Theory Of Magnetotransport Research Articles

Semiclassical Boltzmann magnetotransport theory in anisotropic systems with a nonvanishing Berry curvature

Understanding the transport behavior of an electronic system under the influence of a magnetic field remains a key subject in condensed matter physics. Particularly in topological materials, their nonvanishing Berry curvature can lead to many interesting phenomena in magnetotransport owing to the coupling between the magnetic field and Berry curvature. By fully incorporating both the field-driven anisotropy and inherent anisotropy in the band dispersion, we study the semiclassical Boltzmann magnetotransport theory in topological materials with a nonvanishing Berry curvature. We show that as a solution to the Boltzmann transport equation the effective mean-free-path vector is given by the integral equation, including the effective velocity arising from the coupling between the magnetic field, Berry curvature and mobility. We also calculate the conductivity of Weyl semimetals with an isotropic energy dispersion, and find that the coupling between the magnetic field and Berry curvature induces anisotropy in the relaxation time, showing a substantial deviation from the result obtained assuming a constant relaxation time.

Magnetospectroscopy of terahertz surface plasmons in subwavelength perforated superlattice thin-films

Surface plasmons, the resonant oscillations of conducting electrons at the interface of negative and positive permittivity materials, pave the way for enhanced electromagnetic wave–matter interactions at a subwavelength scale. On the other hand, spin-dependent magnetotransport ushers an ingenious technology by inculcating electron spin to realize miniaturized, energy-efficient electromagnetic devices. Generally, magneto-resistive devices (viz., multilayer un-patterned magnetic–non-magnetic thin films) relying on magnetotransport mechanisms are not recognized for supporting surface plasmons toward enhanced electromagnetic interactions. However, an amalgamation of surface plasmons with spin-dependent magnetotransport can exploit magnetic (spintronic) degree of freedom in plasmonic devices. In this work, we propose a patterned superlattice (non-magnetic/ferromagnetic thin films) terahertz (THz) magneto-resistive device for supporting surface plasmons toward enhanced electromagnetic interactions. Magnetotransport dependent enhancement and dynamic magnetic modulation of resonant THz transmissions are experimentally demonstrated in subwavelength superlattice (Al/Ni) hole arrays for varying lattice parameters. Our experiments reveal that typical non-magnetic electromagnetic phenomena like surface plasmon resonances can be tweaked by externally applied low intensity magnetic fields [∼few tens of milli-tesla (0–30 mT)]. Experimental outcomes are explicated by spin-dependent terahertz magnetotransport theory in perforated superlattice metal sheets and, therefore, can stimulate a paragon for spin-based integrated photonic technology.

Weak localization in disordered spin-1 chiral fermions

We theoretically investigate the quantum interference theory of magnetotransport of the three-component or spin-1 chiral fermions, which possess two linear Dirac bands and a flat band. For isotropic scalar impurities, the correction of conductivity from the coherent backscatter and non-coherent backscatter contributions cancel out in the intravalley scattering, leading to a weak localization correction to the Drude conductivity from the intervalley scattering. For the anisotropic impurities, the above cancelation is removed, we find the approximative quantum interference conductivity in the weak anisotropy case. The contributions from the chiral anomaly and classical Lorentz force are also discussed. Our work reveals some intriguing and detectable transport signatures of the novel spin-1 chiral fermions.

Theory of magnetotransport in shaped topological insulator nanowires

We show that shaped topological insulator (TI) nanowires, i.e. such that their cross-section radius varies along the wire length, can be tuned into a number of different transport regimes when immersed in a homogeneous coaxial magnetic field. This is in contrast with widely studied tubular nanowires with constant cross-section, and is due to magnetic confinement of Dirac surface carriers. In flat 2D systems such a confinement requires non-homogeneous magnetic fields, while for shaped nanowires of standard size homogeneous fields of the order of $B\sim\,1$T are sufficient. We put recent work [Kozlovsky et al., Phys. Rev. Lett. 124, 126804 (2020)] into broader context and extend it to deal with axially symmetric wire geometries with arbitrary radial profile. A dumbbell-shaped TI nanowire is used as a paradigmatic example for transport through a constriction and shown to be tunable into five different transport regimes: (i) conductance steps, (ii) resonant transmission, (iii) current suppression, (iv) Coulomb blockade, and (v) transport through a triple quantum dot. Switching between regimes is achieved by modulating the strength of a coaxial magnetic field and does not require strict axial symmetry of the wire cross-section. As such, it should be observable in TI nanowires fabricated with available experimental techniques.

