Integer and fractional quantum Hall effect in a strip of stripes

We study anisotropic stripe models of interacting electrons in the presence of magnetic fields in the quantum Hall regime with integer and fractional filling factors. The model consists of an infinite strip of finite width that contains periodically arranged stripes (forming supercells) to which the electrons are confined and between which they can hop with associated magnetic phases. The interacting electron system within the one-dimensional stripes are described by Luttinger liquids and shown to give rise to charge and spin density waves that lead to periodic structures within the stripe with a reciprocal wavevector 8k _F in a mean field approximation. This wavevector gives rise to Umklapp scattering and resonant scattering that results in gaps and chiral edge states at all known integer and fractional filling factors ν. The integer and odd denominator filling factors arise for a uniform distribution of stripes, whereas the even denominator filling factors arise for a non-uniform stripe distribution. We focus on the ground state of the system, and identify the quantum Hall regime via the quantized Hall conductance. For this we calculate the Hall conductance via the Streda formula and show that it is given by σ _H = νe ²/h for all filling factors. In addition, we show that the composite fermion picture follows directly from the condition of the resonant Umklapp scattering.     

Study of crystal-field excitations and Raman active phonons in o-DyMnO3

In DyMnO₃ orthorhombic single crystals, the weak Raman active phonon softening below T=100 K is correlated with the study of infrared active Dy³⁺ CF excitations as a function of temperature and under applied magnetic field. We detect five H_13/2 CF transitions that we predict with appropriate CF Hamiltonian and we confirm that the magnetic easy axis lies in the ab plane. While the CF energy level shifts below T=100 K reflect different displacements of the oxygen ions that contribute to the phonon softening, lifting of the ground state Kramers doublet degeneracy (∼30 cm⁻¹) is observed below T_N=39 K due to the anisotropic Mn³⁺−Dy³⁺ interaction, which could be responsible for the stability of the bc-cycloid ferroelectric phase.     

Intermediate phase of the one dimensional half-filled Hubbard-Holstein model

We present a numerical study of the Hubbard-Holstein model in one dimension at half filling, including finite-frequency quantum phonons. At half filling, the effects of the electron-phonon and electron-electron interactions compete with the Holstein phonon coupling acting as an effective negative Hubbard on-site interaction U that promotes on-site electron pairs and a Peierls charge-density wave state. Most previous work on this model has assumed that only Peierls or Mott phases are possible at half filling. However, there has been speculation that a third metallic phase exists between the Peierls and Mott phases. We confirm the intermediate phase, and show that the Luttinger liquid correlation exponent K(rho) >1 in this region, indicating dominant superconducting pair correlations. We explore the full phase diagram as a function of Hubbard U, phonon coupling constant, and phonon frequency.     

Statistical Theory of the Phonon Drag Force Acting on a Conduction Electron

Within the framework of microscopic fluctuation-dissipation theory, we obtain the stochastic equation describing the Brownian motion of an electron in the phonon field of the crystal lattice. An expression for the Green’s function of the phonon field is found in general form and for the case of linear phonon-variable interaction of an electron with the phonon field with allowance for the potential screening of crystal-lattice nuclei. An expression for the phonon drag acting on a conduction electron in the lattice field is found and analyzed with allowance for the interaction. Frequency dependence of the coefficient of the phonon drag acting on a conduction electron is studied and the contribution of the electron-phonon interaction to the effective mass of a charge carrier is determined.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 3, pp. 249–268, March 2005.     

Electronic structure for sliding charge density waves

We present a model for the electron system in NbSe₃ based on its quasi one-dimensional metallic properties. In a one-dimensional metal phonon drag of 2K_F-phonons takes place at temperatures higher than θ_D, since the phonon-electron scattering rate τ^?1_ph?el is greater than the phonon-phonon rate τ^?1_ph?ph. this situation is in contrast to the situation in three dimensional metals, where phonon drag takes place only at very low temperatures. Our model explains the transport properties of the material including the electrical conductivity anistropy, the conductivity in a strong electric field, and the Hall effect data.     

Phonon focusing and electron–phonon drag in semiconductor crystals with degenerate charge-carrier statistics

We study the effect of anisotropy in elastic properties on the electron–phonon drag and thermoelectric phenomena in gapless semiconductors with degenerate charge-carrier statistics. It is shown that phonon focusing leads to a number of new effects in the drag thermopower at low temperatures, when diffusive phonon scattering from the boundaries is the predominant relaxation mechanism. We analyze the effect of phonon focusing on the dependences of the thermoelectromotive force (thermopower) in HgSe:Fe crystals on geometric parameters and the heat-flow directions relative to the crystal axes in the Knudsen regime of the phonon gas flow. The crystallographic directions that ensure the maximum and minimum values of the thermopower are determined and the role of quasi-longitudinal and quasi-transverse phonons in the drag thermopower in HgSe:Fe crystals at low temperatures is analyzed. It is shown that the main contribution to the drag thermopower comes from slow quasi-transverse phonons in the directions of focusing in long samples.     

