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Register a new userEngineering spectral properties of non-interacting lattice Hamiltonians
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We investigate the spectral properties of one-dimensional lattices with position-dependent hopping amplitudes and on-site potentials that are smooth bounded functions of 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.
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We have calculated the low-field magnetic susceptibility $chi$ of a system consisting of non-interacting mono-dispersed nanoparticles using a classical statistical approach. The model makes use of the assumption that the axes of symmetry of all nanoparticles are aligned and oriented at a certain angle $psi$ with respect to the external magnetic field. An analytical expression for the temperature dependence of the susceptibility $chi(T)$ above the blocking temperature is obtained. The derived expression is a generalization of the Curie law for the case of anisotropic magnetic particles. We show that the normalized susceptibility is a universal function of the ratio of the temperature over the anisotropy constant for each angle $psi$. In the case that the easy-axis is perpendicular to the magnetic field the susceptibility has a maximum. The temperature of the maximum allows one to determine the anisotropy energy.
Multilayered van der Waals structures often lack periodicity, which difficults their modeling. Building on previous work for bilayers, we develop a tight-binding based, momentum space formalism capable of describing incommensurate multilayered van der Waals structures for arbitrary lattice mismatch and/or misalignment between different layers. We demonstrate how the developed formalism can be used to model angle-resolved photoemission spectroscopy measurements, and scanning tunnelling spectroscopy which can probe the local and total density of states. The general method is then applied to incommensurate twisted trilayer graphene structures. It is found that the coupling between the three layers can significantly affect the low energy spectral properties, which cannot be simply attributed to the pairwise hybridization between the layers.
We consider the Landau Hamiltonian $H_0$, self-adjoint in $L^2({mathbb R^2})$, whose spectrum consists of an arithmetic progression of infinitely degenerate positive eigenvalues $Lambda_q$, $q in {mathbb Z}_+$. We perturb $H_0$ by a non-local potential written as a bounded pseudo-differential operator ${rm Op}^{rm w}({mathcal V})$ with real-valued Weyl symbol ${mathcal V}$, such that ${rm Op}^{rm w}({mathcal V}) H_0^{-1}$ is compact. We study the spectral properties of the perturbed operator $H_{{mathcal V}} = H_0 + {rm Op}^{rm w}({mathcal V})$. First, we construct symbols ${mathcal V}$, possessing a suitable symmetry, such that the operator $H_{mathcal V}$ admits an explicit eigenbasis in $L^2({mathbb R^2})$, and calculate the corresponding eigenvalues. Moreover, for ${mathcal V}$ which are not supposed to have this symmetry, we study the asymptotic distribution of the eigenvalues of $H_{mathcal V}$ adjoining any given $Lambda_q$. We find that the effective Hamiltonian in this context is the Toeplitz operator ${mathcal T}_q({mathcal V}) = p_q {rm Op}^{rm w}({mathcal V}) p_q$, where $p_q$ is the orthogonal projection onto ${rm Ker}(H_0 - Lambda_q I)$, and investigate its spectral asymptotics.
Precise shaping of coherent electron sources allows the controlled creation of wavepackets into a one dimensional (1D) quantum conductor. Periodic trains of Lorentzian pulses have been shown to induce minimal excitations without creating additional electron-hole pairs in a single non-interacting 1D electron channel. The presence of electron-electron (e-e) interactions dramatically affects the non-equilibrium dynamics of a 1D system. Here, we consider the intrinsic spectral properties of a helical liquid, with a pair of counterpropagating interacting channels, in the presence of time-dependent Lorentzian voltage pulses. We show that peculiar asymmetries in the behavior of the spectral function are induced by interactions, depending on the sign of the injected charges. Moreover, we discuss the robustness of the concept of minimal excitations in the presence of interactions, where the link with excess noise is no more straightforward. Finally, we propose a scanning tunneling microscope setup to spectroscopically access and probe the non-equilibrium behavior induced by the voltage drive and e-e interactions. This allows a diagnosis of fractional charges in a correlated quantum spin Hall liquid in the presence of time-dependent drives.
The dispersion properties of exciton polaritons in multiple-quantum-well based resonant photonic crystals are studied. In the case of structures with an elementary cell possessing a mirror symmetry with respect to its center, a powerful analytical method for deriving and analyzing dispersion laws of the respective normal modes is developed. The method is used to analyze band structure and dispersion properties of several types of resonant photonic crystals, which would not submit to analytical treatment by other approaches. These systems include multiple quantum well structures with an arbitrary periodic modulation of the dielectric function and structures with a complex elementary cell. Special attention was paid to determining conditions for superradiance (Bragg resonance) in these structures, and to the properties of the polariton stop band in the case when this condition is fulfilled (Bragg structures). The dependence of the band structure on the angle of propagation, the polarization of the wave, and the effects due to exciton homogeneous and inhomogeneous broadenings are considered, as well as dispersion properties of excitations in near-Bragg structures.
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