Manifestations of classical size effect and electronic viscosity in the magnetoresistance of narrow two-dimensional conductors: Theory and experiment

We develop a classical kinetic theory of magnetotransport of 2D electrons in narrow channels with partly diffusive boundary scattering and apply it to description of magnetoresistance measured in the temperature interval 4.2-30 K in long mesoscopic bars fabricated from high-purity GaAs quantum well structures. Both experiment and theory demonstrate a number of characteristic features in the longitudinal and Hall resistances caused by the size effect in two dimensions owing to the high ballisticity of the transport. In addition to the features described previously, we also reveal a change in the slope of the first derivative of magnetoresistance when the cyclotron orbit diameter equals to half of the channel width. These features are suppressed with increasing temperature as a result of the electronic viscosity due to electron-electron interaction. By comparing theory and experiment, we determine the characteristic time of relaxation of angular distribution of electrons caused by electron-electron scattering.

Hall anomaly and moving vortex charge in layered superconductors

Magnetotransport theory of layered superconductors in the flux flow steady state is revisited. Longstanding controversies concerning observed Hall sign reversals are resolved. The conductivity separates into a Bardeen-Stephen vortex core contribution, and a Hall conductivity due to moving vortex charge. This charge, which is responsible for Hall anomaly, diverges logarithmically at weak magnetic field. Its values can be extracted from magetoresistivity data by extrapolation of vortex core Hall angle from the normal phase. Hall anomalies in YBa_22Cu_33O_{7}7, Bi_22Sr_22CaCu_22O_{8-x}8−x, and Nd_{1.85}1.85Ce_{0.15}0.15CuO_{4-y}4−y data are consistent with theoretical estimates based on doping dependence of London penetration depths. In the appendices, we derive the Streda formula for the hydrodynamical Hall conductivity, and refute previously assumed relevance of Galilean symmetry to Hall anomalies.

Self-Consistent Theory of Screening and Transport in Narrow, Translation-Invariant Hall Bars under the Conditions of the Integer Quantum-Hall-Effect

We summarize and discuss a self-consistent screening and magneto-transport theory, developed to understand the results of scanning-force-microscope experiments on the current distribution in a two-dimensional electron system (2DES), located in a narrow Hall bar under the conditions of the integer quantum Hall effect (IQHE) and its breakdown. The theory explains why, at low temperatures, at certain intervals of the applied perpendicular magnetic field, the current density is confined to “incompressible stripes” (ISs), in which a fixed number of Landau levels is occupied, and the longitudinal and Hall resistivity assume quantized values. The theory also explains, how the position and shape of these ISs depend on magnetic field and temperature, and why the confinement of the current density on these ISs leads to precisely quantized values of the macroscopic longitudinal and Hall resistance. The theory, which leads, at high temperatures, to the well known Drude results for current density and resistance, shows that the IQHE is a consequence of the peculiar screening properties of a 2DES in a strong magnetic field at low temperatures, and that it can be understood without assumptions about special localization effects.

Current distribution in narrow translation-invariant quantum-Hall-systems with lateral density modulation

A previously developed self-consistent screening and magneto-transport theory for laterally confined, translation-invariant quantum-Hall-systems is applied to two-dimensional electron systems created by a donor sheet with a lateral density modulation. The previous calculations, assuming a homogeneous donor charge density, could explain experimental results on the spatial distribution of an applied source-drain-current, and the resulting Hall potential, only for the ‘edge-dominated’ low-magnetic-field part of a quantum-Hall-plateau, where the current flows through incompressible stripes near the edges. For the high-magnetic-field regime of the plateau, they predicted current flow only in a narrow stripe in the center of the sample, whereas the experiments found current in a wide region of its bulk. Assuming a suitably modulated donor charge density, we can avoid this discrepancy, and we obtain a strong dependence of the distribution of the applied current on magnetic field, lattice temperature, and the current-strength.

