Impurity Strength Research Articles

Current fluctuations in unconventional superconductor junctions with impurity scattering

The order parameter of bulk two-dimensional superconductors is classified as nodal, if it vanishes for a direction in momentum space, or gapful if it does not. Each class can be topologically nontrivial if Andreev bound states are formed at the edges of the superconductor. Non-magnetic impurities in the superconductor affect the formation of Andreev bound states and can drastically change the tunneling spectra for small voltages. Here, we investigate the mean current and its fluctuations for two-dimensional tunnel junctions between a normal-metal and unconventional superconductors by solving the quasi-classical Eilenberger equation self-consistently, including the presence of non-magnetic impurities in the superconductor. As the impurity strength increases, we find that superconductivity is suppressed for almost all order parameters since (i) at zero applied bias, the effective transferred charge calculated from the noise-current ratio tends to the electron charge $e$ and (ii) for finite bias, the current-voltage characteristics follows that of a normal state junction. There are notable exceptions to this trend. First, gapful nontrivial (chiral) superconductors are very robust against impurity scattering due to the linear dispersion relation of their surface Andreev bound states. Second, for nodal nontrivial superconductors, only p_x-wave pairing is almost immune to the presence of impurities due to the emergence of odd-frequency s-wave Cooper pairs near the interface. Owing to their anisotropic dependence on the wave vector, impurity scattering is an effective pair breaking mechanism for the rest of nodal superconductors. All these behaviors are neatly captured by the noise-current ratio, providing a useful guide to find experimental signatures for unconventional superconductivity.

Impurity-induced current in a Chern insulator

Chern insulators arguably provide the simplest examples of topological phases. They are characterized by a topological invariant and can be identified by the presence of protected edge states. In this article, we show that a local impurity in a Chern insulator induces a twofold response: bound states that carry a chiral current and a net current circulating around the impurity. This is a manifestation of broken time symmetry and persists even for an infinitesimal impurity potential. To illustrate this, we consider a Coulomb impurity in the Haldane model. Working in the low-energy long-wavelength limit, we show that an infinitesimal impurity strength suffices to create bound states. We find analytic wavefunctions for the bound states and show that they carry a circulating current. In contrast, in the case of a trivial analogue, graphene with a gap induced by a sublattice potential, bound states occur but carry no current. In the many body problem of the Haldane model at half-filling, we use a linear response approach to demonstrate a circulating current around the impurity. Impurity textures in insulators are generally expected to decay exponentially; in contrast, this current decays polynomially with distance from the impurity. Going beyond the Haldane model, we consider the case of coexisting trivial and non-trivial masses. We find that the impurity induces a local chiral current as long as time reversal symmetry is broken. However, the decay of this local current bears a signature of the overall topology - the current decays polynomially in a non-trivial system and exponentially in a trivial system. In all cases, our analytic results agree well with numerical tight-binding simulations.

Decoherence time, hydrogenic-like impurity effect and Shannon entropy on polaron in RbCl triangular quantum dot qubit

Using Pekar variational method, Eigen energies of the ground and first excited states of the polaron in triangular bound and Coulomb potential quantum dot are derived in view of investigating the density of probability, the decoherence time and the Shannon entropy. Numerical analysis show that the decoherence time is decreasing function of polaron radius and the strength of the Coulombic impurity and the increase function of dispersion coefficient. These results suggest that the decrease of polaron radius and Coulombic impurity lead to the increase of coherence time. Also the entropy shows the oscillatory periodic evolution as function of the time due to the triangular form of the confinement. It’s also seen that entropy is periodic for the lower value of Coulomb impurity parameter and for the higher value of the polaronic radius.

Noise-Modulated Effects of Anisotropy and Position Dependent Effective Mass on the Oscillator Strength of Impurity Doped Quantum Dots

Noise-Modulated Effects of Anisotropy and Position Dependent Effective Mass on the Oscillator Strength of Impurity Doped Quantum Dots

Effect of nonlinearity, magnetic and nonmagnetic impurities, and spin-orbit scattering on the nonlocal microwave response of ad-wave superconductor

