The line shape of the Shubnikov-de Haas (SdH) oscillation has been analyzed in detail for a GaAs/AlGaAs two-dimensional electron gas. The line shape, or equivalently the behavior of the Fourier components, of the experimentally observed SdH oscillation is well reproduced by the sinusoidal density of states at the Fermi energy that oscillates with a magnetic field in a saw-tooth shape to keep the electron density constant. This suggests that the broadening of each Landau level by disorder is better described by a Gaussian than by a Lorentzian.
Recently discovered modulations of Shubnikov-de Haas oscillations in microwave-irradiated two-dimensional electron systems are shown to arise from electron heating induced by the radiation. The electron temperature, obtained by balancing the energy absorption from the microwave field and the energy dissipation to the lattice through realistic electron-phonon couplings, exhibits resonance. The modulation of the Shubnikov de Haas oscillation and the suppression of magnetoresistance are demonstrated together with microwave-induced resistance oscillation, in agreement with experimental findings.
The widely reported magnetoresistance oscillations in LaAlO3/SrTiO3 heterostructures have invariably been attributed to the Shubnikov-de Haas (SdH) effect, despite a pronounced inconsistency with low-field Hall resistance measurements. Here we report SdH-like resistance oscillations in quasi-1D electron waveguides created at the LaAlO3/SrTiO3 interface by conductive atomic force microscopy lithography. These oscillations can be directly attributed to magnetic depopulation of magnetoelectric subbands. Our results suggest that the SdH oscillations in 2D SrTiO3-based systems may originate from na…
We report measurements of the surface Shubnikov de Haas oscillations (SdH) on crystals of the topological insulator Bi$_2$Te$_2$Se. In crystals with large bulk resistivity ($\sim$4 $Ω$cm at 4 K), we observe $\sim$15 surface SdH oscillations (to the $n$ = 1 Landau Level) in magnetic fields $B$ up to 45 Tesla. Extrapolating to the limit $1/B\to 0$, we confirm the $\frac12$-shift expected from a Dirac spectrum. The results are consistent with a very small surface Lande $g$-factor.
We report on quantum magneto-oscillations in an ultra-high mobility GaAs/AlGaAs quantum well at very high tilt angles. Unlike previous studies, we find that the spin and cyclotron splittings become equal over a continuous range of angles, but only near certain, angle-dependent filling factors. At high enough tilt angles, Shubnikov-de Haas oscillations reveal a prominent beating pattern, indicative of consecutive level crossings, all occurring at the same angle. We explain these unusual observations by an in-plane field-induced increase of the carrier mass, which leads to accelerated, filling f…
We report on magnetotransport measurements in a two-dimensional (2D) electron gas subject to subterahertz radiation in the regime where Shubnikov-de Haas oscillations (SdHO) and microwave-induced resistance oscillations (MIRO) coexist over a wide magnetic field range, spanning several harmonics of the cyclotron resonance. Surprisingly, we find that the SdHO amplitude is modified by the radiation in a non-trivial way owing to the oscillatory correction which has the same period and phase as MIRO. This finding challenges our current understanding of microwave photoresistance in 2D electron gas, …
The amplitude and phase of Shubnikov-de Haas oscillations have been analyzed in detail for two-dimensional electron gases subjected to a weak unidirectional periodic potential modulation. The amplitude is suppressed, accompanied by inversion of the phase, at the maximum bandwidth conditions at low magnetic fields. The suppression is gradually taken over by the enhancement with the increase of the magnetic fields. The suppression and the enhancement are attributable to the collisional and the diffusion contribution of the modulated potential to the conductivity, respectively, the former (the la…
We report polarization-resolved resonant reflection spectroscopy of a charge-tunable atomically-thin valley semiconductor hosting tightly bound excitons coupled to a dilute system of fully spin- and valley-polarized holes in the presence of a strong magnetic field. We find that exciton-hole interactions manifest themselves in hole-density dependent, Shubnikov-de Haas-like oscillations in the energy and line broadening of the excitonic resonances. These oscillations are evidenced to be precisely correlated with the occupation of Landau levels, thus demonstrating that strong interactions between…
We study transport in a smooth random magnetic field, with emphasis on composite fermions (CF) near half-filling of the Landau level. When either the amplitude of the magnetic field fluctuations or its mean value $\bar B$ is large enough, the transport is of percolating nature. While at $\bar{B}=0$ the percolation effects enhance the conductivity $σ_{xx}$, increasing $\bar B$ (which corresponds to moving away from half-filling for the CF problem) leads to a sharp falloff of $σ_{xx}$ and, consequently, to the quantum localization of CFs. We demonstrate that the localization is a crucial factor …
