We report on realization of 10 quantum Hall devices in series fabricated using epitaxial graphene on silicon carbide. Precision measurements with a resistance bridge indicates that the quantized Hall resistance across an array at filling factor 2 is equivalent to 5 h/e^2 within the measurement uncertainty of approximately 4 10-8. A quantum-Hall phase diagram for the array shows that a metrological quantization of 5 h/e^2 can be achieved at the magnetic field of 6 T and temperature of 4 K. This experiment demonstrates the possibility of timely unchangeable resistance reference in various ranges in relaxed experimental conditions.
An experimental study of the high mobility GaAs/AlGaAs system at large-$ν$ indicates several distinct phase relations between the oscillatory diagonal- and Hall- resistances, and suggests a new class of integral quantum Hall effect, which is characterized by "anti-phase" Hall- and diagonal- resistance oscillations.
We constructed a Hall resistance formula for the fractional quantum Hall effect by analyzing the experimental data reported in [J. P. Eisenstein and H. L. Stormer, {Science} {\bf 248}, 1510 (1990)]. The formula is given as a function of magnetic induction, chemical potential and temperature. The Hall resistance function contains a single-electron energy spectrum, which has phenomenological perturbation terms with three tunable parameters. The formula yields 12 plateaus that are consistent with the experiment. The perturbations can be interpreted as precession or nutation of a Landau orbital in…
Precision quantum Hall resistance (QHR) measurements were performed on large-area epitaxial graphene device at low magnetic fields (B = 2 T - 8 T) at temperature T = 1.5 K. Hall resistance was measured using Cryogenic Current Comparator resistance bridge with high biasing current Isd = 40 micro ampere. The results showed that at B = 8 T the relative deviation of Hall resistance from the expected quantized value h/2e2 is within experimental uncertainty of 3.5 parts in 108 and remained below 0.35 parts per million (ppm) down to B = 3 T.
We study the four-terminal resistance fluctuations of mesoscopic samples near the transition between the $ν=2$ and the $ν=1$ quantum Hall states. We observe near-perfect correlations between the fluctuations of the longitudinal and Hall components of the resistance. These correlated fluctuations appear in a magnetic-field range for which the two-terminal resistance of the samples is quantized. We discuss these findings in light of edge-state transport models of the quantum Hall effect. We also show that our results lead to an ambiguity in the determination of the width of quantum Hall transiti…
We examine the radiation induced modification of the Hall effect in high mobility GaAs/AlGaAs devices that exhibit vanishing resistance under microwave excitation. The modification in the Hall effect upon irradiation is characterized by (a) a small reduction in the slope of the Hall resistance curve with respect to the dark value, (b) a periodic reduction in the magnitude of the Hall resistance, $R_{xy}$, that correlates with an increase in the diagonal resistance, $R_{xx}$, and (c) a Hall resistance correction that disappears as the diagonal resistance vanishes.
The longitudinal and Hall resistances have recently been measured for quantum Hall bilayers at total filling $ν=1$ in the superfluid state with interlayer pairing, both for currents flowing parallel to one another and for "counterflowing" currents in the two layers. Here I examine the contribution to these resistances from the motion of unpaired vortices in these systems, developing some possible explanations of various qualitative features of these data.
General thermodynamical arguments are used to relate the Hall current to the part of the magnetic moment originated in "macroscopic current loops". The Hall resistance is found to depend only on the electron properties in the vicinity of the Fermi energy, which is the essential advantage of the presented treatment. The obtained relation is analyzed by using Landauer-Buttiker-like view to the electron transport. As one of the possible application the Hall resistance of the periodically modulated two-dimensional electron system in strong magnetic fields is briefly discussed.
