We calculate the correction to the conductivity of a disordered ferromagnetic metal due to spin-wave-mediated electron--electron interactions. This correction is the generalization of the Altshuler-Aronov correction to spin-wave-mediated interactions. We derive a general expression for the conductivity correction to lowest order in the spin-wave-mediated interaction and for the limit that the exchange splitting $Δ$ is much smaller than the Fermi energy. For a "clean" ferromagnet with $Δτ_{\rm el}/\hbar \gg 1$, with $τ_{\rm el}$ the mean time for impurity scattering, we find a correction $δσ\propto -T^{5/2}$ at temperatures $T$ above the spin wave gap. In the opposite, "dirty" limit, $Δτ_{\rm el}/\hbar \ll 1$, the correction is a non-monotonous function of temperature.
Quantum interference phenomena in the conductivity of mesoscopic ferromagnets are considered, particularly with regard to the effects of geometric phases acquired by electrons propagating through regions of spatially varying magnetization (due, e.g., to magnetic domain walls). Weak localization and electron-electron interaction quantum corrections to the conductivity and universal conductance fluctuations are discussed. Experiments are proposed for multiply-connected geometries that should reveal conductance oscillations with variations of the profile of the magnetization.
We study intrinsic DC spin and valley Hall conductivity in doped ferromagnetic silicene in the presence of an electric filed applied perpendicular to silicene sheet. By calculating its energy spectrum and wavefunction and by making use of Kubo formalism, we obtain a general relation for the transverse Hall conductivity which can be used to obtain spin- and valley-Hall conductivity. Our results, in the zero limit of the exchange field, reduces to the previous results. Furthermore we discuss electrically tunable spin and valley polarized transport in ferromagnetic silicene and obtain the necessa…
We study the effect of one-side metallization of a uniform ferromagnetic thin film on its spin-wave dispersion relation in the Damon-Eshbach geometry. Due to the finite conductivity of the metallic cover layer on the ferromagnetic film the spin-wave dispersion relation may be nonreciprocal only in a limited wave-vector range. We provide an approximate analytical solution for the spin-wave frequency, discuss its validity and compare it with numerical results. The dispersion is analyzed systematically by varying the parameters of the ferromagnetic film, the metal cover layer and the value of the…
We investigate the electrical conductivity of spin-polarized graphene in the presence of short-ranged magnetic scatterers within the relaxation time approximation and the semi-classical Boltzmann approach. Spin-flip scattering of the itinerant electrons from the majority spin sub-band into the minority one results in a minimum in the electrical resistivity at a finite temperature. While this behavior is reminiscent of the renowned Kondo effect, it has an entirely different origin and differs from the Kondo effect in several aspects. In particular, unlike the Kondo effect, this is a single part…
It is of great interest to explore intrinsic two-dimensional ferromagnetism and seek better two-dimensional quantum anomalous Hall insulator materials. Here, we show that the FeBr$_3$ monolayer is an intrinsic two-dimensional ferromagnetic material whose Curie temperature is 140 K thanks to its strong spin exchange interaction and giant uniaxial magnetic anisotropy. Our phonon spectra and mechanical analysis indicate that the FeBr$_3$ monolayer is dynamically and mechanically stable. Our electronic structure calculation shows that there is one Dirac cone at K point in the Brillouin zone and th…
We present a theory of the infrared conductivity and absorption coefficients of metallic (III,Mn)V ferromagnetic semiconductors. We find that the conductivity is dominated by inter-valence-band transitions that produce peaks at $\hbar ω\sim 220 {\rm meV}$ and obscure the broadened Drude peak. We demonstrate that transverse f-sum rule measurements can be used to extract accurate values for the free carrier density, bypassing the severe characterization difficulties that have till now been created by the large anomalous Hall effect in these materials.
We investigated the magnetotransport in high quality ferromagnetic (Ga,Mn)As films and wires. At low temperature the conductivity decreases with decreasing temperature without saturation down to 20 mK. Here we show, that the conductivity decrease follows a ln($T/T_0$) dependency in 2D films and a $-1/\sqrt{T}$ dependency in 1D wires and is independent of an applied magnetic field. This behavior can be explained by the theory of electron-electron interaction.
