Random Impurity Potential Research Articles

Local Density of States of Quasi-Particles around a Vortex Core in a Square Superconducting Plate with a Random Impurity Potential

We have solved the Bogoliubov-de Gennes equation with a random impurity potential Vimp(r) under an external magnetic field with the finite element method and obtained the local density of states and the order parameter around a vortex. From these results, we find two properties of a vortex structure in a dirty superconductor. First, the order parameter structure around the vortex is deformed by the impurity potential. Second, distributions of bound states is also deformed, but these deformations of the order parameter and bound states do not correspond with each other.

Impurity effects on nano-structured dirty superconductors: violation of Anderson’s Theorem

It is shown that in nano-structured s-wave superconductor, transition temperature Tc depends on random impurity potentials. This means violation of the Anderson’s theorem, which states that non-magnetic impurity does not affect the Tc of s-wave superconductor. We determine the impurity effects on Tc for nano-structured superconductor, using the finite element method to solve the Bogoliubov-de Gennes equations under spatially a random impurity potential. We show that some impurity potentials increase Tc but other impurity potentials decrease Tc. We find that the superconductor with localized order parameter shows increased Tc, which is contrary to expectation. Our results show that a dirty superconductor does not always mean weak superconductivity.

Proximity effect in a ferromagnetic semiconductor with spin-orbit interactions

We study theoretically the proximity effect in a ferromagnetic semiconductor with Rashba spin-orbit interaction. The exchange potential generates opposite-spin-triplet Cooper pairs which are transformed into equal-spin-triplet pairs by the spin-orbit interaction. In the limit of strong spin-orbit interaction, symmetry of the dominant Cooper pair depends on the degree of disorder in a ferromagnet. In the clean limit, spin-singlet $s$-wave Cooper pairs are the most dominant because the spin-momentum locking stabilizes a Cooper pair consisting of a time-reversal partner. In the dirty limit, on the other hand, equal-spin-triplet $s$-wave pairs are dominant because random impurity potentials release the locking. We also discuss the effects of the spin-orbit interaction on the Josephson current.

Dirty two-band superconductivity with interband pairing order

We study theoretically the effects of random nonmagnetic impurities on the superconducting transition temperature Tc in a two-band superconductor characterized by an equal-time s-wave interband pairing order parameter. Because of the two-band degree of freedom, it is possible to define a spin-triplet s-wave pairing order parameter as well as a spin-singlet s-wave order parameter. The former belongs to odd-band-parity symmetry class, whereas the latter belongs to even-band-parity symmetry class. In a spin-singlet superconductor, Tc is insensitive to the impurity concentration when we estimate the self-energy due to the random impurity potential within the Born approximation. On the other hand in a spin-triplet superconductor, Tc decreases with the increase of the impurity concentration. We conclude that Cooper pairs belonging to odd-band-parity symmetry class are fragile under the random impurity potential even though they have s-wave pairing symmetry.

Disorder-induced vortex lattice melting in a Bose-Einstein condensate

We study the vortex lattice dynamics in presence of single impurity as well as random impurities or disorder. We show that in presence of a single impurity the vortex lattice gets distorted and the distortion depends on the position of the single impurity with respect to the positions of the vortices in the impurity free Abrikosov vortex lattice and also the strength of the impurity potential. We then show that a new type of giant hole with hidden vortices inside it can be created in the vortex lattice by a cluster of impurities. In presence of random impurity potential or disorder the vortex lattice melts. We show that the vortex lattice also melts in presence of pseudorandom potential generated by the superposition of two optical lattices. The absence of long-range order in the melted vortex lattice is demonstrated from the structure factor profile and the histogram of the distances between each pair of the vortices.

Low-temperature spin coulomb drag in a two-dimensional electron gas

The phenomenon of low-temperature spin Coulomb drag in a two-dimensional electron gas is investigated. The spin transresistivity coefficient is essentially enhanced in the diffusive regime, as compared to conventional predictions. The origin of this enhancement is the quantum coherence of spin-up and spin-down electrons propagating in the same random impurity potential and coupled via the Coulomb interaction. A comprehensive analysis of spin and interlayer Coulomb drag effects is presented.

Giant mesoscopic fluctuations of the elastic cotunneling thermopower of a single-electron transistor

We study the thermoelectric transport of a small metallic island weakly coupled to two electrodes by tunnel junctions. In the Coulomb blockade regime, in the case when the ground state of the system corresponds to an even number of electrons on the island, the main mechanism of electron transport at lowest temperatures is elastic cotunneling. In this regime, the transport coefficients strongly depend on the realization of the random impurity potential or the shape of the island. Using the random-matrix theory, we calculate the thermopower and the thermoelectric kinetic coefficient and study the statistics of their mesoscopic fluctuations in the elastic cotunneling regime. The fluctuations of the thermopower turn out to be much larger than the average value.

