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.

Higher-order topological superconductivity from repulsive interactions in kagome and honeycomb systems

We discuss a pairing mechanism in interacting two-dimensional multipartite lattices that intrinsically leads to a second order topological superconducting state with a spatially modulated gap. When the chemical potential is close to Dirac points, oppositely moving electrons on the Fermi surface undergo an interference phenomenon in which the Berry phase converts a repulsive electron-electron interaction into an effective attraction. The topology of the superconducting phase manifests as gapped edge modes in the quasiparticle spectrum and Majorana Kramers pairs at the corners. We present symmetry arguments which constrain the possible form of the electron-electron interactions in these systems and classify the possible superconducting phases which result. Exact diagonalization of the Bogoliubov-de Gennes Hamiltonian confirms the existence of gapped edge states and Majorana corner states, which strongly depend on the spatial structure of the gap. Possible applications to vanadium-based superconducting kagome metals AV$_3$Sb$_3$ (A=K,Rb,Cs) are discussed.

Floquet prethermalization and Rabi oscillations in optically excited Hubbard clusters

We study the properties of Floquet prethermal states in two-dimensional Mott-insulating Hubbard clusters under continuous optical excitation. With exact-diagonalization simulations, we show that Floquet prethermal states emerge not only off resonance, but also for resonant excitation, provided a small field amplitude. In the resonant case, the long-lived quasi-stationary Floquet states are characterized by Rabi oscillations of observables such as double occupation and kinetic energy. At stronger fields, thermalization to infinite temperature is observed. We provide explanations to these results by means of time-dependent perturbation theory. The main findings are substantiated by a finite-size analysis.

Pressure and Temperature Effects on the Magnetic Properties of Donor Impurities in a GaAs/AlGaAs Quantum Heterostructure Subjected to a Magnetic Field

The exact diagonalization method has been used to solve the effective-mass Hamiltonian of a single electron confined parabolically in the GaAs/AlGaAs quantum heterostructure, in the presence of a donor impurity and under the effect of an applied uniform magnetic field. The donor impurity is located at distance (d) along the growth direction which is perpendicular to the motion of the electron in a two-dimensional heterostructure layer. We have investigated the dependence of the magnetization (M) and magnetic susceptibility (χ) of a GaAs/AlGaAs quantum heterostructure nanomaterial on the magnetic field strength (ω_c), confining frequency (ω_o), donor impurity position (d), pressure (P) and temperature (T). Keywords: Exact diagonalization, Donor impurity, Magnetic field, Magnetization, Magnetic susceptibility, Pressure and temperature.

Anomalous and anisotropic nonlinear susceptibility in the proximate Kitaev magnet α-RuCl3

The leading order nonlinear (NL) susceptibility, χ3, in a paramagnet is negative and diverges as T → 0. This divergence is destroyed when spins correlate and the NL response provides unique insights into magnetic order. Dimensionality, exchange interaction, and preponderance of quantum effects all imprint their signatures in the NL magnetic response. Here, we study the NL susceptibilities in the proximate Kitaev magnet α-RuCl3, which differs from the expected antiferromagnetic behavior. For T < Tc = 7.5 K and field B in the ab-plane, we obtain contrasting NL responses in low (<2 T) and high field regions. For low fields, the NL behavior is dominated by a quadratic response (positive χ2), which shows a rapid rise below Tc. This large χ2 > 0 implies a broken sublattice symmetry of magnetic order at low temperatures. Classical Monte Carlo (CMC) simulations in the standard K − H − Γ model secure such a quadratic B dependence of M, only for T ≈ Tc with χ2 being zero as T → 0. It is also zero for all temperatures in exact diagonalization calculations. On the other hand, we find an exclusive cubic term (χ3) that describes the high field NL behavior well. χ3 is large and positive both below and above Tc crossing zero only for T > 50 K. In contrast, for B ∥ c-axis, no separate low/high field behaviors are measured and only a much smaller χ3 is apparent.