Recent work has extended topological band theory to open, non-Hermitian Hamiltonians, yet little is understood about how non-Hermiticity alters the topological quantization of associated observables. We address this problem by studying the quantum anomalous Hall effect (QAHE) generated in the Dirac surface states of a 3D time-reversal-invariant topological insulator (TI) that is proximity-coupled to a metallic ferromagnet. By constructing a contact self-energy for the ferromagnet, we show that in addition to generating a mass gap in the surface spectrum, the ferromagnet can introduce a non-Her…
We have studied the intrinsic spin Hall conductivity of 3d transition metal ferromagnets using first-principles calculations. We find the spin Hall conductivity of bcc Fe and fcc Ni, prototypes of ferromagnetic systems, depends on the direction of magnetization. The spin Hall conductivity of electrons with their spin orientation orthogonal to the magnetization are found to be larger than that when the two are parallel. For example, the former can be more than four times larger than the latter in bcc Fe. Such a difference arises due to the anisotropy of the spin current operator in the spinor s…
We study the quantum corrections to the conductivity of the two-dimensional disordered interacting electron system in the diffusive regime due to inelastic scattering off rare magnetic impurities. We focus on the case of very different g-factors for electrons and magnetic impurities. Within the Born approximation for the inelastic scattering off magnetic impurities we find additional temperature-dependent corrections to the conductivity of the Altshuler-Aronov type. Our results demonstrate that the low temperature transport in interacting disordered electron systems with rare magnetic impuriti…
We present a theory of the intrinsic anomalous Hall effect in a model of a doped Weyl semimetal, which serves here as the simplest toy model of a generic three-dimensional metallic ferromagnet with Weyl nodes in the electronic structure. We analytically evaluate the anomalous Hall conductivity as a function of doping, which allows us to explicitly separate the Fermi surface and non Fermi surface contributions to the Hall conductivity by carefully evaluating the zero frequency and zero wavevector limits of the corresponding response function. We show that this separation agrees with the one sug…
The quantum corrections to the conductivity and the thermopower in monolayer graphene are studied. We use the recursive Green's function method to calculate numerically the conductivity and the thermopower of graphene. We then analyze these weak localization corrections by fitting with the analytical theory as function of the impurity parameters and the gate potential. As a result of the quantum corrections to the thermopower, we find large magnetothermopower which is shown to provide a very sensitive measure of the size and strength of the impurities. We compare these analytical and numerical…
We consider the effect of electron-electron interactions on the current-in-plane (CIP) conductivity and exchange coupling energy of a disordered metallic magnetic multilayer. We analyze its dependence on the value of ferromagnetic splitting of conducting electrons and ferromagnetic layers relative magnetizations orientation. We show that contribution to the CIP conductivity and exchange coupling energy as a periodic function of the angle of magnetizations relative orientation experience $ 2π\to π$ transition depending on the characteristic energies: ferromagnetic splitting of the conducting el…
We report an experimental study of the quantum corrections to the longitudinal conductivity and the Hall coefficient of a low mobility, high density two-dimensional two-dimensional electron gas in a AlGaAs/GaAs/AlGaAs quantum well in a wide temperature range (1.5 K - 110 K). This temperature range covers both the diffusive and the ballistic interaction regimes for our samples. It was therefore possible to study the crossover region for the longitudinal conductivity and the Hall effect.
For an isotropic single-band system, it is well known that the semiclassical Boltzmann transport theory within the relaxation time approximation and the Kubo formula with the vertex corrections provide the same result with the $(1-\cosθ)$ factor in the inverse transport relaxation time. In anisotropic multiband systems, the semiclassical Boltzmann transport equation is generalized to coupled integral equations relating transport relaxation times at different angles in different bands. Using the Kubo formula, we study the vertex corrections to the dc conductivity in anisotropic multiband system…
We report an experimental study of quantum conductivity corrections in a low mobility, high density two-dimensional electron gas in a AlGaAs/GaAs/AlGaAs quantum well in a wide temperature range (1.5K - 110K). This temperature range covers both the diffusive and the ballistic interaction regimes for our samples. It has been therefore possible to study the crossover between these regimes for both the longitudinal conductivity and the Hall effect. We perform a parameter free comparison of our experimental data for the longitudinal conductivity at zero magnetic field, the Hall coefficient, and the…
We calculate the correction to the electronic density of states in a disordered ferromagnetic metal induced by spin-wave mediated interaction between the electrons. Our calculation is valid for the case that the exchange splitting in the ferromagnet is much smaller than the Fermi energy, but we make no assumption on the relative magnitude of the exchange splitting and the elastic electronic scattering time. In the "clean limit", where the exchange splitting is much larger than the electronic scattering rate, we find a correction with a T^{d/2} temperature dependence, where d is the effective d…