It is theoretically possible to combine several Hall bars in arrays to define new quantum standards with perfectly quantized resistance values. We have thus, for the first time, developed and fabricated novel Quantum Hall Array Resistance Standards (QHARS) made of a large number N (N=100, 50) of Hall bars placed in parallel using a triple connections technique. The Hall resistance of these quantum standards is found to be very well quantized. On the i=2 Hall plateau, the resistance of specific good arrays stays equal to RK/2N within 5 parts in 10^9 for supplying currents up to 2 mA at a 1.3 K …
We demonstrate a device concept to fabricate resistance standards made of quantum Hall series arrays by using p-type and n-type graphene. The ambipolar nature of graphene allows fabricating series quantum Hall resistors without complex multi-layer metal interconnect technology, which is required when using conventional GaAs two-dimensional electron systems. As a prerequisite for a precise resistance standard we confirm the vanishing of longitudinal resistance across a p-n junction for metrological relevant current levels in the range of a few \muA.
The influence of microwave irradiation on dissipative and Hall resistance in high-quality bilayer electron systems is investigated experimentally. We observe a deviation from odd symmetry under magnetic field reversal in the microwave-induced Hall resistance $ΔR_{xy}$ whereas the dissipative resistance $ΔR_{xx}$ obeys even symmetry. Studies of $ΔR_{xy}$ as a function of the microwave electric field and polarization exhibit a strong and non-trivial power and polarization dependence. The obtained results are discussed in connection to existing theoretical models of microwave-induced photoconduct…
The symmetry properties of the resistance of mesoscopic samples in the quantum Hall regime are investigated. In addition to the reciprocity relation, our samples obey new symmetries, that relate resistances measured with different contact configurations. Different kinds of symmetries are identified, depending on whether the magnetic field value is such that the system is above, or below, a quantum Hall transition. Related symmetries have recently been reported for macroscopic samples in the quantum Hall regime by Ponomarenko {\it et al.} (Solid State Commun. {\bf 130}, 705 (2004)), and Karmaka…
Magnetic transitions in AlAs two-dimensional electrons give rise to sharp resistance spikes within the quantum Hall effect. Such spikes are likely caused by carrier scattering at magnetic domain walls below the Curie temperature. We report a critical behavior in the temperature dependence of the spike width and amplitude, from which we deduce the Curie temperature of the quantum Hall ferromagnet. Our data also reveal that the Curie temperature increases monotonically with carrier density.
We present precision measurements of the fractional quantized Hall effect where the quantized resistance $R^{[1/3]}$ in the fractional quantum Hall state at filling factor 1/3 was compared with a quantized resistance $R^{[2]}$, represented by an integer quantum Hall state at filling factor 2. A cryogenic current comparator bridge capable of currents down to the nanoampere range was used to directly compare two resistance values of two GaAs-based devices located in two cryostats. A value of $1 - (5.3 \pm 6.3) 10^{-8}$ (95% confidence level) was obtained for the ratio $(R^{[1/3]}/6R^{[2]})$. Thi…
We report the experimental results from a dark study and a photo-excited study of the high mobility GaAs/AlGaAs system at large filling factors, $ν$. At large-$ν$, the dark study indicates several distinct phase relations ("Type-1", "Type-2", and "Type-3") between the oscillatory diagonal- and Hall- resistances, as the canonical Integral Quantum Hall Effect (IQHE) is manifested in the "Type-1" case of approximately orthogonal diagonal- and Hall resistance- oscillations. Surprisingly, the investigation indicates quantum Hall plateaus also in the "Type-3" case characterized by approximately "ant…
We present an experimental study of mesoscopic, two-dimensional electronic systems at high magnetic fields. Our samples, prepared from a low-mobility InGaAs/InAlAs wafer, exhibit reproducible, sample specific, resistance fluctuations. Focusing on the lowest Landau level we find that, while the diagonal resistivity displays strong fluctuations, the Hall resistivity is free of fluctuations and remains quantized at its $ν=1$ value, $h/e^{2}$. This is true also in the insulating phase that terminates the quantum Hall series. These results extend the validity of the semicircle law of conductivity i…
A nonlinear single-particle model is introduced, which captures the characteristic of systems in the quantum Hall regime. The model entails the magnetic Shrödinger equation with spatially variable magnetic flux density. The distribution of flux is prescribed via the postulates of the mesoscopic mechanics (MeM) introduced in my previous articles [cf. J. Phys. Chem. Solids, 65 (2004), 1507-1515; J. Geom. Phys., Vol. 55/1 (2005), 1-18]. The model is found to imply exact integer and fractional quantization of the Hall conductance. In fact, Hall resistance is found to be $R_H = \frac{h}{2e^2}\frac{…
