arXiv subjects

J. K. Freericks

Publications and source records attributed to J. K. Freericks.

At least 145 records · Page 8Linked to original sources

arXiv2008

Theoretical description of time-resolved photoemission spectroscopy: application to pump-probe experiments

The theory for time-resolved photoemission spectroscopy as applied to pump-probe experiments is developed and solved for the generic case of a strongly correlated material. The formal development incorporates all of the nonequilibrium effects of the pump pulse and the finite time width of the probe pulse. While our formal development is completely general, in our numerical illustration for the Hubbard model, we assume the pump pulse drives the electrons into a nonequilibrium configuration, which rapidly thermalizes to create a hot (quasi-equilibrium) electronic system, and we then study the effects of windowing that arise from the finite width of the probe pulse. We find sharp features in the spectra are broadened, particularly the quasiparticle peak of strongly correlated metals at low temperature.

cond-mat.str-el↗

arXiv2008

Effect of anisotropic hopping on the Bose Hubbard model phase diagram: strong-coupling perturbation theory on a square lattice

There has been a recent resurgence of experimental efforts to quantitatively determine the phase diagram of the Bose Hubbard model by carefully analyzing experiments with ultracold bosonic atoms on an optical lattice. In many realizations of these experiments, the hopping amplitudes are not homogeneous throughout the lattice, but instead, the lattice has an anisotropy where hopping along one direction is not exactly equal to hopping along a perpendicular direction. In this contribution, we examine how an anisotropy in the hopping matrix elements affects the Mott lobes of the Bose Hubbard model. For weak anisotropy, we find the phase diagram is only slightly modified when expressed in terms of the average hopping, while for strong anisotropy, one expects to ultimately see dimensional crossover effects.

cond-mat.str-el↗

arXiv2008

Steady-state nonequilibrium density of states of driven strongly correlated lattice models in infinite dimensions

The formalism for exactly calculating the retarded and advanced Green's functions of strongly correlated lattice models in a uniform electric field is derived within dynamical mean-field theory. To illustrate the method, we solve for the nonequilibrium density of states of the Hubbard model in both the metallic and Mott insulating phases at half-filling (with an arbitrary strength electric field) by employing the numerical renormalization group as the impurity solver. This general approach can be applied to any strongly correlated lattice model in the limit of large dimensions.

cond-mat.str-el↗

arXiv2008

Pattern formation in mixtures of ultracold atoms in optical lattices

Regular pattern formation is ubiquitous in nature; it occurs in biological, physical, and materials science systems. Here we propose a set of experiments with ultracold atoms that show how to examine different types of pattern formation. In particular, we show how one can see the analog of labyrinthine patterns (so-called quantum emulsions) in mixtures of light and heavy atoms (that tend to phase separate) by tuning the trap potential and we show how complex geometrically ordered patterns emerge (when the mixtures do not phase separate), which could be employed for low-temperature thermometry. The complex physical mechanisms for the pattern formation at zero temperature are understood within a theoretical analysis called the local density approximation.

cond-mat.str-el↗

arXiv2008

Nonequilibrium sum rules for the retarded self-energy of strongly correlated electrons

We derive the first two moment sum rules of the conduction electron retarded self-energy for both the Falicov-Kimball model and the Hubbard model coupled to an external spatially uniform and time-dependent electric field (this derivation also extends the known nonequilibrium moment sum rules for the Green's functions to the third moment). These sum rules are used to further test the accuracy of nonequilibrium solutions to the many-body problem; for example, we illustrate how well the self-energy sum rules are satisfied for the Falicov-Kimball model in infinite dimensions and placed in a uniform electric field turned on at time t=0. In general, the self-energy sum rules are satisfied to a significantly higher accuracy than the Green's functions sum rules.

cond-mat.str-el↗

arXiv2007

Quenching Bloch oscillations in a strongly correlated material

Dynamical mean-field theory is generalized to solve the nonequilibrium Keldysh boundary problem: a system is started in equilibrium at a temperature T=0.1, a uniform electric field is turned on at t=0, and the system is monitored as it approaches the steady state. The focus here is on the Bloch oscillations of the current and how they decay after their initial appearance near t=0. The system is evolved out to the longest time allowed by our computational resources--in most cases we are unable to reach the steady state. The strongly correlated material is modeled by the spinless Falicov-Kimball model at half-filling on a hypercubic lattice in d=oo dimensions, which has a Mott-like metal-insulator transition at U=sqrt{2}. The computational algorithm employed is highly efficient, parallelizes well, and scales to thousands of processors. For strong fields, we find beats develop with a period of 2 pi/U, while for strong interactions, the Bloch oscillations are sharply damped and become quite irregular in time.