Shubnikov-de Haas (SdH) oscillations under a dc current bias are experimentally studied on a Hall bar sample of single layer graphene. In dc resistance, the bias current shows the common damping effect on the SdH oscillations and the effect can be well accounted for by an elevated electron temperature that is found to be linearly dependent on the current bias. In differential resistance, a novel phase inversion of the SdH oscillations has been observed with increasing dc bias, namely we observe the oscillation maxima develop into minima and vice versa. Moreover, it is found that the onset bias…
We study the magnetoresistance, δρ_{xx}(B)/ρ_0, of a high-mobility 2D electron gas in the domain of magnetic fields, B, intermediate between the weak localization and the Shubnikov-de Haas oscillations, where δρ_{xx}(B)/ρ_0 is governed by the interaction effects. Assuming short-range impurity scattering, we demonstrate that in the {\em second order} in the interaction parameter, $λ$, a {\em linear} B-dependence, δρ_{xx}(B)/ρ_0\sim λ^2ω_c/E_F with {\em temperature-independent} slope emerges in this domain of B (here ω_c and E_F are the cyclotron frequency and the Fermi energy, respectively). Un…
The Shubnikov - de Haas effect in quasi-two-dimensional compounds is studied. The conductivity is calculated from the Kubo formula. Two effects -- the field-dependent phase shift of the beats and the slow oscillations of the conductivity are explained and calculated. The results are applicable to the strongly anisotropic organic metals and other layered compounds.
Topological semimetals characterize a novel class of quantum materials hosting Dirac/Weyl fermions. The important features of topological fermions can be exhibited by quantum oscillations. Here we report the magnetoresistance and Shubnikov-de Haas (SdH) quantum oscillation of longitudinal resistance in the single crystal of topological semimetal Ta3SiTe6 with the magnetic field up to 38 T. Periodic amplitude of the oscillations reveals related information about the Fermi surface. The fast Fourier transformation spectra represent a single oscillatory frequency. The analysis of the oscillations …
Within the semiclassical approach, we calculate contributions of the Berry phase and of the Zeeman coupling of the electron moment with the magnetic field to the phase of the Shubnikov - de Haas oscillations for the surface electrons in the Bi$_2$X$_3$ family of three-dimensional topological insulators (X stands for Te or Se). We also discuss a relation of the obtained results with published experimental data on the Shubnikov-de Haas oscillations for this family of topological insulators.
The spin splitting of conduction band electrons in inversion-asymmetric InGaAs/InP quantum wells is studied by Shubnikov-de Haas measurements combining the analysis of beating patterns and coincidence measurements in doubly tilted magnetic fields. The method allows us to determine the absolute values of the Rashba and linear Dresselhaus spin-orbit interaction coefficients, their relative sign and the full Landé g-tensor. This is achieved by analyzing the anisotropy of the beat node positions with respect to both polar and azimuthal angles between the magnetic field direction and the quantum we…
The momentum dependent splitting of spin-bands in an electronic system is known as the "Rashba effect". Systems with the "Rashba effect" possess a Dirac point in momentum space. An electron in a cyclotron orbit enclosing that Dirac point in the reciprocal space gains a "Berry phase". We report here the Shubnikov-de-Haas oscillations (SdH) at the conducting interface of EuO-KTaO$_3$ (KTO). Observed SdH oscillations suggest the presence of two Fermi surfaces. For both the Fermi surfaces, we have seen the presence of a non-trivial "Berry phase" suggesting that the surfaces enclose the "Dirac poin…
The results of the longitudinal and Hall magnetoresistivity measurements in the Shubnikov - de Haas oscillation regime for the HgCdTe/HgTe/HgCdTe heterostructures with a wide (20.3 nm) HgTe quantum well are presented. An anomalous phase shift of magneto-oscillations is detected: in the region of spin-unsplit peaks the longitudinal resistivity maxima are located at even filling factor numbers in contradiction with a conventional situation in 2D systems. It is shown that the observed features are associated with the inverted nature of the spectrum in the investigated quantum well with the electr…