The influence of dephasing on the quantum spin Hall effect (QSHE) is studied. In the absence of dephasing, the longitudinal resistance in a QSHE system exhibits the quantum plateaus. We find that these quantum plateaus are robust against the normal dephasing but fragile with the spin dephasing. Thus, these quantum plateaus only survive in mesoscopic samples. Moreover, the longitudinal resistance increases linearly with the sample length but is insensitive to the sample width. These characters are in excellent agreement with the recent experimental results [science {\bf 318}, 766 (2007)]. In ad…
Phase randomizing processes in mesoscopic systems can be described in a phenomenological way within the Landauer-Büttiker formalism by attaching extra voltage probes to the sample. In this paper, it is shown that a perturbation treatment of this idea allows for the incorporation of such effects without the need of giving up the efficiency of recursive techniques commonly used for calculating the transmission coefficients. The technique is applied to a 4-probe ring, where a Hall effect can be observed that originates from quantum interference rather than a Lorentz force acting on the electrons.…
In some recent experiments [A. J. Bestwick, et. al., Phys. Rev. Lett. 114, 187201 (2015), Cui-Zu Chang, et. al., Nat. Materials. 14, 473-477 (2015)] it has been shown that in observations of the quantum anomalous Hall (QAH) effect the longitudinal resistance $R_L$ increases as temperature $T$ increases, while Hall resistance $R_H$ loses its quantization with increase in $T$. This behavior was explained due to increased thermal fluctuations as $T$ increases. We show that similar effects arise in QAH samples with quasi-helical edge modes as disorder increases in presence of inelastic scattering …
The longitudinal resistances of a six-terminal graphene p-n junction under a perpendicular magnetic field are investigated. Because of the chirality of the Hall edge states, the longitudinal resistances on top and bottom edges of the graphene ribbon are not equal. In the presence of suitable disorder, the top-edge and bottom-edge resistances well show the plateau structures in the both unipolar and bipolar regimes and the plateau values are determined by the Landau filling factors only. These plateau structures are in excellent agreement with the recent experiment. For the unipolar junction, t…
Resistance fluctuation phenomenon in antidot lattices in the quantum Hall regime are studied. Magnetoresistance of finite antidot array systems in the quantum Hall plateau transition regime exhibits two types of oscillatory effect. One is the aperiodic resistance fluctuations (RFs) and the other is the Aharonov-Bohm (AB)-type oscillations. Their dependences on the magnetic field and the gate voltage are quite distinct. While the aperiodic RFs are attributed to the complex evolution of the conducting network of compressible channels, the AB-type oscillations are interpreted in terms of edge sta…
At total Landau level filling factor $ν_{tot}=1$ a double layer two-dimensional electron system with small interlayer separation supports a collective state possessing spontaneous interlayer phase coherence. This state exhibits the quantized Hall effect when equal electrical currents flow in parallel through the two layers. In contrast, if the currents in the two layers are equal, but oppositely directed, both the longitudinal and Hall resistances of each layer vanish in the low temperature limit. This finding supports the prediction that the ground state at $ν_{tot}=1$ is an excitonic superfl…
The magneto resistance of a narrow single quantum well is spectacularly different from the usual behavior. At filling factors 2/3 and 3/5 we observe large and sharp maxima in the longitudinal resistance instead of the expected minima. The peak value of the resistance exceeds those of the surrounding magnetic field regions by a factor of up to three. The formation of the maxima takes place on very large time scales which suggests a close relation with nuclear spins. We discuss the properties of the observed maxima due to a formation of domains of different electronic states.
We study a $ν=1$ topological system with one twisting edge-state band and one normal edge-state band. For the twisting edge-state band, Fermi energy goes through the band three times, thus, having three edge states on one side of the sample; while the normal edge band contributes only one edge state on the other side of the sample. In such a system, we show that it consists of both topologically protected and unprotected edge states, and as a consequence, its Hall resistance depends on the location where the Hall measurement is done even for a translationally invariant system. This unique prop…
We demonstrate quantum Hall resistance measurements with metrological accuracy in a small cryogen-free system operating at a temperature of around 3.8K and magnetic fields below 5T. Operating this system requires little experimental knowledge or laboratory infrastructure, thereby greatly advancing the proliferation of primary quantum standards for precision electrical metrology. This significant advance in technology has come about as a result of the unique properties of epitaxial graphene on SiC.
