Weak Localization Theory Research Articles

Anomalous magnetoresistance of two-dimensional systems in the presence of spin-orbit scattering

A theory of weak localization in two-dimensional semiconductor structures and metal films is developed for spin relaxation by the Elliott-Yafet mechanism. The theory is valid in the entire range of classically weak magnetic fields. It is shown that effects due to spin-orbit interaction substantially modify magnetoresistance in both diffusive and ballistic regimes.

Anomalous magnetoresistivity of the superconducting Zr80Pt20 system in quasicrystalline and amorphous states

The binary icosahedral Zr80Pt20 system has been synthesized during the crystallization of an initially amorphous alloy fabricated by melt quenching on the surface of a rotating copper wheel. The temperature and field dependences of the electrical resistivity and magnetoresistivity of the icosahedral and amorphous phases are studied and compared in a temperature range of 1.5–300 K and magnetic fields up to 8 T. Superconductivity has been detected for the first time in the icosahedral and amorphous phases of the Zr80Pt20 system. For both phases, the magnetoresistivity is positive and depends anomalously on the magnetic field. The anomalous behavior of magnetoresistivity is satisfactorily described by the theory of weak localization and electron-electron interaction in three-dimensional disordered systems, which takes into account electron scattering by superconducting fluctuations. The absolute values and temperature dependences of the electron-electron interaction constant and the times of inelastic scattering of conduction electrons are estimated for the icosahedral and amorphous phases of this binary system.

Low field magnetotransport in strainedSi∕SiGecavities

Low field magnetotransport revealing signatures of ballistic transport effects in strained $\mathrm{Si}∕\mathrm{SiGe}$ cavities is investigated. We fabricated strained $\mathrm{Si}∕\mathrm{SiGe}$ cavities by confining a high mobility $\mathrm{Si}∕\mathrm{SiGe}$ two-dimensional electron gas in a bended nanowire geometry defined by electron-beam lithography and reactive ion etching. The main features observed in the low temperature magnetoresistance curves are the presence of a zero-field magnetoresistance peak and of an oscillatory structure at low fields. By adopting a simple geometrical model we explain the oscillatory structure in terms of electron magnetic focusing. A detailed examination of the zero-field peak line shape clearly shows deviations from the predictions of ballistic weak localization theory.

Electron–Phonon Scattering in a Disordered Ti41V41Al18 Alloy

The results of a systematic study of electron–electron interaction and weak localization on Ti41V41Al18 alloy are being reported in this work. The results indicate an anomalous resistivity behaviour with variation in temperature that follows a T2 variation at high temperature and shows a T1/2 variation at low temperature. Attempt has been made to explain this anomalous behaviour of resistivity with the help of the existing theories concerning low temperature physics. The low field magnetoresistivity is described by weak localization theory under strong spin–orbit interaction. The electron–phonon scattering rate obeys a T4 dependence, which is interpreted by the existing theories of electron–phonon interaction.

Weak localization and spin‐orbit interaction in self‐organized In 0.2 Ga 0.8 As quantum wires on GaAs (221)A substrates

Anisotropic negative magnetoresistance (MR) parallel and perpendicular to the wires in the regime of quantum interference of hole gas has been investigated in self-organized In0.2Ga0.8As quantum wires (QWRs) grown on GaAs (221)A substrates by MBE and separated from p-type Si-doped Al0.35Ga0.75As by an undoped spacer layer of it (thickness Ls) in order to address issues concerning the dimensionality in weak localization (WL) as well as spin-orbit (SO) interaction. For Ls = 3 nm, the best fits of the parallel MR to the 2D WL theory have been obtained with τso ∼ 24 ps, being well described by the model of anisotropic 2D WL for strong lateral coupling of the wires. For Ls = 20 nm, on the other hand, the best fits to 1D WL theory have been obtained with τso ∼ 150 ps assuming diffusive boundary scattering and the data cannot be fit to 2D WL, being well described by the model of quasi-1D WL. In addition, the data for Ls = 10 nm show a featureof the crossover between 2D WL and 1D WL, indicating the intermediate lateral coupling between the wires. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Electronic transport studies onSb1−x(SiO2)x films

Sb1−x(SiO2)x granular films were prepared by the co-sputtering method with the volume fraction ofSiO2,x, ranging from 0 (i.e. pure Sb) to about 30%. Systematic electronic transportstudies, including resistivity, magnetoresistance, Hall effect and Seebeck effect,were carried out against the temperature, magnetic field and volume fractionx ofSiO2. With the gradualincrease of the SiO2 content, the mean grain size of the Sb decreases, and eventually the film becomesamorphous, as illustrated by the changes of the x-ray diffraction patterns. The temperaturecoefficient of resistivity also changes its sign from positive to negative, indicating asemimetal–semiconductor or insulator transition. Magnetoresistance studies using the weaklocalization theory revealed that the electron dephasing time follows approximately aT−2 law. This behaviour indicates that the electron–phonon (e–ph) scattering still dominatesthe electron dephasing processes in these granular systems with a fair number ofSiO2 inclusions. The Hall coefficient decreases monotonically with temperature and with the volume fractionof SiO2.The giant Hall effect is absent in these granular films. Finally, an interesting but rather complicatedbehaviour of the Seebeck coefficient versus temperature was observed when the volume content ofthe SiO2 exceeded 18%.

