Dirty Metal Research Articles

Robust room temperature perpendicular magnetic anisotropy and anomalous Hall effect of sputtered NiCo2O4 film

Inverse spinel ferrimagnetic NiCo2O4 (NCO) exhibits volatile physical properties due to the complex ion/valence occupation, which complicates the study its intrinsic properties. In this work, robust room temperature perpendicular magnetic anisotropy (PMA) is distinctly observed in high-quality RF-sputtered NCO film down to 3 uc (2.4 nm), confirmed by the room temperature anomalous Hall effect. The NCO films show a good metallic conductivity with a dimensional driven metal-insulator transition. The scaling relation between anomalous Hall conductivity ( σxy ) and the longitudinal conductivity ( σxx ) reveals the dirty metal behavior in conjunction with the contribution of intrinsic Berry phase or disorder-enhanced electron correlation contribute to the anomalous Hall effect for thick films while the dirty scaling law dominates for the thin films. This work introduces an oxide candidate with robust room temperature PMA as well as massive production ability for the functional spintronic applications.

Strong enhancement of spin-orbit torques in ferrimagnetic Ptx(Si3N4)1–x /CoTb bilayers by Si3N4 doping

We report strong enhancement of spin-orbit torques by incorporating ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ impurities into the dirty metal Pt. We find that the ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ impurities lower the spin Hall conductivity and the charge conductivity of the Pt host at different rates, leading to a twofold increase in the dampinglike spin-orbit torque per unit current density for ferrimagnetic ${\mathrm{Pt}}_{x}{({\mathrm{Si}}_{3}{\mathrm{N}}_{4})}_{1--x}/{\mathrm{Co}}_{0.65}{\mathrm{Tb}}_{0.35}$ bilayers. This torque enhancement is attributed to the optimized trade-off between the intrinsic spin Hall conductivity and the spin carrier lifetime in the dirty limit. We also find that only 58% of the angular momentum of the spin current entering the ferrimagnetic ${\mathrm{Co}}_{0.65}{\mathrm{Tb}}_{0.35}$ relaxes via exchange interaction and thus makes a contribution to spin torque generation. This work establishes ${\mathrm{Pt}}_{0.7}{({\mathrm{Si}}_{3}{\mathrm{N}}_{4})}_{0.3}$ with a high spin Hall ratio of 0.8 and a high charge conductivity of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}$ as a compelling spin Hall metal for spin-orbitronics. This work also reaffirms the variation of the spin-orbit torque with relative spin relaxation rates within the magnetic layer.

Theory of disordered superconductors with applications to nonlinear current response

Abstract I present a review of the theory and basic equations for charge transport in superconducting alloys starting from the Keldysh formulation of the quasiclassical transport equations developed by Eilenberger, Larkin and Ovchinnikov, and Eliashberg. This formulation is the natural extension of Landau’s theory of normal Fermi liquids to the superconducting state of strongly correlated metals. For dirty metals the transport equations reduce to equations for charge diffusion, with the current response given by the Drude conductivity at low temperatures. The extension of the diffusion equation for the charge and current response of a strongly disordered normal metal to the superconducting state yields Usadel’s equations for the nonequilibrium quasiclassical Keldysh propagator. The conditions for the applicability of the Usadel equations are discussed, the pair-breaking effect of disorder on the current response, including the nonlinear current response to an electromagnetic field in the dirty limit, τ ≪ ℏ/Δ, are reported. The same nonlinearity is shown to lead to source currents for photon generation and nonlinear Kerr rotation driven by the nonlinear response to excitation of the superconductor by a multi-mode electromagnetic field. The potential relevance of the nonlinear source currents to superconducting radio-frequency cavities as detectors of axion-like dark matter candidates is briefly discussed.

