Nonmagnetic Disorder Research Articles

Effects of heavy-ion irradiation on the microwave surface impedance of (Ba1−xKx)Fe2As2 single crystals

The electrodynamic response of Ba1−xKxFe2As2 single crystals at the microwave frequencies has been investigated by means of a coplanar resonator technique, at different values of non-magnetic disorder introduced into the samples by heavy-ion irradiation. The surface impedance Zs = Rs + iXs conforms to the classical skin effect above the critical temperature. Below Tc, Rs monotonically decreases while Xs shows a peak, which evolves as a function of the irradiation fluence. The disorder-dependent Zs(T) curves are analyzed within a two-fluid model, suitably modified to account for a finite quasiparticle fraction at T = 0. The analysis gives, for the unirradiated crystal, quasiparticle relaxation times τ that are in good agreement with previous literature. Smaller τ values are deduced for the disordered crystals, both in the normal and in the superconducting states. The limits of application of the model are discussed.

Crossover from impurity-controlled to granular superconductivity in (TMTSF)2ClO4

Using a proper cooling procedure, a controllable amount of non-magnetic structural disorder can be introduced at low temperature in (TMTSF)2ClO4. Here we performed simultaneous measurements of transport and magnetic properties of (TMTSF)2ClO4 in its normal and superconducting states, while finely covering three orders of magnitude of the cooling rate around the anion ordering temperature. Our result reveals, with increasing density of disorder, the existence of a crossover between homogeneous defect-controlled d-wave superconductivity and granular superconductivity. At slow cooling rates, with small amount of disorder, the evolution of superconducting properties is well described with the Abrikosov-Gorkov theory, providing further confirmation of non-s-wave pairing in this compound. In contrast, at fast cooling rates, zero resistance and diamagnetic shielding are achieved through a randomly distributed network of superconducting puddles embedded in an normal conducting background and interconnected by proximity effect coupling. The temperature dependence of the AC complex susceptibility reveals features typical for a network of granular superconductors. This makes (TMTSF)2ClO4 a model system for granular superconductivity where the grain size and their concentration are tunable within the same sample.

Effects of nonmagnetic disorder on the energy of Yu-Shiba-Rusinov states

We study the sensitivity of Yu-Shiba-Rusinov states, bound states that form around magnetic scatterers in superconductors, to the presence of nonmagnetic disorder in both two and three dimensional systems. We formulate a scattering approach to this problem and reduce the effects of disorder to two contributions: disorder-induced normal reflection and a random phase of the amplitude for Andreev reflection. We find that both of these are small even for moderate amounts of disorder. In the dirty limit in which the disorder-induced mean free path is smaller than the superconducting coherence length, the variance of the energy of the Yu-Shiba-Rusinov state remains small in the ratio of the Fermi wavelength and the mean free path. This effect is more pronounced in three dimensions, where only impurities within a few Fermi wavelengths of the magnetic scatterer contribute. In two dimensions the energy variance is larger by a logarithmic factor because impurities contribute up to a distance of the order of the superconducting coherence length.

Hydrogenation-induced cerium valence change in CeNiZn

Polycrystalline CeNiZn (ZrNiAl type, P6¯2m, a = 715.6 (4), c = 388.4 (2) pm) forms a new hydride CeNiZnH1.2(1) under hydrogen exposure (10 bar) at 423 K. The resulting hydride crystallizes in a hexagonal structure (P6/mmm) with the unit cell parameters a = 433.19 (2) and c = 424.37 (2) pm. Thus, hydrogen atom insertion yields a structural transition from a ZrNiAl- to an AlB2-type structure with a high volume cell expansion of +20.1%. The magnetic, thermal and transport properties of CeNiZnH1.2(1) were investigated. Susceptibility and specific heat measurements do not reveal magnetic order down to 1.8 K but most likely the presence of ferromagnetic correlations due to the proximity of a ferromagnetic order or a nonmagnetic atom disorder spin-glass state. Moreover, the cerium valence is modified from an intermediate to a trivalent state, a change that results from the decrease of the hybridization strength between conduction and Ce (4f) electrons upon hydrogenation. Transport measurements also evidence a deviation from the typical resistivity behavior of metallic systems. Several scenarios are conceived to explain this change, in particular weak localization effect, knowing that it rarely occurs upon hydrogenation of intermetallics.

The influence of anisotropic Rashba spin–orbit coupling on current-induced spin polarization in graphene

We consider a disordered graphene layer with anisotropic Rashba spin–orbit coupling subjected to a longitudinal electric field. Using the linear response theory we calculate current-induced spin polarization including in-plane normal and parallel components with respect to the electric field direction. Unlike the case of isotropic Rashba spin–orbit where the normal component of spin polarization is linear in terms of Fermi energy around the Dirac point, anisotropic Rashba spin–orbit can result in non-linear dependence of this component at such energies within the Lifshitz points. Furthermore, we show that anisotropic Rashba interaction allows for tuning the direction of spin polarization from perpendicular direction to the parallel one such that for certain values of Rashba parameters the magnitudes of both components can also be quenched. The effect of carriers scattering on randomly distributed non-magnetic disorders is also taken into account by calculating vertex correction. This results in modification of spin polarization components depending on the relative strength of Rashba parameters.

