Emergence of Wigner molecules in one-dimensional systems of repulsive fermions under harmonic confinement

A Bethe-Ansatz spin-density functional approach is developed to evaluate the ground-state density profile in a system of repulsively interacting spin-1/2 fermions inside a quasi-one-dimensional harmonic well. The approach allows for the formation of antiferromagnetic quasi-order with increasing coupling strength and reproduces with high accuracy the exact solution that is available for the two-fermion system.Comment: 3 pages, 2 figures, submitte

Thermoelectric alloys between PbSe and PbS with effective thermal conductivity reduction and high figure of merit

The n-type alloys between PbSe and PbS are studied. The effect of alloy composition on transport properties is evaluated and the results are interpreted with theories based on random atomic site substitution. The alloying in PbSe_(1−x)S_x brings thermal conductivity reduction, carrier mobility reduction as well as change of effective mass. When all these factors are evaluated, both experimentally and theoretically, the optimized thermoelectric performance is found to change gradually with alloy composition. High zT can be found in all PbSe_(1−x)S_x alloys. The possibility of achieving significant improvement of zT through alloying is also discussed

Higher mobility in bulk semiconductors by separating the dopants from the charge-conducting band – a case study of thermoelectric PbSe

In the rigid band approximation dopants in semiconductors only change the Fermi level and carrier concentration such that different dopants are thought equivalent when fully ionized. In this work we examine the small but significant difference in mobility due to the type of dopant in heavily doped PbSe by studying n-type samples doped with Br, In and Bi. We propose that cation and anion dopants lead to a difference in mobility at high concentrations. This can be understood considering the predominance of cation states to the conduction band and anion states to the valence band. For higher mobility and better performance for most applications of heavily doped semiconductors, dopants should be on the site that is of less influence on the charge-conducting band. This concept can be viewed as an analog of modulation doping on the atomic level. Its physical origin is the random potential due to disorder that perturbs carriers, which is also the origin of Anderson localization at low temperature, a well-studied topic in theoretical physics. In thermoelectric PbSe, the selection of dopant can lead to 10% difference in mobility and in zT

Density-functional theory of inhomogeneous electron systems in thin quantum wires

Motivated by current interest in strongly correlated quasi-one-dimensional (1D) Luttinger liquids subject to axial confinement, we present a novel density-functional study of few-electron systems confined by power-low external potentials inside a short portion of a thin quantum wire. The theory employs the 1D homogeneous Coulomb liquid as the reference system for a Kohn-Sham treatment and transfers the Luttinger ground-state correlations to the inhomogeneous electron system by means of a suitable local-density approximation (LDA) to the exchange-correlation energy functional. We show that such 1D-adapted LDA is appropriate for fluid-like states at weak coupling, but fails to account for the transition to a ``Wigner molecules'' regime of electron localization as observed in thin quantum wires at very strong coupling. A detailed analyzes is given for the two-electron problem under axial harmonic confinement.Comment: 8 pages, 7 figures, submitte

Linear Continuum Mechanics for Quantum Many-Body Systems

We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the time-dependent wave function in a locally co-moving reference frame can be described as a geometric deformation of the ground-state wave function. We show that this equation of motion is exact for systems consisting of a single particle, and for all systems at sufficiently high frequency, and that it leads to an excitation spectrum that has the correct integrated strength. The theory is illustrated by simple model applications to one- and two-electron systems.Comment: 4 pages, 1 figure, 1 tabl

Effects of interaction and polarization on spin-charge separation: A time-dependent spin-density-functional theory study

We calculate the nonequilibrium dynamic evolution of a one-dimensional system of two-component fermionic atoms after a strong local quench by using a time-dependent spin-density-functional theory. The interaction quench is also considered to see its influence on the spin-charge separation. It is shown that the charge velocity is larger than the spin velocity for the system of on-site repulsive interaction (Luttinger liquid), and vise versa for the system of on-site attractive interaction (Luther-Emery liquid). We find that both the interaction quench and polarization suppress the spin-charge separation.Comment: 8 pages, 9 figure

Density-functional theory of strongly correlated Fermi gases in elongated harmonic traps

