Theory of the linewidth of intersubband plasmons in quantum wells

Computing the self-consistent field in Kohn-Sham density functional theory

A new framework is presented for evaluating the performance of self-consistent field methods in Kohn-Sham density functional theory (DFT). The aims of this work are two-fold. First, we explore the properties of Kohn-Sham DFT as it pertains to the convergence of self-consistent field iterations. Sources of inefficiencies and instabilities are identified, and methods to mitigate these difficulties are discussed. Second, we introduce a framework to assess the relative utility of algorithms in the present context, comprising a representative benchmark suite of over fifty Kohn-Sham simulation inputs, the scf-x _n suite. This provides a new tool to develop, evaluate and compare new algorithms in a fair, well-defined and transparent manner.

Superradiant Emission from a Collective Excitation in a Semiconductor

We report an anomalous wide broadening of the emission spectra of an electronic excitation confined in a two-dimensional potential. We attribute these results to an extremely fast radiative decay rate associated with superradiant emission from the ensemble of confined electrons. Lifetimes extracted from the spectra are below 100 fs and, thus, 6 orders of magnitude faster than for single particle transitions at similar wavelength. Moreover, the spontaneous emission rate increases with the electronic density, as expected for superradiant emission. The data, all taken at 300 K, are in excellent agreement with our theoretical model, which takes into account dipole-dipole Coulomb interaction between electronic excitations. Our experimental results demonstrate that the interaction with infrared light, which is usually considered a weak perturbation, can be a very efficient relaxation mechanism for collective electronic excitations in solids.

Representing the thermal state in time-dependent density functional theory

Classical molecular dynamics (MD) provides a powerful and widely used approach to determining thermodynamic properties by integrating the classical equations of motion of a system of atoms. Time-Dependent Density Functional Theory (TDDFT) provides a powerful and increasingly useful approach to integrating the quantum equations of motion for a system of electrons. TDDFT efficiently captures the unitary evolution of a many-electron state by mapping the system into a fictitious non-interacting system. In analogy to MD, one could imagine obtaining the thermodynamic properties of an electronic system from a TDDFT simulation in which the electrons are excited from their ground state by a time-dependent potential and then allowed to evolve freely in time while statistical data are captured from periodic snapshots of the system. For a variety of systems (e.g., many metals), the electrons reach an effective state of internal equilibrium due to electron-electron interactions on a time scale that is short compared to electron-phonon equilibration. During the initial time-evolution of such systems following electronic excitation, electron-phonon interactions should be negligible, and therefore, TDDFT should successfully capture the internal thermalization of the electrons. However, it is unclear how TDDFT represents the resulting thermal state. In particular, the thermal state is usually represented in quantum statistical mechanics as a mixed state, while the occupations of the TDDFT wavefunctions are fixed by the initial state in TDDFT. We work to address this puzzle by (A) reformulating quantum statistical mechanics so that thermodynamic expectations can be obtained as an unweighted average over a set of many-body pure states and (B) constructing a family of non-interacting (single determinant) TDDFT states that approximate the required many-body states for the canonical ensemble.

Time-dependent density functional theory for open quantum systems with unitary propagation

We extend the Runge-Gross theorem for a very general class of open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS) time-dependent density functional theory, it is possible to rigorously include the effects of the environment within a bath functional in the KS potential. A Markovian bath functional inspired by the theory of nonlinear Schrödinger equations is suggested, which can be readily implemented in currently existing real-time codes. Finally, calculations on a helium model system are presented.

Real-time electron dynamics with exact-exchange time-dependent density-functional theory

The exact exchange potential in time-dependent density-functional theory is defined as an orbital functional through the time-dependent optimized effective potential (TDOEP) method. We numerically solve the TDOEP integral equation for the real-time nonlinear intersubband electron dynamics in a semiconductor quantum well with two occupied subbands. It is found that memory effects become significant in the vicinity of intersubband resonances.

Generator coordinate method in time-dependent density-functional theory: Memory made simple

The generator coordinate (GC) method is a variational approach to the quantum many-body problem in which interacting many-body wave functions are constructed as superpositions of (generally nonorthogonal) eigenstates of auxiliary Hamiltonians containing a deformation parameter. This paper presents a time-dependent extension of the GC method as a new approach to improve existing approximations of the exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT). The time-dependent GC method is shown to be a conceptually and computationally simple tool to build memory effects into any existing adiabatic XC potential. As an illustration, the method is applied to driven parametric oscillations of two interacting electrons in a harmonic potential (Hooke's atom). It is demonstrated that a proper choice of time-dependent generator coordinates in conjunction with the adiabatic local-density approximation reproduces the exact linear and nonlinear two-electron dynamics quite accurately, including features associated with double excitations that cannot be captured by TDDFT in the adiabatic approximation.

