Analytical expressions for the charge-charge local-field factor and the exchange-correlation kernel of a two-dimensional electron gas

We present an analytical expression for the static many-body local field factor $G_{+}(q)$ of a homogeneous two-dimensional electron gas, which reproduces Diffusion Monte Carlo data and embodies the exact asymptotic behaviors at both small and large wave number $q$. This allows us to also provide a closed-form expression for the exchange and correlation kernel $K_{xc}(r)$, which represents a key input for density functional studies of inhomogeneous systems.Comment: 5 pages, 3 figure

Orbital ordering in undoped manganites via a generalized Peierls instability

We study the ground state orbital ordering of $LaMnO_3$, at weak electron-phonon coupling, when the spin state is A-type antiferromagnet. We determine the orbital ordering by extending to our Jahn-Teller system a recently developed Peierls instability framework for the Holstein model [1]. By using two-dimensional dynamic response functions corresponding to a mixed Jahn-Teller mode, we establish that the $Q_2$ mode determines the orbital order.Comment: A few changes made. Accepted in Phys. Rev.

Peierls to superfluid crossover in the one-dimensional, quarter-filled Holstein model

We use continuous-time quantum Monte Carlo simulations to study retardation effects in the metallic, quarter-filled Holstein model in one dimension. Based on results which include the one- and two-particle spectral functions as well as the optical conductivity, we conclude that with increasing phonon frequency the ground state evolves from one with dominant diagonal order---2k_F charge correlations---to one with dominant off-diagonal fluctuations, namely s-wave pairing correlations. In the parameter range of this crossover, our numerical results support the existence of a spin gap for all phonon frequencies. The crossover can hence be interpreted in terms of preformed pairs corresponding to bipolarons, which are essentially localised in the Peierls phase, and "condense" with increasing phonon frequency to generate dominant pairing correlations.Comment: 11 pages, 5 figure

Correlation energy of a two-dimensional electron gas from static and dynamic exchange-correlation kernels

We calculate the correlation energy of a two-dimensional homogeneous electron gas using several available approximations for the exchange-correlation kernel $f_{\rm xc}(q,\omega)$ entering the linear dielectric response of the system. As in the previous work of Lein {\it et al.} [Phys. Rev. B {\bf 67}, 13431 (2000)] on the three-dimensional electron gas, we give attention to the relative roles of the wave number and frequency dependence of the kernel and analyze the correlation energy in terms of contributions from the $(q, i\omega)$ plane. We find that consistency of the kernel with the electron-pair distribution function is important and in this case the nonlocality of the kernel in time is of minor importance, as far as the correlation energy is concerned. We also show that, and explain why, the popular Adiabatic Local Density Approximation performs much better in the two-dimensional case than in the three-dimensional one.Comment: 9 Pages, 4 Figure

Interaction-Induced Enhancement of Spin-Orbit Coupling in Two-Dimensional Electronic System

We study theoretically the renormalization of the spin-orbit coupling constant of two-dimensional electrons by electron-electron interactions. We demonstrate that, similarly to the $g$ factor, the renormalization corresponds to the enhancement, although the magnitude of the enhancement is weaker than that for the $g$ factor. For high electron concentrations (small interaction parameter $r_s$) the enhancement factor is evaluated analytically within the static random phase approximation. For large $r_s\sim 10$ we use an approximate expression for effective electron-electron interaction, which takes into account the local field factor, and calculate the enhancement numerically. We also study the interplay between the interaction-enhanced Zeeman splitting and interaction-enhanced spin-orbit coupling.Comment: 18 pages, 2 figures, REVTe