Josephson current signatures of Majorana flat bands on the surface of time-reversal-invariant Weyl and Dirac semimetals

A linear Josephson junction mediated by the surface states of a time-reversal-invariant Weyl or Dirac semimetal localizes Majorana flat bands protected by the time-reversal symmetry. We show that as a result, the Josephson current exhibits a discontinuous jump at $\pi$ phase difference which can serve as an experimental signature of the Majorana bands. The magnitude of the jump scales proportionally to the junction width and the momentum space distance between the Weyl nodes. It also exhibits a characteristic dependence on the junction orientation. We demonstrate that the jump is robust against the effects of non-zero temperature and weak non-magnetic disorder.

Magnetic-proximity-induced magnetoresistance on topological insulators

We theoretically study the magnetoresistance (MR) of two-dimensional massless Dirac electrons as found on the surface of three-dimensional topological insulators (3D TIs) that is capped by a ferromagnetic insulator (FI). We calculate charge and spin transport by Kubo and Boltzmann theories, taking into account the ladder-vertex correction and the in-scattering due to normal and magnetic disorder. The induced exchange splitting is found to generate an electric conductivity that depends on the magnetization orientation, but its form is very different from both the anisotropic and spin Hall MR. The in-plane MR vanishes identically for non-magnetic disorder, while out-of-plane magnetizations cause a large MR ratio. On the other hand, we do find an in-plane MR and planar Hall effect in the presence of magnetic disorder aligned with the FI magnetization. Our results may help understand recent transport measurements on TI|FI systems.

Realization of Valley and Spin Pumps by Scattering at Nonmagnetic Disorders.

The recent success in optical pumping of valley polarization in two-dimensional transition metal dichalcogenides (TMDs) has greatly promoted the concept of valley-based informatics and electronics. However, between the demonstrated valley polarization of transient electron-hole pair excitations and practical valleytronic operations, there exist obvious gaps to fill, among which is the valley pump of long-lived charge carriers. Here we discover that the quested valley pump of electrons or holes can be realized simply by scattering at the ubiquitous nonmagnetic disorders, not relying on any specific material property. The mechanism is rooted in the nature of the valley as a momentum space index: the intervalley backscattering in general has a valley contrasted rate due to the distinct momentum transfers, causing a net transfer of population from one valley to another. As examples, we numerically demonstrate the sizable valley pump effects driven by charge current in nanoribbons of monolayer TMDs, where the spin-orbit scattering by nonmagnetic disorders also realizes a spin pump for the spin-valley locked holes. Our finding points to a new opportunity towards valley spintronics, turning disorders from a deleterious factor to a resource of valley and spin polarization.

Disorder enabled band structure engineering of a topological insulator surface

Three-dimensional topological insulators are bulk insulators with Z2 topological electronic order that gives rise to conducting light-like surface states. These surface electrons are exceptionally resistant to localization by non-magnetic disorder, and have been adopted as the basis for a wide range of proposals to achieve new quasiparticle species and device functionality. Recent studies have yielded a surprise by showing that in spite of resisting localization, topological insulator surface electrons can be reshaped by defects into distinctive resonance states. Here we use numerical simulations and scanning tunnelling microscopy data to show that these resonance states have significance well beyond the localized regime usually associated with impurity bands. At native densities in the model Bi2X3 (X=Bi, Te) compounds, defect resonance states are predicted to generate a new quantum basis for an emergent electron gas that supports diffusive electrical transport.

Unconventional Disorder Effects in Correlated Superconductors.

We study the effects of disorder on unconventional superconductors in the presence of correlations, and explore a novel correlated disorder paradigm dominated by strong deviations from standard Abrikosov-Gor'kov theory due to generation of local bound states and cooperative impurity behavior driven by Coulomb interactions. Specifically we explain under which circumstances magnetic disorder acts as a strong poison destroying high-T_{c} superconductivity at the sub-1% level, and when nonmagnetic disorder, counterintuitively, hardly affects the unconventional superconducting state while concomitantly inducing an inhomogeneous full-volume magnetic phase. Recent experimental studies of Fe-based superconductors have discovered that such unusual disorder behavior seems to be indeed present in those systems.