Ballistic phonon studies in the lowest Landau level

We report time-resolved studies of ballistic phonon absorption in the fractional quantum Hall regime at Landau level filling factors of and . The technique used can resolve the interaction of the two-dimensional electron system with LA and TA phonons and has been used to measure the temperature variation of the heat capacity of a single layer of electrons at . The energy gaps at have also been measured and found to be in good agreement with theory. The roles of compressible and incompressible regions in the phonon absorption process are discussed. Angle resolved measurements at are also in good agreement with theory.     

Exotic electronic phases in the second Landau level

Recent experiments have shown that two-dimensional electron systems with an externally applied magnetic field are an extremely rich ground for many-body physics. In particular, when only two of the Landau levels (LL) are filled an intricate magnetoresistance is found. This result stems from an interesting competition of electronic phases such as fractional quantum Hall liquids, reentrant integer Hall states, and unique quantized states at even denominator LL filling factors. We present a brief review of the transport properties of these electronic phases and discuss in detail the effects of an added in-plane magnetic field.     

Exotic electronic phases in the second Landau level

Recent experiments have shown that two-dimensional electron systems with an externally applied magnetic field are an extremely rich ground for many-body physics. In particular, when only two of the Landau levels (LL) are filled an intricate magnetoresistance is found. This result stems from an interesting competition of electronic phases such as fractional quantum Hall liquids, reentrant integer Hall states, and unique quantized states at even denominator LL filling factors. We present a brief review of the transport properties of these electronic phases and discuss in detail the effects of an added in-plane magnetic field.     

Phonon drag thermopower in doped bismuth

The low-temperature (2<T<80 K) thermopower in bismuth doped by tellurium, a donor impurity (0<c≤0.07 at. % Te), is dominated by the phonon component, which shifts to higher temperatures with increasing dopant concentration. The temperature and concentration dependences of the phonon thermopower of doped bismuth are satisfactorily described by the theory of phonon drag of electrons. The theory is developed for a strongly anisotropic electron spectrum and includes both direct and two-step phonon drag.     

On the fractional quantum hall effect

We show in the Hartree-Fock approximation that the formation of a two dimensional electron lattice allows for a natural explanation of the anomalous fractional quantum Hall effect. Landau levels are broadened and split in a number of bands in such a way that if the number of electrons per unit cell is a half odd integer the Fermi energy is in a gap for an odd filling fraction denominator, and at the center of a band if the denominator is even.     

First principles calculations of the low temperature electrical resistivity of potassium

The results of first principles calculations of the low temperature (2 K ?T?20 K) phonon-limited electrical resistivity of potassium are presented for both the Bloch limit (possible phonon drag effects are completely ignored) and the phonon drag limit (phonon-phonon collisions, which tend to suppress phonon drag, are neglected). In the former case the agreement with experiment is very good; in the latter, the calculated results are much too low. These results are at serious variance with the conclusions of Kaveh and Wiser and reopen the question of whether or not there is any evidence for important phonon drag effects in the low temperature electrical resistivity of potassium.     

Nonohmic behavior of semiconductors in a quantizing magnetic field

We have investigated the nonohmic resistivity of a nondegenerate semiconductor in quantizing magnetic fields for the case where acoustic phonons are the dominant scattering mechanism. The type of I-V characteristics found depends upon which of three mechanism are dominant. The three mechanisms are due to collisional broadening, inelasticities due to the finite phonon energy and phonon drag. When collistion broadening is important, the nonlinearities in the current voltage characteristic arise only from electron heating, while when the inelasticities are dominant, there is also an intrinsic nonlinearity in the characteristic. Finally, when phonon drag is dominant, high frequency acoustoelectric amplification will occur when the Hall velocity exceeds the sound velocity, i.e. V_H > S.For the case where inelasticities dominate, a region of negative differential resistance is obtained that should persist even when there is considerable optical phonon scattering.     

Atomistic simulation of the motion of dislocations in metals under phonon drag conditions

The mobility of dislocations in the over-barrier motion in different metals (Al, Cu, Fe, Mo) has been investigated using the molecular dynamics method. The phonon drag coefficients have been calculated as a function of the pressure and temperature. The results obtained are in good agreement with the experimental data and theoretical estimates. For face-centered cubic metals, the main mechanism of dislocation drag is the phonon scattering. For body-centered cubic metals, the contribution of the radiation friction becomes significant at room temperature. It has been found that there is a correlation between the temperature dependences of the phonon drag coefficient and the lattice constant. The dependences of the phonon drag coefficient on the pressure have been calculated. In contrast to the other metals, iron is characterized by a sharp increase in the phonon drag coefficient with an increase in the pressure at low temperatures due to the α-∈ phase transition.     