Correlated singlet phase in the one-dimensional Hubbard-Holstein model

We show that a nearest-neighbor singlet phase results (from an effective Hamiltonian) for the one-dimensional Hubbard-Holstein model in the regime of strong electron-electron and electron-phonon interactions and under non-adiabatic conditions ($t/\omega_0 \leq 1$). By mapping the system of nearest-neighbor singlets at a filling $N_p/N$ onto a hard-core-boson (HCB) $t$-$V$ model at a filling $N_p/(N-N_p)$, we demonstrate explicitly that superfluidity and charge-density-wave (CDW) occur mutually exclusively with the diagonal long range order manifesting itself only at one-third filling. Furthermore, we also show that the Bose-Einstein condensate (BEC) occupation number $n_0$ for the singlet phase, similar to the $n_0$ for a HCB tight binding model, scales as $\sqrt N$; however, the coefficient of $\sqrt N$ in the $n_0$ for the interacting singlet phase is numerically demonstrated to be smaller.Comment: Corrected a few reference

Correlation energy and spin polarization in the 2D electron gas

The ground state energy of the two--dimensional uniform electron gas has been calculated with fixed--node diffusion Monte Carlo, including backflow correlations, for a wide range of electron densities as a function of spin polarization. We give a simple analytic representation of the correlation energy which fits the density and polarization dependence of the simulation data and includes several known high- and low-density limits. This parametrization provides a reliable local spin density energy functional for two-dimensional systems and an estimate for the spin susceptibility. Within the proposed model for the correlation energy, a weakly first--order polarization transition occurs shortly before Wigner crystallization as the density is lowered.Comment: Minor typos corrected, see erratum: Phys. Rev. Lett. 91, 109902(E) (2003

Collapse of Spin-Splitting in the Quantum Hall Effect

It is known experimentally that at not very large filling factors $\nu$ the quantum Hall conductivity peaks corresponding to the same Landau level number $N$ and two different spin orientations are well separated. These peaks occur at half-integer filling factors $\nu = 2 N + 1/2$ and $\nu = 2 N + 3/2$ so that the distance between them $\delta\nu$ is unity. As $\nu$ increases $\delta\nu$ shrinks. Near certain $N = N_c$ two peaks abruptly merge into a single peak at $\nu = 2N + 1$. We argue that this collapse of the spin-splitting at low magnetic fields is attributed to the disorder-induced destruction of the exchange enhancement of the electron $g$-factor. We use the mean-field approach to show that in the limit of zero Zeeman energy $\delta\nu$ experiences a second-order phase transition as a function of the magnetic field. We give explicit expressions for $N_c$ in terms of a sample's parameters. For example, we predict that for high-mobility heterostructures $N_c = 0.9 d n^{5/6} n_i^{-1/3},$ where $d$ is the spacer width, $n$ is the density of the two-dimensional electron gas, and $n_i$ is the two-dimensional density of randomly situated remote donors.Comment: 14 pages, compressed Postscript fil

Experimental evidence for the formation of stripe phases in Si/SiGe

We observe pronounced transport anisotropies in magneto-transport experiments performed in the two-dimensional electron system of a Si/SiGe heterostructure. They occur when an in-plane field is used to tune two Landau levels with opposite spin to energetic coincidence. The observed anisotropies disappear drastically for temperatures above 1 K. We propose that our experimental findings may be caused by the formation of a unidirectional stripe phase oriented perpendicular to the in-plane field.Comment: 4 pages, 3 figure

Emergence of quasi-metallic state in disordered 2D electron gas due to strong interactions

The interrelation between disorder and interactions in two dimensional electron liquid is studied beyond weak coupling perturbation theory. Strong repulsion significantly reduces the electronic density of states on the Fermi level. This makes the electron liquid more rigid and strongly suppresses elastic scattering off impurities. As a result the weak localization, although ultimately present at zero temperature and infinite sample size, is unobservable at experimentally accessible temperature at high enough densities. Therefore practically there exists a well defined metallic state. We study diffusion of electrons in this state and find that the diffusion pole is significantly modified due to "mixture" with static photons similar to the Anderson - Higgs mechanism in superconductivity. As a result several effects stemming from the long range nature of diffusion like the Aronov - Altshuler logarithmic corrections to conductivity are less pronounced.Comment: to appear in Phys. Rev.