We provide the first observation of weak localization in high carrier density two-dimensional electron gas in AlInN/GaN heterostructures; at low temperatures and low fields the conductivity increases with increasing magnetic field. Weak localization is further confirmed by the lnT dependence of the zero-field conductivity and angle dependence of magnetoresistance. The inelastic scattering rate is linearly proportional to temperature, demonstrating that electron-electron scattering is the principal phase breaking mechanism. Shubnikov-de Haas (SdH) oscillations at high magnetic fields are also o…
We record fine oscillations of 20 to 60 mT superimposed on larger oscillations having periodicity ~ 2 T at temperatures up to 100 K and fields up to 10 T from silicon nanowires. Having confirmed that these features appear from the edge states associated with skipping orbits at nanowire edges and confined pure orbits in the interior of the nanowires we derive electron effective mass of 0.001 me to 0.006 me, carrier lifetime in the range 3 to 19 fs and carrier density that varies from 2x10^11 cm^-2 to 9x10^12 cm^-2. However, at low temperature the observed oscillation amplitude invariant of the …
We study the Landau level spectrum using a multi-band $\mathbf{k}\cdot\mathbf{p}$ theory in monolayer transition metal dichalcogenide semiconductors. We find that in a wide magnetic field range the Landau levels can be characterized by a harmonic oscillator spectrum and a linear-in-magnetic field term which describes the valley degeneracy breaking. The effect of the non-parabolicity of the band-dispersion on the Landau level spectrum is also discussed. Motivated by recent magnetotransport experiments, we use the self-consistent Born approximation and the Kubo formalism to calculate the Shubnik…
Topological insulators are ideally represented as having an insulating bulk with topologically protected, spin-textured surface states. However, it is increasingly becoming clear that these surface transport channels can be accompanied by a finite conducting bulk, as well as additional topologically trivial surface states. To investigate these parallel conduction transport channels, we studied Shubnikov-de Haas oscillations in Bi$_2$Se$_3$ thin films, in high magnetic fields up to 30 T so as to access channels with a lower mobility. We identify a clear Zeeman-split bulk contribution to the osc…
The Haldane model on a honeycomb lattice is a paradigmatic example of a system featuring quantized Hall conductivity in the absence of an external magnetic field, that is, a quantum anomalous Hall effect. Recent theoretical work predicted that the anomalous Hall conductivity of massive Dirac fermions can display Shubnikov-de Haas (SdH) oscillations, which could be observed in topological insulators and honeycomb layers with strong spin--orbit coupling. Here, we investigate the electronic transport properties of Chern insulators subject to high magnetic fields by means of accurate spectral expa…
We have studied Shubnikov-de Haas oscillations in a two-dimensional electron system in silicon at low electron densities. Near the metal-insulator transition, only "spin" minima of the resistance at Landau-level filling factors 2, 6, 10, and 14 are seen, while the "cyclotron" minima at filling factors 4, 8, and 12 disappear. A simple explanation of the observed behavior requires a giant enhancement of the spin splitting near the metal-insulator transition.
A gate-defined quantum dot in bilayer graphene is utilized as a sensitive electrometer for probing the charge density of its environment. Under the influence of a perpendicular magnetic field, the charge carrier density of the channel region next to the quantum dot oscillates due to the formation of Landau levels. This is experimentally observed as oscillations in the gate-voltage positions of the Coulomb resonances of the nearby quantum dot. From the frequency of the oscillations, we extract the charge carrier density in the channel and from the amplitude the shift of the quantum dot potentia…
Monolayer jacutingaite (Pt$_2$HgSe$_3$) has been recently identified as a candidate quantum spin Hall system with a 0.5 eV band gap, but no transport measurements have been performed so far on this material, neither in monolayer nor in the bulk. By using a dedicated high-pressure technique, we grow crystals enabling the exfoliation of 50-100 nm thick layers and the realization of devices for controlled transport experiments. Magnetoresistance measurements indicate that jacutingaite is a semimetal, exhibiting Shubnikov-de Haas (SdH) resistance oscillations with a multi-frequency spectrum. We ad…
We investigate the 2-dimensional Fermi surface of high-mobility LaAlO$_3$/SrTiO$_3$ interfaces using Shubnikov-de Haas oscillations. Our analysis of the oscillation pattern underscores the key role played by the Rashba spin-orbit interaction brought about by the breaking of inversion symmetry, as well as the dominant contribution of the heavy $d_{xz}$/$d_{yz}$ orbitals on electrical transport. We furthermore bring into light the complex evolution of the oscillations with the carrier density, which is tuned by the field effect.
