Strong vertex corrections from weak disorder in 2D d-wave superconductors

We show that weak static random potentials have pronounced effects on the quasiparticle states of a 2Dd-wave superconductor close to a node. We prove that the vertex correction coming from the simplest crossed diagram is important even for a nonmagnetic potential. The leading frequency and momentum dependent logarithmic singularities in the self-energy are calculated exactly to second order in perturbation theory. The self-energy corrections lead to a modified low energy density of states which depends strongly on the type of random potential and which can be measured in experiments. There is an exceptional case for a potential with extremely local scatterers and opposite nodes separated by (, ) where an exact cancelation takes place eliminating the leading frequency dependent singularity in the simplest crossed diagram. A comparison of the perturbative results with a self-consistent CPA (coherent potential approximation) for the nonmagnetic disorder reveals qualitative differences in the self-energy at the smallest energies which are due to the neglectance of vertex corrections in CPA.     

Quantum transport in topological semimetals under magnetic fields

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.     

Persistent current in an almost staggered Harper model

In this paper we study the persistent current (PC) of a staggered Harper model, close to the half-filling. The Harper model is different than other one dimensional disordered systems which are always localized, since it is a quasi-periodic system with correlated disorder resulting in the fact that it can be in the metallic regime. Nevertheless, the PC for a wide range of parameters of the Harper model does not show typical metallic behavior, although the system is in the metallic regime. This is a result of the nature of the central band states, which are a hybridization of Gaussian states localized in superlattice points. When the superlattice is not commensurate with the system length, the PC behaves as an insulator. Thus even in the metallic regime a typical finite Harper model may exhibit a PC expected from an insulator.     

Assessment of the coherent potential approximation for the absorption spectra of a one-dimensional Frenkel exciton system with a Gaussian distribution of fluctuations in the optical transition frequency

We investigate the accuracy of the coherent potential approximation (CPA) for the optical absorption spectra of a one-dimensional Frenkel exciton system with nearest-neighbor interactions and a Gaussian distribution of fluctuations in the optical transition frequency (diagonal Gaussian disorder). Our earlier studies have established that the CPA gives highly accurate results for the integral of the density of states of this system. In this paper we compare the CPA results for the normalized optical absorption with the finite-array calculations of Schreiber and Toyozawa and Schreiber for the same model. It is found that the CPA results for the absorption are in good agreement with their findings. It is pointed out that an expansion of the density of states in terms of the eigenstates of the ideal (no disorder) array contains a term proportional to the normalized absorption. Since the density of states is accurately approximated by the CPA, the presence of this term explains the success of the CPA in reproducing the absorption spectra. Our findings support the use of the Gaussian disorder model to interpret the absorption spectra of one and quasi-one dimensional exciton systems.     

Anisotropic fluctuation magnetoconductivity in Bi2Sr2Ca2Cu3Ox thin films

Measurements of the fluctuation magnetoconductivity as a function of both the magnetic field up to 13 T and the temperature in thin films of Bi₂Sr₂Ca₂Cu₃O_x are presented. The variation of the magnetoconductivity with the magnetic field strength is quadratic at temperatures distantly above the critical temperatureT _c and changes to an entirely negative curvature nearT _c . The latter behavior is attributed to an inhomogeneous critical temperature in the films. The results are analyzed in terms of recent theoretical models for fluctuation-enhanced magnetoconductivity in layered superconductors. The magnetoconductivity in a magnetic field oriented normal to the copper-oxide layers is dominated by the orbital contribution of the Aslamazov-Larkin effect. The magnetoconductivity in the parallel orientation is distinctly smaller and provides evidence for the corresponding Zeeman contribution. The latter measurement also indicates that the Maki-Thompson process may be insignificant in Bi₂Sr₂Ca₂Cu₃O_x.     

The CPA solution of the anomalous Lyapunov exponent for disordered binary chains

The Coherent Potential Approximation (CPA) self-consistent equation is calculated for a binary disordered chain introducing a simple transformation. The transformation reduces the CPA equation to a cubic polynomial whose complex roots are related to the Green function and their relation to the complex Lyapunov exponent is also established. This solution fruitfully captures essential aspects of the well-known anomalous scaling behaviors in a different and advantageous way. It is found that the anomalous behavior is strongly effected by the nature of these roots. A small disorder expansion is carried out for comparison with the previous weak disorder calculations. We found that the CPA reproduced the anomalous behavior of the exact calculations. Received 22 April 2002 Published online 1st October 2002 RID="a" ID="a"e-mail: avgin@bornova.ege.edu.tr     

Transport properties of intermediate valence compounds studied within the alloy analog approximation of the Periodic Anderson Model

