Weiss Oscillations Research Articles

Exploring the effects of a one-dimensional periodic potential on a three-dimensional topological insulator

High mobility two-dimensional systems with superposed 1D lateral periodic potentials exhibit characteristic commensurability (Weiss) oscillations that reflect the interplay of the cyclotron radius at the Fermi level and the superlattice period. Here, we impose a one-dimensional periodic potential on strained HgTe, which is a strong 3D topological insulator. By tuning the Fermi level with top gates, the effects of the artificial potential can be studied in the bulk gap, where only Dirac surface states exist, in the conduction band, and in the valence band, where Dirac electrons and holes coexist. On the electron side, we observe clear commensurability oscillations whose period is governed by the carrier density of the top-surface Dirac electrons. Unexpectedly, weak commensurability oscillations are also observed in the valence band with a period that depends on both electron and hole density. Published by the American Physical Society 2024

Magnetotransport of thin film topological insulators in proximity with helical spin density wave

The magnetoconductivity of an ultrathin film of topological insulator in proximity with helical spin density wave is calculated. Pronounced Weiss oscillations periodic in the inverse magnetic field appear for upper and bottom surfaces. With finite Zeeman coupling and hybridization across the surfaces Weiss oscillations for the top surface are more pronounced than the bottom surface. However in the absence of Zeeman coupling both the surfaces show same magnitude of oscillations.

Band conductivity oscillations in a gate-tunable graphene superlattice

Electrons exposed to a two-dimensional (2D) periodic potential and a uniform, perpendicular magnetic field exhibit a fractal, self-similar energy spectrum known as the Hofstadter butterfly. Recently, related high-temperature quantum oscillations (Brown-Zak oscillations) were discovered in graphene moiré systems, whose origin lies in the repetitive occurrence of extended minibands/magnetic Bloch states at rational fractions of magnetic flux per unit cell giving rise to an increase in band conductivity. In this work, we report on the experimental observation of band conductivity oscillations in an electrostatically defined and gate-tunable graphene superlattice, which are governed both by the internal structure of the Hofstadter butterfly (Brown-Zak oscillations) and by a commensurability relation between the cyclotron radius of electrons and the superlattice period (Weiss oscillations). We obtain a complete, unified description of band conductivity oscillations in two-dimensional superlattices, yielding a detailed match between theory and experiment.

Magnetoconductivity in quasiperiodic graphene superlattices

The magnetoconductivity in Fibonacci graphene superlattices is investigated in a perpendicular magnetic field B. It was shown that the B-dependence of the diffusive conductivity exhibits a complicated oscillatory behavior whose characteristics cannot be associated with Weiss oscillations, but rather with Shubnikov-de Haas ones. The absense of Weiss oscillations is attributed to the existence of two incommensurate periods in Fibonacci superlattices. It was also found that the quasiperiodicity of the structure leads to a renormalization of the Fermi velocity v_{F} of graphene. Our calculations revealed that, for weak B, the dc Hall conductivity sigma _{yx} exhibits well defined and robust plateaux, where it takes the unexpected values pm 4e^{2}/hslash left( 2N+1right) , indicating that the half-integer quantum Hall effect does not occur in the considered structure. It was finally shown that sigma _{yx} displays self-similarity for magnetic fields related by tau ^{2} and tau ^{4}, where tau is the golden mean.

Acoustomagnetoelectric effect in two-dimensional materials: Geometric resonances and Weiss oscillations

We study electron transport in two-dimensional materials with parabolic and linear (graphene) dispersions of the carriers in the presence of surface acoustic waves and an external magnetic field using semiclassical Boltzmann equations approach. We observe an oscillatory behavior of both the longitudinal and Hall electric currents as functions of the surface acoustic wave frequency at a fixed magnetic field and as functions of the inverse magnetic field at a fixed frequency of the acoustic wave. We explain the former by the phenomenon of geometric resonances, while we relate the latter to the Weiss-like oscillations in the presence of the dynamic superlattice created by the acoustic wave. Thus we demonstrate the dual nature of the acoustomagnetoelectric effect in two-dimensional electron gas.