Magnetotransport properties of nonstoichiometric Si–Mn alloys with an excess of manganese relative to silicides Mn4Si7 and MnSi

Comparative examination of magnetotransport properties of nonstoichiometric Si1–xMnx alloys with roughly the same (δх/x ≈ 7%) excess of Mn relative to silicides Mn4Si7 and MnSi has been performed. Films of Si1–xMnx (х ≈ 0.39 and 0.535) with a thickness of 60–70 nm have been fabricated by means of pulsed laser deposition on Al2O3 (0001) substrates at a temperature of 340°С. It has been found that the excess of Mn produces the strongest effect on the Curie temperature in the case of MnSi (ТС increases from 30 K to 300 K and higher), while no such effect is observed in Mn4Si7. This may be attributed to strong nonmagnetic disorder in Si1–xMnx with x ≈ 0.39 and the associated unusual behavior of negative magnetoresistance (NMR): The NMR varies linearly with magnetic field at В ≤ 1.3 T and exhibits almost no temperature dependence at T = 40–85 K.

Nanoscale magnetization of a single vortex in d-wave superconductors

A finite-size scaling of the nanoscale magnetization m on size averaging R of a single vortex in d-wave bulk superconductor is developed using quasiclassical Eilenberger equations. Nanoscaling is anchoring around the linear London approximation for bulk superconductors. Comparing the results with those obtained in local nonlinear approach demonstrated the importance of the nonlocal contribution. Temperature dependences of two-point correlation function χ(T,R1,R2)=m(T,R2)/m(0,R2)−m(T,R1)/m(0,R1) with R2 > R1 and one-point function χ(T, R1 → ∞, R2) are calculated. It is found that χ(T, R1, R2), R2 > R1, is a nonmonotonous function of temperature and changes sign at high temperatures. This nonmonotonous temperature dependence can be understood as a result of competition between various effects i) Volovik effect and nonlocal corrections to superconducting electron density dominating in low temperature range, and ii) current-induced suppression of the order parameter dominating at high temperatures. The introduced nonmagnetic disorder greatly suppresses the low temperature nonlocal and nonlinear effects, leaving the order parameter effects to prevail in the whole temperature range. Nonlocal pairing and tunneling effects are investigated at the superconductor - normal metal border by considering a d-wave superconducting dot (d-dot) inside a normal diffusive metal. These effects result in a suppression of the supercurrent in the vortex core and are essential in nanodots with relatively small sizes. At sizes larger than a temperature dependent characteristic length the nanoscale physics transforms into bulk solution.

Ferromagnetic clusters induced by a nonmagnetic random disorder in diluted magnetic semiconductors

In this work, we analyze the nonmagnetic random disorder leading to a formation of ferromagnetic clusters in diluted magnetic semiconductors. The nonmagnetic random disorder arises from randomness in the host lattice. Including the disorder to the Kondo lattice model with random distribution of magnetic dopants, the ferromagnetic–paramagnetic transition in the system is investigated in the framework of dynamical mean-field theory. At a certain low temperature one finds a fraction of ferromagnetic sites transiting to the paramagnetic state. Enlarging the nonmagnetic random disorder strength, the paramagnetic regimes expand resulting in the formation of the ferromagnetic clusters.

Low field magnetoresistance in a 2D topological insulator based on wide HgTe quantum well

Low field magnetoresistance is experimentally studied in a two-dimensional topological insulator (TI) in both diffusive and quasiballistic samples fabricated on top of a wide (14 nm) HgTe quantum well. In all cases a pronounced quasi-linear positive magnetoresistance is observed similar to that found previously in diffusive samples based on a narrow (8 nm) HgTe well. The experimental results are compared with the main existing theoretical models based on different types of disorder: sample edge roughness, nonmagnetic disorder in an otherwise coherent TI and metallic puddles due to locally trapped charges that act like local gate on the sample. The quasiballistic samples with resistance close to the expected quantized values also show a positive low-field magnetoresistance but with a pronounced admixture of mesoscopic effects.

Impurity-Induced Smearing of the Spin Resonance Peak in Fe-Based Superconductors

The spin resonance peak in the iron-based superconductors is observed in inelastic neutron scattering experiments and agrees well with predicted results for the extended s-wave ($s_\pm$) gap symmetry. On the basis of four-band and three-orbital tight binding models we study the effect of nonmagnetic disorder on the resonance peak. Spin susceptibility is calculated in the random phase approximation with the renormalization of the quasiparticle self-energy due to the impurity scattering in the static Born approximation. We find that the spin resonance becomes broader with the increase of disorder and its energy shifts to higher frequencies. For the same amount of disorder the spin response in the $s_\pm$ state is still distinct from that of the $s_{++}$ state.

