We study quantum many-body effects in the long-wavelength optical response of confined electrons at finite temperatures. We simulate homogeneous electron gas confined in one dimension into a slab of nanoscale thickness. We demonstrate how the slab boundaries break down the ideal Drude response of free charge carriers, giving rise to scattering effects due to both the surfaces and quantum many-body interactions. We use a recent path-integral Monte Carlo (PIMC) approach developed in [Tiihonen et al. Phys. Rev. A 113, 053711] to quantify these effects in high accuracy. We perform phenomenological fits to Drude and Drude-Lorentz models parameters, manifesting various trends of the optical response with physical parameters like density and temperature, and numerical effects like finite size and the quantum statistics.
We study quantum many-body effects in the long-wavelength optical response of confined electrons at finite temperatures. We simulate homogeneous electron gas confined in one dimension into a slab of nanoscale thickness. We demonstrate how the slab boundaries break down the ideal Drude response of free charge carriers, giving rise to scattering effects due to both the surfaces and quantum many-body interactions. We use a recent path-integral Monte Carlo (PIMC) approach developed in [Tiihonen et al. Phys. Rev. A 113, 053711] to quantify these effects in high accuracy. We perform phenomenological fits to Drude and Drude-Lorentz models parameters, manifesting various trends of the optical response with physical parameters like density and temperature, and numerical effects like finite size and the quantum statistics.
Ultra-thin films are fundamental components of modern nanoelectronics, where reducing thickness to the few-nanometer scale leads to a dramatic increase in electrical resistivity. For decades, this behavior has been interpreted in terms of classical size effects, primarily surface scattering within the Fuchs--Sondheimer theory and grain-boundary scattering in the Mayadas--Shatzkes model. While these approaches successfully describe transport when the film thickness is comparable to the electronic mean free path, growing experimental evidence indicates that they become insufficient under extreme confinement. This review discusses the crossover from classical scattering to a quantum-confinement regime in which the electronic states available for transport are fundamentally restructured by finite size. We review the recently proposed reciprocal-space confinement theory, which predicts an exponential increase of resistivity with decreasing thickness at the nanoscale, and discuss how it can be combined with classical surface-scattering models to provide a unified description of ultra-thin metallic and semiconducting films. Finally, we summarize recent experimental evidence supporting this picture and discuss its implications for future nanoelectronic devices, nanoscale interconnects, and quantum transport under extreme spatial confinement.
Ab initio quantum Monte Carlo methods, in principle, allow for the calculation of exact properties of correlated many-electron systems but are, in general, limited to the simulation of a finite number of electrons N under periodic boundary conditions. Therefore, an accurate theory of finite-size effects is indispensable to bridge the gap to realistic applications in the thermodynamic limit. In this work, we revisit the uniform electron gas at finite temperature, as it is relevant to contemporary research, e.g., in the field of warm dense matter. In particular, we present a new scheme to eliminate finite-size effects both in the static structure factor S(q) and in the interaction energy v, which is based on the density response formalism. We demonstrate that this method often allows us to obtain v in the thermodynamic limit within a relative accuracy of ∼0.2% from as few as N = 4 electrons without any empirical choices or knowledge of results for other values of N. Finally, we evaluate the applicability of our method upon increasing the density parameter rs and decreasing the temperature T.
Abstract Nonlinear density response theory is revisited focusing on the harmonically perturbed finite temperature uniform electron gas. Within the non-interacting limit, brute force quantum kinetic theory calculations for the quadratic, cubic, quartic and quintic responses reveal a deep connection with the linear response. Careful analysis of the static long wavelength limit led us to conjecture a canonical non-interacting form that expresses arbitrary order nonlinear responses as the weighted sum of the linear responses evaluated at all multiple harmonics. This harmonic expansion is successfully validated against ab initio path integral Monte Carlo simulations.
We use quantum Monte Carlo (QMC) simulations to study the combined effects of harmonic confinement and temperature for bosons in a two-dimensional(2D) optical lattice. The scale-invariant, finite temperature state diagram is presented for the Bose-Hubbard model in terms of experimental parameters -- the particle number, confining potential and interaction strength. To distinguish the nature of the spatially separated superfluid, Mott insulator, and normal Bose liquid phases, we examine the local density, compressibility, superfluid density, and Green's function. In the annular superfluid rings, as the width of the ring decreases, the long-range superfluid correlations start to deviate from an equivalent homogeneous 2D system. At zero temperature, the correlation decay is intermediate between one-dimension and two-dimensions, while at a finite temperature, the decay is similar to that in one-dimension at a much lower temperature. The calculations reveal shortcomings of the local density approximation in describing superfluid properties of trapped bosons. We also present the finite-temperature phase diagram for the homogeneous two dimensional Bose-Hubbard model. We compare our state diagram with the results of a recent experiment at NIST on a harmonically trapped 2D lattice [Phys. Rev. Lett. 105, 110401 (2010)], and identify a finite-temperature effect in the experiment.
Electron and hole excitations in semiconductors may be approximated as particles with effective masses which interact via Coulomb potentials. We study systems of electrons and holes with quantum Monte Carlo (QMC) techniques, covering three related areas: (1) elastic scattering of excitons, (2) thermodynamics of electron-hole plasmas, and (3) electrons confined in a quantum dot. Excitons are bound states of an electron and a hole, and obey Bose statistics. A low density exciton gas is an experimentally realizable dilute Bose gas. The scattering length a8 of a dilute Bose gas determines its properties, but is difficult to calculate. We present an essentially exact QMC treatment of exciton-exciton scattering, and find scattering lengths for different spin orientations of the excitons. At some mass ratios mh/me the scattering lengths diverge in conjunction with the appearance of biexciton vibrational states, an effect not found by earlier perturbative treatments. Path integral Monte Carlo (PIMC) is used to model the thermodynamics of the electron-hole plasma. Our primary interest is the Bose condensation of an excitonic gas. At low density and low temperature the spin-unpolarized system forms biexcitons. Since we are interested in Bose condensation, we study a spin-polarized system, which has no biexcitons. Restricted paths are used to handle the Fermion sign problem. With an appropriate choice of paired nodes for the restricted path approximation we find an excitonic Bose condensate. The energy of the low temperature, low density exciton gas determined from PIMC agrees well with the theory of dilute Bose gases, in which our previously calculated scattering length is used to model the exciton-exciton interactions. At higher densities the excitons are less well defined and the transition changes character. Finally, we study electrons in the inhomogeneous environment of a self-assembled InAs-GaAs quantum dot. We combine our ground state QMC treatment with another method, density functional theory (DFT) within the local spin density approximation (LSDA). Our comparison shows that LSDA is acceptable for treating interactions in the case considered, but recommend further tests for application of LSDA to larger dots or coupled dot systems.
Further developments are introduced in the theory of finite-size errors in quantum many-body simulations of extended systems using periodic boundary conditions. We show that our recently introduced model periodic Coulomb interaction [A. J. Williamson et al., Phys. Rev. B 55, R4851 (1997)] can be applied consistently to all Coulomb interactions in the system. The model periodic Coulomb interaction greatly reduces the finite-size errors in quantum many-body simulations. We illustrate the practical application of our techniques with Hartree-Fock and variational and diffusion quantum Monte Carlo calculations for ground- and excited-state calculations. We demonstrate that the finite-size effects in electron promotion and electron addition/subtraction excitation energy calculations are very similar.