Signatures of the Berry curvature in the frequency dependent interlayer magnetoresistance in tilted magnetic fields.

We show that in a layered metal, the angle dependent, finite frequency, interlayer magnetoresistance is altered due to the presence of a non-zero Berry curvature at the Fermi surface. At zero frequency, we find a conservation law which demands that the 'magic angle' condition for interlayer magnetoresistance extrema as a function of magnetic field tilt angle is essentially both field and Berry curvature independent. In the finite frequency case, however, we find that surprisingly large signatures of a finite Berry curvature occur in the periodic orbit resonances. We outline a method whereby the presence and magnitude of the Berry curvature at the Fermi surface can be extracted.

Localized many-particle Majorana modes with vanishing time-reversal symmetry breaking in double quantum dots.

We introduce the concept of spinful many-particle Majorana modes with local odd operator products, thereby preserving their local statistics. We consider a superconductor-double-quantum-dot system where these modes can arise with negligible Zeeman splitting when Coulomb interactions are present. We find a reverse Mott-insulator transition, where the even- and odd-parity bands become degenerate. Above this transition, Majorana operators move the system between the odd-parity ground state, associated with elastic cotunneling, and the even-parity ground state, associated with crossed Andreev reflection. These Majorana modes are described in terms of one, three, and five operator products. Parity conservation results in a 4π periodic supercurrent in the even state and no supercurrent in the odd state.

Realising Haldane's vision for a Chern insulator in buckled lattices.

The Chern insulator displays a quantum Hall effect with no net magnetic field. Proposed by Haldane over 20 years ago, it laid the foundation for the fields of topological order, unconventional quantum Hall effects, and topological insulators. Despite enormous impact over two decades, Haldane's original vision of a staggered magnetic field within a crystal lattice has been prohibitively difficult to realise. In fact, in the original paper Haldane stresses his idea is probably merely a toy model. I show that buckled lattices with only simple hopping terms, within in-plane magnetic fields, can realise these models, requiring no exotic interactions or experimental parameters. As a concrete example of this very broad, and remarkably simple principle, I consider silicene, a honeycomb lattice with out-of-plane sublattice anisotropy, in an in-plane magnetic field, and show that it is a Chern insulator, even at negligibly small magnetic fields, which is analogous to Haldane's original model.