Signature of tilted Dirac cones in Weiss oscillations of8−Pmmnborophene

Polymorph of $8\ensuremath{-}Pmmn$ borophene exhibits anisotropic tilted Dirac cones. In this work, we explore the consequences of the tilted Dirac cones in magnetotransport properties of a periodically modulated borophene. We evaluate modulation-induced diffusive conductivity by using linear response theory in low temperature regime. The application of weak spatial modulation (electric, magnetic or both) gives rise to the magnetic-field-dependent nonzero oscillatory drift velocity which causes Weiss oscillation in the longitudinal conductivity at low magnetic field. The Weiss oscillation is studied in the presence of a weak spatial electric, magnetic, and both modulations individually. The tilting of the Dirac cones gives rise to an additional contribution to the Weiss oscillation in longitudinal conductivity. Moreover, it also enhances the frequency of the Weiss oscillation and modifies its amplitude too. Most remarkably, it is found that the presence of both out-of-phase electric and magnetic modulations can cause a sizable valley polarization in diffusive conductivity. The origin of valley polarization lies in the opposite tilting of the two Dirac cones at two valleys.

Angle-dependent Weiss oscillations in a nanocorrugated two-dimensional electron gas

We investigate the diffusive magnetotransport properties of a two-dimensional electron gas residing in a wrinkled nanostructure. The curved geometry of the nanostructure renders an effective inhomogeneous magnetic field which, in turn, yields Weiss oscillations. Since the relative strength of the effective inhomogeneous magnetic field can be tailored by changing the direction of the externally applied magnetic field, these Weiss oscillations exhibit a strong directional dependence. For large external magnetic fields we also find an anisotropic positive magnetoresistance.

Commensurability oscillations in a periodically modulated phosphorene

The recent experimental realization of high-quality phosphorene leads to novel electronic and optical properties with possible new device applications due to its huge direct band gap. We study the commensurability or Weiss oscillations in monolayer phosphorene in the presence of a weak perpendicular magnetic field B and a weak and periodic, electric or magnetic one-dimensional modulation. Either modulation broadens the Landau levels into bands, whose width oscillates with B, and the oscillations appear in the electrical conductivity perpendicular to the modulation taken along the direction (x) of the smaller effective mass. Compared with the oscillations of the diffusive conductivity in a two-dimensional electron gas (2DEG) for typical electron densities , the ones in phosphorene, with typical , have approximately similar height but a period significantly smaller when plotted versus while plotted versus B they occur at significantly higher fields. The Shubnikov–de Haas oscillations exhibit a similar behaviour. When the modulation is taken along the direction (y) of the larger effective mass, the oscillation period is close to that of a 2DEG. For equal modulation strengths the bandwidth due to a magnetic modulation is one order of magnitude larger than that due to an electric one and the amplitude of the oscillations in the diffusive conductivity about 50 times larger. Numerical results are presented for experimentally relevant parameters.

Valley-polarized magnetoconductivity and particle-hole symmetry breaking in a periodically modulated α−T3 lattice

We explore the transport properties of a periodically modulated $\alpha$-$\mathcal{T}_3$ lattice in the presence of a perpendicular magnetic field. The effect of the Berry phase on electrical conductivity oscillation, so-called Weiss oscillation, caused by the modulation induced non-zero drift velocity of charge carriers is investigated. Employing linear response theory within the low temperature regime, we analyze Weiss oscillation as a function of the external magnetic field for both electrically and magnetically modulated $\alpha$-$\mathcal{T}_3$ lattice numerically as well as analytically. The Berry phase makes this hexagonal lattice structure behave differently than other two-dimensional fermionic systems. It causes a significant valley polarization in magnetoconductivity. Most interestingly, the combined effect of both modulations breaks the particle-hole symmetry and causes a smooth transition from even (odd) to odd (even) filling fraction corresponding to the density of states peaks by means of the Berry phase.

Weiss oscillations and particle-hole symmetry at the half-filled Landau level

Particle-hole symmetry in the lowest Landau level of the two-dimensional electron gas requires the electrical Hall conductivity to equal $\pm e^2/2h$ at half-filling. We study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half-filling in the presence of an applied periodic one-dimensional electrostatic potential using the Dirac composite fermion theory proposed by Son. At fixed electron density, the oscillation minima are asymmetrically biased towards higher magnetic fields, while at fixed magnetic field, the oscillations occur symmetrically as the electron density is varied about half-filling. We find an approximate "sum rule" obeyed for all pairs of oscillation minima that can be tested in experiment. The locations of the magnetoresistance oscillation minima for the composite fermion theory of Halperin, Lee, and Read (HLR) and its particle-hole conjugate agree exactly. Within the current experimental resolution, the locations of the oscillation minima produced by the Dirac composite fermion coincide with those of HLR. These results may indicate that all three composite fermion theories describe the same long wavelength physics.

