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.

Full Assignment of Ab-Initio Raman Spectra at Finite Temperatures Using Wannier Polarizabilities: Application to Cyclohexane Molecule in Gas Phase

We demonstrate how to fully ascribe Raman peaks simulated using ab initio molecular dynamics to specific vibrations in the structure at finite temperatures by means of Wannier functions. Here, we adopt our newly introduced method for the simulation of the Raman spectra in which the total polarizability of the system is expressed as a sum over Wannier polarizabilities. The assignment is then based on the calculation of partial Raman activities arising from self- and/or cross-correlations between different types of Wannier functions in the system. Different types of Wannier functions can be distinguished based on their spatial spread. To demonstrate the predictive power of this approach, we applied it to the case of a cyclohexane molecule in the gas phase and were able to fully assign the simulated Raman peaks.

Does filling-dependent band renormalization aid pairing in twisted bilayer graphene?

Magic-angle twisted bilayer graphene (MATBG) exhibits a panoply of many-body phenomena that are intimately tied to the appearance of narrow and well-isolated electronic bands. The microscopic ingredients that are responsible for the complex experimental phenomenology include electron–electron (phonon) interactions and nontrivial Bloch wavefunctions associated with the narrow bands. Inspired by recent experiments, we focus on two independent quantities that are considerably modified by Coulomb interaction-driven band renormalization, namely the density of states and the minimal spatial extent associated with the Wannier functions. First, we show that a filling-dependent enhancement of the density of states, caused by band flattening, in combination with phonon-mediated attraction due to electron-phonon umklapp processes, increases the tendency towards superconducting pairing in a range of angles around magic-angle. Second, we demonstrate that the minimal spatial extent associated with the Wannier functions, which contributes towards increasing the superconducting phase stiffness, also develops a nontrivial enhancement due to the interaction-induced renormalization of the Bloch wavefunctions. While our modeling of superconductivity (SC) assumes a weak electron-phonon coupling and does not consider many of the likely relevant correlation effects, it explains simply the experimentally observed robustness of SC in the wide range of angles that occurs in the relevant range of fillings.

Optical spectral weight, phase stiffness, and Tc bounds for trivial and topological flat band superconductors

We present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat-band superconductors that lead to upper bounds for the superfluid stiffness and the two-dimensional (2D) Tc. We focus on on-site attraction |U| on the Lieb lattice with trivial flat bands and on the π-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weight D̃low≤ñ|U|Ω/2 with ñ=minn,2−n , where n is the flat-band density and Ω is the Marzari–Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound for D̃low linear in |U|. We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte Carlo results.