By using linear response theory the low-temperature microwave response of a nonlocal and nonlinear d-wave superconductor with magnetic and nonmagnetic impurities is calculated. We will show that for the local, linear, and pure sample, penetration depth, Δλ(T), and conductivity, Δσ1(T), vary linearly with temperature, consequently the resistance, ΔR(T), would change linearly with temperature in agreement with experimental results and for the nonlocal, nonlinear sample the linear temperature dependences ΔR(T) change to quadratic function. For impure samples the nonlocality and nonlinearity effects are completely hidden by impurities and the temperature dependences Δλ(T) and Δσ1(T) are determined by temperature interval namely the ranges of T < T* and T* ≪ T ≪ Tc which T* is determined by nonmagnetic impurity concentration and the strength of impurity scattering. For T < T*, ΔR(T) varies as T2, on the other hand for, T* ≪ T ≪ Tc, ΔR(T) varies linearly with temperature. We will also show that the temperature dependence of surface resistance is unaffected by spin-orbit interaction and magnetic impurities.

Majorana fermions at odd junctions in a wire network of ferromagnetic impurities

We consider a wire network of ferromagnetic impurities on the surface of an $s$-wave superconductor with strong Rashba spin-orbit interaction. Within the topological phase, zero-energy Majorana fermions appear at wire end-points as well as at junctions between an odd number of wire segments, while no low-energy states are present at junctions between an even number of wire segments, providing strong experimentally accessible signatures for Majorana fermions. We also investigate the quasiparticle energy gap with respect to varying the Rashba spin-orbit coupling and magnetic impurity strength.

Theory of ballistic quantum transport in the presence of localized defects

We present an efficient numerical approach for treating ballistic quantum transport across devices described by tight binding (TB) Hamiltonians designated to systems with localized potential defects. The method is based on the wave function matching approach, Lippmann-Schwinger equation (LEQ) and the scattering matrix formalism. We show that the number of matrix elements of the Green's function to be evaluated for the unperturbed system can be essentially reduced by projection of the time reversed scattering wave functions on LEQ which radically improves the speed and lowers the memory consumption of the calculations. Our approach can be applied to quantum devices of an arbitrary geometry and any number of degrees of freedom or leads attached. We provide a couple of examples of possible applications of the theory, including current equilibration at the p-n junction in graphene and scanning gate microscopy mapping of electron trajectories in the magnetic focusing experiment on a graphene ribbon. Additionally, we provide a simple toy example of electron transport through 1D wire with added onsite perturbation and obtain a simple formula for conductance showing that Green's function of the device can be obtained from the conductance versus impurity strength characteristics.

Heat capacity, electrical and thermal conductivity of silicene

We investigate the electronic heat capacity, electrical and thermal conductivity of monolayer planar and buckled silicon sheets (silicene) through tight binding approximation and Kubo-Greenwood formula. Applying and increasing dopant atoms to the system leads to opening a gap in the band structures and density of states that causes to decrease (increase) the heat capacity before (after) the Schottky anomaly. The electrical and electronic thermal conductivity of doped silicene reduces with increasing impurity strength.

Direct coupling between charge current and spin polarization by extrinsic mechanisms in graphene

Spintronics---the all-electrical control of the electron spin for quantum or classical information storage and processing---is one of the most promising applications of the two-dimensional material graphene. Although pristine graphene has negligible spin-orbit coupling (SOC), both theory and experiment suggest that SOC in graphene can be substantially enhanced by extrinsic means, such as functionalization by adatom impurities. We present a theory of transport in graphene that accounts for the full spin-coherent dynamics of the carriers, including hitherto-neglected spin precession processes during resonant scattering with dilute impurities. We identify a novel "anisotropic spin precession scattering" process, specific to two dimensions and extrinsic SOC, which contributes to a large current-induced spin polarization in graphene. The theory also yields a comprehensive description of the spin relaxation mechanisms in impurity-decorated graphene: the Elliot-Yafet and Dyakonov-Perel relaxation rates are both present, and we find that the latter can dominate for some choices of carrier density and impurity strength. This provides theoretical foundations for designing future graphene-based integrated spintronic devices.

Anomalous Hall Effect in a 2D Rashba Ferromagnet

Skew scattering on rare impurity configurations is shown to dominate the anomalous Hall effect in a 2D Rashba ferromagnet. The mechanism originates in scattering on rare impurity pairs separated by distances of the order of the Fermi wavelength. The corresponding theoretical description goes beyond the conventional noncrossing approximation. The mechanism provides the only contribution to the anomalous Hall conductivity in the most relevant metallic regime and strongly modifies previously obtained results for lower energies in the leading order with respect to impurity strength.

