Abstract: We find localized electron and hole states in a ring-shaped potential kink in biased bilayer graphene. Within the continuum description, we show that for sharp potential steps the Dirac equation describing carrier states close to the K (or K′) point of the first Brillouin zone can be solved analytically for a circular kink/antikink dot. The solutions exhibit interfacial states which exhibit AharonovBohm oscillations as functions of the height of the potential step and/or the radius of the ring.

Abstract: The Dirac equation is solved for triangular and hexagonal graphene quantum dots for different boundary conditions in the presence of a perpendicular magnetic field. We analyze the influence of the dot size and its geometry on their energy spectrum. A comparison between the results obtained for graphene dots with zigzag and armchair edges, as well as for infinite-mass boundary condition, is presented and our results show that the type of graphene dot edge and the choice of the appropriate boundary conditions have a very important influence on the energy spectrum. The single-particle energy levels are calculated as a function of an external perpendicular magnetic field that lifts degeneracies. Comparing the energy spectra obtained from the tight-binding approximation to those obtained from the continuum Dirac equation approach, we verify that the behavior of the energies as a function of the dot size or the applied magnetic field are qualitatively similar, but in some cases quantitative differences can exist.

Abstract: Van der Waals quantum wells, naturally formed in two-dimensional layered materials with nanoscale thickness, possess many inherent advantages over conventional molecular beam epitaxy grown counterparts, and could bring up intriguing physics and applications. However, optical transitions originated from the series of quantized states in these emerging quantum wells are still elusive. Here, we show that multilayer black phosphorus appears to be an excellent candidate for van der Waals quantum wells with well-defined subbands and high optical quality. Using infrared absorption spectroscopy, we probe subband structures of multilayer black phosphorus with tens of atomic layers, revealing clear signatures for optical transitions with subband index as high as 10, far from what was attainable previously. Surprisingly, in addition to allowed transitions, an unexpected series of “forbidden” transitions is also evidently observed, which enables us to determine energy spacings separately for conduction and valence subbands. Furthermore, the linear tunability of subband spacings by temperature and strain is demonstrated. Our results are expected to facilitate potential applications for infrared optoelectronics based on tunable van der Waals quantum wells.