Magnetoresistance of Carbon Nanotube with the Kane Dispersion Law

Considering the nanotube as effective conducting media the magnetoresistance is calculated. For an electron motion along nanotube axis the spin–orbital interaction is considered as perturbation and the Dirac equation is solved for longitudinal wave functions. It is shown that in this case a magnetic field can be considered as perturbation for energy spectrum and density matrix diagonal components for each spin orientation are needed to calculate the nanotube conductivity. For narrow gap nanotube the magnetoresistance depends linearly on a weak magnetic field. Our results show that in nanotubes the negative magnetoresistance (NMR) can be described without theory of weak localization.

Weak localization and electron–electron interaction in disordered V 80Al 20− xFe x alloys at low temperature

In this Letter we report on the electrical resistivity and magneto-resistivity of disordered V 80Al 20− x Fe x alloys in the temperature range 1.5⩽ T⩽300 K and analyze them in the light of weak localization and electron–electron interaction. The low temperature zero field resistivity obeys a T 1/2 law, which is explained by electron–electron interaction. The low field magneto-resistivity is described by weak localization theory under strong spin–orbit interaction. The electron–phonon scattering rate obeys a quadratic temperature dependence. This observation is interpreted by the existing theories of electron–phonon interaction.

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.

Weak localization and magnetointersubband scattering effects in anAlxGa1−xN/GaNtwo-dimensional electron gas

Magnetotransport measurements have been carried out on a two-dimensional electron gas in a modulation-doped ${\mathrm{Al}}_{0.22}{\mathrm{Ga}}_{0.78}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ heterostructure. The weak localization and magnetointersubband scattering effects have been studied. The measurements show that the inelastic scattering time is inversely proportional to the temperature, following the prediction by weak localization theory. Furthermore, fitting the inelastic scattering time indicates an enhanced phase-breaking rate compared to the theoretical predication. At the same time, a magnetoresistance oscillation induced by intersubband scattering has also been observed. This magnetoresistance oscillation persists to a relatively high temperature in contrast to the Shubnikov--de Haas oscillation.

Magnetic and electrical properties of a Cu–Ga–Mg–Sc icosahedral quasicrystal

We have investigated the magnetic susceptibility and the electrical resistivity of a new P-type icosahedral quasicrystal Cu 48.2Ga 33.8Mg 3Sc 15 and a cubic phase Cu 49Ga 36Sc 15, interpreted as a 1/1 approximant crystal of the quasicrystal. The magnetic susceptibility of the Cu 48.2Ga 33.8Mg 3Sc 15 quasicrystal showed an increase from −3.51 × 10 −4 to −2.78 × 10 −4 m 3 kg −1 with a rise in temperature from 120 to 300 K. The Cu 49Ga 36Sc 15 cubic phase showed also a rise from −6.18 × 10 −4 to −4.50 × 10 −4 m 3 kg −1 between 100 and 300 K. The increase in the susceptibility was accounted for by the temperature dependence of the Pauli paramagnetism. The experimental results strongly suggest the existence of a pseudogap in the electronic density of states at Fermi energy for the Cu 48.2Ga 33.8Mg 3Sc 15 quasicrystal and the Cu 49Ga 36Sc 15 approximant, which has been observed in various stable icosahedral quasicrystals. The electrical resistivity of the Cu 47.1Ga 32.9Mg 5Sc 15 quasicrystal showed a negative temperature coefficient in the temperature region between 2 and 270 K. The Cu 49Ga 35.8Sc 15.2 cubic phase showed a positive temperature coefficient in the temperature region. The tendency of the quasicrystal was qualitatively accounted for by the weak localization theory.

Magnetic and electrical properties of a new type Zn–Mg–Sc icosahedral quasicrystal

The magnetic susceptibility of the Zn–Mg–Sc icosahedral quasicrystals, which have a new type of atomic cluster structure, was found to increase with a rise in temperature from 100 to 300 K. The increase of the susceptibility was accounted for by the temperature dependent term of the Pauli paramagnetism, which indicated a pseudogap in the electronic density of states (DOS) near the Fermi energy. This new type quasicrystal may be stabilized by the pseudogap in the DOS, as in various stable icosahedral quasicrystals discovered to date. We measured the temperature dependence of the electrical resistivity. In the temperature range between 2 and 300 K, the resistivity increased by 0.08% with a decrease in temperature. These measurements were analyzed on the basis of the weak localization theory of electrons in quasicrystals.