Controlling dynamical thermal transport of biased bilayer graphene by impurity atoms

We address the dynamical thermal conductivity of biased bilayer graphene doped with acceptor impurity atoms for AA-stacking in the context of tight binding model Hamiltonian. The effect of scattering by dilute charged impurities is discussed in terms of the self-consistent Born approximation. Green’s function approach has been exploited to find the behavior of thermal conductivity of bilayer graphene within the linear response theory. We have found the frequency dependence of thermal conductivity for different values of concentration and scattering strength of dopant impurity. Also the dependence of thermal conductivity on the impurity concentration and bias voltage has been investigated in details.

Role of Spin–Orbit Interaction and Impurity Doping in Thermodynamic Properties of Monolayer MoS2

Using linear response theory, a tight-binding Hamiltonian model, and the Green’s function technique, the influences of spin–orbit interaction (SOI) and impurity doping on the electronic heat capacity (EHC) and magnetic susceptibility (MS) of monolayer MoS2 have been investigated. The effect of scattering on dilute charged impurities is discussed in terms of the self-consistent Born approximation. We have calculated the temperature dependence of the EHC and MS for different values of SOI, concentration, and scattering strength of dopant impurity. The results show that, in the presence of impurities, the heat capacity of MoS2 decreases (increases) before (after) the Schottky anomaly, as does the MS. It is also found that the EHC and MS of the doped MoS2 reduce with the SOI in all temperature ranges.

The effects of impurity doping on the optical properties of biased bilayer graphene

We address the optical conductivity of doped AA-stacked bilayer graphene in the presence of a finite bias voltage at finite temperature. The effect of scattering by dilute charged impurities is discussed in terms of the self-consistent Born approximation. Green's function approach has been implemented to find the behavior of optical conductivity of bilayer graphene within linear response theory. We have found the frequency dependence of optical conductivity for different values of concentration and scattering strength of dopant impurity. Also the dependence of optical conductivity on the impurity concentration and bias voltage has been investigated in details. A peak appears in the plot of optical conductivity versus impurity concentration for different values of chemical potential. Furthermore we find optical conductivity reduces with frequency for any impurity concentration and scattering strength.

Graphene quantum dot with a hydrogenic impurity

We investigate the electronic energy levels of a circular graphene quantum dot with a hydrogenic impurity placed at the center of the dot. We have adopted a variational scheme in such a way that the trial wave functions take into account the carrier confinement due to the dot geometry as well as the effect of the magnetic field. We found that the presence of impurity strongly modifies the electronic spectrum of the graphene quantum dot. We also calculated the critical value of the impurity strength as a function of dot radius.

Graphene quantum dot with a hydrogenic impurity

We investigate the electronic energy levels of a circular graphene quantum dot with a hydrogenic impurity placed at the center of the dot. We have adopted a variational scheme in such a way that the trial wave functions take into account the carrier confinement due to the dot geometry as well as the effect of the magnetic field. We found that the presence of impurity strongly modifies the electronic spectrum of the graphene quantum dot. We also calculated the critical value of the impurity strength as a function of dot radius.

Existence of zero-energy impurity states in different classes of topological insulators and superconductors and their relation to topological phase transitions

We consider the effects of impurities on topological insulators and superconductors. We start by identifying the general conditions under which the eigenenergies of an arbitrary Hamiltonian H belonging to one of the Altland-Zirnbauer symmetry classes undergo a robust zero energy crossing as a function of an external parameter which can be, for example, the impurity strength. We define a generalized root of \det H, and use it to predict or rule out robust zero-energy crossings in all symmetry classes. We complement this result with an analysis based on almost degenerate perturbation theory, which allows a derivation of the asymptotic low-energy behavior of the ensemble averaged density of states $\rho \sim E^\alpha$ for all symmetry classes, and makes it transparent that the exponent \alpha\ does not depend on the choice of the random matrix ensemble. Finally, we show that a lattice of impurities can drive a topologically trivial system into a nontrivial phase, and in particular we demonstrate that impurity bands carrying extremely large Chern numbers can appear in different symmetry classes of two-dimensional topological insulators and superconductors. We use the generalized root of \det H(k) to reveal a spiderweblike momentum space structure of the energy gap closings that separate the topologically distinct phases in p_x + i p_y superconductors in the presence of an impurity lattice.