We use the Periodic Anderson Model (PAM) to describe the transport properties of intermediate valence compounds. The transport quantities of interest are related to the current-current response function. Therefore, a current operator being consistent with the PAM Hamiltonian must be defined. This aim is achieved by defining a proper particle density operator and using the continuity equation. The PAM is treated within the alloy analog approximation, i.e. it is replaced by the sum of two effective single-particle “alloy”-Hamiltonians, which are treated within the coherent potential approximation (CPA). Then the CPA for transport quantities is used to calculate the current-current response function. It is shown that for all reasonable assumptions for the conduction band and the hybridization dispersion the current vertex corrections vanish within the CPA. For different assumptions concerning the hybridization dispersion, we present numerical results for the temperature and parameter dependence of some transport quantities, in particular the static resistivity. The relevance of these results for the understanding of the typical experimental resistivity behaviour obtained for different intermediate valence compounds and possible shortcomings of our approach are discussed.     

Dimensional crossover of quantum interference effects in thin quasicrystalline Al-Cu-Fe films

We present a study of the electrical transport properties of thin i-Al-Cu-Fe films. We observe clear signatures of a dimensional crossover in the temperature and magnetic field dependence of the conductivity for films thinner that ≃ 10³?. In particular for the thinnest sample the magnetoconductivity is strongly anisotropic, as is expected for the weak localisation contribution in two dimensions. These experiments show direct qualitative manifestations of the disorder induced quantum interference effects occurring in quasicrystals. Estimates of the electronic microscopic parameters are in accordance with those obtained in bulk samples. Their values and significance are discussed. Received 16 February 2001 and Received in final form 20 June 2001     

Frequency dependent magnetoconductivity and conductivity study in Ni-dispersed silica nano-composite produced by sol-gel technique

The low frequency (20 Hz to 1 MHz) ac conductivity and magnetoconductivity behaviour of ceramic nanocomposite (Ni-SiO₂) at low temperature down to 77 K are reported. The frequency dependent conductivity followed the power law, σ(ω) ∝ ω ^s . The fractional exponent s is a function of temperature and was found to increase with increasing temperature. This type of variation may be attributed to small polaron hopping. A peak present in the loss tangent indicates the presence of a Debye relaxation process. The magnetoconductivity of the samples is positive, which strongly depends on frequency. A firm theoretical explanation of frequency dependent magnetoconductivity is still lacking.     

Electrical conductivity of electrons in a model binary disordered alloy with long range order

The CPA d. c. electrical conductivity for a bcc based random binary substitutional alloy with long range ordering is determined for a single band model with diagonal disorder and arbitrary alloy parameters. The CPA vertex corrections to vanish, off-diagonal elements of the Green function are most important. The conductivity obeys general symmetries with respect to alloy parameters and can be brought to closed form resembling the standard expression = ne²/m. To interpret various terms in correctly, limits with available Boltzmann equation solutions are analyzed in detail.     

Magnetic properties and a combined recursive-CPA calculation of pseudobinary intermetallics: Application to Hf(FeAl)2

The pseudobinary compounds Hf(Fe_1−xAl_x)₂, 0.15×0.30, show a pure C14 phase. Since the structure is stabilized in the presence of impurities, a combined recursive method — extended CPA is applied. The local densities of states for C14 are obtained within the recursive method and then the CPA describes the disorder. The changes with x of the local densities, and Fe magnetic moment are estimated.     

Quantum galvanomagnetic properties of n-type inversion layers on Si(100) MOSFET

Transverse magnetoconductivity σ_xx and Hall effect in n-type inversion layers of Si(100) MOSFET are measured for various source-drain fields between 0.08 and 40 V/cm under magnetic fields up to 150 kOe at 1.4 K. Conductivity peaks in low Landau levels are in good agreement with theory. Effect of the source-drain field in the magnetoconductivity is found to be very important in higher Landau levels as well as in the appearance of the lowest Landau level peak. Immobile electrons are clearly observed in conductivity bottoms. Electrode geometry effect for Hall effect measurement under strong magnetic fields is discussed.     

On the homomorphic cluster CPA

Among the various extensions of the CPA, the homomorphic cluster CPA (HCPA) was presented recently as the only approximation (i) having the correct analytical properties, (ii) taking multiple scattering into account and (iii) preserving the symmetry of the original lattice. Though very appealing mathematically, we show in this paper that it does not give the right position for the impurity states in the dilute limit with non zero diagonal disorder. Consequently, even if HCPA satisfies points (i) to (iii) and even if it gives the correct dilute limit for purely off-diagonal disorder, it is to be rejected as a method to study systems with non negligible diagonal disorder.     