Positive and negative linear magnetoresistance of graphite

The magnetoresistance (MR) of bulk graphite with different particle sizes is investigated. The MR of the graphite decreases with the particle size decreases. The graphite with micro-sized particles has a positive MR and exhibits positive linear field dependence of MR at about 50 K, whereas the graphite with particle size of 30.2 nm has a negative MR and exhibits negative linear field dependence of MR at about 25 K. The possible mechanism for the MR of graphite can be partially understood using ordinary MR theory, weak localization theory and diffuse scattering theory.

Weak-field magnetoresistance anomaly and Shubnikov–de Haas oscillations in Sn-doped InSb thin films on GaAs (100) substrates

Distinctive magnetoresistance (MR) effects in weak magnetic fields before the appearance of Shubnikov–de Haas (SdH) oscillations at low temperatures in Sn-doped (7×10 16 cm −3) InSb films grown on GaAs(100) substrates by MBE have been investigated with decreasing film thickness d from 1 μm . The negative MR found in weak magnetic fields for d⩾0.5 μm can be broadly divided into two regimes: T-sensitive negative MR below B c observed with anisotropy between parallel and perpendicular magnetic field and a T-insensitive parabolic one above B c observable only under in-plane magnetic fields. The latter is ascribable to the skipping orbit effect due to surface boundary scattering. In vanishing magnetic fields far below B c, the negative MR reduces with decreasing d and the different positive MR overlaps with it below 0.5 μm , eventually dominating the positive MR at d∼0.2 μm . These results have been analyzed using a two-layer model for the films, where the composition of the upper layer under the surface and the lower one adjacent to the InSb/GaAs interface is assumed. The MR data in the extremely weak magnetic fields below 100 G for each layer have been successfully fitted to the two-dimensional (2D) weak localization (WL) theory. These results explain that the crossover from the 2D WL to the weak anti-localization (WAL) occurs when the interface is approached with the increase of SO interaction in the layers caused by the increased influence of the asymmetric potential at the hetero interface (Rashba term) and the SO rate in the intrinsic InSb film due to the crystal field of the zinc-blende structure (Dresselhaus term) is as small as τ so −1⩽3×10 8 s −1 .

Unitary limit and quantum interference effect in disordered two-dimensional crystals with nearly half-filled bands

Based on the self-consistent $T$-matrix approximation, the quantum interference (QI) effect is studied with the diagrammatic technique in weakly-disordered two-dimensional crystals with nearly half-filled bands. In addition to the usual 0-mode cooperon and diffuson, there exist $\pi$-mode cooperon and diffuson in the unitary limit due to the particle-hole symmetry. The diffusive $\pi$-modes are gapped by the deviation from the exactly-nested Fermi surface. The conductivity diagrams with the gapped $\pi$-mode cooperon or diffuson are found to give rise to unconventional features of the QI effect. Besides the inelastic scattering, the thermal fluctuation is shown to be also an important dephasing mechanism in the QI processes related with the diffusive $\pi$-modes. In the proximity of the nesting case, a power-law anti-localization effect appears due to the $\pi$-mode diffuson. For large deviation from the nested Fermi surface, this anti-localization effect is suppressed, and the conductivity remains to have the usual logarithmic weak-localization correction contributed by the 0-mode cooperon. As a result, the dc conductivity in the unitary limit becomes a non-monotonic function of the temperature or the sample size, which is quite different from the prediction of the usual weak-localization theory.

Electron Transport and Time-Dependent Perturbation in a Two-Dimensional Symplectic System

Electron transport in a two-dimensional symplectic system with time-dependent perturbations is investigated numerically by the equation of motion method. The effect of time-dependent perturbations on the conductivity is examined in the critical regime as well as in the metallic regime. The universal correction to the conductivity, which is consistent with the weak localization theory, is indeed observed in the metallic regime. In the critical regime, it is found that the dependence of the conductivity on the frequency of perturbations can be described by the one-parameter scaling.

Spin precession observation in quantum corrections to resistance of Si 0.7Ge 0.3/Si 0.2Ge 0.8 heterostructure with 2DHG

The two-dimensional hole gas (2DHG) magnetoresistivity of a Si 0.7Ge 0.3/Si 0.2Ge 0.8 heterostructure in a wide range of temperatures T=0.335– 20 K and transport currents I=100– 50 μA is measured. In the vicinity of zero magnetic field, a sharp and positive in sign feature on smooth negative magnetoresistance is observed at the lowest temperatures. The amplitude of this feature quickly fades with increasing temperature and transport current. For the analysis of the experimental data the theory of weak localization for 2DHG is applied. The values of τ so and τ tr obtained are used for the first time to define zero magnetic field splitting in the hole energy spectrum for a Si 0.7Ge 0.3/Si 0.2Ge 0.8 heterostructure: Δ=2.97 meV .