Impurity Effects on Caroli–de Gennes–Matricon Mode in Vortex Core in Superconductors

We develop a scheme of Gor'kov Green's functions to treat impurity effects on Caroli-de Gennes-Matricon (CdGM) mode in superconductors (SCs) by improving the Kopnin-Kravtsov scheme with respect to the coherence factors and applicability to various SCs. We can study the impurity effects keeping the discreteness of the energy spectrum in contrast to the quasiclassical theory. We can thus apply this scheme to the SCs with the small quasiclassical parameter $k_{\mathrm{F}}\xi_{0}$ (which is the product of the Fermi wavenumber $k_{\mathrm{F}}$ and the coherence length $\xi_{0}$ in pure SC at zero temperature) and/or superclean regime $\Delta_{\mathrm{mini}} \tau \gg1$ ($\Delta_{\mathrm{mini}}$ and $\tau$ denote, respectively, the level spacing of the CdGM mode called minigap and the relaxation time for CdGM mode and we take $\hbar =1$). We investigate the impurity effects as a white noise for a vortex in an s-wave SC and two types of vortices in a chiral p-wave SC, for various values of the quasiclassical parameters and impurity strengths (from moderately clean regime to superclean regime), and confirm the validity of this scheme.

Evidence for broken Galilean invariance at the quantum spin Hall edge

We study transport properties of the helical edge channels of a quantum spin Hall (QSH) insulator, in the presence of electron-electron interactions and weak, local Rashba spin-orbit coupling. The combination of the two allows for inelastic backscattering that does not break time-reversal symmetry (TRS), resulting in interaction-dependent power law corrections to the conductance. Here, we use a non-equilibrium Keldysh formalism to describe the situation of a long, one-dimensional edge channel coupled to external reservoirs, where the applied bias is the leading energy scale. By calculating explicitly the corrections to the conductance up to fourth order of the impurity strength, we analyse correlated single- and two-particle backscattering processes on a microscopic level. Interestingly, we show that the modeling of the leads together with the breaking of Galilean invariance has important consequences on the transport properties. Such breaking occurs, because the Galilean invariance of the bulk spectrum transforms into an emergent Lorentz invariance of the edge spectrum. With this broken Galilean invariance at the QSH edge, we find a contribution to single particle backscattering with a very low power scaling, while in the presence of Galilean invariance the leading contribution would be due to correlated two-particle backscattering only. This difference is further reflected in different values of the Fano factor of the shot noise, an experimentally observable quantity. The described behaviour is specific to the Rashba scatterer, and does not occur in the case of backscattering off a time-reversal breaking, magnetic impurity.

Spin-polarized currents and impurity-induced bound states in mesoscopic s-wave superconducting loops

The spin current is investigated in mesoscopic s-wave superconducting loops with spin-orbit interaction by solving the Bogoliubov-de Gennes equations self-consistently. Due to the breaking of spin-reversal symmetry, the spin-polarized currents with opposite chirality flowing near the inner and outer edges of the sample can be observed. A universal state bound to the introduced magnetic and nonmagnetic impurities appears in the strong scattering limit. Differently from the case of a nonmagnetic impurity, midgap bound states arise for the magnetic case, and the energy level can cross the Fermi level at some weak impurity strength. Consequently, the spin current jumps at the crossing point and shows novel features with impurity strength. Further, the current evolution depends sensitively on the located site of a single impurity, and more zero-energy modes can show up for an appropriate relative position between many magnetic impurities due to the quantum interference effect.

Conductance stability in chaotic and integrable quantum dots with random impurities.

For a quantum dot system of fixed geometry, in the presence of random impurities the average conductance over an appropriate range of the Fermi energy decreases as the impurity strength is increased. Can the nature of the corresponding classical dynamics in the dot region affect the rate of decrease? Utilizing graphene quantum dots with two semi-infinite, single-mode leads as a prototypical model, we address the device stability issue by investigating the combined effects of classical dynamics and impurities on the average conductance over the energy range of the first transverse mode. We find that, for chaotic dot systems, the rate of decrease in the average conductance with the impurity strength is in general characteristically smaller than that for integrable dots. We develop a semiclassical analysis for the phenomenon and also obtain an understanding based on the random matrix theory. Our results demonstrate that classical chaos can generally lead to a stronger stability in the device performance, strongly advocating exploiting chaos in the development of nanoscale quantum transport devices.