组分调制合金的表面电子结构——CPA方法

本文在紧束缚近似下,用CPA方法结合无限级微扰理论讨论了组分调制合金的表面电子结构。数值计算包括了替位无序模型及Anderson无序模型。 关键词：     

Transport properties of intermediate valence compounds studied within the alloy analog approximation of the Periodic Anderson Model

We use the Periodic Anderson Model (PAM) to describe the transport properties of intermediate valence compounds. The transport quantities of interest are related to the current-current response function. Therefore, a current operator being consistent with the PAM Hamiltonian must be defined. This aim is achieved by defining a proper particle density operator and using the continuity equation. The PAM is treated within the alloy analog approximation, i.e. it is replaced by the sum of two effective single-particle alloy-Hamiltonians, which are treated within the coherent potential approximation (CPA). Then the CPA for transport quantities is used to calculate the current-current response function. It is shown that for all reasonable assumptions for the conduction band and the hybridization dispersion the current vertex corrections vanish within the CPA. For different assumptions concerning the hybridization dispersion, we present numerical results for the temperature and parameter dependence of some transport quantities, in particular the static resistivity. The relevance of these results for the understanding of the typical experimental resistivity behaviour obtained for different intermediate valence compounds and possible shortcomings of our approach are discussed.Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köln, FRG     

Magneto-oscillations due to electron-electron interactions in the ac conductivity of a two-dimensional electron gas

Electron-electron interactions give rise to the correction, deltasigma(int)(omega), to the ac magnetoconductivity, sigma(omega), of a clean 2D electron gas that is periodic in omega_(c)(-1), where omega_(c) is the cyclotron frequency. Unlike conventional harmonics of the cyclotron resonance, which are periodic with omega, this correction is periodic with omega(3/2). Oscillations in deltasigma(int)(omega) develop at low magnetic fields, omega_(c)相似文献   

Microwave-induced giant oscillations of the magnetoconductivity in 2D electronic corbino disks with capacitance contacts

Using Corbino disks with capacitance contacts, the microwave photoconductivity of the 2D electron gas in selectively doped GaAs/AlAs heterostructures has been studied at 4.2 K in magnetic fields up to 0.6 T. The giant oscillations of the magnetoconductivity have been revealed in the samples exposed to microwave radiation at high filling factors similar to those earlier discovered in the 2D Corbino disks with ohmic contacts. The results demonstrate that the presence of ohmic contacts is of no importance for the observation of the microwave-induced giant oscillations of the magnetoconductivity in the 2D electron system.     

Cluster coherent potential approximation for disordered photonic crystals using photonic Wannier functions

We present an investigation of disordered photonic crystals (PhCs) based on the combination of photonic Wannier functions with the concept of the coherent potential approximation (CPA). In particular, we provide the theoretical foundation of a real-space cluster CPA that is causal, enforces the proper symmetries of the effective medium, and includes effects of multiple scattering of the same and nearby defects, which is essential for strong defects. Based on this, we present results for the density of states of disordered PhCs for different types of disorder. Our results are thus relevant to such diverse areas as random lasing and the analysis of fabricational imperfections in PhCs.     

Cluster approaches to random alloys: An appraisal

Some of the cluster extensions of the coherent potential approximation (CPA) based on the effective medium theory have been critically studied with respect to the decoupling schemes involved in them. Their computational tractability has been examined and it has been found that theself-consistent calculations in three-dimensional systems are immensely difficult to perform. A self-consistent calculation has been reported for simple cubic lattices with diagonal and off-diagonal disorder using a pair-CPA method. A significant finding of the paper is that it has been shown thatnon-analyticities are a general feature of extensions of CPA within multiple scattering framework. The non-analyticities were reported several times but a general proof of their existence was not noticed. It was also believed that the so-called molecular—CPA is analytic, this has been shown to be wrong here. The density of states results with off-diagonal randomness have been qualitatively understood to yield some information about the influence of off-diagonal randomness on Anderson localisation of an electron.     

Current-pinch effect in inhomogeneous two-dimensional electron systems and its role in the photoresponse to microwave radiation

An analysis of the classical problem demonstrates that the current-pinch effect exists near one of the sides of a rectangular sample when the two-dimensional electron density has a gradient along the current direction and the ratio of the Hall component of the magnetoconductivity tensor to its dissipative component is large. This conclusion is confirmed by the numerical calculations. It has been shown that the results explain a number of experimental observations in the regime of microwave-induced states with near-zero dissipative components of the magnetoconductivity and magnetoresistivity tensors.