Theory of coupled spin-charge transport due to spin-orbit interaction in inhomogeneous two-dimensional electron liquids

Spin-orbit interactions in two-dimensional electron liquids are responsible for many interesting transport phenomena in which particle currents are converted to spin polarizations and spin currents and vice versa. Prime examples are the spin Hall effect, the Edelstein effect, and their inverses. By similar mechanisms, it is also possible to partially convert an optically induced electron-hole density wave to a spin density wave and vice versa. In this paper, we present a unified theoretical treatment of these effects based on quantum kinetic equations that include not only the intrinsic spin-orbit coupling from the band structure of the host material, but also the spin-orbit coupling due to an external electric field and a random impurity potential. The drift-diffusion equations we derive in the diffusive regime are applicable to a broad variety of experimental situations, both homogeneous and nonhomogeneous, and include on equal footing ``skew scattering'' and ``side jump'' from electron-impurity collisions. As a demonstration of the strength and usefulness of the theory we apply it to the study of several effects of current experimental interest: the inverse Edelstein effect, the spin-current swapping effect, and the partial conversion of an electron-hole density wave to a spin density wave in a two-dimensional electron gas with Rashba and Dresselhaus spin-orbit couplings, subject to an electric field.

Nonperturbative expression for the transmission through a leaky chiral edge mode

Chiral edge modes of topological insulators and Hall states exhibit nontrivial behavior of conductance in the presence of impurities or additional channels. We present a simple formula for the conductance through a chiral edge mode coupled to a disordered bulk. For a given coupling matrix between the chiral mode and bulk modes, and a Green's function matrix of bulk modes in real space, the renormalized Green's function of the chiral mode is expressed in closed form as a ratio of determinants. We demonstrate the usage of the formula in two systems: (i) a 1d wire with random on-site impurity potentials for which we found that the disorder averaging is made simpler with the formula, and (ii) a quantum Hall fluid with impurities in the bulk for which the phase picked up by the chiral mode due to the scattering with the impurities can be conveniently estimated.

Series-Coupled Triple Quantum Dot Molecules

We present the electronic properties of a triple quantum dot molecule embedded inside a sub-micron mesa, made from a quadruple-barrier triple-quantum-well structure, and surrounded by a single gate electrode. We outline the design principles of the quadruple-barrier triple-quantum-well structure and calculate the energy of the three lowest states as a function of center well thickness. We observe regular and irregular shaped Coulomb diamond regions similar to those for double quantum dot devices. Variation in the Coulomb blockade region shape is introduced by fluctuation in the offset energies between the quantum dots likely associated with device processing and random impurity potential in the material. We also present Coulomb blockade patterns calculated with a constant interaction model for sequential tunneling through the three series-coupled quantum dots.

Series-Coupled Triple Quantum Dot Molecules

We present the electronic properties of a triple quantum dot molecule embedded inside a sub-micron mesa, made from a quadruple-barrier triple-quantum-well structure, and surrounded by a single gate electrode. We outline the design principles of the quadruple-barrier triple-quantum-well structure and calculate the energy of the three lowest states as a function of center well thickness. We observe regular and irregular shaped Coulomb diamond regions similar to those for double quantum dot devices. Variation in the Coulomb blockade region shape is introduced by fluctuation in the offset energies between the quantum dots likely associated with device processing and random impurity potential in the material. We also present Coulomb blockade patterns calculated with a constant interaction model for sequential tunneling through the three series-coupled quantum dots.

Modeling of the Light Emission Spectra of InGaN/GaN Quantum Well with Highly Doped Barriers

We investigate light emission spectra at different excitation levels of nanoscale thin InGaN film participating in an InGaN/GaN quantum well (QW) with heavily doped barriers for green and blue light emitting diodes (LEDs). We model the spectral shape and energy position in frames of the free electron recombination model created first for highly doped 3D direct gap III-V semiconductor films and applied for QWs at low excitation. The model accounts for the influence on the potential width of the QW of the random impurity potential of the doped barriers which penetrates into the QW. The blue shift at high excitation is supposed to be due to the filling of the conduction band with degenerate 2D nonequilibrium electrons. A structure in the emission bands is observed and it is assumed to be a result from step-like 2D density-of-states (DOS) in the QW. A good agreement is obtained between the calculated and experimental spectra assuming that the barriers are graded.

Frequency and temperature dependence of the anomalous ac Hall conductivity in a chiralpx+ipysuperconductor with impurities

We calculate frequency and temperature dependence of the anomalous ac Hall conductivity induced by impurity scattering in a chiral ${p}_{x}+i{p}_{y}$ superconductor, such as ${\text{Sr}}_{2}{\text{RuO}}_{4}$, with spontaneous time-reversal-symmetry breaking in the absence of an external magnetic field. We consider two models of disorder, Gaussian and non-Gaussian, characterized by the second and third moments of the random impurity potential, respectively. Within both models, we find that the anomalous Hall conductivity has a finite real value at zero frequency, exhibits singularities at the threshold of photon absorption across the superconducting gap, and decays as some power of the high frequency $\ensuremath{\omega}$. The Hall conductivity increases linearly with the decrease in temperature below the superconducting transition and saturates at zero temperature. Using our results for the high-frequency Hall conductivity, we estimate the polar Kerr angle for light reflection from the material and compare it with the experimental measurements in ${\text{Sr}}_{2}{\text{RuO}}_{4}$ by Xia et al., Phys. Rev. Lett. 97, 167002 (2006).

