Engineering spectral properties of non-interacting lattice Hamiltonians

We investigate the spectral properties of one-dimensional lattices with position-dependent hopping amplitudes and on-site potentials that are smooth bounded functions of the position. We find an exact integral form for the density of states (DOS) in the limit of an infinite number of sites, which we derive using a mixed Bloch-Wannier basis consisting of piecewise Wannier functions. Next, we provide an exact solution for the inverse problem of constructing the position-dependence of hopping in a lattice model yielding a given DOS. We confirm analytic results by comparing them to numerics obtained by exact diagonalization for various incarnations of position-dependent hoppings and on-site potentials. Finally, we generalize the DOS integral form to multi-orbital tight-binding models with longer-range hoppings and in higher dimensions.

Morphology-induced spectral modification of self-assembled WS2 pyramids

We characterize the optical response of hollow WS2 pyramids, that exhibit a strongly reduced photoluminescence with respect to horizontally layered WS2. Studying the position dependence of the spectral Raman features reveals local variations in the atomic arrangement.

Effective Photoluminescence Imaging of Bubbles in hBN-Encapsulated WSe2 Monolayer

Interfacial bubbles are unintentionally created during the transfer of atomically thin 2D layers, a required process in the fabrication of van der Waals heterostructures. By encapsulating a WSe2 monolayer in hBN, we study the differing photoluminescence (PL) properties of the structure resulting from bubble formation. Based on the differentiated absorption probabilities at the bubbles compared to the pristine areas, we demonstrate that the visibility of the bubbles in PL mapping is enhanced when the photoexcitation wavelength lies between the n = 1 and n = 2 resonances of the A-exciton. An appropriate choice of detection window, which includes localized exciton emission but excludes free exciton emission, further improves bubble imaging capability. The interfacial position dependence of the bubbles, whether they are located above or below the WSe2 monolayer, gives rise to measurable consequences in the PL shape.

Understanding Beam Induced Electronic Excitations in Materials

A time dependent self consistent field based method for determining the rates of electronic excitations induced in materials by the presence of external point charges is presented. The method utilizes the full scalar potential of the external point charge in the interaction Hamiltonian instead of relying on multipolar expansions thereof. A general method is presented for determining the conditions under which dipole selection rules are adequate to describe the electronic response of the material to perturbation by external point charges. The position dependence of point charge induced transition rates between the ground and lowest few excited electronic states was resolved for a small polybenzoid. Notably, electronic excitations that are optically forbidden can be strongly allowed for particular positions of the perturbing point charge. Application of the methods detailed here can lead to an improved understanding of the electronic response of materials under irradiation by beams of charged particles.

Understanding Beam Induced Electronic Excitations in Materials

A time dependent self consistent field based method for determining the rates of electronic excitations induced in materials by the presence of external point charges is presented. The method utilizes the full scalar potential of the external point charge in the interaction Hamiltonian instead of relying on multipolar expansions thereof. A general method is presented for determining the conditions under which dipole selection rules are adequate to describe the electronic response of the material to perturbation by external point charges. The position dependence of point charge induced transition rates between the ground and lowest few excited electronic states was resolved for a small polybenzoid. Notably, electronic excitations that are optically forbidden can be strongly allowed for particular positions of the perturbing point charge. Application of the methods detailed here can lead to an improved understanding of the electronic response of materials under irradiation by beams of charged particles.