Transport through quantum spin Hall insulator/metal junctions in graphene ribbons
Elsa Prada, Georgo Metalidis
备注：
12 pages, 9 figures. Order of authors exchanged. Published version in the special issue of the Journal of Computational Electronics: "Electronic transport in graphene nanostructures and devices"
Quantum spin Hall insulator/metal interfaces are formed in graphene ribbons with intrinsic spin-orbit coupling by selectively doping two regions creating a potential step. For a clean graphene ribbon, the transmission of the topological edge states through a n-n or p-p junction is perfect irrespective of the ribbon termination, width, and potential step parameters due to the orthogonality of incoming and outgoing edge channels. This is shown numerically for an arbitrary crystallographic orientation of the ribbon and proven analytically for zigzag and metallic armchair boundary conditions. In disordered ribbons, the orthogonality between left- and right-movers is in general destroyed and backscattering sets in. However, transmission approaches one by increasing the ribbon's width, even in the presence of strong edge roughness.
Using self-consistent calculations based on Non-Equilibrium Green's Function (NEGF) formalism, the origin of negative differential resistance (NDR) in molecular junctions and quantum wires is investigated. Coupling of the molecule to electrodes becomes asymmetric at high bias due to asymmetry between its highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) levels. This causes appearance of an asymmetric potential profile due to a depletion of charge and reduction of screening near the source electrode. With increasing bias, this sharp potential drop leads to…
Quantum dynamics and kinetics of electrically gated graphene ribbons with lateral n-p and e-n-p junctions under magnetic field are investigated. It is shown that the snake-like states of quasiparticles skipping along the n-p interface do not manifest themselve in the main semiclassical part of the ribbon conductance. Giant oscillations of the conductance of a ribbon with an n-p-n junction are predicted and analytically calculated. Depending on the number of junctions inside the ribbon its magnetoresistance may be controllably changed by 50% - 90% by an extremely small change of the magnetic fi…
Based on the nearest-neighbor tight-binding model, we present analytical description of low-energy electron transport through a symmetrical junction of two semimetal armchair ribbons. The results obtained demonstrate the transmission suppression in the vicinity of the neutrality point except for the junction of the ribbons consisting of 3p-1 and 3p+5 dimer lines, p/2 is odd. Unlike other interconnections, these compounds are shown to be free of even local levels arising at the junction interface and exhibit electron backscattering to be inversely as the square of p+1.
Graphene nano-ribbons junctions based electronic devices are proposed in this Letter. Non-equilibrium Green function calculations show that nano-ribbon junctions tailored from single layer graphene with different edge shape and width can act as metal-semiconductor junctions and quantum dots can be implemented. In virtue of the possibilities of patterning monolayer graphene down to atomic precision, these structures, quite different from the previously reported two-dimensional bulk graphene or carbon nanotube devices, are expected to be used as the building blocks of the future nano-electronics…
Coulomb blockade is observed in a graphene nanoribbon device with a top gate. When two pn junctions are formed via the back gate and the local top gate, electrons are confined between the pn junctions which act as the barriers. When no pn junctions are induced by the gate voltages, electrons are still confined, as a result of strong disorder, but in a larger area. Measurements on five other devices with different dimensions yield consistent results.
