Multiphase superconductivity in PdBi.

Unconventional superconductivity, where electron pairing does not involve electron-phonon interactions, is often attributed to magnetic correlations in a material. Well known examples include high-T cuprates and uranium-based heavy fermion superconductors. Less explored are unconventional superconductors with strong spin-orbit coupling, where interactions between spin-polarised electrons and external magnetic field can result in multiple superconducting phases and field-induced transitions between them, a rare phenomenon in the superconducting state.

Giant Atomic Swirl in Graphene Bilayers with Biaxial Heterostrain.

The study of moiré engineering started with the advent of van der Waals heterostructures, in which stacking 2D layers with different lattice constants leads to a moiré pattern controlling their electronic properties. The field entered a new era when it was found that adjusting the twist between two graphene layers led to strongly-correlated-electron physics and topological effects associated with atomic relaxation. A twist is now routinely used to adjust the properties of 2D materials.

Magnetization Signature of Topological Surface States in a Non-Symmorphic Superconductor.

Superconductors with nontrivial band structure topology represent a class of materials with unconventional and potentially useful properties. Recent years have seen much success in creating artificial hybrid structures exhibiting the main characteristics of 2D topological superconductors. Yet, bulk materials known to combine inherent superconductivity with nontrivial topology remain scarce, largely because distinguishing their central characteristic-the topological surface states-has proved challenging due to a dominant contribution from the superconducting bulk.

Charge-polarized interfacial superlattices in marginally twisted hexagonal boron nitride.

When two-dimensional crystals are brought into close proximity, their interaction results in reconstruction of electronic spectrum and crystal structure. Such reconstruction strongly depends on the twist angle between the crystals, which has received growing attention due to interesting electronic and optical properties that arise in graphene and transitional metal dichalcogenides. Here we study two insulating crystals of hexagonal boron nitride stacked at small twist angle.

Twists and the Electronic Structure of Graphitic Materials.

We analyze the effect of twists on the electronic structure of configurations of infinite stacks of graphene layers. We focus on three different cases: an infinite stack where each layer is rotated with respect to the previous one by a fixed angle, two pieces of semi-infinite graphite rotated with respect to each other, and finally a single layer of graphene rotated with respect to a graphite surface. In all three cases, we find a rich structure, with sharp resonances and flat bands for small twist angles.

Electrostatic effects, band distortions, and superconductivity in twisted graphene bilayers.

Bilayer graphene twisted by a small angle shows a significant charge modulation away from neutrality, as the charge in the narrow bands near the Dirac point is mostly localized in a fraction of the Moiré unit cell. The resulting electrostatic potential leads to a filling-dependent change in the low-energy bands, of a magnitude comparable to or larger than the bandwidth. These modifications can be expressed in terms of new electron-electron interactions, which, when expressed in a local basis, describe electron-assisted hopping terms.

Edge Modes and Nonlocal Conductance in Graphene Superlattices.

We study the existence of edge modes in gapped moiré superlattices of graphene monolayer ribbons on a hexagonal boron nitride substrate. We find that the superlattice bands acquire finite Chern numbers, which lead to a valley Hall effect. The presence of dispersive edge modes is confirmed by calculations of the band structure of realistic nanoribbons using tight binding methods.

Quantum phase transitions and the extended coupled cluster method.

We discuss the application of an extended version of the coupled cluster method to systems exhibiting a quantum phase transition. We use the lattice O(4) nonlinear sigma model in (1+1) and (3+1) dimensions as an example. We show how simple predictions get modified, leading to the absence of a phase transition in (1+1) dimensions, and strong indications for a phase transition in (3+1) dimensions.