Transverse Magnetoconductivity Research Articles

π Oscillation phase shift between transverse and longitudinal magnetoconductivities in Weyl semimetals

In the presence of a magnetic field $\mathbf{B}$, the negative transverse magnetoconductivity (TMC) for $\mathbf{E}\ensuremath{\perp}\mathbf{B}$, with $\mathbf{E}$ being the applied electric field, and anomalous positive longitudinal magnetoconductivity (LMC) for $\mathbf{E}\ensuremath{\parallel}\mathbf{B}$ of a three-dimensional (3D) Weyl semimetal (WSM) both exhibit periodic-in-$1/B$ quantum oscillations. We develop a semiclassical theory of the magnetoconductivities of a 3D WSM, taking into account the effect of the Landau level broadening and finite temperatures. We find that if one fixes the direction of $\mathbf{B}$ and switches the direction of $\mathbf{E}$ to be perpendicular and parallel to $\mathbf{B}$, there exists an interesting peak-valley correspondence, or, say, a relative $\ensuremath{\pi}$ oscillation phase shift, between the oscillating TMC and LMC. This can serve as unambiguous measurable evidence manifesting the distinct underlying physical mechanisms of the TMC and LMC in WSMs, which has so far not been reported in theories or experiments.

Competition between the inter-valley scattering and the intra-valley scattering on magnetoconductivity induced by screened Coulomb disorder in Weyl semimetals

Recent experiments on Weyl semimetals reveal that charged impurities may play an important role. We use a screened Coulomb disorder to model the charged impurities, and study the magneto-transport in a two-node Weyl semimetal. It is found that when the external magnetic field is applied parallel to the electric field, the calculated longitudinal magnetoconductivity shows positive in the magnetic field, which is just the negative longitudinal magnetoresistivity (LMR) observed in experiments. When the two fields are perpendicular to each other, the transverse magnetoconductivities are measured. It is found that the longitudinal (transverse) magnetoconductivity is suppressed (enhanced) sensitively with increasing the screening length. This feature makes it hardly to observe the negative LMR in Weyl semimetals experimentally owing to a small screening length. Our findings gain insight into further understanding on recently actively debated magneto-transport behaviors in Weyl semimetals. Furthermore we studied the relative weight of the inter-valley scattering and the intra-valley scattering. It shows that the former is as important as the latter and even dominates in the case of strong magnetic fields and small screening length. We emphasize that the discussions on inter-valley scattering is out of the realm of one-node model which has been studied.

Terahertz quantum Hall effect for spin-split heavy-hole gases in strained Ge quantum wells

Spin-split heavy-hole gases in strained germanium quantum wells were characterized by polarisation-resolved terahertz time-domain spectroscopy. Effective masses, carrier densities, g-factors, transport lifetimes, mobilities and Rashba spin-splitting energies were evaluated, giving quantitative insights into the influence of strain. The Rashba coefficient was found to lower for samples with higher biaxial compressive strain, while heavy-hole mobilities were enhanced to over cm2 V−1 s−1 at 3 K. This high mobility enabled the observation of the optical quantum Hall effect at terahertz frequencies for spin-split two-dimensional heavy-holes, evidenced as plateaux in the transverse magnetoconductivity at even and odd filling factors.

Linear magnetoconductivity in an intrinsic topological Weyl semimetal

Searching for the signature of the violation of chiral charge conservation in solids has inspired a growing passion for the magneto-transport in topological semimetals. One of the open questions is how the conductivity depends on magnetic fields in a semimetal phase when the Fermi energy crosses the Weyl nodes. Here, we study both the longitudinal and transverse magnetoconductivity of a topological Weyl semimetal near the Weyl nodes with the help of a two-node model that includes all the topological semimetal properties. In the semimetal phase, the Fermi energy crosses only the 0th Landau bands in magnetic fields. For a finite potential range of impurities, it is found that both the longitudinal and transverse magnetoconductivity are positive and linear at the Weyl nodes, leading to an anisotropic and negative magnetoresistivity. The longitudinal magnetoconductivity depends on the potential range of impurities. The longitudinal conductivity remains finite at zero field, even though the density of states vanishes at the Weyl nodes. This work establishes a relation between the linear magnetoconductivity and the intrinsic topological Weyl semimetal phase.

Thermoelectric transport in double-Weyl semimetals

We study the thermoelectric properties of a double-Weyl fermion system, possibly realized in $\mathrm{HgCr_2Se_4}$ and $\mathrm{SrSi_2}$, by a semi-classical Boltzmann transport theory. We investigate different relaxation processes including short-range disorder and electron-electron interaction on the thermoelectric transport coefficients. It is found that the anisotropy of the band dispersion for in-plane and out-of-plane momentum directions affects the relaxation time for transport in different directions. The transport also exhibits an interesting directional dependence on the chemical potential and model parameters, differing from a simple isotropic quadratic or linearly dispersing electron gas. By applying a static magnetic field along the linearly dispersing direction, the longitudinal and transverse electrical and thermal magnetoconductivity show a similar dependence on the in-plane cyclotron frequency to the linear dispersing Weyl nodes. By including internode scattering, we find that the chiral anomaly contribution to the thermoelectric coefficients doubles that of a linearly dispersing Weyl node in both the semi-classical and quantum regimes. A magnetic field applied along the quadratically dispersing direction will split the double Weyl point into two single Weyl points with the same chirality.