We have studied the effect of an in-plane magnetic field on Hall field-induced resistance oscillations in high mobility two-dimensional electron systems. We have found that the oscillation frequency depends only on the perpendicular component of the magnetic field but the oscillation amplitude decays exponentially with an in-plane component. While these findings cannot be accounted for by existing theories of nonlinear transport, our analysis suggests that the decay can be explained by an in-plane magnetic field-induced modification of the quantum scattering rate.
We explain the recent observation of resistance spikes and hysteretic transport properties in Ising quantum Hall ferromagnets in terms of the unique physics of their domain walls. Self-consistent RPA/Hartree-Fock theory is applied to microscopically determine properties of the ground state and domain-wall excitations. In these systems domain wall loops support one-dimensional electron systems with an effective mass comparable to the bare electron mass and may carry charge. Our theory is able to account quantitatively for the experimental Ising critical temperature and to explain characteristic…
We show that quantum resistance standards made of transferred graphene reach the uncertainty of semiconductor devices, the current reference system in metrology. A large graphene device (150 \times 30 \mum2), exfoliated and transferred onto GaAs, revealed a quantization with a precision of (-5.1 \pm 6.3) \times 10-9 accompanied by a vanishing longitudinal resistance at current levels exceeding 10 \muA. While such performance had previously only been achieved with epitaxially grown graphene, our experiments demonstrate that transfer steps, inevitable for exfoliated graphene or graphene grown by…
In view of the progress achieved in the field of the ac quantum Hall effect, the Working Group of the Comite Consultatif d'Electricite et Magnetisme (CCEM) on the AC Quantum Hall Effect asked the authors of this paper to write a compendium which integrates their experiences with ac measurements of the quantum Hall resistance. In addition to the important early work performed at the Bureau International des Poids et Mesures and the National Physical Laboratory, UK, further experience has been gained during a collaboration of the authors' institutes NRC, METAS, and PTB, and excellent agreement b…
We present a systematical experimental investigation of an unusual transport phenomenon observed in two dimensional electron gases in Si/SiGe heterostructures under integer quantum Hall effect (IQHE) conditions. This phenomenon emerges under specific experimental conditions and in different material systems. It is commonly referred to as Hall resistance overshoot, however, lacks a consistent explanation so far. Based on our experimental findings we are able to develop a model that accounts for all of our observations in the framework of a screening theory for the IQHE. Within this model the or…
We use spin-density-functional theory to study recently reported hysteretic magnetoresistance ρ_{xx} spikes in Mn-based 2D electron gases [Jaroszyński et al. Phys. Rev. Lett. (2002)]. We find hysteresis loops in our calculated Landau fan diagrams and total energies signaling quantum-Hall-ferromagnet phase transitions. Spin-dependent exchange-correlation effects are crucial to stabilize the relevant magnetic phases arising from distinct symmetry-broken excited- and ground-state solutions of the Kohn-Sham equations. Besides hysteretic spikes in ρ_{xx}, we predict hysteretic dips in the Hall resi…
We describe transport properties of two-dimensional arrays of low capacitance tunnel junctions, such as the current voltage characteristic and its dependence on external magnetic field and temperature. We discuss several experiments in which the small capacitance of the junctions plays an important role. In arrays where the junctions have a relatively large charging energy, (i.e. when they have a low capacitance) and a high normal state resistance, the low bias resistance increases with decreasing temperature and eventually at very low temperature the array becomes insulating even though the e…
In this work we provide a systematic explanation to the unusual non-monotonic behavior of the Hall resistance observed at two-dimensional electron systems. We use a semi-analytical model based on the interaction theory of the integer quantized Hall effect to investigate the existence of the anomalous, \emph{i.e} overshoot, Hall resistance $R_{H}$. The observation of the overshoot resistance at low magnetic field edge of the plateaus is elucidated by means of overlapping evanescent incompressible strips, formed due to strong magnetic fields and interactions. Utilizing a self-consistent numerica…