Doping efficiency and electron transport in Al-doped ZnO films grown by atomic layer deposition

Transparent conducting Al-doped ZnO films were grown by atomic layer deposition (ALD). Al-doping was introduced by inserting 1 Al2O3 cycle per 28 ZnO cycles. The x-ray photoelectron spectroscopy showed that the density of the Al donors is 2×1021–3×1021 cm−3, while the Hall-effect measurements showed a ten times lower electron density. This low doping efficiency is a well-known inherent problem of the ALD method, and we wanted to explain its origin. We have found that the electron density is reduced by electron traps at the grain surface; however, the effect was too weak to explain the low doping efficiency. Therefore, the mechanism of the Al2O3 doping was analyzed. We have proposed that each Al2O3 molecule ideally provides two single-electron Al donors accompanied by one Zn vacancy, which acts as a two-electron acceptor. This would cause a perfect compensation; however, the compensation is in reality not perfect, which results in weakly efficient doping. Calculations also showed that each Zn vacancy creates a bound pair with an Al donor. To verify our doping model experimentally, it was inserted into the metallic transport theory and compared with the electron transport measurements. A good agreement was found for a broad range of experimental conditions. In the regime of weak localization, the conductivity showed the temperature dependence σ(T)=a+bT3/4, which is a signature of weak localization and electron–electron scattering in a 3D dirty metal.

Droplets of the Order Parameter in a Low Density Attracting Electron System in the Presence of a Strong Random Potential

The properties of a two-dimensional low density (n<<1) electron system with strong onsite Hubbard attraction U>W (W is the bandwidth) in the presence of a strong random potential V uniformly distributed in the range from -V to +V are considered. Electronic hoppings only at neighboring sites on the square lattice are taken into account, thus W=8t. The calculations were carried out for a lattice of 24x24 sites with periodic boundary conditions. In the framework of the Bogoliubov - de Gennes approach we observed an appearance of inhomogeneous states of spatially separated Fermi-Bose mixture of Cooper pairs and unpaired electrons with the formation of bosonic droplets of different size in the matrix of the unpaired normal states We observed a decrease in the droplet size (from larger droplets to individual bielectronic pairs) when we decrease the electron density at fixed values of the Hubbard attraction and random potential. The obtained results are important for the construction of the gross phase diagram and understanding of the nature of the phase transition between superconducting, normal metallic and localized states in quasi-2D (thin) film of a dirty metal. In a more practical sense it is interesting also for the experimental implementation of superconducting qubits on quantum circuits with high impedances in granular superconductors.

Cluster formation and non-metal-to-metal transition in a diamond-shaped graphene-like lattice

This work is a numerical simulation of the bond percolation in an array of junctions and bifurcations mimicking a section of a graphene slab. We calculate the size distribution of graphene clusters as a filler of a polymer aiming to obtain the percolation threshold. We obtained the sigmoidal distribution of graphene clusters as a function of concentration of persistent conducting bonds creating these clusters. The probability density of this distribution shows a universal complementary Fermi–Dirac behavior as a signature of a topological response. Using a tight-binding model for the transmission from the source to the drain, we obtain a smooth transition from an insulator to a conductor through a dirty metal as the concentration of conductive bonds increases for small arrays. As the array size increases, the simulation shows a sharp non-metal-to-metal transition from a pure polymer into a pristine suspended graphene layer.

Enhanced Spin Hall Effect in S‐Implanted Pt

AbstractHigh efficiency of charge–spin interconversion in spin Hall materials is a prime necessity to apprehend intriguing functionalities of spin–orbit torque for magnetization switching, auto‐oscillations, and domain wall motion in energy‐efficient and high‐speed spintronic devices. To this end, innovations in fabricating advanced materials that possess not only large charge–spin conversion efficiency but also viable electrical and spin Hall conductivity are of importance. Here, a new spin Hall material designed by implanting low energy 12 keV sulfur ions in heavy metal Pt, named as Pt(S), is reported that demonstrates eight times higher conversion efficiency as compared to pristine Pt. The figure of merit, spin Hall angle (θSH), up to of 0.502 together with considerable electrical conductivity of 1.65 × 106 Ω–1 m–1 is achieved. The spin Hall conductivity increases with increasing , as , implying an intrinsic mechanism in a dirty metal conduction regime. A comparatively large of 8.32 × 105 () Ω–1 m–1 among the reported heavy‐metals‐based alloys can be useful for developing next‐generation spintronic devices using spin–orbit torque.

