Quantum Interference Corrections Research Articles

Density of States in Two-DimensionalSquare Lattices Around Half Filling with Strong Impurities

We calculate the lowest-order quantum-interference correction tothe density of states (DOS) of weakly-disordered two-dimensional(2D) tight-binding square lattices around half filling. Theimpurities are assumed to be randomly distributed on smallfractions of the sites, and have a strong potential yielding aunitary-limit scattering. In addition to the usual diffusive modesin the retarded-advanced channel, there appear diffusive πmodes in the retarded-retarded (or advanced-advanced) channel dueto the existence of particle-hole symmetry. It is found that theπ-mode diffuson gives rise to a logarithmic suppression to theDOS near the band center, which prevails over the positivecorrection contributed by π-mode cooperon. As a result, theDOS is subject to a negative total correction. This result isqualitatively different from the divergent behavior of the DOS atthe band center predicted previously for disordered 2Dtwo-sublattice models with the particle-hole symmetry.

Quantum Corrections to the Conductivity of a Natural Nd[sub 2 – ][sub x]Ce[sub x]CuO[sub 4] Superlattice

Temperature and magnetic field dependences of the resistivity and Hall coefficient in layered single-crystal Nd2−x CexCuO4 (x = 0.12) films are experimentally investigated and analyzed. It is shown that this material clearly exhibits quantum effects characteristic of 2D semiconductor structures: negative magnetoresistance caused by suppression of the interference quantum correction by a magnetic field, a near-logarithmic temperature dependence of the conductivity, and a temperature dependence of the Hall coefficient related to e-e interaction. It is shown that, when analyzing experimental data, it is necessary to take interlayer transitions into account. Such an approach provides quantitative agreement between experiment and the standard theory of quantum corrections.

Effect of Roughness of Two-Dimensional Heterostructures on Weak Localization

The effect that a longitudinal magnetic field exerts on the transverse negative magnetoresistance by suppressing the interference quantum correction is studied in GaAs/InxGal−x As/GaAs structures with a single quantum well. It is shown that the variation in the shape of the transverse magnetoresistance curve caused by a longitudinal magnetic field depends strongly on the relation between the mean free path, the phase-breaking length, and the correlation length characterizing the roughness of the two-dimensional layer. It is shown that the experimental results allow one to estimate the parameters of large-scale and small-scale roughness of the two-dimensional layer in the structures under study. The results obtained are in good agreement with the data of probe microscopy.

DYNAMICAL CONDUCTIVITY IN DISORDERED TWO-DIMENSIONAL SQUARE LATTICES AROUND HALF FILLING

Quantum interference (QI) correction to dynamical conductivity is calculated with the diagrammatic technique in a weakly-disordered two-dimensional (2D) square lattice around half filling, in which the pointlike nonmagnetic impurities are assumed to be substituted randomly for the host atoms. It is found that the conductivity correction is inversely proportional to the frequency for the case of perfectly-nested Fermi surface, resulting from the contribution of diffusive π modes to the QI effect. Such an antilocalization effect is strikingly different from the logarithmic weak-localization correction predicted for 2D free electron systems.

Electronic thermal conductivity of disordered metals

We calculate the thermal conductivity of interacting electrons in disordered metals. In our analysis we point out that the interaction affects thermal transport through two distinct mechanisms, associated with quantum interference corrections and energy exchange of the quasiparticles with the electromagnetic environment, respectively. The latter is seen to lead to a violation of the Wiedemann-Franz law. Our theory, valid to all orders in perturbation theory, predicts a strong enhancement of the Lorenz ratio $\ensuremath{\kappa}∕\ensuremath{\sigma}T$ over the value predicted by the Wiedemann-Franz law, when the electrons encounter a large environmental impedance.