Strain induced novel quantum magnetotransport properties of topological insulators

Recent theoretical and experimental researches have revealed that the strained bulk HgTe can be regarded as a three-dimensional topological insulator (TI). Motivated by this, we explore the strain effects on the transport properties of the HgTe surface states, which are modulated by a weak 1D in-plane electrostatic periodic potential in the presence of a perpendicular magnetic field. We analytically derive the zero frequency (dc) diffusion conductivity for the case of quasielastic scattering in the Kubo formalism, and find that, in strong magnetic field regime, the Shubnikov–de Haas oscillations are superimposed on top of the Weiss oscillations due to the electric modulation for null and finite strain. Furthermore, the strain is shown to remove the degeneracy in inversion symmetric Dirac cones on the top and bottom surfaces. This accordingly gives rise to the splitting and mixture of Landau levels, and the asymmetric spectrum of the dc conductivity. These phenomena, not known in a conventional 2D electron gas and even in a strainless TI and graphene, are a consequence of the anomalous spectrum of surface states in a fully stained TI. These results should be valuable for electronic and spintronic applications of TIs, and thus we fully expect to see them in the further experiment.

The coupled electromagnetic field effects on quantum transport in an electrically modulated graphene

Recent experiments have revealed that the periodic graphene ripples can cause a periodic potential. Motivated by this, we have explored the electromagnetic field effects on the transport of graphene subjected to an electric periodic potential. Comparing with recently obtained results for magnetically modulated graphene, we also find an abrupt disappearance of oscillations in the magnetoconductivity at γe=1, and in a strong magnetic field, the Shubnikov–de Haas oscillations on it are superimposed on the Weiss oscillations. However, these oscillations with the electric and magnetic modulations have a π phase shift. Our results should be valuable for electronic applications of graphene.

Mechanical strain induced valley-dependent quantum magnetotransport of Dirac particles in graphene

We have explored the mechanical strain effects on the magnetotransport in graphene with a 1D electrostatic periodic potential in the presence of a perpendicular magnetic field. We find that, in a strong magnetic field regime, the conductivity exhibits a superposition of the Shubnikov–de Haas and Weiss oscillations in each valley due to the electrical modulation. Especially, the strain removes the valley degeneracy of Landau levels in inversion symmetric Dirac cones. Accordingly, this causes the valley-dependence of the conductivity. These phenomena, absent in a freestanding graphene, are a consequence of the anomalous spectrum of carriers in a fully stained graphene.

Fourier transform analysis of irradiated Weiss oscillations

We present a theoretical approach to study the effect of microwave radiation on the magnetoresistance of a one-dimensional superlattice. In our proposal the magnetoresistance of a unidirectional spatial periodic potential (superlattice), is modulated by microwave radiation due to an interference effect between both space- and time-dependent potentials. The final magnetoresistance will mainly depend on the spatial period of the superlattice and the radiation frequency. We consider an approach to study these effects based on the fast Fourier transform of the obtained magnetoresistance profiles in function of the inverse of the magnetic field. Based on this theory we propose the design of a novel radiation sensor for the terahertz band.

Influence of electrostatic field on the Weiss oscillations in graphene

Abstract Recent theoretical works have predicated the appearance of Weiss oscillations in the magnetoconductivity with a one-dimensional periodic electrical or magnetic modulation in graphene. This paper further explores the electrostatic field effect on the Weiss oscillations in the presence of crossed uniform in-plane electric field and perpendicular magnetic field that is weakly and periodically modulated along one direction. We find that the oscillation amplitude (OA) of Weiss oscillations and the value of conductivity are both shown to increase as the electric field E increases for a given magnetic field B. More interestingly, the electric field leads to an abrupt disappearance of the Weiss oscillations, when the value of electric to magnetic field ratio approaches a threshold value, i.e., γ e = E υ F B = 1 . These phenomena, not known in the conventional 2D electron gas, are a consequence of the anomalous spectrum of electron in graphene.