The transport properties of Bi-riched Bi2Sr2CuO6+δ single crystal

As-grown superconducting Bi-riched Bi2Sr2CuO6+δ single crystals have been grown by the traveling solvent floating zone technique. The superconducting transition temperature Tc was about 6 K and the room temperature resistivity was about 2×10−3 Ohm-cm. Transport properties, such as resistivity, magnetoresistance and Hall effect were measured from overdoped to underdoped samples annealed in inert atmosphere at 650°C. The transition temperature can be raised to 12 K after post annealing. The Hall measurement shows that the hole carrier density decrease after annealing. The temperature dependence of Hall angle is T1.5, not quadratic as observed for most high-Tc superconducting oxides such as YBa2Cu3O7. The variation of onset Tc with different external magnetic field is very different from high-Tc superconductors. The in-plane conductivity shows the dependence of ln T and can be explained by weak localization theory.

INFLUENCE OF ELECTRON IRRADIATION DEFECTS ON THE TRANSPORT PROPERTIES OF CUPRATES

We use electron irradiation at low temperature to introduce defects in a controlled manner in the cuprates. We have shown in YBCO 7 that the main influence on transport properties is due to stable defects in the CuO 2 plane. They are found analogous to Zn substitution on the copper planar site.1 Compared to impurity substitutions, the great advantage of electron irradiation is to allow to study the physical properties of a single sample with an increasing defect content. Tc and electrical resistivity measurements have been performed on electron irradiated single crystals of different cuprates (YBCO, Bi-2212, Hg-1223, T1-2201) for a wide range of hole dopings nh. A simple correlation between the decrease of Tc and the increase of residual resistivity ΔR2D is found, as expected for d ware superconductivity. The ratio ΔTc/ΔR2D, which is expected to be proportional to nh/m* is found to reproduce the variation of nh from the under-doped to the over-doped regime.2 This demonstrates that the hole content is the relevant parameter to describe the transport properties all over the phase diagram. For large defect contents, low T upturns of the resistivity are observed in under-doped YBCO 6.6 and over-doped T1-2201 (see Ref. [3]). In the highly over-doped T1 compound the decrease of conductivity scales as expected from weak localization theory. For YBCO 6.6 the large low T contribution to the resistivity is shown to be initially proportional to the defect content. It might therefore be associated to Kondo like spin flip scattering term. This would be consistent with the results on the magnetic properties induced by spinless defects such as Li (see Ref. [4]).

Weak localization in InSb thin films heavily doped with lead

We study the weak localization (WL) in three-dimensional polycrystalline thin films of InSb. The films are closely compensated showing the electron concentration $n>{10}^{16} {\mathrm{cm}}^{\ensuremath{-}3}$ at the total concentration of the donor- and acceptor-type structural defects ${N}_{t}>{10}^{18} {\mathrm{cm}}^{\ensuremath{-}3}.$ Unless Pb doped, the InSb films do not show any measurable or show very small WL effect at 4.2 K. The Pb doping to the concentration of the order of ${10}^{18} {\mathrm{cm}}^{\ensuremath{-}3}$ leads to pronounced WL effects below 7 K. From the comparison of the experimental data on temperature dependence of the magnetoresistivity and sample resistance with the WL theory, the dependence of the phase destroying time ${\ensuremath{\tau}}_{\ensuremath{\varphi}}(T)$ is determined. It is concluded that the dephasing is connected to three separate processes. The first is due to the spin-orbit scatterings and is characterized by temperature-independent relaxation time ${\ensuremath{\tau}}_{\mathrm{so}}\ensuremath{\simeq}{10}^{\ensuremath{-}12} \mathrm{s}.$ The second is associated with the electron-phonon interaction $({\ensuremath{\tau}}_{i}\ensuremath{\sim}{T}^{\ensuremath{-}3}).$ The third dephasing process is characterized by temperature-independent relaxation time ${\ensuremath{\tau}}_{c}=(1--7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12} \mathrm{s},$ which is tentatively ascribed to inelastic scattering at extended structural defects. The resulting time ${\ensuremath{\tau}}_{\ensuremath{\varphi}}$ shows saturation in its temperature dependence for $\stackrel{\ensuremath{\rightarrow}}{T}0.$ The temperature dependence of the resistance can be explained by the electron-electron interaction for $T<1 \mathrm{K},$ and by the WL effect for $T>2 \mathrm{K}.$