Non-Wigner-Dyson level statistics and fractal wave function of disordered Weyl semimetals

Finding fingerprints of disordered Weyl semimetals (WSMs) is an unsolved task. Here we report such findings in the level statistics and the fractal nature of electron wave function around Weyl nodes (WNs) of disordered WSMs. The nearest-neighbor level spacing follows a new universal distribution ${P}_{c}(s)={C}_{1}{s}^{2}exp[\ensuremath{-}{C}_{2}{s}^{2\ensuremath{-}{\ensuremath{\gamma}}_{0}}]$ originally proposed for the level statistics of critical states in the integer quantum Hall systems or normal dirty metals (diffusive metals) at metal-to-insulator transitions, instead of the Wigner-Dyson distribution for diffusive metals. Numerically we find ${\ensuremath{\gamma}}_{0}=0.62\ifmmode\pm\else\textpm\fi{}0.07$. In contrast to the Bloch wave functions of clean WSMs that uniformly distribute over the whole space of $(D=3)$ at large length scale, the wave function of disordered WSMs at a WN occupies a fractal space of dimension $D=2.18\ifmmode\pm\else\textpm\fi{}0.05$. Away from the WN, wave function is a fractal at a length scale below a correlation length diverging at the WN as $\ensuremath{\xi}\ensuremath{\propto}{|E|}^{\ensuremath{-}\ensuremath{\nu}}$ with $\ensuremath{\nu}=0.89\ifmmode\pm\else\textpm\fi{}0.05$. Beyond the length scale, the wave function is homogeneous. In the ergodic limit, the level number variance ${\mathrm{\ensuremath{\Sigma}}}_{2}$ around Weyl nodes increases linearly with the average level number $N,{\mathrm{\ensuremath{\Sigma}}}_{2}=\ensuremath{\chi}N$, where $\ensuremath{\chi}=0.2\ifmmode\pm\else\textpm\fi{}0.1$ is independent of system sizes and disorder strengths.

Local trigonal modes and the suppression of the charge density wave in TiSe2−xTex

Finding fingerprints of disordered Weyl semimetals (WSMs) is an unsolved task. Here we report such findings in the level statistics and the fractal nature of electron wavefunction around Weyl nodes of disordered WSMs. The nearest-neighbor level spacing follows a new universal distribution $P_c(s)=C_1 s^2\exp[-C_2 s^{2-\gamma_0}]$ originally proposed for the level statistics of critical states in the integer quantum Hall systems or normal dirty metals (diffusive metals) at metal-to-insulator transitions, instead of the Wigner-Dyson distribution for diffusive metals. Numerically, we find $\gamma_0=0.62\pm0.07$. In contrast to the Bloch wavefuntions of clean WSMs that uniformly distribute over the whole space of ($D=3$) at large length scale, the wavefunction of disordered WSMs at a Weyl node occupies a fractal space of dimension $D=2.18\pm 0.05$. The finite size scaling of the inverse participation ratio suggests that the correlation length of wavefunctions at Weyl nodes ($E=0$) diverges as $\xi\propto |E|^{-\nu}$ with $\nu=0.89\pm0.05$. In the ergodic limit,the level number variance $\Sigma_2$ around Weyl nodes increases linearly with the average level number $N$, $\Sigma_2=\chi N$, where $\chi= 0.2\pm0.1$ is independent of system sizes and disorder strengths.

Symmetry conditions of a nodal superconductor for generating robust flat-band Andreev bound states at its dirty surface

We discuss the symmetry property of a nodal superconductor that hosts robust flat-band zero-energy states at its surface under potential disorder. Such robust zero-energy states are known to induce the anomalous proximity effect in a dirty normal metal attached to a superconductor. A recent study has shown that a topological index ${\cal N}_\mathrm{ZES}$ describes the number of zero-energy states at the dirty surface of a $p$-wave superconductor. We generalize the theory to clarify the conditions required for a superconductor that enables ${\cal N}_\mathrm{ZES}\neq 0$. Our results show that ${\cal N}_\mathrm{ZES}\neq 0$ is realized in a topological material that belongs to either the BDI or CII class. We also present two realistic Hamiltonians that result in ${\cal N}_\mathrm{ZES}\neq 0$.

Quantum ergodicity in the SYK model

We present a replica path integral approach describing the quantum chaotic dynamics of the SYK model at large time scales. The theory leads to the identification of non-ergodic collective modes which relax and eventually give way to an ergodic long time regime (describable by random matrix theory). These modes, which play a role conceptually similar to the diffusion modes of dirty metals, carry quantum numbers which we identify as the generators of the Clifford algebra: each of the 2N different products that can be formed from N Majorana operators defines one effective mode. The competition between a decay rate quickly growing in the order of the product and a density of modes exponentially growing in the same parameter explains the characteristics of the system's approach to the ergodic long time regime. We probe this dynamics through various spectral correlation functions and obtain favorable agreement with existing numerical data.