Multiband theory of superconductivity at theLaAlO3/SrTiO3interface

We present a multi-band model for superconductivity at the metallic interface between insulating oxides LaAlO$_3$ and SrTiO$_3$ (001). Using a self-consistent Bogoliubov-de Gennes theory, formulated with the realistic bands at the interface, we investigate the spin-singlet and spin-triplet pairings in intra-band and inter-band channels. We find that the Rashba and atomic spin-orbit interactions at the interface induce singlet pairing in the inter-band channel and triplet pairing in both the intra-band and inter-band channels when the pairing amplitude in the singlet intra-band channel is finite. The gate-voltage variation of superconductivity is resolved in different pairing channels, compared with experimental results and found to match quite well. Interestingly, an enhancement of the superconducting transition temperature by external in-plane magnetic field is found revealing the existence of a hidden superconducting state above the observed one. As the interface is known to possess high level of inhomogeneity, we explore the role of non-magnetic disorder incorporating thermal phase fluctuations by using a Monte-Carlo method. We show that even after the transition to the non-superconducting phase, driven by temperature or magnetic field, the interface possesses localized Cooper pairs whose signature was observed in previous experiments.

Bulk disorder in the superconductor affects proximity-induced topological superconductivity

We investigate effects of ordinary nonmagnetic disorder in the bulk of a superconductor on magnetic adatom-induced Shiba states and on the proximity-induced superconductivity in a nanowire that is tunnel coupled to the bulk superconductor. Within the formalism of self-consistent Born approximation, we show that, contrary to widespread belief, the proximity-induced topological superconductivity can be adversely affected by the bulk superconducting disorder even in the absence of any disorder in the nanowire (or the superconductor-nanowire interface) when the proximity tunnel coupling is strong. In particular, bulk disorder can effectively randomize the Shiba-state energies. In the case of a proximate semiconductor nanowire, we numerically compute the dependence of the effective disorder and pairing gap induced on the wire as a function of the semiconductor-superconductor tunnel coupling. We find that the scaling exponent of the induced disorder with respect to coupling is always larger than that of the induced gap, implying that at weak coupling, the proximity-induced pairing gap dominates, whereas at strong coupling, the induced disorder dominates. These findings bring out the importance of improving the quality of the bulk superconductor itself (in addition to the quality of the nanowire and the interface) in the experimental search for solid-state Majorana fermions in proximity-coupled hybrid structures and, in particular, points out the pitfall of pursuing strong coupling between the semiconductor and the superconductor in a goal toward having a large proximity gap. In particular, our work establishes that the bulk superconductor in strongly coupled hybrid systems for Majorana studies must be in the ultraclean limit, since otherwise the bulk disorder is likely to completely suppress all induced topological superconductivity effects.

Spin-selective localization of correlated lattice fermions

The interplay between local, repulsive interactions and disorder acting only on one spin orientation of lattice fermions ("spin-dependent disorder") is investigated. The nonmagnetic disorder vs. interaction phase diagram is computed using Dynamical Mean-Field Theory in combination with the geometric average over disorder. The latter determines the typical local density of states and is therefore sensitive to Anderson localization. The effect of spin-dependent disorder is found to be very different from that of conventional disorder. In particular, it destabilizes the metallic solution and leads to a novel spin-selective, localized phase at weak interactions and strong disorder.

Exchange and collective behavior of magnetic impurities in a disordered helical metal

We study the exchange interaction and the subsequent collective behavior of magnetic impurities embedded in a disordered two-dimensional (2D) helical metal. The exchange coupling follows a statistical distribution whose moments are calculated to the lowest order in $\left(p_F\ell\right)^{-1}$, where $p_F$ is the Fermi momentum of itinerant electrons and $\ell$ is the mean free path. We find that i) the first moment of the distribution decays exponentially, and ii) the variance of the interaction is long-range, however, it becomes independent of the orientation of the localized magnetic moments due to the locking between spin and momentum of the electrons that mediate the interaction. As consequence, long-range magnetic order tends to be suppressed, and a spin glass phase emerges. The formalism is applied to the surface states of a three-dimensional (3D) topological insulator. The lack of a net magnetic moment in the glassy phase and the full randomization of spin polarization at distances larger than $\ell$ excludes a spectral gap for surface states. Hence, non-magnetic disorder may explain the dispersion in results for photoemission experiments in magnetically-doped topological insulators.

Influence of Quenched Nonmagnetic Impurities on Phase Transitions in Two-Dimensional 3-State Antiferromagnetic Potts Model on Triangular Lattice

An influence of quenched nonmagnetic disorder on the phase transitions in the two dimensional antiferromagnetic Potts model with a number of spin state q=3 on a triangular lattice is calculated by the Monte-Carlo method. The systems with linear sizes L=20÷144 at spin concentrations p=1.00, 0.90, 0.80 are studied. By means of the fourth order Binder cumulant method, the inclusion of a quenched disorder as nonmagnetic impurities into a pure antiferromagnetic Potts model is shown to be the cause of the change of the first order phase transition into the second one.