Recent experiments reporting unexpectedly large spin Hall effect (SHE) in graphene decorated with adatoms have raised a fierce controversy. We apply numerically exact Kubo and Landauer- Buttiker formulas to realistic models of gold-decorated disordered graphene (including adatom clustering) to obtain the spin Hall conductivity and spin Hall angle, as well as the nonlocal resistance as a quantity accessible to experiments. Large spin Hall angles of 0.1 are obtained at zero-temperature, but their dependence on adatom clustering differs from the predictions of semiclassical transport theories. F…
In contrast to the case of ordinary quantum Hall effect, the resistance of ballistic helical edge channels in typical quantum spin-Hall experiments is non-vanishing, additive and poorly quantized. Here we present a simple argument connecting this qualitative difference with a spin relaxation in the current/voltage leads in an experimentally relevant multi-terminal bar geometry. Both the finite lead resistance and the spin relaxation contribute to a non-vanishing four-terminal edge resistance, explaining poor quantization quality. We show that corrections to the four-terminal and two-terminal r…
We considered the nonequlibrium spin dipoles induced around spin independent elastic scatterers by the intrinsic spin-Hall effect associated with the Rashba spin-orbit coupling. The normal to 2DEG spin polarization has been calculated in the diffusion range around the scatterer. We found that although around each impurity this polarization is finite, the corresponding macroscopic spin density, obtained via averaging of individual spin dipole distributions over impurity positions is zero in the bulk. At the same time, the spin density is finite near the boundary of 2DEG, except for a special ca…
In this work we report experiments on defined by shallow etching narrow Hall bars. The magneto-transport properties of intermediate mobility two-dimensional electron systems are investigated and analyzed within the screening theory of the integer quantized Hall effect. We observe a non-monotonic increase of Hall resistance at the low magnetic field ends of the quantized plateaus, known as the overshoot effect. Unexpectedly, for Hall bars that are defined by shallow chemical etching the overshoot effect becomes more pronounced at elevated temperatures. We observe the overshoot effect at odd and…
We show how a dc current can be generated in a Hall bar without applying a bias voltage. The Hall resistance $R_H$ that corresponds to this pumped current is quantized, just as in the usual integer quantum Hall effect (IQHE). In contrast with the IQHE, however, the longitudinal resistance $R_{xx}$ does not vanish on the plateaus, but equals the Hall resistance. We propose an experimental geometry to measure the pumped current and verify the predicted behavior of $R_H$ and $R_{xx}$.
The resistance due to the convergence from bulk to a constriction, for example, a nanopore, is a mainstay of transport phenomena. In classical electrical conduction, Maxwell, and later Hall for ionic conduction, predicted this access or convergence resistance to be independent of the bulk dimensions and inversely dependent on the pore radius, $a$, for a perfectly circular pore. More generally, though, this resistance is contextual, it depends on the presence of functional groups/charges and fluctuations, as well as the (effective) constriction geometry/dimensions. Addressing the context generi…
An intriguing observation on the quantum anomalous Hall effect (QAHE) in magnetic topological insulators (MTIs) is the dissipative edge states, where quantized Hall resistance is accompanied by nonzero longitudinal resistance. We numerically investigate this dissipative behavior of QAHE in MTIs with a three-dimensional tight-binding model and non-equilibrium Greens function formalism. It is found that, in clean samples, the geometric mismatch between the detecting electrodes and the MTI sample leads to additional scattering in the central Hall bar, which is similar to the effect of splitting g…
Motivated by the recent experiment by Marguerite et al. [1] on imaging in graphene samples, we investigate theoretically the dissipation induced by resonant impurities in the quantum Hall regime. The impurity induced forward scattering of electrons at quantum Hall edges leads to an enhanced phonon emission, which reaches its maximum when the impurity state is tuned to resonance by a scanning tip voltage. Our analysis of the effect of the tip potential on the dissipation reveals peculiar thermal rings around the impurities, in consistency with experimental observations. Remarkably, this impurit…