A theoretical study of electron multiplication coefficient in a cold-cathode Penning ion generator

The discharge mechanism of a Penning ion generator (PIG) is seriously influenced by the electron ionization process. A theoretical approach has been proposed to formulate the electron multiplication coefficient, M, of a PIG as a function of the axial magnetic field and the applied voltage. A numerical simulation was used to adjust the free parameters of expression M. Using the coefficient M, the values of the effective secondary electron emission coefficient, γeff, were obtained to be from 0.09 to 0.22. In comparison to the experimental results, the average value of γeff differs from the secondary coefficient of clean and dirty metals by the factors 1.4 and 0.5, respectively.

Bosonic Confinement and Coherence in Disordered Nanodiamond Arrays.

In the presence of disorder, superconductivity exhibits short-range characteristics linked to localized Cooper pairs which are responsible for anomalous phase transitions and the emergence of quantum states such as the bosonic insulating state. Complementary to well-studied homogeneously disordered superconductors, superconductor-normal hybrid arrays provide tunable realizations of the degree of granular disorder for studying anomalous quantum phase transitions. Here, we investigate the superconductor-bosonic dirty metal transition in disordered nanodiamond arrays as a function of the dispersion of intergrain spacing, which ranges from angstroms to micrometers. By monitoring the evolved superconducting gaps and diminished coherence peaks in the single-quasiparticle density of states, we link the destruction of the superconducting state and the emergence of bosonic dirty metallic state to breaking of the global phase coherence and persistence of the localized Cooper pairs. The observed resistive bosonic phase transitions are well modeled using a series-parallel circuit in the framework of bosonic confinement and coherence.

Effect of disorder on the resistivity of CoFeCrAl films

Structural and electron-transport properties of thin films of the ferrimagnetic Heusler compound CoFeCrAl have been investigated to elucidate structure-property relationships. The alloy is, ideally, a spin-gapless semiconductor, but structural disorder destroys the spin-gapless character and drastically alters the transport behavior. Two types of CoFeCrAl films were grown by magnetron sputtering deposition at 973 K, namely polycrystalline films on Si substrates and epitaxial films on MgO (001) substrates. The resistivity decreases with increasing temperature, with relatively small temperature coefficients of –0.19 μΩcm/K for the polycrystalline films and –0.12 μΩcm/K for the epitaxial films. The residual resistivity of the polycrystalline films deposited on Si is higher than that of the epitaxial film deposited on MgO, indicating that the polycrystalline films behave as so-called dirty metals.

Charge diffusion and the butterfly effect in striped holographic matter

Recently, it has been proposed that the butterfly velocity - a speed at which quantum information propagates - may provide a fundamental bound on diffusion constants in dirty incoherent metals. We analytically compute the charge diffusion constant and the butterfly velocity in charge-neutral holographic matter with long wavelength "hydrodynamic" disorder in a single spatial direction. In this limit, we find that the butterfly velocity does not set a sharp lower bound for the charge diffusion constant.

Gyrotropic Magnetic Effect and the Magnetic Moment on the Fermi Surface.

The current density j^{B} induced in a clean metal by a slowly-varying magnetic field B is formulated as the low-frequency limit of natural optical activity, or natural gyrotropy. Working with a multiband Pauli Hamiltonian, we obtain from the Kubo formula a simple expression for α_{ij}^{GME}=j_{i}^{B}/B_{j} in terms of the intrinsic magnetic moment (orbital plus spin) of the Bloch electrons on the Fermi surface. An alternate semiclassical derivation provides an intuitive picture of the effect, and takes into account the influence of scattering processes in dirty metals. This "gyrotropic magnetic effect" is fundamentally different from the chiral magnetic effect driven by the chiral anomaly and governed by the Berry curvature on the Fermi surface, and the two effects are compared for a minimal model of a Weyl semimetal. Like the Berry curvature, the intrinsic magnetic moment should be regarded as a basic ingredient in the Fermi-liquid description of transport in broken-symmetry metals.