Ultra‐low acoustic‐phonon‐limited mobility and giant phonon‐drag thermopower in MgZnO/ZnO heterostructures

We present numerical simulations of the acoustic‐phonon‐limited mobility, $ \mu _{\rm ac}, $ and phonon‐drag thermopower, S^{\rm g},$ in two‐dimensional electron gases confined in MgZnO/ZnO heterostructures. The calculations are based on the Boltzmann equation and are made for temperatures in the range 0.3–20 K and sheet densities 0.5–30 × 10¹⁵ m^–2. The theoretical estimations of \mu _{\rm ac} $ are in good agreement with the experiment without any adjustable parameters. We find that the magnitude of \mu _{\rm ac} $ is dramatically decreased in relation to GaAs‐based heterostructures. The phonon‐drag thermopower, S^{\rm g},$ which according to Herring's expression is inversely proportional to \mu _{\rm ac} is severely increased exceeding 200 mV/K at T = 5 K depending on sheet density. The giant values of S^{\rm g} $ lead to a strong improvement of the figure of merit ZT at low temperatures. Our findings suggest that MgZnO/ZnO heterostructures can be candidates for good thermoelectric materials at cryogenic temperatures. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermoelectric power of p-doped single-wall carbon nanotubes and the role of phonon drag

We measured thermoelectric power S of bulk single-wall carbon nanotube materials p doped with acids. In contrast to oxygen-exposed or degassed samples, S is very small at the lowest temperatures, increases superlinearly above a characteristic and sample-dependent T, and then levels off. We attribute this unusual behavior to 1D phonon drag, in which the depression of the Fermi energy cuts off electron-phonon scattering at temperatures below a characteristic T0. This idea is supported by a model calculation in which the low temperature behavior of phonon drag is specifically related to the one-dimensional character of the electronic spectrum.     

Frictional magnetodrag between spatially separated two-dimensional electron systems: Coulomb versus phonon mediated electron-electron interaction

We study the frictional drag due to Coulomb and phonon mediated electron-electron interaction in a double layer electron system exposed to a perpendicular magnetic field. We calculate the transresistivity as a function of magnetic field, temperature, and inter-layer spacing Λ. We find the strikingly different magnetic field and temperature dependence of the transresistivity for Λ=30 and 200 nm and ascribe this to the weak screening effect at large inter-layer separations.     

Phonon drag resistivity of potassium

The phonon drag resistivity for potassium is calculated by solving the Boltzman equations for both the electrons and phonons as opposed to the conventional method of Ziman where the phonon equation is not considered. By an application of the Schwartz inequality we can show that the drag resistivity in the present formalism is larger than that obtained by the conventional method. We substantiate this result by numerical calculation for potassium at very low temperatures, using a realistic phonon spectrum obtained from inelastic neutron scattering data. Parts of this paper were presented as partial fulfilment for a Ph.D. degree at Cornell University. The work was partially supported by CSIR funding.     

Drag effect of one-dimensional electrons upon photoionization of D<Superscript>(−)</Superscript> centers in a longitudinal magnetic field

A theory is elaborated for the impurity photon drag effect in a semiconductor quantum wire exposed to a longitudinal magnetic field B directed along the axis of the quantum wire. The phonon drag effect is associated with the transfer of the longitudinal photon momentum to localized electrons in optical transitions from D^(?) states to hybrid-quantized states of the quantum wire, which is described by a confinement parabolic potential. An analytical expression for the drag current density is derived within the model of a zero-range potential in the effective mass approximation, and the spectral dependence of the drag current density is examined at different magnitudes of B and parameters of the quantum wire upon electron scattering by a system of impurities with short-range potentials. It is established that the spectral dependence of the drag current density exhibits a Zeeman doublet with a clear beak-shaped peak due to optical transitions of electrons from D^(?) states to states with the magnetic quantum number m=1. The possibility of using the photon drag effect in a longitudinal magnetic field for the development of laser radiation detectors is analyzed.     

Thermoelectric Coefficients of Silicon MOSFETS in Quantizing Magnetic Field

The phonon drag and electron diffusion contribution to the tensor M which determines 3 the heat flux U = M·E is calculated for a silicon MOSFETS in a perpendicular magnetic field B. We used nearly the same theoretical formalism as Ref [6], but improvements are made in several respects. First of all the dielectric function of Fermi-Thomas approximation which has been proved to result in overscreening of the interaction is replaced by rigorous Lindhard-type dielectric function to take account of the screening between electrons and phonons. Secondly the contributions of localized electrons are separated from those of the free state electrons which are the only part that contributes to both conductivity tensor and magnetothermopower tensor. The calculated M_yx and S_xx reveal magneto-oscillationsoriginating Gom oscillations in the density of states at the Fermi level. At T = 5.02 K, our new results show that the diffusion components of thermopower are negligibly small compared with those due to phonon drag. All the theoretical values of M_yx, S_xx and S_yx are in accordance with the experimental data better than previous theoretical results.