We investigated the magnetic field dependence of the Hall and the bend resistances in the ballistic regime for a single layer graphene Hall bar structure containing a pn-junction. When both regions are n-type the Hall resistance dominates and Hall type of plateaus are formed. These plateaus occur as a consequence of the restriction on the angle imposed by Snell's law allowing only electrons with a certain initial angles to transmit though the potential step. The size of the plateau and its position is determined by the position of the potential interface as well as the value of the applied pot…
The use of multiple current terminals on millimeter-scale graphene $p-n$ junction devices fabricated with Corbino geometries, or quantum Hall resistance dartboards, have enabled the measurement of several fractional multiples of the quantized Hall resistance at the $ν=2$ plateau ($R_H\approx 12906 Ω$). Experimentally obtained values agreed with corresponding numerical simulations performed with the LTspice circuit simulator. More complicated designs of the quantum Hall resistance dartboard were simulated to establish the potential parameter space within which these Corbino-type devices could o…
We report on a comparison of four GaAs/AlGaAs-based quantum resistance standards using an original technique adapted from the well-known Wheatstone bridge. This work shows that the quantized Hall resistance at Landau level filling factor $ν=2$ can be reproducible with a relative uncertainty of $32\times 10^{-12}$ in the dissipationless limit of the quantum Hall effect regime. In the presence of a very small dissipation characterized by a mean macroscopic longitudinal resistivity $\bar{R_{xx}(B)}$ of a few $μΩ$, the discrepancy $ΔR_{\mathrm{H}}(B)$ measured on the Hall plateau between quantum H…
We have observed commensurability oscillations (CO) in the Hall resistance $R_{yx}$ of a unidirectional lateral superlattice (ULSL). The CO, having small amplitudes ($\sim$ 1 $Ω$) and being superposed on a roughly three-orders of magnitude larger background, are obtained by directly detecting the difference in $R_{yx}$ between the ULSL area and the adjacent unmodulated two-dimensional electron gas area, and then extracting the odd part with respect to the magnetic field. The CO thus obtained are compared with a theoretical calculation and turn out to have the amplitude much smaller than the th…
We report on a magnetotransport study in a high-mobility 2D hole gas hosted in a pure Ge/SiGe quantum well subject to dc electric fields and high frequency microwave radiation. We find that under applied dc bias the differential resistivity exhibits a pronounced maximum at a magnetic field which increases linearly with the applied current. We associate this maximum with the fundamental peak of Hall field-induced resistance oscillations (HIRO) which are known to occur in 2D electron gases in GaAs/AlGaAs systems. After taking into account the Dingle factor correction, we find that the position o…
We report the first observation of the quantum Hall effect in epitaxial graphene. The result described in the submitted manuscript fills the yawning gap in the understanding of the electronic properties of this truly remarkable material and demonstrate suitability of the silicon carbide technology for manufactiring large area high quality graphene. Having found the quantum Hall effect in several devices produced on distant parts of a single large-area wafer, we can confirm that material synthesized on the Si-terminated face of SiC promises a suitable platform for the implementations of quantum…
We report on the stability of the quantum Hall plateau in wide Hall bars made from a chemically gated graphene film grown on SiC. The $ν=2$ quantized plateau appears from fields $B \simeq 5$ T and persists up to $B \simeq 80$ T. At high current density, in the breakdown regime, the longitudinal resistance oscillates with a $1/B$ periodicity and an anomalous phase, which we relate to the presence of additional electron reservoirs. The high field experimental data suggest that these reservoirs induce a continuous increase of the carrier density up to the highest available magnetic field, thus en…
Measurements of fractional multiples of the ν=2 plateau quantized Hall resistance (R_H {\approx} 12906 Ω) were enabled by the utilization of multiple current terminals on millimetre-scale graphene p-n junction devices fabricated with interfaces along both lateral directions. These quantum Hall resistance checkerboard devices have been demonstrated to match quantized resistance outputs numerically calculated with the LTspice circuit simulator. From the devices' functionality, more complex embodiments of the quantum Hall resistance checkerboard were simulated to highlight the parameter space wit…