Weak-Localization Effect on the Density of States in Disordered d-wave Superconductors**The project supported by National Natural Science Foundation of China under Grant Nos. 10274008, 10174011, and 10347105 and Natural Science Foundation of Jiangsu Province of China under Grant Nos. BK2002050 and BK2001002

The weak-localization effect on the quasiparticle density of states (DOS) is studied with the diagrammatic technique in the binary-alloy model of disordered two-dimensional -wave superconductors both in the Born and the unitary limits. We derive in details the expressions of the Goldstone modes (cooperon and diffuson) for quasiparticle diffuson. For generic Fermi surfaces, the DOS is shown to be subject to a quantum interference correction of logarithmic suppression. In the combined limit of unitarity and nested Fermi surface (the UN limit), it is found that the self-energy diagrams with two -mode diffusons make additional contributions to the weak-localization effect, which has not been considered in the previous diagrammatic analysis. Due to the contributions of these new diagrams, the DOS in the UN limit is shown to have also a negative logarithmic correction, which is qualitatively different from the previous prediction.

Weak-localization theory for quasiparticle dynamical conductivities of disorderedd-wave superconductors

By the diagrammatic technique, we calculate the quantum interference (QI) contributions to the quasiparticle dynamical conductivities of two-dimensional d-wave superconductors with dilute nonmagnetic impurities either near the Born or near the unitary limit. For generic situations, only the 0-mode cooperon has QI contributions to the charge and spin conductivities. It is found that with decreasing frequency, the spin conductivity increases logarithmically while the charge one decreases logarithmically. Such a qualitative difference originates from a novel QI process related to the intrinsic particle-hole symmetry. In the combined limit of unitarity and nested Fermi surface, there exist additional diffusive $\ensuremath{\pi}$ modes in addition to the usual diffusive 0 modes. The QI corrections in this limit are shown to vanish due to the cancellation of the contributions from 0-mode and $\ensuremath{\pi}$-mode cooperons, so that both the charge and spin conductivities approach their universal values.

Test-Particle Approach to Electron Dephasing in an Open Mesoscopic Cavity

The quantum interference effect is suppressed by dephasing processes. The dephasing in mesoscopic systems at low temperatures is mainly caused by electron–electron Coulomb interactions. Usually, the magnitude of the suppression is characterized by the dephasing time . It has been shown that its T-dependence changes according to the effective dimensionality of a system. Using nano-fabrication technology, we can prepare a mesoscopic cavity which is connected to reservoirs through a pair of thin leads. A mesoscopic cavity with a weak opening can be regarded as a quasi-zero-dimensional system, and the quantum transport properties in such a system are qualitatively different from those in higher dimensional systems. We expect that the dephasing nature is also qualitatively different. We hereafter focus on the case where the classical electron motion is diffusive or chaotic. If the width of the leads is reduced, the dwelling time d for electrons becomes very long. Due to the confining effect, there arises a nearly uniform diffusion mode with the lowest eigenvalue 0 1⁄4 h = d. This mode dominantly contributes the quantum interference corrections to conductance when temperature T is sufficiently low. The present author has studied the Tdependence of for the mode by a self-consistent renormalization approach (SCRA), and found an interesting crossover behavior of . It has been shown that behaves as 1 / T when T 0=kB. If T is decreased below 0=kB, the T-dependence of crosses over to 1 / T and the dephasing effect becomes nearly negligible. In this short note, we reconsider the dephasing problem in an open mesoscopic cavity by adopting a test-particle approach. We explicitly calculate the dephasing factor for the weak-localization correction arising from a timereversed pair of paths with duration . In the long-time regime of h ðkBTÞ , the dephasing factor obeys a simple exponential law expð = 1Þ, as usually expected. However, much slower decay expð ð = 2ÞÞ is observed in the short-time regime of h ðkBTÞ . Here, 1 and 2 are characteristic time scales and satisfy h 1 1 , h 1 2 kBT . It is shown that in the case of T 0=kB is determined by the slow decay expð ð = 2ÞÞ. This is the reason why the dephasing effect becomes nearly negligible in the lowtemperature regime. On the other hand, the exponential law expð = 1Þ determines in the high-temperature regime. The resulting is in agreement with that of the SCRA apart from numerical factors. We set h 1⁄4 kB 1⁄4 1 in the following. We adapt the test-particle approach to our problem. Let us consider a time-reversed pair of paths with duration . We introduce a classical path x1ðtÞ which starts from x1ð0Þ and ends at x1ð Þ, and express its time-reversed path as x2ðtÞ. Let us assume that wave packets 1ðr; tÞ and 2ðr; tÞ follow the classical paths x1ðtÞ and x2ðtÞ, respectively. The test particle interacts with a bath of environment electrons. We introduce the density operator WenvðtÞ for the environment and the state vectors j1i and j2i which correspond to 1ðr; tÞ and 2ðr; tÞ, respectively. The test-particle state is described by a linear combination of j1i and j2i. We assume that the environment at t 1⁄4 0 is in thermal equilibrium with respect to the Hamiltonian Henv for the environment electrons including the Coulomb interactions between them. The density operator at t 1⁄4 0 is given by Wð0Þ 1⁄4 WS Wenvð0Þ, where WS 1⁄4 P i;j1⁄41;2 jiiwijhjj. The interference amplitude is Fð Þ 1⁄4 h1j trenvfWð Þgj2i. The dephasing is characterized by the dephasing factor ð Þ Fð Þ=Fð0Þ. In terms of the density of environment electrons ðrÞ and its average value 0, we define ðrÞ as ðrÞ 1⁄4 ðrÞ 0. The Coulomb interaction of the test particle with the environment electrons is expressed as