The Hikami-Larkin-Nagaoka (HLN) formula [Prog. Theor. Phys. 63, 707 (1980)] describes the quantum corrections to the magnetoconductivity of a quasi-2D electron gas (quasi-2DEG) with parabolic dispersion. It predicts a crossover from weak localization to antilocalization as a function of the strength of scattering off spin-orbit impurities. Here, we derive the conductivity correction for massless Dirac fermions in 3D topological insulators (TIs) in the presence of spin-orbit impurities. We show that this correction is always positive and therefore we predict weak antilocalization for every valu…
We consider a disordered topological insulator thin film placed on the top of a ferromagnetic insulator with a perpendicular exchange field $M$ and subjected to a perpendicular electric field. The presence of ferromagnetic insulator causes that bottom surface states of the topological insulator thin film become spin polarized and the electric field provides a potential difference $V$ between the two surface states, resulting in breaking of time-reversal and inversion symmetry in the system. Using Kubo formalism and employing the first Born approximation as well as the self-consistent Born appr…
It is known that the anomalous Hall conductivity (AHC) in a disordered two dimensional electron system with Rashba spin-orbit interaction and finite ferromagnetic spin-exchange energy is zero in the metallic weak-scattering regime because of the exact cancellation of the bare-bubble contribution by the vertex correction. We study the effect of inhomogeneous longitudinal electric field on the AHC in such a system. We predict that AHC increases from zero (at zero wavenumber), forms a peak, and then decreases as the wavenumber for the variation of electric field increases. The peak-value of AHC i…
We study the effect of disorder on the intrinsic anomalous Hall (AH) conductivity in a spin-polarized two-dimensional electron gas with a Rashba-type spin-orbit interaction. We find that AH conductivity vanishes unless the lifetime is spin-dependent, similar to the spin Hall (SH) conductivity in the non-magnetic system. In addition, we find that the SH conductivity does not vanish in the presence of magnetic scatterers. We show that the SH conductivity can be controlled by changing the amount of the magnetic impurities.
Conductivity of a disorder-free intrinsic graphene is studied to the first order in the long-range Coulomb interaction and is found to be σ=σ_0(1+0.01 g), where 'g' is the dimensionless ("fine structure") coupling constant. The calculations are performed using three different methods: i) electron polarization function, ii) Kubo formula for the conductivity, iii) quantum transport equation. Surprisingly, these methods yield different results unless a proper ultraviolet cut-off procedure is implemented, which requires that the interaction potential in the effective Dirac Hamiltonian is cut-off a…
We study one-dimensional transport in focused-ion-beam written in-plane-gate transistors on III-V heterostructures at moderately low temperatures at zero bias without any external magnetic field applied. In accordance with a recent proposal of A. Gold and L. Calmels, Valley- and spin-occupancy instability in the quasi-one-dimensional electron gas, Phil. Mag. Lett. 74, 33-42 (1996) and earlier experimental data, we observe plateaux in the source-drain conductivity considered as a function of the gate voltage, not only at multliples of 2e^2/h but also clearly at e^2/h, just before the channel cl…
Emergence of multiple topological phases with a series of Chern numbers, $\pm 1$, $\mp 1$, $\pm 2$, $\mp 2$, $\pm 3$ and $\mp 4$, are observed in a ferromagnetic Kitaev-Heisenberg-spin-anisotropic model on honeycomb lattice with further neighbor interactions in the presence of an external magnetic field. Magnon Chern insulating dispersions of this two-band model are studied by using linear spin-wave theory formulated on the exact ferromagnetic ground state. Magnon edge states are obtained for the respective topological phases along with density of states. A topological phase diagram of this mo…
Thermal Hall conductivity from semiclassical spin dynamics simulations: implementation and applications to chiral ferromagnets and Kitaev magnets
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；University of Münster（明斯特大学）；Imperial College London（帝国理工学院）
We study quantum corrections to conductivity in a 2D system with a smooth random potential and strong spin-orbit splitting of the spectrum. We show that the interference correction is positive and down to the very low temperature can exceed the negative correction related to electron-electron interactions. We discuss this result in the context of the problem of the metal-insulator transition in Si-MOSFET structures.
The electron-electron interaction quantum correction to the conductivity of the gated double well Al$_x$Ga$_{1-x}$As/GaAs structures is investigated experimentally. The analysis of the temperature and magnetic field dependences of the conductivity tensor allows us to obtain reliably the diffusion part of the interaction correction for the regimes when the structure is balanced and when only one quantum well is occupied. The surprising result is that the interaction correction does not reveal resonant behavior; it is practically the same for both regimes.