The edge states in the integer quantum Hall effect are known to be significantly affected by electrostatic interactions leading to the formation of compressible and incompressible strips at the boundaries of Hall bars. We show here, in a combined experimental and theoretical analysis, that this does not hold for the quantum Hall effect in narrow graphene ribbons. In our graphene Hall bar, which is only 60 nm wide, we observe the quantum Hall effect up to Landau level index k=2 and show within a zero free-parameter model that the spatial extent of the compressible and incompressible strips is o…
The quantum Hall effect in Graphene nano-ribbons (GNR) is investigated with the non-equilibrium Green s function (NEGF) based quantum transport model in the ballistic regime. The nearest neighbor tight-binding model based on pz orbital constructs the device Hamiltonian. GNRs of different edge geometries (Zigzag and Armchair) are considered. The magnetic field is included in both the channels and contact through Peierls substitution. Efficient algorithms for calculating the surface Green function are used to save computation time while simulating realistically large dimensions comparable to tho…
The electronic transport properties through junctions in nanographite ribbons are investigated using the Landauer approach. In the low-energy regime ribbons with zigzag boundary have a single conducting channel of edge states. The conductance as a function of the chemical potential shows a rich structure with sharp dips of zero conductance. Each zero-conductance resonance is connected with a resonant state which can be interpreted as the superposition of two degenerate flux states with Kekulé-like current patterns. These zero-conductance dips are connected with a pronounced negative magneto re…
In the presence of crossed electric and magnetic fields, a graphene ribbon has chiral states running along sample edges and along boundaries between $p$-doped and $n$-doped regions. We here consider the scattering of edge states into interface states, which takes place whereever the $pn$ interface crosses the sample boundary, as well as the reverse process. For a graphene ribbon with armchair boundaries, the evolution of edge states into interface states and {\em vice versa} is governed by the conservation of valley isospin. Although valley isospin is not conserved in simplified models of a ri…
We consider theoretically a wide graphene ribbon, that on both ends is attached to electronic reservoirs which generally have different temperatures. The graphene ribbon is assumed to be deposited on a substrate, that leads to a spin-orbit coupling of Rashba type. We calculate the thermally induced charge current in the ballistic transport regime as well as the thermoelectric voltage (Seebeck effect). Apart from this, we also consider thermally induced spin current and spin polarization of the graphene ribbon. The spin currents are shown to have generally two components; one parallel to the te…
Characterized by zigzag and armchair boundaries, the narrow ribbons display the very different characteristics in Hall conductivities. It is shown that the multi-band-crossings occur in the energy spectrum for armchair ribbons, and the number of them depends on the width of ribbons. Theoretically, it is predicated that the conductivities exhibit drastic sign reversals for narrow ribbons as the Fermi energy sweep over the band-crossings. A new classification of armchair ribbons is suggested based on the emergence of a flat band in the energy spectrum only for odd armchair ribbons. The evolution…
Magnetic Weyl semimetals exhibit intriguing transport phenomena due to their non-trivial band structure. Recent experiments in bulk crystals of the shandite-type Co$_3$Sn$_2$S$_2$ have shown that this material system is a magnetic Weyl semimetal. To access the length scales relevant for chiral transport, it is mandatory to fabricate microstructures of this fascinating compound. We therefore have cut micro-ribbons (typical size $0.3~\times~3~\times~50$μ$m^3$) from Co$_3$Sn$_2$S$_2$ single crystals using a focused beam of Ga$^{2+}$-ions and investigated the impact of the sample dimensions and po…
In graphene nanoribbon junctions, the nearly perfect transmission occurs in some junctions while the zero conductance dips due to anti-resonance appear in others. We have classified the appearance of zero conductance dips for all combinations of ribbon and junction edge structures. These transport properties do not attribute to the whole junction structure but the partial corner edge structure, which indicates that one can control the electric current simply by cutting a part of nanoribbon edge. The ribbon width is expected to be narrower than 10 nm in order to observe the zero conductance dip…
Suspended graphene nano-ribbons formed during current annealing of suspended graphene flakes have been investigated experimentally. Transport measurements show the opening of a transport gap around charge neutrality due to the formation of "Coulomb islands", coexisting with quantum Hall conductance plateaus appearing at moderate values of magnetic field $B$. Upon increasing $B$, the transport gap is rapidly suppressed, and is taken over by a much larger energy gap due to electronic correlations. Our observations show that suspended nano-ribbons allow the investigation of phenomena that could n…