Positive magnetoresistance in a weak magnetic field in germanium with impurity concentration near the metal‐insulator transition

On the metallic side of the metal-insulator transition (MIT) the theory of quantum corrections to the conductivity provides an accurate description of the temperature dependence of conductivity and magnetoconductivity in a wide variety of disordered conductors. However, we found that there exists a concentration region 1 ≤ N/Nc < 1.4 (here Nc is the critical concentration of the MIT) where the quantum interference corrections do not manifest themselves in the low-temperature resistivity and magnetoresistance experiments. Experiments have been done on isotopically engineered bulk n-type Ge with a high homogeneity of the impurity distribution, which was obtained by neutron-transmutation doping on the metallic side of the MIT close to Nc. We observed an abnormal positive magnetoresistance at relatively small magnetic fields and low temperatures (down to 30 mK) which we consider to be due to the Maki-Thomson correction to the metallic conductivity [1] and a second contribution which we attribute to be due to the tunneling between neighboring electron lakes localized in long range potential fluctuations. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Experimental study of weak antilocalization effects in a high-mobilityInxGa1−xAs/InPquantum well

The magnetoresistance associated with quantum interference corrections in a high mobility, gated InGaAs/InP quantum well structure is studied as a function of temperature, gate voltage, and angle of the tilted magnetic field. Particular attention is paid to the experimental extraction of phase-breaking and spin-orbit scattering times when weak anti- localization effects are prominent. Compared with metals and low mobility semiconductors the characteristic magnetic field $B_{tr} = \hbar/4eD \tau$ in high mobility samples is very small and the experimental dependencies of the interference effects extend to fields several hundreds of times larger. Fitting experimental results under these conditions therefore requires theories valid for arbitrary magnetic field. It was found, however, that such a theory was unable to fit the experimental data without introducing an extra, empirical, scale factor of about 2. Measurements in tilted magnetic fields and as a function of temperature established that both the weak localization and the weak anti-localization effects have the same, orbital origin. Fits to the data confirmed that the width of the low field feature, whether a weak localization or a weak anti-localization peak, is determined by the phase-breaking time and also established that the universal (negative) magnetoresistance observed in the high field limit is associated with a temperature independent spin-orbit scattering time.