We report the electron doping in the surface vicinity of KTaO_3 by inducing oxygen-vacancies via Ar^+ -irradiation. The doped electrons have high mobility (> 10^4 cm^2/Vs) at low temperatures, and exhibit Shubnikov-de Haas oscillations with both two- and three-dimensional components. A disparity of the extracted in-plane effective mass, compared to the bulk values, suggests mixing of the orbital characters. Our observations demonstrate that Ar^+ -irradiation serves as a flexible tool to study low dimensional quantum transport in 5d semiconducting oxides.
The Shubnikov - de Haas effect in quasi-two-dimensional normal metals is studied. The interlayer conductivity is calculated using the Kubo formula. The electron scattering on short-range is considered in the self-consistent Born approximation. The result obtained differs from that derived from the Boltzmann transport equation. This difference is shown to be a general feature of conductivity in magnetic field. A detailed description of the two new qualitative effects -- the field-dependent phase shift of beats and of the slow oscillations of conductivity is provided. The results obtained are ap…
Metallic Bi2Te3 crystalline sheets with the room-temperature resistivity of above 10 mΩ cm were prepared and their magnetoresistive transport was measured in a field of up to 9 Tesla. The Shubnikov de Haas oscillations were identified from the secondly-derived magnetoresistance curves. While changing the angle between the field and normal axis of the sheets, we find that the oscillation periods present a cosine dependence on the angle. This indicates a two-dimensional transport due to the surface state. The work reveals a resolvable surface contribution to the overall conduction even in a meta…
Quantum magnetic oscillations in SrTiO3/\LaAlO3 interface are observed. The evolution of their frequency and amplitude at various gate voltages and temperatures is studied. The data are consistent with the Shubnikov de-Haas theory. The Hall resistivity rho exhibits nonlinearity at low magnetic field. It is fitted assuming multiple carrier contributions. The comparison between the mobile carrier density inferred from the Hall data and the oscillation frequency suggests multiple valley and spin degeneracy. The small amplitude of the oscillations is discussed in the framework of the multiple band…
Shubnikov-de Haas (SdH) oscillations are observed in Bi2Se3 flakes with high carrier concentration and low bulk mobility. These oscillations probe the protected surface states and enable us to extract their carrier concentration, effective mass and Dingle temperature. The Fermi momentum obtained is in agreement with angle resolved photoemission spectroscopy (ARPES) measurements performed on crystals from the same batch. We study the behavior of the Berry phase as a function of magnetic field. The standard theoretical considerations fail to explain the observed behavior.
Probing Fermi-surface spin-textures via the nonlinear Shubnikov-de Haas effect
RIKEN Center for Quantum Computing（理化学研究所量子计算中心）；University of St Andrews（圣安德鲁斯大学）；University of Basel（巴塞尔大学）；King Fahd University of Petroleum and Minerals（法赫德国王石油与矿物大学）；Center for Advanced Quantum Computing, KFUPM（KFUPM先进量子计算中心）
We present a model for microwave photoconductivity in two-dimensional electron systems (2DESs) in a magnetic field at the microwave frequencies lower that the electron cyclotron frequency when the intra-Landau level (LL) transitions dominate. Using this model, we explain the effect of decrease in the 2DES dissipative conductivity (and resistivity) and smearing of its Shubnikov -- de Haas oscillations by microwave radiation observed recently \cite{1,2}. The model invokes the concept of suppression of elastic impurity scattering of electrons by the microwave electric field. We calculated the dep…
We study the magnetotransport properties of high mobility holes in monolayer and bilayer WSe$_2$, which display well defined Shubnikov-de Haas (SdH) oscillations, and quantum Hall states (QHSs) in high magnetic fields. In both mono and bilayer WSe$_2$, the SdH oscillations and the QHSs occur predominantly at even filling factors, evincing a two-fold Landau level degeneracy. The Fourier transform analysis of the SdH oscillations in bilayer WSe$_2$ reveal the presence of two subbands localized in the top or the bottom layer, as well as negative compressibility. From the temperature dependence of…
Shubnikov de Haas (SdH) oscillations and Angle Resolved PhotoEmission Spectroscopy (ARPES) are used to probe the Fermi surface of single crystals of Bi2Se3. We find that SdH and ARPES probes quantitatively agree on measurements of the effective mass and bulk band dispersion. In high carrier density samples, the two probes also agree in the exact position of the Fermi level EF, but for lower carrier density samples discrepancies emerge in the position of EF. In particular, SdH reveals a bulk three-dimensional Fermi surface for samples with carrier densities as low as 10^17cm-3. We suggest a sim…
Double-Carrier Fitting of Hall Resistance Assisted by Gate-Induced Shubnikov-de Haas Oscillations in Possible Excitonic Insulator Ta2Pd3Te5
School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Hangzhou Key Laboratory of Quantum Matter, School of Physics, Hangzhou Normal University（杭州师范大学物理学院量子物质杭州市重点实验室）
We report the magneto-transport properties of CaAl$_4$ single crystals with $C2/m$ structure at low temperature. CaAl$_4$ exhibits large unsaturated magnetoresistance $\sim$3000$\%$ at 2.5 K and 14 T. The nonlinear Hall resistivity is observed, which indicates the multi-band feature. The first-principles calculations show the electron-hole compensation and the complex Fermi surface in CaAl$_4$, to which the two-band model with over-simplified carrier mobility can't completely apply. Evident quantum oscillations have been observed with B//c and B//ab configurations, from which the nontrivial Be…
