fields in a deconfinement transition. This follows from a nontrivial infrared fixed point caused by matter, and an anomalous scaling dimension of the gauge field. This leads to a logarithmic interaction between the defects of the gauge fields, which form a gas of magnetic monopoles.