Zitterbewegung of Moiré Excitons in Twisted MoS_{2}/WSe_{2} Heterobilayers.

The moiré pattern observed in stacked noncommensurate crystal lattices, such as heterobilayers of transition metal dichalcogenides, produces a periodic modulation of their band gap. Excitons subjected to this potential landscape exhibit a band structure that gives rise to a quasiparticle dubbed the moiré exciton. In the case of MoS_{2}/WSe_{2} heterobilayers, the moiré trapping potential has honeycomb symmetry and, consequently, the moiré exciton band structure is the same as that of a Dirac-Weyl fermion, whose mass can be further tuned down to zero with a perpendicularly applied field. Here we show that, analogously to other Dirac-like particles, the moiré exciton exhibits a trembling motion, also known as Zitterbewegung, whose long timescales are compatible with current experimental techniques for exciton dynamics. This promotes the study of the dynamics of moiré excitons in van der Waals heterostructures as an advantageous solid-state platform to probe Zitterbewegung, broadly tunable by gating and interlayer twist angle.

Composite super-moiré lattices in double-aligned graphene heterostructures.

When two-dimensional (2D) atomic crystals are brought into close proximity to form a van der Waals heterostructure, neighbouring crystals may influence each other's properties. Of particular interest is when the two crystals closely match and a moiré pattern forms, resulting in modified electronic and excitonic spectra, crystal reconstruction, and more. Thus, moiré patterns are a viable tool for controlling the properties of 2D materials. However, the difference in periodicity of the two crystals limits the reconstruction and, thus, is a barrier to the low-energy regime. Here, we present a route to spectrum reconstruction at all energies. By using graphene which is aligned to two hexagonal boron nitride layers, one can make electrons scatter in the differential moiré pattern which results in spectral changes at arbitrarily low energies. Further, we demonstrate that the strength of this potential relies crucially on the atomic reconstruction of graphene within the differential moiré super cell.

Quantum rotor in nanostructured superconductors.

Despite its apparent simplicity, the idealized model of a particle constrained to move on a circle has intriguing dynamic properties and immediate experimental relevance. While a rotor is rather easy to set up classically, the quantum regime is harder to realize and investigate. Here we demonstrate that the quantum dynamics of quasiparticles in certain classes of nanostructured superconductors can be mapped onto a quantum rotor. Furthermore, we provide a straightforward experimental procedure to convert this nanoscale superconducting rotor into a regular or inverted quantum pendulum with tunable gravitational field, inertia, and drive. We detail how these novel states can be detected via scanning tunneling spectroscopy. The proposed experiments will provide insights into quantum dynamics and quantum chaos.

Surface correlation effects in two-band strongly correlated slabs.

Using an extension of the Gutzwiller approximation for an inhomogeneous system, we study the two-band Hubbard model with unequal band widths for a slab geometry. The aim is to investigate the mutual effect of individual bands on the spatial distribution of quasi-particle weight and charge density, especially near the surface of the slab. The main effect of the difference in band width is the presence of two different length scales corresponding to the quasi-particle profile of each band. This is enhanced in the vicinity of the critical interaction of the narrow band where an orbitally selective Mott transition occurs and a surface dead layer forms for the narrow band. For the doped case, two different regimes of charge transfer between the surface and the bulk of the slab are revealed. The charge transfer from surface/center to center/surface depends on both the doping level and the average relative charge accumulated in each band. Such effects could also be of importance when describing the accumulation of charges at the interface between structures made of multi-band strongly correlated materials.

Unconventional vortex states in nanoscale superconductors due to shape-induced resonances in the inhomogeneous cooper-pair condensate.

Vortex matter in mesoscopic superconductors is known to be strongly affected by the geometry of the sample. Here we show that in nanoscale superconductors with coherence length comparable to the Fermi wavelength the shape resonances of the order parameter results in an additional contribution to the quantum topological confinement-leading to unconventional vortex configurations. Our Bogoliubov-de Gennes calculations in a square geometry reveal a plethora of asymmetric, giant multivortex, and vortex-antivortex structures, stable over a wide range of parameters and which are very different from those predicted by the Ginzburg-Landau theory. These unconventional states are relevant for high-T(c) nanograins, confined Bose-Einstein condensates, and graphene flakes with proximity-induced superconductivity.

Rectification by an imprinted phase in a Josephson junction.

A Josephson phase shift can be induced in a Josephson junction by a strategically nearby pinned Abrikosov vortex (AV). For an asymmetric distribution of an imprinted phase along the junction (controlled by the position of the AV) such a simple system is capable of rectification of ac current in a broad and tunable frequency range. The resulting rectified voltage is a consequence of the directed motion of a Josephson antivortex which forms a pair with the AV when at local equilibrium. The proposed realization of the ratchet potential by an imprinted phase is more efficient than the asymmetric geometry of the junction itself, is easily realizable experimentally, and provides rectification even in the absence of an applied magnetic field.

Efficient numerical approach to inhomogeneous superconductivity: the Chebyshev-Bogoliubov-de Gennes method.

We propose a highly efficient numerical method to describe inhomogeneous superconductivity by using the kernel polynomial method in order to calculate the Green's functions of a superconductor. Broken translational invariance of any type (impurities, surfaces, or magnetic fields) can be easily incorporated. We show that limitations due to system size can be easily circumvented and therefore this method opens the way for the study of scenarios and/or geometries that were unaccessible before. The proposed method is highly efficient and amenable to large scale parallel computation. Although we only use it in the context of superconductivity, it is applicable to other inhomogeneous mean-field theories.