cond-mat.str-el↗

arXiv2007

Optical and dc transport properties of a strongly correlated charge density wave system: exact solution in the ordered phase of the spinless Falicov-Kimball model with dynamical mean-field theory

We derive the dynamical mean-field theory equations for transport in an ordered charge-density-wave phase on a bipartite lattice. The formalism is applied to the spinless Falicov-Kimball model on a hypercubic lattice at half filling. We determine the many-body density of states, the dc charge and heat conductivities, and the optical conductivity. Vertex corrections continue to vanish within the ordered phase, but the density of states and the transport coefficients show anomalous behavior due to the rapid development of thermally activated subgap states. We also examine the optical sum rule and sum rules for the first three moments of the Green's functions within the ordered phase and see that the total optical spectral weight in the ordered phase either decreases or increases depending on the strength of the interactions.

cond-mat.str-el↗

arXiv2006

Nonequilibrium dynamical mean-field theory of strongly correlated electrons

We present a review of our recent work in extending the successful dynamical mean-field theory from the equilibrium case to nonequilibrium cases. In particular, we focus on the problem of turning on a spatially uniform, but possibly time varying, electric field (neglecting all magnetic field effects). We show how to work with a manifestly gauge-invariant formalism, and compare numerical calculations from a transient-response formalism to different types of approximate treatments, including the semiclassical Boltzmann equation and perturbation theory in the interaction. In this review, we solve the nonequilibrium problem for the Falicov-Kimball model, which is the simplest many-body model and the easiest problem to illustrate the nonequilibrium behavior in both diffusive metals and Mott insulators. Due to space restrictions, we assume the reader already has some familiarity both with the Kadanoff-Baym-Keldysh nonequilibrium formalism and with equilibrium dynamical mean-field theory; we provide a guide to the literature where additional details can be found.

cond-mat.str-el↗

arXiv2006

Electronic charge reconstruction of doped Mott insulators in multilayered nanostructures

Dynamical mean-field theory is employed to calculate the electronic charge reconstruction of multilayered inhomogeneous devices composed of semi-infinite metallic lead layers sandwiching barrier planes of a strongly correlated material (that can be tuned through the metal-insulator Mott transition). The main focus is on barriers that are doped Mott insulators, and how the electronic charge reconstruction can create well-defined Mott insulating regions in a device whose thickness is governed by intrinsic materials properties, and hence may be able to be reproducibly made.

cond-mat.str-el↗

arXiv2006

Nonequilibrium perturbation theory of the spinless Falicov-Kimball model

We perform a perturbative analysis for the nonequilibrium Green functions of the spinless Falicov-Kimball model in the presence of an arbitrary external time-dependent but spatially uniform electric field. The conduction electron self-energy is found from a strictly truncated second-order perturbative expansion in the local electron-electron repulsion U. We examine the current at half-filling, and compare to both the semiclassical Boltzmann equation and exact numerical solutions for the contour-ordered Green functions from a transient-response formalism (in infinite dimensions) on the Kadanoff-Baym-Keldysh contour. We find a strictly truncated perturbation theory in the two-time formalism cannot reach the long-time limit of the steady state; instead it illustrates pathological behavior for times larger than approximately 2/U.

cond-mat.str-el↗

arXiv2006

Electronic thermal transport in strongly correlated multilayered nanostructures

The formalism for a linear-response many-body treatment of the electronic contributions to thermal transport is developed for multilayered nanostructures. By properly determining the local heat-current operator, it is possible to show that the Jonson-Mahan theorem for the bulk can be extended to inhomogeneous problems, so the various thermal-transport coefficient integrands are related by powers of frequency (including all effects of vertex corrections when appropriate). We illustrate how to use this formalism by showing how it applies to measurements of the Peltier effect, the Seebeck effect, and the thermal conductance.

cond-mat.str-el↗

arXiv2006

Nonequilibrium dynamical mean-field theory

The many-body formalism for dynamical mean-field theory is extended to treat nonequilibrium problems. We illustrate how the formalism works by examining the transient decay of the oscillating current that is driven by a large electric field turned on at time t=0. We show how the Bloch oscillations are quenched by the electron-electron interactions, and how their character changes dramatically for a Mott insulator.

cond-mat.str-el↗

arXiv2005

Real-time formalism for studying the nonlinear response of "smart" materials to an electric field

