Luttinger Model Research Articles

Luttinger model for current and spin-Hall conductivities

We evaluate, based on a dimensional analysis, the ration of the spin-Hall conductivity to current conductivity in a sample where the electric current is dominated by the Luttinger model. The ratio is composed of a size-dependent factor multiplied by the corresponding ratio in the Drude model.

Introduction to integrable many-body systems I

Introduction to integrable many-body systems IThis is the first volume of a three-volume introductory course about integrable (exactly solvable) systems of interacting bodies. The aim of the course is to derive and analyze, on an elementary mathematical and physical level, the Bethe ansatz solutions, ground-state properties and the thermodynamics of integrable many-body systems in many domains of physics: Nonrelativistic one-dimensional continuum Fermi and Bose gases; One-dimensional quantum models of condensed matter physics like the Heisenberg, Hubbard and Kondo models; Relativistic models of the (1+1)-dimensional Quantum Field Theory like the Luttinger model, the sine-Gordon model and its fermionic analog the Thirring model; Two-dimensional classical models, especially the symmetric Coulomb gas. In the first part of this volume, we deal with nonrelativistic one-dimensional continuum Fermi and Bose quantum gases of spinless (identical) particles with specific types of pairwise interactions like the short-range δ-function and hard-core interactions, and the long-range 1/

Exact Jastrow-Slater wave function for the one-dimensional Luttinger model

We show that it is possible to describe the ground state of the Luttinger model in terms of a Jastrow-Slater wave function. Moreover, our findings reveal that one-particle excitations and their corresponding dynamics can be faithfully represented only when a Jastrow factor of a similar form is applied to a coherent superposition of many Slater determinants. We discuss the possible relevance of this approach for the theoretical description of photoemission spectra in higher dimensionality, where the present wave function can be straightforwardly generalized and can be used as a variational ansatz, which is exact for the one-dimensional (1D) Luttinger model.

Optical anisotropy of strained quantum wells on high index substrates

AbstractWe investigate anisotropic properties of strained InGaAs quantum wells on the high index (11n)A (n = 3,4,5) GaAs substrates. The polarization dependence of photoluminescence of strained InGaAs quantum wells were measured, and optical anisotropy was observed. We calculated anisotropy of the optical transition matrix elements based on the 4x4 and 6x6 Luttinger model for the quantum wells with uniaxial strain. The calculated anisotropy taking into account of split‐off band qualitaively agree with our experiment. This indicates that the band mixing of split‐off band into the heavy‐hole band largely contributes to the the optical anisotropy in the strained InGaAs quantum wells on the high index substrates. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Tunable Aharonov-Anandan phase in transport through mesoscopic hole rings

We present a theoretical study of spin-3/2 hole transport through mesoscopic rings, based on the spherical Luttinger model. The quasi-one-dimensional ring is created in a symmetric two-dimensional quantum well by a singular-oscillator potential for the radial in-plane coordinate. The quantum-interference contribution to the two-terminal ring conductance exhibits an energy-dependent Aharonov-Anandan phase, even though Rashba and Dresselhaus spin splittings are absent. Instead, confinement-induced heavy-hole - light-hole mixing is found to be the origin of this phase, which has ramifications for magneto-transport measurements in gated hole rings.

Electronic transport in inhomogeneous quantum wires

We study the transport properties of a long non-uniform quantum wire where theelectron–electron interactions and the density vary smoothly at large length scales. Weshow that these inhomogeneities lead to a finite resistivity of the wire, due to a weakviolation of momentum conservation in the collisions between electrons. Estimating therate of change of momentum associated with non-momentum-conserving scatteringprocesses, we derive the expression for the resistivity of the wire in the regime of weaklyinteracting electrons and find a contribution linear in temperature for a broadrange of temperatures below the Fermi energy. By estimating the energy dissipatedthroughout the wire by low-energy excitations, we then develop a different method forderiving the resistivity of the wire, which can be combined with the bosonizationformalism. This allows us to compare our results with previous works relyingon an extension of the Tomonaga–Luttinger model to inhomogeneous systems.

Kondo screening cloud and charge staircase in one-dimensional mesoscopic devices

We propose that the finite size of the Kondo screening cloud, xi(K), can be probed by measuring the charge quantization in a one-dimensional system coupled to a small quantum dot. When the chemical potential mu in the system is varied at zero temperature, one should observe charge steps whose locations are at values of mu that are controlled by the Kondo effect when the system size L is comparable to xi(K). We show that, if the standard Kondo model is used, the ratio between the widths of the Coulomb blockade valleys with odd or even number of electrons is a universal scaling function of xi(K)/L. If we take into account electron-electron interactions in a single-channel wire, this ratio also depends on the parameters of the effective Luttinger model; in addition, the scaling is weakly violated by a marginal bulk interaction. For the geometry of a quantum dot embedded in a ring, we show that the dependence of the charge steps on a magnetic flux through the ring is controlled by the size of the Kondo screening cloud.