Weak localization and integer quantum Hall effect in a periodic potential

We consider magnetotransport in a disordered two-dimensional electron gas in the presence of a periodic modulation in one direction. Existing quasiclassical and quantum approaches to this problem account for Weiss oscillations in the resistivity tensor at moderate magnetic fields, as well as a strong modulation-induced modification of the Shubnikov-de Haas oscillations at higher magnetic fields. They do not account, however, for the operation at even higher magnetic fields of the integer quantum Hall effect, for which quantum interference processes are responsible. We then introduce a field-theory approach, based on a nonlinear sigma model, which encompasses naturally both the quasiclassical and quantum-mechanical approaches, as well as providing a consistent means of extending them to include quantum interference corrections. A perturbative renormalization-group analysis of the field theory shows how weak localization corrections to the conductivity tensor may be described by a modification of the usual one-parameter scaling, such as to accommodate the anisotropy of the bare conductivity tensor. We also show how the two-parameter scaling, conjectured as a model for the quantum Hall effect in unmodulated systems, may be generalized similarly for the modulated system. Within this model we illustrate the operation of the quantum Hall effect in modulated systems for parameters that are realistic for current experiments.

Dephasing due to Spin–Wave Excitations in Ferromagnetic Metals

The dephasing due to spin–wave excitations is studied for ferromagnetic wires of mesoscopic dimensions in the diffusive regime. The spin–wave dephasing time τ φ for conduction electrons is calculated as a function of temperature T on the basis of the s – d interaction model. It is shown that in the absence of an external magnetic field, the spin–wave dephasing in some cases becomes comparable to, or even dominates, the ordinary dephasing due to Coulomb interactions. It is also shown that if a magnetic field H is applied parallel to the wire, the spin–wave dephasing is exponentially suppressed with the increase of H at the low-temperature regime of γ H ≫ T (γ: gyromagnetic ratio). This strong H -dependence can be used to examine the influence of the spin–wave dephasing on quantum interference corrections.

Quantum Interference Effect on the Conductance of a Ferromagnetic Wire with a Domain Wall

We study quantum interference corrections to the conductance of a thin wire of a disordered ferromagnetic metal in the presence of a domain wall (DW). The DW is a source of the decoherence of electron wavefunctions. We calculate the weak-localization correction and the mesoscopic conductance fluctuations to show how the DW suppresses these quantum corrections. We explicitly take the location of the DW into account in calculating the quantum corrections. It is shown that the magnitude of the quantum corrections depends on the location of the DW when the system length is of the order of, or shorter than, the phase coherence length. We find that the quantum interference corrections are most remarkably suppressed when the DW is located at the center of the ferromagnetic wire. It is also shown that the decoherence effect becomes pronounced with decrease of the thickness of the DW.

Dephasing of the Quantum Interference Effect in Open Ballistic Billiards

Quantum interference corrections to conductance are suppressed by the dephasing due to electron-electron interactions. The dephasing in open ballistic billiards is studied at low temperatures. It is shown that if the classical electron motion is chaotic, the interference correction arising from a time-reversed pair of paths with duration τ is suppressed by the factor of exp (-τ/τ φ ), where τ φ should be identified as the dephasing time. Consequently, the weak-localization correction to conductance is suppressed by the factor of 1/(1+ t B /τ φ ) ( t B : classical escape time). In contrast, it is also shown that the interference correction in non-chaotic billiards (i.e., integrable or mixed case) cannot be characterized by such a simple exponential decay. This implies that the dephasing time is not well defined in non-chaotic billiards.

Quantum interference in intentionally disordered dopedGaAs/AlxGa1−xAssuperlattices

The processes of quantum interference are studied in intentionally disordered doped short-period $\mathrm{GaAs}/{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ superlattices where the conductivity can be controlled by the artificial disorder. We found that the usual formula for the weak localization correction to the classical conductivity of superlattices obtained in the propagative Fermi-surface approximation [W. Szott, C. Jedrzejek, and W.P. Kirk, Phys. Rev. Lett. $63,$ 1980 (1989)] does not allow to one explain the observed negative magnetoresistance. An excelent agreement was obtained between our results and recently published calculations of the quantum interference correction to the conductivity of the strongly disordered superlattices, where the transport regime corresponding to the diffusive Fermi surface was considered [A. Cassam-Chenai and D. Mailly, Phys. Rev. B 52, 1984 (1995)]. We found a tendency toward a propagative regime with an increase of the electron concentration, when the influence of disorder was weakened. The decrease of the dephasing of the electron wave function was observed with an increase of both the doping concentration and the disorder strength. The observed temperature dependence of the dephasing time manifested that the process of the dephasing is modified in the presence of strong disorder.