Negative viscosity and eddy flow of the imbalanced electron-hole liquid in graphene

We present a hydrodynamic theory for electron-hole magnetotransport in graphene incorporating carrier-population imbalance, energy, and momentum relaxation processes. We focus on the electric response and find that the carrier and energy imbalance relaxation processes strongly modify the shear viscosity, so that an effective viscosity can be negative in the vicinity of charge neutrality. We predict an emergent eddy flow pattern of swirling currents and explore its manifestation in nonlocal resistivity oscillations in a strip of graphene driven by a source current.

Quantum interference magnetoconductance of polycrystalline germanium films in the variable-range hopping regime

Direct evidence of quantum interference magnetotransport in polycrystalline germanium films in the variable-range hopping (VRH) regime is reported. The temperature dependence of the conductivity of germanium films fulfilled the Mott VRH mechanism with the form of in the low-temperature regime (). For the magnetotransport behaviour of our germanium films in the VRH regime, a crossover, from negative magnetoconductance at the low-field to positive magnetoconductance at the high-field, is observed while the zero-field conductivity is higher than the critical value (). In the regime of , the magnetoconductance is positive and quadratic in the field for some germanium films. These features are in agreement with the VRH magnetotransport theory based on the quantum interference effect among random paths in the hopping process.

Magnetoresistance of compensated semimetals in confined geometries

Two-component conductors -- e.g., semi-metals and narrow band semiconductors -- often exhibit unusually strong magnetoresistance in a wide temperature range. Suppression of the Hall voltage near charge neutrality in such systems gives rise to a strong quasiparticle drift in the direction perpendicular to the electric current and magnetic field. This drift is responsible for a strong geometrical increase of resistance even in weak magnetic fields. Combining the Boltzmann kinetic equation with sample electrostatics, we develop a microscopic theory of magnetotransport in two and three spatial dimensions. The compensated Hall effect in confined geometry is always accompanied by electron-hole recombination near the sample edges and at large-scale inhomogeneities. As the result, classical edge currents may dominate the resistance in the vicinity of charge compensation. The effect leads to linear magnetoresistance in two dimensions in a broad range of parameters. In three dimensions, the magnetoresistance is normally quadratic in the field, with the linear regime restricted to rectangular samples with magnetic field directed perpendicular to the sample surface. Finally, we discuss the effects of heat flow and temperature inhomogeneities on the magnetoresistance.

Theory of Magneto-Transport in Spin–Charge Composite Order Phase of Sm Skutterudite

The transport properties of conduction electrons in a novel spin–charge composite order phase of Sm skutterudite are studied in the framework of an extended Kondo lattice model derived from the p–f hybridization. It is demonstrated that the external magnetic field changes drastically a semiconducting transport to a half-metallic one under the interference of the composite order parameters. The resulting magneto-resistivity is shown to reproduce the features of complicated experimental results for SmRu4P12, particularly when the effect of the Lorentz force is properly taken into account at low temperatures.

Effect of Joule heating on current-induced asymmetries and breakdown of the quantum Hall effect in narrow Hall bars

Recent low-temperature scanning-force-microscopy experiments on narrow Hall bars, under the conditions of the integer quantum Hall effect (IQHE) and its breakdown, have revealed an interesting position dependence of the Hall potential, which changes drastically with the applied magnetic field and the strength of the imposed current through the sample. The present paper shows, that inclusion of Joule heating into an existing self-consistent theory of screening and magneto-transport, which assumes translation invariant Hall bars with a homogeneous background charge due to doping, can explain the experimental results on the breakdown of the IQHE in the so called edge-dominated regime.

Memory matrix theory of magnetotransport in strange metals

We model strange metals as quantum liquids without quasiparticle excitations, but with slow momentum relaxation, and with slow diffusive dynamics of a conserved charge and energy. General expressions are obtained for electrical, thermal and thermoelectric transport in the presence of an applied magnetic field using the memory matrix formalism. In the appropriate limits, our expressions agree with previous hydrodynamic and holographic results. We discuss the relationship of such results to thermoelectric and Hall transport measurements in the strange metal phase of the hole-doped cuprates.

Chiral anomaly and diffusive magnetotransport in Weyl metals.

We present a microscopic theory of diffusive magnetotransport in Weyl metals and clarify its relation to the chiral anomaly. We derive coupled diffusion equations for the total and axial charge densities and show that the chiral anomaly manifests as a magnetic-field-induced coupling between them. We demonstrate that a universal experimentally observable consequence of this coupling in magnetotransport in Weyl metals is a quadratic negative magnetoresistance, which will dominate all other contributions to magnetoresistance under certain conditions.