New Luttinger-liquid physics from angle-resolved photoemission on a paradigm material

Li 0.9Mo 6O 17 is a paradigm material for studying Luttinger-liquid physics in the solid state. This paper summarizes recent and new photoemission studies directed at the quantum critical behavior that is expected for such a system. A theoretical description of the results requires a two-band Tomonaga–Luttinger model augmented by marginal interactions.

Boundary Effect on NMR Relaxation Rate for Tomonaga–Luttinger Model

The NMR relaxation rate, 1/ T 1 , in one-dimensional Tomonaga–Luttinger model with an open boundary has been investigated to comprehend the electronic state, which depends on x , the distance from the boundary. Based on the bosonization scheme, we examine the spin response function, R ( x , T ) [∝1/( T 1 T )], as the function of x , temperature ( T ) and interaction. It is shown that, with increasing x , R ( x , T ) increases from zero with an oscillation and reduces to a finite value after taking a maximum of the peak height. The amplitude of the oscillation is enhanced by interaction but decreases exponentially due to thermal fluctuation. We demonstrate properties associated with the Tomonaga–Luttinger liquid from the view point of the interplay of boundary, interaction and temperature.

Transport of Charge-Density Waves in the Presence of Disorder: Classical Pinning Versus Quantum Localization

We consider the interplay of the elastic pinning and the Anderson localization in the transport properties of a charge-density wave in one dimension, within the framework of the Luttinger model in the limit of strong repulsion. We address a conceptually important issue of which of the two disorder-induced phenomena limits the mobility more effectively. We argue that the interplay of the classical and quantum effects in transport of a very rigid charge-density wave is quite nontrivial: the quantum localization sets in at a temperature much smaller than the pinning temperature, whereas the quantum localization length is much smaller than the pinning length.

Polarization-dependent quantum beats of four-wave mixing in the Luttinger model for bulk semiconductors

We examine the description of quantum beats in four-wave mixing with bulk semiconductors within the framework of the Luttinger-Kohn model. An analytic expression for their dependence on the relative linear polarization of pump and probe is derived, taking only the band structure and coherent interaction of the light waves with the semiconductor medium into account. Herewith all features seen in experiments are very well reproduced, e.g., the vanishing of the beats for an angle ${\ensuremath{\theta}}_{0}\ensuremath{\approx}76\ifmmode^\circ\else\textdegree\fi{}$ between the polarizations of pump and probe. Therefore, as opposed to general belief based on earlier theoretical work, no ad hoc exciton-exciton Coulomb interaction has to be invoked to describe the observed phase and magnitude of the quantum beats for copolarized or for cross-polarized test and pump pulses.

A strongly correlated electron state at one-dimensional quantum points

The method of exact diagnoalization is applied to find the distribution of electrons over single-particle states at a 1D quantum point and the Fourier spectrum of the electron density. It is shown that the distribution function contains an unexpected signularity at the Fermi level. It is found that (i) the singularity results from the Wigner electron ordering and (ii) the Wigner ordering involves suppression of spatial Fourier harmonics of the electron density observed when the interaction potential grows over the entire range of wave vectors except for the double Fermi wave vector. It is demonstrated that the distribution function calculated within the Luttinger model also has a singularity at the Fermi level and this singularity is of an irregular shape.

Forward scattering approximation and bosonization in integer quantum Hall systems

In this work, we present a model and a method to study integer quantum Hall (IQH) systems. Making use of the Landau levels structure we divide these two-dimensional systems into a set of interacting one-dimensional gases, one for each guiding center. We show that the so-called strong field approximation, used by Kallin and Halperin and by MacDonald, is equivalent, in first order, to a forward scattering approximation and analyze the IQH systems within this approximation. Using an appropriate variation of the Landau level bosonization method we obtain the dispersion relations for the collective excitations and the single-particle spectral functions. For the bulk states, these results evidence a behavior typical of non-normal strongly correlated systems, including the spin-charge splitting of the single-particle spectral function. We discuss the origin of this behavior in the light of the Tomonaga–Luttinger model and the bosonization of two-dimensional electron gases.

Current in a spin-orbit-coupling system

The formulas of particle current as well as spin and angular momentum currents are studied for most spin-orbit coupling (SOC) systems. It is shown that the conventional expression of currents in some literatures are not complete for some SOC systems. The particle current in the Dresselhaus system must have extra terms in addition to the conventional one, but no extra term for the Rashba or Luttinger model. Furthermore, we also prove that the extra terms of total angular momentum appear in the Rashba current in addition to the conventional one.