Stochastic time-dependent current-density-functional theory

A time-dependent current-density-functional theory for many-particle systems in interaction with arbitrary external baths is developed. We prove that, given the initial quantum state |Psi0> and the particle-bath interaction operator, two external vector potentials A(r,t) and A'(r,t) that produce the same ensemble-averaged current density, j(r,t), must necessarily coincide up to a gauge transformation. This result greatly expands the applicability of time-dependent density-functional theory to open quantum systems, and allows for first-principles calculations of many-particle time evolution beyond Hamiltonian dynamics.

Time-dependent density-functional theory beyond the local-density approximation

Approximations for the ground-state exchange-correlation potential of density-functional theory have reached a high level of sophistication. By contrast, time- or frequency-dependent exchange-correlation potentials are still being treated in a local approximation. Here we propose a novel approximation scheme, which effectively brings the power of the generalized gradient approximation (GGA) and meta-GGA to time-dependent density-functional theory. The theory should allow a more accurate treatment of strongly inhomogeneous electronic systems (e.g. molecular junctions) while remaining essentially exact for slowly varying densities and slowly varying external potentials.

Two-electron linear intersubband light absorption in a biased quantum well

We point out a novel manifestation of many-body correlations in the linear optical response of electrons confined in a quantum well. Namely, we demonstrate that along with the conventional absorption peak at a frequency omega close to the intersubband energy delta, there exists an additional peak at frequency h omega approximately = 2delta. This new peak is solely due to electron-electron interactions, and can be understood as excitation of two electrons by a single photon. The actual peak line shape is comprised of a sharp feature, due to excitation of pairs of intersubband plasmons, on top of a broader band due to absorption by two single-particle excitations. The two-plasmon contribution allows us to infer intersubband plasmon dispersion from linear absorption experiments.

Time-dependent Kohn-Sham theory with memory

In time-dependent density-functional theory, exchange and correlation (xc) beyond the adiabatic approximation can be described by viscoelastic stresses in the electron liquid. In the time domain, the resulting velocity-dependent xc vector potential has a memory containing short- and long-range components, leading to decoherence and energy relaxation. We solve the associated time-dependent Kohn-Sham equations, including the dependence on densities and currents at previous times, for the case of charge-density oscillations in a quantum well. We illustrate xc memory effects, clarify the dissipation mechanism, and extract intersubband relaxation rates for weak and strong excitations.

Excitation energies from time-dependent density-functional theory beyond the adiabatic approximation

Time-dependent density-functional theory in the adiabatic approximation has been very successful for calculating excitation energies in molecular systems. This paper studies nonadiabatic effects for excitation energies, using the current-density functional of Vignale and Kohn [Phys. Rev. Lett. 77, 2037 (1996)]. We derive a general analytic expression for nonadiabatic corrections to excitation energies of finite systems and calculate singlet s-->s and s-->p excitations of closed-shell atoms. The approach works well for s-->s excitations, giving a small improvement over the adiabatic local-density approximation, but tends to overcorrect s-->p excitations. We find that the observed problems with the nonadiabatic correction have two main sources: (1) the currents associated with the s-->p excitations are highly nonuniform and, in particular, change direction between atomic shells, (2) the so-called exchange-correlation kernels of the homogeneous electron gas, f(xc) (L) and f(xc) (T), are incompletely known, in particular in the high-density atomic core regions.

Intersubband transport in quantum wells in strong magnetic fields mediated by single- and two-electron scattering

We show theoretically that in quantum wells subjected to a strong magnetic field the intersubband current peaks at magnetic field values, which reveal the underlying specific intersubband scattering mechanism. We have designed and grown a superlattice structure in which such current oscillations are clearly visible, and in which the transition from the purely single-electron to the mixed single- and two-electron scattering regimes can be observed by tuning the applied voltage bias. The measurements were conducted in ultrahigh magnetic fields (up to 45 T) to obtain the full spectrum of the current oscillations.

Ultranonlocality in time-dependent current-density-functional theory: application to conjugated polymers

We solve the long-standing problem of the large overestimation of the static polarizability of conjugated polymers obtained using the local density approximation within density-functional theory. The local approximation is unable to describe the highly nonlocal exchange and correlation (xc) effects found in these quasi-one-dimensional systems. Time-dependent current-density-functional theory enables a local current description of ultranonlocal xc effects using the Vignale-Kohn functional [G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996)]. Except for the model hydrogen chain, our results are in excellent agreement with the best available correlated methods.

Dissipation of intersubband plasmons in wide quantum wells

This Letter reports detailed measurements of the dissipation times tau(d) of approximately 10 meV intersubband (ISB) plasmons, and of the (single-particle) transport lifetimes tau(mu), in a remotely doped 40 nm GaAs quantum well. Introduced here as the time for ISB plasmons to dissipate into other modes of the electron gas, tau(d) is deduced from the homogeneous ISB absorption linewidth, measured as a function of sheet concentration and perpendicular dc electric field. Modeling in this and the next Letter [C. A. Ullrich and G. Vignale, Phys. Rev. Lett. 87, 037402 (2001)] indicates that scattering from rough interfaces dominates tau(d), while scattering from ionized impurities dominates tau(mu).