The intrinsic spin Hall conductivity and the anomalous Hall conductivity of ferromagnetic L1$_0$-CoPt are studied using first principle calculations of the spin Berry and Berry curvatures, respectively. We find that the Berry curvature and the spin Berry curvature exhibit different symmetry with respect to that of the band structure. The Berry curvature preserves the $C_{4v}$ crystal rotation symmetry along the c-axis whereas the symmetry of the spin Berry curvature reduces to $C_{2v}$. Contributions to the Berry curvature and the spin Berry curvature are classified by the spin character of ba…
Simultaneous nanoscale imaging of local conductivity and chemical potential in a quantum Hall isospin ferromagnet
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院）；Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science, Westlake University（西湖大学理学院物理学系浙江省量子材料重点实验室）；Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), School of Physics, Renmin University of China（中国人民大学物理学院量子态构建与操控教育部重点实验室）；Department of Physics and Astronomy, University of Manchester（曼彻斯特大学物理与天文学系）
We present a systematic study of the corrections to both the longitudinal conductivity and Hall resistivity due to electron-electron interactions in high quality GaAs systems using the recent theory of Zala et al. [Phys. Rev. B 64, 214204 (2001)]. We demonstrate that the interaction corrections to the longitudinal conductivity and Hall resistivity predicted by the theory are consistent with each other. This suggests that the anomalous metallic drop in resistivity at B=0 is due to interaction effects and supports the theory of Zala et al.
In this article, we investigate the temperature and chemical potential dependence of the optical conductivity of graphene, within a field theoretical representation in the continuum approximation, arising from an underlying tight-binding atomistic model, that includes up to next-to-nearest neighbor coupling. Our calculations allow us to obtain the dependence of the optical conductivity on frequency, temperature and finite chemical potential, generalizing our previously reported calculations at zero temperature, and reproducing the universal and experimentally verified value at zero frequency.
We compute the two-loop interaction correction to the minimal conductivity of disorder-free intrinsic graphene with the help of dimensional regularization. The calculation is done in two different ways: via density-density and via current-current correlation functions. Upon properly renormalizing the perturbation theory, in both cases, we find that: $σ= σ_0\,( 1 + \al\,(19-6π)/12) \approx σ_0 \,(1 + 0.01\, \al)$, where $\al = e^2 / (4 π\hbar v)$ is the renormalized fine structure constant and $σ_0 = e^2 / (4 \hbar)$. Our results are consistent with experimental uncertainties and resolve a theo…
We consider the correction $Δσ_\mathrm{ee}$ due to electron-electron interaction to the conductivity of a weakly disordered metal (Al'tshuler-Aronov correction). The correction is related to the spectral determinant of the Laplace operator. The case of a large square metallic network is considered. The variation of $Δσ_\mathrm{ee}(L_T)$ as a function of the thermal length $L_T$ is found very similar to the variation of the weak localization $Δσ_\mathrm{WL}(L_ϕ)$ as a function of the phase coherence length. Our result for $Δσ_\mathrm{ee}$ interpolates between the known 1d and 2d results, but th…
We report a complete analytical expression for the one-loop correction to the ac conductivity $σ(ω)$ of a disordered two-dimensional electron system in the diffusive regime. The obtained expression includes the weak localization and Altshuler-Aronov corrections as well as the corrections due to superconducting fluctuations above superconducting transition temperature. The derived expression has no $1/(iω)$ divergency in the static limit, $ω\to 0$, in agreement with general expectations for the normal state conductivity of a disordered electron system.