Shubnikov-de Haas (SdH) oscillations, the most well-known magneto-oscillations caused by the quantization of electron energy levels in the presence of magnetic fields in two-dimensional (2D) electron systems, can be used to determine Fermi-surface properties and directly measure the Berry phase of the 2D systems. It is usually thought that transport measurements are required to measure the SdH oscillations. Contradicting this belief, we demonstrate that the SdH oscillations can be measured in graphene systems by carrying out scanning tunneling spectroscopy (STS) measurements. The energy-moment…
Quantum wire superlattices (1D) realized by controlled dislocation slipping in quantum well superlattices (2D) (atomic saw method) have already shown magnetophonon oscillations. This effect has been used to investigate the electronic properties of such systems and prove the quantum character of the physical properties of the wires. By cooling the temperature and using pulsed magnetic field up to 35 T, we have observed both quantum Hall effect (QHE) and Shubnikov de Haas (SdH) oscillations for various configurations of the magnetic field. The effective masses deduced from the values of the fund…
We explore theoretically the magnetoresistance of Weyl semimetals in transversal magnetic fields away from charge neutrality. The analysis within the self-consistent Born approximation is done for the two different models of disorder: (i) short-range impurties and (ii) charged (Coulomb) impurities. For these models of disorder, we calculate the conductivity away from charge neutrality point as well as the Hall conductivity, and analyze the transversal magnetoresistance (TMR) and Shubnikov-de Haas oscillations for both types of disorder. We further consider a model with Weyl nodes shifted in en…
We show Shubnikov-de Haas oscillations in topological insulator (Bi$_{x}$Sb$_{1-x}$)$_{2}$Te$_{3}$ films whose carrier type is p-type (x = 0.29, 0.34) and n-type (x = 0.42). The physical properties such as the Berry phase, mobility, and the scattering time are significantly changed by tuning the Fermi-level position with the concentration x. The Landau-level fan diagram in the sample with x = 0.42 showed the $π$ Berry phase and its mobility was as high as 17,000 cm$^{2}$/V/s, whereas the others had the 2$π$ Berry phase and much lower mobility. This suggests that because the bulk band of the sa…
We analyze the behavior of the longitudinal conductivity $σ_{zz}$ in a field perpendicular to the highly conducting plane of a quasi-2D {\em multiband} metal in the case of closed system and open systems where $τ$ is fixed, $τ$ oscillates due to intra-band scattering and $τ$ oscillates due to inter-band scattering. In all but one case, we find that there are also mixing frequencies present -- however they exhibit different qualitative behaviors, as befits their different origins, and in the case of inter-band scattering in an opensystem, may in fact be absent in the dHvA oscillations of that s…
We have studied the quantum oscillations in the conductivity of metallic, p-type Bi$_2$Se$_{2.1}$Te$_{0.9}$. The dependence of the oscillations on the angle of the magnetic field with the surface as well as the Berry phase determined from the Landau level fan plot indicate that the observed oscillations arise from surface carriers with the characteristic Dirac dispersion. Several quantities characterizing the surface conduction are calculated employing the Lifshitz-Kosevich theory. The low value of the Fermi energy with respect to the Dirac point is consistent with the metallic character of th…
We study Shubnikov-de Haas oscillations in a p-type WSe$_2$ monolayer under very high magnetic field. The oscillation pattern is complex due to a large spin and valley splitting, in the non-fully-resolved Landau level regime. Our experimental data can be reproduced with a model in which the main parameter is the ratio between the Zeeman energy and the cyclotron energy. The model takes into account the Landau levels from both valleys with the same Gaussian broadening, which allows to predict the relative amplitude of the resistance oscillation originating from each valley. The Zeeman energy is …
Up to know all the experimental results concerning the integer and fractional quantum Hall effect are related to semiconductor heterostructures (and more recently with graphene). The common characteristic of all these systems is the presence of a reservoir of electrons, which, in fact, in the initial stage is the source of the electrons, providing the two-dimensional electron gas (2DES). Then, any physical realization of a 2DES is necessarily embedded in a 3D structure, which establishes the Fermi level. Hence, the 2DES appears to be an open system. In this paper we present an analytical appro…
Shubnikov-de Haas oscillations of two-dimensional electron gases in AlYN/GaN and AlScN/GaN heterostructures
Cornell University（康奈尔大学）；Fraunhofer Institute for Applied Solid State Physics IAF（弗劳恩霍夫应用固态物理研究所）；Kavli Institute at Cornell for Nanoscale Science（康奈尔纳米科学卡弗里研究所）
The "one-dimensional" coherent states are applied to describe the Shubnikov - de Haas and the de Haas-van Alphen oscillation effects in metals, semimetals, and degenerate semiconductors. The oscillatory part of the electron density of states in a magnetic field is calculated. A substantial simplification of calculations is achieved.