The nonlinear response of a material to a large electric field (steady or pulsed) often determines the ultimate performance of the material for electronics applications. The formalism for understanding nonlinear effects in conventional semiconductors is well understood. The formalism is less well developed for so-called ``smart'' materials that are tuned to lie close to the metal-insulator transition. Here we show that the nonlinear response of a strongly correlated electronic material can be calculated with a massively parallel algorithm by discretizing a continuous matrix operator on the Kadanoff-Baym contour in real time. We benchmark the technique by examining the solutions when the field vanishes and comparing the results to exact results from an equilibrium formalism. We briefly discuss the numerical issues associated with the case of a large electric field and present results that show how the Bloch oscillations become damped as the scattering due to electron correlations increases.

cond-mat.str-el↗

arXiv2005

Steady-state nonequilibrium dynamical mean-field theory and the quantum Boltzman

We derive the formalism for steady state nonequilibrium dynamical mean-field theory in a real-time formalism along the Kadanoff-Baym contour. The resulting equations of motion are first transformed to Wigner coordinates (average and relative time), and then re-expressed in terms of differential operators. Finally, we perform a Fourier transform with respect to the relative time, and take the first-order limit in the electric field to produce the quantum Boltzmann equation for dynamical mean-field theory. We next discuss the structure of the equations and their solutions, describing how these equations reduce to the Drude result in the limit of a constant relaxation time. We also explicitly demonstrate the equivalence between the Kubo and nonequilibrium approaches to linear response. There are a number of interesting modifications of the conventional quantum Boltzmann equation that arise due to the underlying bandstructure of the lattice.

cond-mat.str-el↗

arXiv2005

Spectral moment sum rules for strongly correlated electrons in time-dependent electric fields

We derive exact operator average expressions for the first two spectral moments of nonequilibrium Green's functions for the Falicov-Kimball model and the Hubbard model in the presence of a spatially uniform, time-dependent electric field. The moments are similar to the well-known moments in equilibrium, but we extend those results to systems in arbitrary time-dependent electric fields. Moment sum rules can be employed to estimate the accuracy of numerical calculations; we compare our theoretical results to numerical calculations for the nonequilibrium dynamical mean-field theory solution of the Falicov-Kimball model at half-filling.

cond-mat.str-el↗

arXiv2005

Optical sum rules that relate to the potential energy of strongly correlated systems

A class of sum rules for inelastic light scattering is developed. We show that the first moment of the non-resonant response provides information about the potential energy in strongly correlated systems. The polarization dependence of the sum rules provide information about the electronic excitations in different regions of the Brillouin zone. We determine the sum rule for the Falicov-Kimball model, which possesses a metal-insulator transition, and compare our results to the light scattering experiments in SmB_6.

cond-mat.str-el↗

arXiv2004

Nonlinear response of Bloch electrons in infinite dimensions

The exact nonlinear response of noninteracting (Bloch) electrons is examined within a nonequilibrium formalism on the infinite-dimensional hypercubic lattice. We examine the effects of a spatially uniform, but time-varying electric field (ignoring magnetic-field effects). The electronic Green's functions, Wigner density of states, and time-varying current are all determined and analyzed. We study both constant and pulsed electric fields, focusing on the transient response region. These noninteracting Green's functions are an important input into nonequilibrium dynamical mean field theory for the nonlinear response of strongly correlated electrons.

cond-mat.stat-mech↗

arXiv2004

Electronic Raman scattering in correlated materials: exact treatment of nonresonant, mixed, and resonant scattering with dynamical mean field theory

We solve for the electronic Raman scattering response functions on an infinite-dimensional hypercubic lattice employing dynamical mean field theory. This contribution extends previous work on the nonresonant response to include the mixed and resonant contributions. We focus our attention on the spinless Falicov-Kimball model, where the problem can be solved exactly, and the system can be tuned to go through a Mott-Hubbard-like metal-insulator transition. Resonant effects vary in different scattering geometries, corresponding to the symmetries of the charge excitations scattered by the light. We do find that the Raman response is large near the double resonance, where the transfered frequency is close to the incident photon frequency. We also find a joint resonance of both the charge-transfer peak and the low-energy peak when the incident photon frequency is on the order of the interaction strength. In general, the resonance effects can create order of magnitude (or more) enhancements of features in the nonresonant response, especially when the incident photon frequency is somewhat larger than the frequency of the nonresonant feature. Finally, we find that the resonant effects also exhibit isosbestic behavior, even in the A1g and B2g sectors, and it is most prominent when the incident photon frequency is on the order of the interaction energy.

cond-mat.str-el↗