Semiclassical spin-spin dynamics and feedback control in transport through a quantum dot

We present a theory of magnetotransport through an electronic orbital, where the electron spin interacts with a (sufficiently) large external spin via an exchange interaction. Using a semiclassical approximation, we derive a set of equations of motions for the electron density matrix and the mean value of the external spin that turns out to be highly nonlinear. The dissipation via the electronic leads is implemented in terms of a quantum master equation that is combined with the nonlinear terms of the spin-spin interaction. With an anisotropic exchange coupling a variety of dynamics is generated, such as self-sustained oscillations with parametric resonances or even chaotic behavior. Within our theory we can integrate a Maxwell-demon-like closed-loop feedback scheme that is capable of transporting particles against an applied bias voltage and that can be used to implement a spin filter to generate spin-dependent oscillating currents of opposite directions.

Nonlinear magnetotransport theory and Hall induced resistance oscillations in graphene

The quantum oscillations of nonlinear magnetoresistance in graphene that occur in response to a dc current bias are investigated. We present a theoretical model for the nonlinear magnetotransport of graphene carriers. The model is based on the exact solution of the effective Dirac equation in crossed electric and magnetic fields, while the effects of randomly distributed impurities are perturbatively added. To compute the nonlinear current effects, we develop a covariant formulation of the migration center theory. The current is calculated for short- and large-range scatterers. The analysis of the differential resistivity in the large magnetic field region, shows that the extrema of the Shubnikov de Hass oscillations invert when the dc currents exceed a threshold value. These results are in good agreement with experimental observations. In the small magnetic field regime, corresponding to large filling factors, the existence of Hall induced resistance oscillations are predicted for ultra clean graphene samples. These oscillations originate from Landau–Zener tunneling between Landau levels, that are tilted by the strong electric Hall field.

Theory of strain-controlled magnetotransport and stabilization of the ferromagnetic insulating phase in manganite thin films.

We show that applying strain on half-doped manganites makes it possible to tune the system to the proximity of a metal-insulator transition and thereby generate a colossal magnetoresistance (CMR) response. This phase competition not only allows control of CMR in ferromagnetic metallic manganites but can be used to generate CMR response in otherwise robust insulators at half-doping. Further, from our realistic microscopic model of strain and magnetotransport calculations within the Kubo formalism, we demonstrate a striking result of strain engineering that, under tensile strain, a ferromagnetic charge-ordered insulator, previously inaccessible to experiments, becomes stable.

Transport and semiclassical dynamics of coupled quantum dots interacting with a local magnetic moment

We present a theory of magnetotransport through a system of two coupled electronic orbitals, where the electron spin interacts with a (large) local magnetic moment via an exchange interaction. For the physical realization of such a set-up we have in mind, for example, semiconductor quantum dots coupled to an ensemble of nuclear spins in the host material or molecular orbitals coupled to a local magnetic moment. Using a semiclassical approximation, we derive a set of Ehrenfest equations of motion for the electron density matrix and the mean value of the external spin (Landau equations): Due to the spin coupling they turn out to be nonlinear and, importantly, also coherences between electron states with different spin directions need to be considered. The electronic spin-polarized leads are implemented in form of a Lindblad-type dissipator in the infinite bias limit. We have solved this involved dynamical system numerically for various isotropic and anisotropic coupling schemes. For isotropic spin coupling and spin-polarized leads we study the effect of current-induced magnetization of the attached spin and compare this with a single quantum dot set-up. We further demonstrate that an anisotropic coupling can lead to a rich variety of parametric oscillations in the average current reflecting the complicated interplay between the Larmor precession of the external spin and the dissipative coherent dynamics of the electron spin.

Nonequilibrium magnetooscillations in spatially non-uniform quantum Hall systems

A theory of nonequilibrium magnetotransport in high Landau levels of inhomogeneous quantum Hall systems is presented. A nonlinear current is calculated in response to given local gradients of the chemical and electrostatic potential in the presence of moderately strong microwave radiation. In the regime of high temperature, theory generalizes previously obtained results describing microwave- and Hall-induced oscillations of magnetoresistivity for the case of spatially non-uniform systems. Additionally, the regime of low temperatures is studied, where strong modification of Shubnikov-de Haas oscillations by the ac and dc fields is demonstrated.