Transport of a two-dimensional electron gas in a lattice of diffusive and thermalizing scatterers

Classical and quantum transport in a new kind of two-dimensional (2D) systems with artificial scatterers—2D electron gas in an array of diffusive and thermalizing scatterers (AuGeNi alloy dots)—was studied experimentally. It is shown that this array leads to a strong diffusive and inelastic scattering of the 2D electrons. As a result, several features in transport properties were observed: commensurability magnetoresistance peak, anomalies of the Hall resistance, unusual behavior (linear temperature dependence, saturation of the negative magnetoresistance) of the quantum interference corrections to the conductivity, which is due to the nontrivial dephasing in the system.

Analysis of negative magnetoresistance: Statistics of closed paths. I. Theory

Statistics of closed paths in two-dimensional (2D) systems, which just determines the interference quantum correction to conductivity and anomalous magnetoconductance, has been studied by computer simulation of a particle motion over the plane with randomly distributed scatterers. Both ballistic and diffusion regimes have been considered. The results of simulation have been analyzed in the framework of diffusion approximation. They are used for calculation of the magnetic-field dependence of magnetoconductance in the model 2D system. It is shown that the anomalous magnetoconductance can be, in principle, described by the well-known expression, obtained in the diffusion approximation, but with the prefactor less than unity and phase breaking, which differs from true value.

Quantum interference effects in quasi-two-dimensional metals

In connection with two groups of experimental data, a calculation is performed of quantum interference corrections in a quasi-two-dimensional metal to conductivity as a function of temperature and magnetic field. For the temperature dependence a cross-over between a two-dimensional (2D) (higher temperatures) and 3D (lower temperatures) behavior is obtained. In the 3D limit the relative correction is isotropic. In the 2D limit it is extremely anisotropic having a logarithmic dependence in the ab plane, and a power law for the c conductivity. The interaction correction to the density of states is calculated as a function of temperature. A criterion for the crossover from 2D to 3D behavior differs strongly from the interference correction, and makes the 2D limit unlikely. In the 3D limit this correction is proportional to $\sqrt{T}.$ Comparison between corrections of different origins favors the interference logarithmic correction for the in-plane conductivity, in agreement with experiment. The c-axis correction can be of either origin, and is nonlogarithmic, as observed in some experiments. The dependence of the relative correction on magnetic field in the 3D limit is always proportional to $\sqrt{H},$ in agreement with experiment, and the coefficient depends only on the orientation of the magnetic field.

Weak localization in thin Cs films

Thin, quench condensed films of Cs change their resistance and Hall effect dramatically when covered with surface impurities. In this paper we investigate the quantum interference corrections to the resistance (weak localization) and determine the inelastic dephasing rate of the conduction electrons. The dephasing rate is proportional to the temperature-dependent resistance. For pure Cs films the magnetoresistance curves show a rather poor agreement with the theory, which is exceptional for quench condensed metal films. In particular, at 4.5 K a linear magnetoresistance is observed at large magnetic fields, which defies explanation. Sandwiches of AgCs yield a much better agreement between the experimental results and the theory. However, the dephasing rate of Cs in Ag/Cs and Au/Cs sandwiches has only half the value of that in pure Cs films with the same thickness and mean free path.

Weak antilocalization in a 2D electron gas with chiral splitting of the spectrum

Motivated by the recent observation of the metal-insulator transition in Si-MOSFETs we consider the quantum interference correction to the conductivity in the presence of the Rashba spin splitting. For a small splitting, a crossover from the localizing to antilocalizing regime is obtained. The symplectic correction is revealed in the limit of a large separation between the chiral branches. The relevance of the chiral splitting for the 2D electron gas in Si-MOSFETs is discussed.