We present magnetotransport measurements performed on two-dimensional hole gases embedded in carbon doped p-type GaAs/AlGaAs heterostructures grown on [001] oriented substrates. A pronounced beating pattern in the Shubnikov-de Haas oscillations proves the presence of strong spin-orbit interaction in the device under study. We estimate the effective masses of spin-orbit split subbands by measuring the temperature dependence of the Shubnikov-de Haas oscillations at different hole densities. While the lighter heavy-hole effective mass is not energy dependent, the heavier heavy-hole effective mass…
We present magnetotransport experiments on high-quality InAs-AlSb quantum wells that show a perfectly clean single-period Shubnikov-de Haas oscillation down to very low magnetic fields. In contrast to theoretical expectations based on an asymmetry induced zero-field spin splitting, no beating effect is observed. The carrier density has been changed by the persistent photo conductivity effect as well as via the application of hydrostatic pressure in order to influence the electric field at the interface of the electron gas. Still no indication of spin splitting at zero magnetic field was observ…
We consider quantum lifetime derived from low-field Shubnikov-de Haas oscillations as a metric of quality of the two-dimensional electron gas in GaAs quantum wells that expresses large excitation gaps in the fractional quantum Hall states of the N=1 Landau level. Analysis indicates two salient features: 1) small density inhomogeneities dramatically impact the amplitude of Shubnikov-de Haas oscillations such that the canonical method (cf. Coleridge, Phys. Rev. B \textbf{44}, 3793) for determination of quantum lifetime substantially underestimates $τ_q$ unless density inhomogeneity is explicitly…
We have studied the effect of structural disorder on the de Haas van Alphen (dHvA) and Shubnikov de Haas (SdH) quantum oscillations measured in single-crystal and highly oriented pyrolytic graphite samples at temperatures down to 30 mK and at magnetic fields up to 14 T. The measurements were performed on different samples characterized by means of x-ray diffraction, transmission electron microscopy and atomic-force microscopy techniques. Our results reveal a correlation between the amplitude of quantum oscillations and the surface roughness.
A two-dimensional electron gas (2DEG) in SrTiO3 is created via modulation doping by interfacing undoped SrTiO3 with a wider-band-gap material, SrTi1-xZrxO3, that is doped n-type with La. All layers are grown using hybrid molecular beam epitaxy. Using magnetoresistance measurements, we show that electrons are transferred into the SrTiO3, and a 2DEG is formed. In particular, Shubnikov-de Haas oscillations are shown to depend only on the perpendicular magnetic field. Experimental Shubnikov-de Haas oscillations are compared with calculations that assume multiple occupied subbands.
It is known that the Shubnikov--de Haas oscillations can be observed in the Hall resistivity, although their amplitude is much weaker than the amplitude of the diagonal resistivity oscillations. Employing a model of two-dimensional massive Dirac fermions that exhibits anomalous Hall effect, we demonstrate that the amplitude of the Shubnikov--de Haas oscillations of the anomalous Hall conductivity is the same as that of the diagonal conductivity. We argue that the oscillations of the anomalous Hall conductivity can be observed by studying the valley Hall effect in graphene superlattices and the…