Evolution of the photoresponse time of the GaAs/AlGaAs cyclotron resonance quantum Hall effect detector

The photoresponse time of the cyclotron resonance detector to terahertz radiation under integer quantum Hall effect conditions in the GaAs/AlGaAs heterostructure is shown to have a deep minimum at the Hall plateau center and two sharp maxima at the plateau edges. The minimum at the plateau center is associated with the fundamental property of vanishing of the random impurity potential screening under quantum Hall effect conditions. The decrease in the response time outside the plateau is related to the equilibrium population of the Landau level above (under) the Fermi level by electrons (holes), respectively, which increases the probability of photoexcited carrier recombination. It is shown that, under conditions of background radiation (300 K), relaxation times decrease by two orders of magnitude while retaining the characteristic magnetic field dependence.

Band-filling effect on the light emission spectra of InGaN/GaN quantum wells with highly doped barriers

We investigate spectra of InGaN/GaN quantum well (QW) light-emitting diode (LED) structures with heavily doped barriers at different excitation levels. We model the spectral shape and energy position in frames of dominating mechanism of free electron recombination accounting for the influence on the potential width of the QW of the random impurity potential penetrating from the doped barriers. The blue shift at high excitation is supposed to be due to the filling of the conduction band with degenerate 2D non-equilibrium electrons. A structure in the emission bands is observed and it is assumed to be a result from step-like 2D density of states in the QW. A good accordance is obtained between the calculated and experimental spectra assuming that the barriers are graded.

Microscopic theory of impurity states in coupled quantum wells and superlattices

We present a theory of impurity states in quantum wells and superlattices which treats the confining heterostructure potential and the random impurity potential on the same footing. The relevant three-dimensional Hamiltonian is diagonalized in the low-doping regime. The results are used to calculate infrared absorption spectra which contain contributions of impurity and intersubband transitions. We mainly discuss the excited impurity states, which are pinned to higher subbands and are resonant states in the continuum. After a detailed analysis of a coupled quantum well system, we study the transition to a superlattice. In particular, we are able to explain existing experimental data on a quadruple quantum well.

Anomalous Josephson Effect inp-Wave Dirty Junctions

The Josephson effect in p-wave superconductor/diffusive normal metal/p-wave superconductor junctions is studied theoretically. Amplitudes of Josephson currents are several orders of magnitude larger than those in s-wave junctions. Current-phase (J-phi) relations in low temperatures are close to those in ballistic junctions such as J proportional to sin(phi/2) and J proportional to phi even in the presence of random impurity potentials. A cooperative effect between the midgap Andreev resonant states and the proximity effect causes such anomalous properties and is a character of the spin-triplet superconductor junctions.

Recombination mechanism of photoluminescence in InN epilayers

We report an investigation of the recombination mechanism for photoluminescence (PL) in InN epilayers grown by molecular beam epitaxy and metal-organic chemical vapor deposition with a wide range of free electron concentrations from 3.5×10 17–5×10 19 cm −3. We found that the PL spectra are strongly blueshifted with increasing excitation intensity. For all the samples studied, the exponent of the relationship between the integrated PL intensity and the excitation intensity is very close to unity and independent of the temperature. By assuming Gaussian fluctuations of the random impurity potential, calculation based on the ‘free-to-bound’ recombination model can be used to interpret our results very well and it correctly reproduces the development of the total PL peak shift as a function of carrier concentration. It is concluded that the PL transition mechanism in InN epifilms can be characterized as the recombination of free electrons in the conduction band to nonequilibrium holes in the valence band tail.

Dirty quantum Hall ferromagnets and quantum Hall spin glasses

We study quantum Hall ferromagnets in the presence of a random electrostatic impurity potential, within the framework of a classical non-linear sigma model. We discuss the behaviour of the system using a heuristic picture for the competition between exchange and screening, and test our conclusions with extensive numerical simulations. We obtain a phase diagram for the system as a function of disorder strength and deviation of the average Landau level filling factor from unity. Screening of an impurity potential requires distortions of the spin configuration. In the absence of Zeeman coupling there is a disorder-driven, zero-temperature phase transition from a ferromagnet at weak disorder and small deviation from integer filling to a spin glass at stronger disorder or large charge deviation. We characterise the spin glass phase in terms of its magnetic and charge response, as well as its ac conductivity.

Quantum Hall ferromagnet in a parabolic well

We report the observation of an anomalous magnetoresistance peak in a tilted magnetic field corresponding to filling factor of 2 in several parabolic wells of different width. This phenomenon is due to the unpolarized-ferromagnetic transitions in quantum Hall ferromagnets. The domain formation induced by the random impurity potential is responsible for this magnetoresistance peak. The shift of the peak position with the tilt angle is attributed to the magnetic-field dependence of the exchange-correlation energy across the transition.