Two-component Fermi gases with tunable repulsive or attractive interactions inside quasi-one-dimensional (Q1D) harmonic wells may soon become the cleanest laboratory realizations of strongly correlated Luttiger and Luther-Emery liquids under confinement. We present a microscopic Kohn-Sham density-functional theory of these systems, with specific attention to a gas on the approach to a confinement-induced Feshbach resonance. The theory employs the one-dimensional Gaudin-Yang model as the reference system and transfers the appropriate Q1D ground-state correlations to the confined inhomogeneous gas {\it via} a suitable local-density approximation to the exchange and correlation energy functional. Quantitative understanding of the role of the interactions in the bulk shell structure of the axial density profile is thereby achieved. While repulsive intercomponent interactions depress the amplitude of the shell structure of the noninteracting gas, attractive interactions stabilize atomic-density waves through spin pairing. These should be clearly observable in atomic clouds containing of the order of up to a hundred atoms.Comment: 13 pages, 9 figures, submitte

Persisting quantum effects in the anisotropic Rabi model at thermal equilibrium

Quantum correlations and nonclassical states are at the heart of emerging quantum technologies. Efforts to produce long-lived states of such quantum resources are a subject of tireless pursuit. Among several platforms useful for quantum technology, the mature quantum system of light-matter interactions offers unprecedented advantages due to current on-chip nanofabrication, efficient quantum control of its constituents, and its wide range of operational regimes. Recently, a continuous transition between the Jaynes-Cummings model and the Rabi model has been proposed by exploiting anisotropies in their light-matter interactions, known as the anisotropic quantum Rabi model. In this work, we study the long-lived quantum correlations and nonclassical states generated in the anisotropic Rabi model and how these indeed persist even at thermal equilibrium. To achieve this, we thoroughly analyze several quantumness quantifiers, where the long-lived quantum state is obtained from a dressed master equation that is valid for all coupling regimes and with the steady state ensured to be the canonical Gibbs state. Furthermore, we demonstrate a stark distinction between virtual excitations produced beyond the strong coupling regime and the quantumness quantifiers once the light-matter interaction has been switched off. This raises the key question about the nature of the equilibrium quantum features generated in the anisotropic quantum Rabi model and paves the way for future experimental investigations, without the need for challenging ground-state cooling

Continuum Mechanics for Quantum Many-Body Systems: The Linear Response Regime

We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-particle orbitals. We refer to our approach as continuum mechanics for quantum many-body systems. In the linear response regime, the equation of motion for the displacement field becomes a linear fourth-order integro-differential equation, whose only inputs are the one-particle density matrix and the pair correlation function of the ground-state. The complexity of this equation remains essentially unchanged as the number of particles increases. We show that our equation of motion is a hermitian eigenvalue problem, which admits a complete set of orthonormal eigenfunctions under a scalar product that involves the ground-state density. Further, we show that the excitation energies derived from this approach satisfy a sum rule which guarantees the exactness of the integrated spectral strength. Our formulation becomes exact for systems consisting of a single particle, and for any many-body system in the high-frequency limit. The theory is illustrated by explicit calculations for simple one- and two-particle systems.Comment: 23 pages, 4 figures, 1 table, 6 Appendices This paper is a follow-up to PRL 103, 086401 (2009

Nonexponential Solid State 1H and 19F Spin–Lattice Relaxation, Single-crystal X-ray Diffraction, and Isolated-Molecule and Cluster Electronic Structure Calculations in an Organic Solid: Coupled Methyl Group Rotation and Methoxy Group Libration in 4,4′-Dimethoxyoctafluorobiphenyl

We investigate the relationship between intramolecular rotational dynamics and molecular and crystal structure in 4,4′-dimethoxyoctafluorobiphenyl. The techniques are electronic structure calculations, X-ray diffractometry, and 1H and 19F solid state nuclear magnetic resonance relaxation. We compute and measure barriers for coupled methyl group rotation and methoxy group libration. We compare the structure and the structure-motion relationship in 4,4′-dimethoxyoctafluorobiphenyl with the structure and the structure-motion relationship in related compounds in order to observe trends concerning the competition between intramolecular and intermolecular interactions. The 1H spin–lattice relaxation is nonexponential in both the high-temperature short-correlation time limit and in the low-temperature long-correlation time limit, albeit for different reasons. The 19F spin–lattice relaxation is nonexponential at low temperatures and it is exponential at high temperatures