Plasmon-resonant Raman spectroscopy in metallic nanoparticles: Surface-enhanced scattering by electronic excitations

Since the discovery of surface-enhanced Raman scattering (SERS) 40 years ago, the origin of the ``background'' that is systematically observed in SERS spectra has remained questionable. To deeply analyze this phenomenon, plasmon-resonant Raman scattering was recorded under specific experimental conditions on a panel of composite multilayer samples containing noble metal (Ag and Au) nanoparticles. Stokes, anti-Stokes, and wide, including very low, frequency ranges have been explored. The effects of temperature, size (in the nm range), embedding medium (${\text{SiO}}_{\text{2}}, {\text{Si}}_{\text{3}}{\text{N}}_{\text{4}}$, or ${\text{TiO}}_{\text{2}}$) or ligands have been successively analyzed. Both lattice (Lamb modes and bulk phonons) and electron (plasmon mode and electron-hole excitations) dynamics have been investigated. This work confirms that in Ag-based nanoplasmonics composite layers, only Raman scattering by single-particle electronic excitations accounts for the background. This latter appears as an intrinsic phenomenon independently of the presence of molecules on the metallic surface. Its spectral shape is well described by revisiting a model developed in the 1990s for analyzing electron scattering in dirty metals, and used later in superconductors. The ${g}_{s}$ factor, that determines the effective mean-free path of free carriers, is evaluated, ${g}_{s}^{\mathrm{expt}}=0.33\ifmmode\pm\else\textpm\fi{}0.04$, in good agreement with a recent evaluation based on time-dependent local density approximation ${g}_{s}^{\mathrm{theor}}=0.32$. Confinement and interface roughness effects at the nanometer range thus appear crucial to understand and control SERS enhancement and more generally plasmon-enhanced processes on metallic surfaces.

Anderson Localization and the Quantum Phase Diagram of Three Dimensional Disordered Dirac Semimetals.

We study the quantum phase diagram of a three dimensional noninteracting Dirac semimetal in the presence of either quenched axial or scalar potential disorder, by calculating the average and the typical density of states as well as the inverse participation ratio using numerically exact methods. We show that as a function of the disorder strength a half-filled (i.e., undoped) Dirac semimetal displays three distinct ground states, namely an incompressible semimetal, a compressible diffusive metal, and a localized Anderson insulator, in stark contrast to a conventional dirty metal that only supports the latter two phases. We establish the existence of two distinct quantum critical points, which respectively govern the semimetal-metal and the metal-insulator quantum phase transitions and also reveal their underlying multifractal nature. Away from half-filling the (doped) system behaves as a diffusive metal that can undergo Anderson localization only, which is shown by determining the mobility edge and the phase diagram in terms of energy and disorder.

Anomalous Hall Effect of the Co Thin Film Deposited by High-Pressure Magnetron Sputtering

In this paper, we studied the dependence of temperature and weak localization (WL) effect on the anomalous Hall effect (AHE) in strong disordered and poorly crystallized metal Co thin film deposited by high-pressure magnetron sputtering. The temperature coefficients of resistivity is positive at high temperatures and becomes negative at low temperatures, which is the typical characteristic of weak localization effect in dirty metal regime due to the strong disorder. The saturation anomalous Hall resistivity (ρAxy) have no scaling relation between ρxy and ρxx in weak localization region with temperature below 50 K. In metal region, temperature ranged from 50 K to 300 K, the relation between ρAxy and ρxxis ρAxy=A+bρ2xx, which indicates that the AHE in this Co thin film is scattering-independence at high temperature. The results also shows that the WL effect have a significant impact on the AHE of the Co thin film at low temperature.

Anomalous proximity effect and theoretical design for its realization

We discuss the stability of zero-energy states appearing in a dirty normal metal attached to a superconducting thin film with Dresselhaus [110] spin-orbit coupling under the in-plane Zeeman field. The Dresselhaus superconductor preserves an additional chiral symmetry and traps more than one zero-energy state at its edges. All the zero-energy states at an edge belong to the same chirality in large Zeeman field due to the effective $p$-wave pairing symmetry. The pure chiral nature in the wave function enables the penetration of the zero-energy states into the dirty normal metal with keeping their high degree of degeneracy. By applying a theorem, we prove the the perfect Andreev reflection into the dirty normal metal at the zero-energy. This paper gives a microscopic understanding of the anomalous proximity effect.