Beating pattern in quantum magnetotransport coefficients of spin–orbit coupled Dirac fermions in gated silicene

We report a theoretical study of magnetotransport coefficients of spin–orbit coupled gated silicene in the presence and absence of spatial periodic modulation. The combined effect of spin–orbit coupling and perpendicular electric field manifests through the formation of a regular beating pattern in Weiss and SdH oscillations. Analytical results, in addition to the numerical results, of the beating pattern formation are provided. The analytical results yield a beating condition which will be useful to determine the spin–orbit coupling constant by simply counting the number of oscillation between any two successive nodes. Moreover, the numerical results of modulation effect on collisional and Hall conductivities are presented.

Spin- and valley-dependent commensurability oscillations and electric-field-induced quantum Hall plateaux in periodically modulated silicene

We study the commensurability oscillations in silicene subject to a perpendicular electric field Ez, a weak magnetic field B, and a weak periodic potential V=V0cos(Cy),C=2π/a0 with a0 its period. The field Ez and/or the modulation lift the spin degeneracy of the Landau levels and lead to spin and valley resolved Weiss oscillations. The spin resolution is maximal when the field Ez is replaced by a periodic one Ez=E0cos(Dy),D=2π/b0, while the valley one is maximal for b0 = a0. In certain ranges of B values, the current is fully spin or valley polarized. Additional quantum Hall conductivity plateaux arise due to spin and valley intra-Landau-level transitions.

Transport properties of a 2DEG in the presence of tilted magnetic field: the influence of a 1D modulation

The effect of 1D periodic modulation on the transport and thermodynamic properties of a non-interacting two-dimensional electron gas (2DEG) is investigated. The Hamiltonian used also includes a tilted magnetic field, Rashba, and Dresselhauss spin-orbit interactions. The 1D periodic modulation introduces non-quantized regions on Hall conductivity and a non-zero diffusive conductivity. A method to estimate the modulation periodicity is given using the periodicity of Weiss oscillations on the diffusive conductivity.

Magnetotransport properties of a magnetically modulated two-dimensional electron gas with the spin–orbit interaction

We study the electrical transport properties of a two-dimensional electron gas (2DEG) with the Rashba spin–orbit interaction in the presence of a constant perpendicular magnetic field which is weakly modulated by , where B1 ≪ B0 and q = 2π/a with a the modulation period. We obtain the analytical expressions of the diffusive conductivities for spin-up and spin-down electrons. The conductivities for spin-up and spin-down electrons oscillate with different frequencies and produce beating patterns in the amplitude of the Weiss and Shubnikov–de Haas oscillations. We show that the Rashba strength can be determined by analyzing the beating pattern in the Weiss oscillation. We find a simple equation which determines the Rashba spin–orbit interaction strength if the number of Weiss oscillations between any two successive nodes is known from the experiment. We compare our results with the electrically modulated 2DEG with the Rashba interaction. For completeness, we also study the beating pattern formation in the collisional and the Hall conductivities.

The Landau band effects in the quantum magnetic oscillations and the deviations from the quasiclassical Lifshitz–Kosevich theory in quasi-two-dimensional conductors

The quantum magnetic oscillations (QMO) in the layered and quasi-two-dimensional (2D) conductors deviate from the quasiclassical Lifshitz–Kosevich (LK) theory developed for 3D conventional metals. We discuss deviations related to the broadening of the Landau levels into Landau bands by various mechanisms (layer-stacking, magnetic breakdown, incoherence, disorder, localization etc.). Each mechanism yields a specific factor modulating the QMO amplitudes depending on the density of states and electron velocities within the Landau bands. In contrast to the LK theory, these factors differ for the thermodynamic (de Haas–van Alphen (dHvA)) and kinetic (Shubnikov–de Haas (SdH)) oscillations. We calculated the magnetic breakdown damping factors for the SdH and dHvA oscillations in the 2D conductors and analyzed their difference as well as the analogy between the bandwidth and Weiss oscillations. In case of an isotropic 3D metals the kinetic factors become proportional to the thermodynamic ones as is assumed in the LK theory.