We study thermal conductivity in the disordered two-dimensional electron liquid in the presence of long-range Coulomb interactions. We describe a microscopic analysis of the problem using as a starting point the partition function defined on the Keldysh contour. We extend the Renormalization Group (RG) analysis developed for thermal transport in the disordered Fermi liquid, and include scattering processes induced by the long-range Coulomb interaction in the sub-temperature energy range. For the thermal conductivity, unlike for the electric conductivity, these scattering processes yield a loga…
Low temperature quantum corrections to the density of states (DOS) and the conductivity are examined for a two-dimensional(2D) square crystal with substitutional impurities. By summing the leading logarithmic corrections to the DOS its energy dependence near half-filling is obtained. It is shown that substitutional impurities do not suppress the van Hove singularity at the middle of the band, however they change its energy dependence strongly. Weak disorder due to substitutional impurities in the three-dimensional simple cubic lattice results in a shallow dip in the center of the band. The cal…
Quantum transport in magnetic topological insulators reveals the strong interplay between the magnetism and topology of electronic band structures. A recent experiment on magnetically doped topological insulator Bi2Se3 thin films showed the anomalous temperature dependence of the magnetoconductivity while their field dependence presents a clear signature of weak anti-localization [Tkac et al., Phys. Rev. Lett. 123, 036406(2019)]. Here we demonstrate that the tiny mass of the surface electrons induced by the bulk magnetization leads to a temperature-dependent correction to the πBerry phase, and…
In computing electric conductivity based on the Kubo formula, the vertex corrections describe such effects as anisotropic scattering and quantum interference and are important to quantum transport properties. These vertex corrections are obtained by solving Bethe-Salpeter equations, which can become numerically intractable when a large number of k-points and multiple bands are involved. We introduce a non-iterative approach to the vertex correction based on rank factorization of the impurity vertices, which significantly alleviate the computational burden. We demonstrate that this method can b…
Based on a tight-binding model and a recursive Green's function technique, spin-depentent ballistic transport through tinny graphene sheets (flakes) is studied. The main interest is focussed on: electrical conductivity, giant magnetoresistance (GMR) and shot noise. It is shown that when graphene flakes are sandwiched between two ferromagnetic electrodes, the resulting GMR coefficient may be quite significant. This statement holds true both for zigzag and armchair chiralities, as well as for different aspect (width/length) ratios. Remarkably, in absolute values the GMR of the armchair-edge grap…
The two-loop interaction correction coefficient to the universal ac conductivity of disorder-free intrinsic graphene is computed with the help of a field theoretic renormalization study using the BPHZ prescription. Non-standard Ward identities imply that divergent subgraphs (related to Fermi velocity renormalization) contribute to the renormalized optical conductivity. Proceeding either via density-density or via current-current correlation functions, a single well-defined value is obtained: $\mathcal{C}= (19-6π)/12) = 0.01$ in agreement with the result first obtained by Mishchenko and which i…
We consider the quantum corrections to the conductivity of fermions interacting via a Chern-Simons gauge field, and concentrate on the Hartree-type contributions. The first-order Hartree approximation is only valid in the limit of weak coupling λto the gauge field, and results in an antilocalizing conductivity correction, \sim λ^2 g \ln^2 T (g is the conductance). In the case of strong coupling, an infinite summation of higher-order terms is necessary, including both the virtual (renormalization) and real (dephasing) processes. At intermediate temperatures 1/g^2τ<<T<<1/gτ(τis the transport tim…
A new type of anomalous Hall effect is shown to arise from the interaction of conduction electrons with dipolar spin waves in ferromagnets. This effect exists even in homogeneous ferromagnets without relativistic spin-orbit coupling. The leading contribution to the Hall conductivity is proportional to the chiral spin correlation of dynamical spin textures and is physically understood in terms of the skew scattering by dipolar magnons.
Spin-orbit torque (SOT) magnetization switching of ferromagnets with large perpendicular magnetic anisotropy has a great potential for the next-generation non-volatile magnetoresistive random-access memory (MRAM). It requires a high-performance pure spin current source with a large spin Hall angle and high electrical conductivity, which can be fabricated by a mass production technique. In this work, we demonstrate ultrahigh efficient and robust SOT magnetization switching in all-sputtered BiSb topological insulator - perpendicularly magnetized Co/Pt multilayers. Despite fabricated by the indus…
It is well known that conductivity of disordered metals is suppressed in the limit of low frequencies and temperatures by quantum corrections. Although predicted by theory to exist up to much higher energies, such corrections have so far been experimentally proven only for $\lesssim$80 meV. Here, by a combination of transport and optical studies, we demonstrate that the quantum corrections are present in strongly disordered conductor MoC up to at least $\sim$4 eV, thereby extending the experimental window where such corrections were found by a factor of 50. The knowledge of both, the real and …
Coulomb interaction might have important effects on the physical observables in topological semimetals with vanishing density of states at the band touching due to the weak screening. In this work, we show that Kohn's theorem is not fulfilled in nodal-line semimetals (NLSMs), which implies non-vanishing interaction corrections to the conductivity. Using renormalized perturbation theory, we determine the first-order optical conductivity in a clean NLSM to be $σ_{\perp \perp}(Ω) = 2 σ_{\parallel \parallel}(Ω) = σ_0 [1 + C_2 α_R(Ω)]$, where $\perp$ and $\parallel$ denote the perpendicular and par…
We study the thermal conductivity in disordered $s$-wave superconductors. Expanding on previous works for normal metals, we develop a formalism that tackles particle diffusion as well as the weak localization (WL) and weak anti-localization (WAL) effects. Using a Green's functions diagrammatic technique, which takes into account the superconducting nature of the system by working in Nambu space, we identify the system's low-energy modes, the diffuson and the Cooperon. The time scales that characterize the diffusive regime are energy dependent; this is in contrast with the the normal state, whe…