Four-terminal resistances, both longitudinal and diagonal, of a locally gated graphene device are measured in the quantum-Hall (QH) regime. In sharp distinction from previous two-terminal studies [J. R. Williams \textit{et al.}, Science {\bf 317}, 638 (2007); B. Özyilmaz \textit{et al.}, Phys. Rev. Lett. {\bf 99}, 166804 (2007)], asymmetric QH resistances are observed, which provide information on reflection as well as transmission of the QH edge states. Most quantized values of resistances are well analyzed by the assumption that all edge states are equally populated. Contrary to the expectat…
We report on the emergence of bulk, valley-polarized currents in graphene-based devices, driven by spatially varying regions of broken sublattice symmetry, and revealed by non-local resistance ($R_\mathrm{NL}$) fingerprints. By using a combination of quantum transport formalisms, giving access to bulk properties as well as multi-terminal device responses, the presence of a non-uniform local bandgap is shown to give rise to valley-dependent scattering and a finite Fermi surface contribution to the valley Hall conductivity, related to characteristics of $R_\mathrm{NL}$. These features are robust…
Microwave induced resistance oscillations (MIROs) were studied experimentally over a very wide range of frequencies ranging from ~20 GHz up to ~4 THz, and from the quasi-classical regime to the quantum Hall effect regime. At low frequencies regular MIROs were observed, with a periodicity determined by the ratio of the microwave to cyclotron frequencies. For frequencies below 150 GHz the magnetic field dependence of MIROs waveform is well described by a simplified version of an existing theoretical model, where the damping is controlled by the width of the Landau levels. In the THz frequency ra…
The quantum oscillations of nonlinear magnetoresistance in graphene that occurs 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 we develop a covariant formulation of the migration center theory. The analysis of the differential resistivity in the large magnetic field region, shows t…
The Hall (RH) and bend (RB) resistance of a graphene Hall bar structure containing a pn-junction are calculated when in the ballistic regime. The simulations are done using the billiard model. Introducing a pn-junction--dividing the Hall bar geometry in two regions--leads to two distinct regimes exhibiting very different physics: 1) both regions are of n-type and 2) one region is n-type and the other p-type. In regime (1) a 'Hall plateau'--an enhancement of the resistance--appears for RH. On the other hand, in regime (2), we found a negative RH, which approaches zero for large B. The bend resi…
Replacing GaAs by graphene to realize more practical quantum Hall resistance standards (QHRS), accurate to within $10^{-9}$ in relative value, but operating at lower magnetic fields than 10 T, is an ongoing goal in metrology. To date, the required accuracy has been reported, only few times, in graphene grown on SiC by sublimation of Si, under higher magnetic fields. Here, we report on a device made of graphene grown by chemical vapour deposition on SiC which demonstrates such accuracies of the Hall resistance from 10 T up to 19 T at 1.4 K. This is explained by a quantum Hall effect with low di…
Following recent experiments, we consider current flow in two dimensional electronic systems in the quantum Hall regime where a gradient in the electron density induces a spatial variation in the Hall resistivity. Describing the system in terms of a spatially varying local resistivity tensor, we show that in such a system the current density is generically non-uniform, with the current being pushed towards one side of the sample. We show that, for sufficiently large density gradient, the voltage along that side is determined by the change of the Hall resistivity, and is independent of the micr…
The magneto- and Hall resistance of a locally gated cross shaped graphene Hall bar is calculated. The edge of the top gate is placed diagonally across the center of the Hall cross. Four-probe resistance is calculated using the Landauer-Büttiker formalism, while the transmission coefficients are obtained using the non-equilibrium Green's function approach. The interplay between transport due to edge channels and snake states is investigated. When two edge channels are occupied we predict oscillations in the Hall and the bend resistance as function of the magnetic field which are a consequence o…
This paper reports on an experimental study of the contact resistance of Hall bars in the Quantum Hall Effect regime while increasing the current through the sample. These measurements involve also the longitudinal resistance and they have been always performed before the breakdown of the Quantum Hall Effect. Our investigations are restricted to the $i=2$ plateau which is used in all metrological measurements of the von Klitzing constant $R_K$. A particular care has been taken concerning the configuration of the measurement. Four configurations were used for each Hall bar by reversing the curr…