Quantum Critical Proximity of the One-Dimensional Ferromagnetic Phase

We consider the influence of the temperature on the normal state in a one-dimensional ferromagnetic phase transition. This transition occurs only at T = 0 in the Luttinger model but the proximity of the critical point can give drastic effects on the physical properties of the normal phase Using the flow equations of the Renormalization group and a Φ4model with a dynamical critical exponent z = 2, we calculated the temperature dependence of coherence length, magnetic susceptibility, and specific heat.

Surface states, Friedel oscillations, and spin accumulation inp-doped semiconductors

We consider a hole-doped semiconductor with a sharp boundary and study the boundary spin accumulation in response to a charge current. First, we solve exactly a single-particle quantum-mechanics problem described by the isotropic Luttinger model in half-space and construct an orthonormal basis for the corresponding Hamiltonian. It is shown that the complete basis includes two types of eigenstates. The first class of states contains conventional incident and reflected waves, while the other class includes localized surface states. Second, we consider a many-body system in the presence of a charge current flowing parallel to the boundary. It is shown that the localized states contribute to spin accumulation near the surface. We also show that the spin density exhibits current-induced Friedel oscillations with three different periods determined by the Fermi momenta of the light and heavy holes. We find an exact asymptotic expression for the Friedel oscillations far from the boundary. We also calculate numerically the spin density profile and compute the total spin accumulation, which is defined as the integral of the spin density in the direction perpendicular to the boundary. The total spin accumulation is shown to fit very well the simple formula ${S}_{\mathrm{tot}}\ensuremath{\propto}(1\ensuremath{-}{m}_{L}∕{m}_{H}{)}^{2}$, where ${m}_{L}$ and ${m}_{H}$ are the light- and heavy-hole masses. The effects of disorder are discussed. We estimate the spin relaxation time in the Luttinger model and argue that spin physics cannot be described within the diffusion approximation.

Effect of Suddenly Turning on Interactions in the Luttinger Model

The evolution of correlations in the exactly solvable Luttinger model (a model of interacting fermions in one dimension) after a suddenly switched-on interaction is analytically studied. When the model is defined on a finite-size ring, zero-temperature correlations are periodic in time. However, in the thermodynamic limit, the system relaxes algebraically towards a stationary state which is well described, at least for some simple correlation functions, by the generalized Gibbs ensemble recently introduced by Rigol et al. (cond-mat/0604476). The critical exponent that characterizes the decay of the one-particle correlation function is different from the known equilibrium exponents. Experiments for which these results can be relevant are also discussed.

Generalized Kubo formula for spin transport: A theory of linear response to non-Abelian fields

The traditional Kubo formula is generalized to describe the linear response with respect to non-Abelian fields. To fulfill the demand for studying spin transport, the SU(2) Kubo formula is derived by two conventional approaches with different gauge fixings. Those two approaches are shown to be equivalent where the nonconservation of the SU(2) current plays an essential role in guaranteeing the consistency. Some concrete examples relating spin Hall effect are considered. The dc spin conductivity in response to an SU(2) electric field vanishes in the system with parabolic unperturbed dispersion relation. By applying a time-dependent Rashba field, the spin conductivity can be measured directly. Our formula is also applied to the high-dimensional representation for the interests of some important models, such as Luttinger model and bilayer spin Hall system.

Spin Hall conductance of the two-dimensional hole gas in a perpendicular magnetic field

The charge and spin Hall conductance of the two-dimensional hole gas within the Luttinger model with and without inversion symmetry breaking terms in a perpendicular magnetic field are studied, and two key phenomena are predicted. The sign of the spin Hall conductance is modulated periodically by the external magnetic field, which means a possible application in the future. Furthermore, a resonant spin Hall conductance in the two-dimensional hole gas with a certain hole density at a typical magnetic field is indicated, which implies a likely way to firmly establish the intrinsic spin Hall effect. The charge Hall conductance is unaffected by the spin-orbit coupling.

Nontrivial ac spin response in the effective Luttinger model

Based on the three-dimensional effective Luttinger Hamiltonian and the exact Heisenberg equations of motion and within a self-consistent semiclassical approximation, we present a theoretical investigation on the nontrivial ac spin responses due to the intrinsic spin–orbit coupling of holes in p-doped bulk semiconductors. We show that the nontrivial ac spin responses induced by the combined action of an ac external electric field and the intrinsic spin–orbit coupling of holes may lead to the generation of a nonvanishing ac spin Hall current in a p-doped bulk semiconductor, which shares some similarities with the dissipationless dc spin Hall current conceived previously and also exhibits some interesting new features that was not found before.