Transverse Magnetoconductivity in a Semiconductor Superlattice under the Stark Quantization Conditions

The transverse magnetoconductivity has been calculated for a one-dimensional semiconductor superlattice under the action of an external quantizing electric field. The dependence of the conductivity on the electric and magnetic fields is analyzed and found to exhibit a strongly pronounced resonance character. The maximum values of conductivity are evaluated.

Transverse magnetoconductivity of quasi-two-dimensional semiconductor layers in the presence of magnon scattering

We have calculated the transverse dc electrical conductivity of a quasi-two-dimensional quantum well in the presence of a magnetic field normal to the barriers of the well for electron–magnon interaction in dilute magnetic semiconductors. The electron gas is considered to be quasi-two-dimensional, while the magnons are considered to be bulk type. By using the formalism of linear response theory an expression for the transverse magnetoconductivity is explicitly calculated for a quasi two-dimensional electron gas confined to a square quantum-well-type structure interacting with three-dimensional magnons. We found that the magnetoconductivity develops an oscillation as the magnetic field is changed. Application was made for a Ga1–xMnxAs sample for which magnetic order occurs below 110 K for manganese concentration about 5%. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Electric field-induced magnetophonon resonance

The additional structure and the sign reversal of the magnetophonon resonance extrema at high electric fields are explained in terms of the electric field induced inelastic inter-Landau level scattering, longitudinal optic phonon scattering. The calculated transverse magnetoconductivity shows a good agreement with experimental observations in thin n +nn + GaAs structures reported by Eaves et al. and Guimaraes et al.

Theory of magnetoconductivity in a two-dimensional electron-gas system: Self-consistent screening model.

Transverse magnetoconductivity ${\ensuremath{\sigma}}_{\mathrm{xx}}$ is investigated for a two-dimensional electron-gas (2D EG) system in magnetic fields. A scattering model commonly applicable to both Si metal-oxide-semiconductor (MOS) and ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As-GaAs heterostructure field-effect transistors (FET's) is investigated. Ionized impurities are taken to exert a Coulomb force which is screened by the 2D EG. The screened Coulomb force determines widths of Landau subbands and, hence, the density of states at the Fermi energy in Landau subbands, which specifies the degree of screening. Thus, when calculating the widths, broadening of subbands and static dielectric response (i.e., screening) are considered self-consistently (self-consistent screening model). Both widths and ${\ensuremath{\sigma}}_{\mathrm{xx}}$ are solved analytically as well as numerically. Calculations are carried out both when impurities exist within the 2D EG and when they are in a remote sheet. Calculated ${\ensuremath{\sigma}}_{\mathrm{xx}}$ is compared with the experiment by Narita et al. and good agreement, though qualitative, is obtained. The real-space behavior of the screened potential is also discussed. The force range becomes short or remains long, depending on the degree of screening.

Enhancement of the valley splitting in silicon (100) n-type inversion layers by lossless edge currents around Wigner magneto-quantum crystals

It is shown that the picture of a quasi-2D electron liquid (interacting electron gas) for the quantum oscillations in high magnetic fields is not in agreement with the transverse magneto-conductivity theory (based on the Kubo formalism deduced for an electron gas) including the influence of the many-body self-energy. The enhancement of all energy splittings above their bare value from the difference of the self-energy is automatically zero for the level coincidences in the intra-Landau level cases and, to a high degree, vanishes for the 'spin level coincidences' where levels of different Landau quantum numbers are involved. In contrast, the model of an electron crystallisation in quantising magnetic fields, including lossless edge currents, allows a comprehensive explanation of all current experimental data, where for two occupied lattices near the Fermi energy with 2/3 and 1/3 filling, respectively, effectively an enhancement of the valley splitting results from the diamagnetic energy of both opposite magnetic moments, due to the lossless edge currents (orbit-orbit interaction), and from the Zeeman energy of each spin interacting with the magnetic moment of the orbital edge current of the other lattice (spin-orbit interaction). The many-body self-energy, in the crystalline state corresponding to the binding energy, loses significance compared to that of an interacting electron gas owing to the lossless edge currents which actually enhance the valley splitting and adjust the energies for a 2/3/1/3 filling (or 1/0 occupation for complete separation) of both quantum levels neighbouring the Fermi energy.

Transverse magnetoconductivity of quasi-two-dimensional semiconductor layers in the presence of phonon scattering.

The transverse magnetoconductivity of quasi-two-dimensional layers, such as those occurring in heterojunctions of superlattices and in metal-oxide-semiconductor field-effect transistor inversion layers, is computed using the formalism of linear response theory, developed previously. The electron gas is considered to be quasi-two-dimensional, while the phonons are considered to be three dimensional. Explicit results for magnetophonon resonances are obtained for various kinds of phonon scattering (acoustic, nonpolar optical, polar optical, and piezoelectric). Collision broadening of the Landau levels is included to avoid divergences.

Electric field-induced quasi-elastic inter-landau level scattering in the space-charge-limited magnetoconductivity of n +n −n + InP structures

Magnetophonon resonance and quasi-elastic inter-Landau level scattering (QUILLS) are investigated in the transverse magnetoconductivity, σ xx, of short (1 μm) n +n −n + InP structures under conditions of space-charge-limited conduction. The damping of the magnetophonon resonance amplitudes at large E is also investigated. The electric field dependence of the QUILLS process in InP is in excellent agreement with a model that we have previously proposed to describe the process in n +nn + GaAs layers. The observed form of the space-charge-limited current-voltage characteristics (I ∝ V 2) is discussed in terms of the behaviour of electrons in short, lightly doped semiconductor layers under the influence of large, mutually perpendicular electric and magnetic fields.

Resonant magnetoresistance measurements in short (∼ 1 μm) n+nn+ GaAs structures: Investigation of the electric field dependence of quasi-elastic inter-Landau level scattering processes

The contribution of quasi-elastic inter-Landau level scattering (QUILLS) by acoustic phonons to the high field transverse magnetoconductivity σ xx of short (∼ 1 μm) n + nn + GaAs devices is investigated experimentally and theoretically. It is shown that the very strong electric field dependence of QUILLS can be understood in terms of the inter-Landau level acoustic phonon scattering matrix.

Shubnikov-de haas effect in kinetic approximation

The transverse and longitudinal magneto-conductivity of an electron-impurity system is calculated using a kinetic approximation based on the Mori formalism. The numerical results agree qualitatively with measurements on narrow gap semiconductors.

Linear response theory revisited. IV. Applications

The one-body linear response expressions (diagonal and nondiagonal) for the dc electrical conductivity, obtained in a previous paper, are applied to specific situations. In the case of ‘‘no collisional current’’ we evaluate the relaxation times which enter an expression (diagonal) for the longitudinal magnetoconductivity; in the case of ‘‘collisional current’’ another expression (diagonal) for the transverse magnetoconductivity is evaluated. The calculations are carried out in the framework of electron–phonon interaction in crystalline materials; various kinds of phonons are considered. The formula for ‘‘collisional current’’ is also used for an analytic evaluation of the phonon assisted hopping conductivity in crystalline and amorphous materials. The results are in harmony with those of the literature or are new. Further, the nondiagonal expression leads to a result for the oscillatory Hall effect, which, in contrast with previous results, is independent of the interaction (e.g., interaction with impurities).

Anomalous magnetoresistivity of bismuth with dilute ionized impurities in quantizing magnetic field

Transverse magnetoconductivity tensor components have been measured in dilute Bi:Sn and Bi:Te alloys up to magnetic field/temperature = 13T / 0.5 K and compared with those of high purity sample. As was expected, perfect phase inversion and enhancement of the quantum oscillation of the magnetoresistivity component were observed. It was also found that peaks of Hall resistivity tensor component due to the hole Fermi surface in the highest magnetic field region revealed dispersion-type line shape in Bi:Sn alloy in contrast to those in Bi:Te alloy or in pure Bi, which may be ascribed to the difference between the screening of anions and that of cations by electrons and holes in these semimetals.

Theory of the transverse static magnetoconductivity in a two-dimensional electron-phonon system

The theory of the transverse static magnetoconductivity (σ xx) in a two-dimensional system under the simultaneous influence of electron-phonon and electron-impurity interactions is presented. The memory function technique is employed to obtain explicit expression for σ xx under conditions appropriate for typical Shubnikov-deHaas measurements. It is shown that σ xx involves two different effective masses and scattering times, of which one is the scattering time in the absence of the magnetic field. In addition, the Landau level width appears in σ xx, thus providing an experimental means for extracting the same from a study of the background conductivity.

Quantum theory of magnetotransport in two-dimensional systems with electron-impurity, electron-phonon and electron-electron interactions

The theory of the transverse static magnetoconductivity ( σ xx ) in a two-dimensional system under the simultaneous influence of electron-impurity, electron-phonon and electron-electron interactions is presented. An explicit expressions for σ xx under conditions appropriate for typical Shubnikov-De Haas measurements is obtained and the renormalized masses and scattering times arc clearly identified.

On transverse magnetoconductivity in strict born approximation

Various assumptions and approximations used in the quantum theory of magnetotransport in the strict Born approximation are critically discussed. It is concluded that the motion about the center of cyclotron orbit with proper damping of the Breit-Wigner type gives correct form of magnetoconducctivity which explains the observed behaviour of magnetoresistance.

On the theory of the transverse dynamic magneto-conductivity in two-dimensional electron-impurity systems

The dynamic magneto-conductivity of a two-dimensional electron-impurity system is calculated in the lowest-order correlation approximation. Explicit results are obtained concerning the dependence of the cyclotron resonance linewidth and the static transverse magnetoresistance on the magnetic field and the effective range of the electron-impurity potential in the quantum limit.