We theoretically study Josephson junctions with a transition metal dichalcogenide zigzag ribbon as a weak link. We demonstrate that the spatial profile of the supercurrent carried by the edge modes determines the critical current dependence on the perpendicular magnetic field. We explore this finding and analyze the impact of Zeeman interaction and the orbital effects of the magnetic field on the Andreev bound states energies. We show that the unequal Fermi velocities of the spin-opposite edge modes lead to an anomalous shift of the Andreev bound states in the presence of the magnetic field. T…
A study of the effect of unscreened Coulomb interactions on the quantum spin Hall (QSH) phase of finite-width neutral zigzag graphene ribbons is presented. By solving a tight-binding Hamiltonian that includes the intrinsic spin-orbit interaction (I-SO), exact expressions for band-structures and edge-states wavefunctions are obtained. These analytic results, supported by tight-binding calculations, show that chiral spin-filtered edge states are composed of localized and damped oscillatory wavefunctions, reminiscent of the ones obtained in armchair ribbons. The addition of long-range Coulomb int…
We study Andreev reflection in graphene nanoribbon/superconductor hybrid junctions. By using a tight-binding approach and the scattering formalism we show that finite-size effects lead to notable differences with respect to the bulk graphene case. At subgap voltages, conservation of pseudoparity, a quantum number characterizing the ribbon states, yields either a suppression of Andreev reflection when the ribbon has an even number of sites in the transverse direction or perfect Andreev reflection when the ribbon has an odd number of sites. In the former case the suppression of Andreev reflectio…
We present an exact calculation of the effective geometry-induced quantum potential for a particle confined on a helicoidal ribbon. This potential leads to the appearance of localized states at the rim of the helicoid. In this geometry the twist of the ribbon plays the role of an effective transverse electric field on the surface and thus this is reminiscent of the quantum Hall effect.
Hall effect in SN and SNS junctions is considered. It is shown that at small temperature the Hall voltage is significantly suppressed as compared to its normal metal value. The time dependence of the Hall voltage in SNS junctions has a form of narrow pulses with the Josephson frequency.
We report on a theoretical study of one-dimensional (1D) states localized at few-layer graphene system ribbon edges, and at interfaces between few-layer graphene systems with different valley Hall conductivities. These 1D states are topologically protected when valley mixing is neglected. We address the influence on their properties of stacking arrangement, interface structure, and external electric field perpendicular to the layers. We find that 1D states are generally absent at multilayer ribbon armchair direction edges, but present irrespective of crystallographic orientation at any interna…
Using the tight-binding BHZ model and Landauer-Büttiker formalism, the topological invariant of the finite width of ribbons of HgTe/CdTe quantum well is studied in the absence and presence of an external transverse electric field. It will be recognized that a critical current changes topological invariant of ribbons of quantum well. This topological phase transition, which occurred by adjustment of the bias voltage, depends on the width of the sample and the gate voltage. The profound effects of an external transverse electric field are considered to the separation of spin-up and spin-down ban…
Both quantum spin Hall and quantum anomalous Hall states are novel states of quantum matter with promising applications. We propose junction quantum wells comprising II-VI, III-V or IV semiconductors as a large class of new materials realizing the quantum spin Hall state. Especially, we find that the bulk band gap for the quantum spin Hall state can be as large as 0.1 eV. Further more, magnetic doping would induce the ferromagnetism in these junction quantum wells due to band edge singularities in the band-inversion regime and to realize the quantum anomalous Hall state.
We show that novel fixed points (characterized by matrices which specify the splitting of the currents at the junction) can be accessed in a system which contains a junction of three quantum Hall line junctions. For such a junction of fractional quantum Hall edge states, we find that it is possible for both the flower (single droplet) and islands (three droplets) configurations to be stable in an intermediate region, for a range of values of the inter-edge repulsive interactions. A measurement of the tunneling conductance as a function of the gate voltage controlling inter-edge repulsions can …
Recent quantum Hall experiments conducted on disordered graphene pn junction provide evidence that the junction resistance could be described by a simple Ohmic sum of the n and p mediums' resistances. However in the ballistic limit, theory predicts the existence of chirality-dependent quantum Hall plateaus in a pn junction. We show that two distinctively separate processes are required for this ballistic-Ohmic plateau transition, namely (i) hole/electron Landau states equilibration and (ii) valley iso-spin dilution of the incident Landau edge state. These conclusions are obtained by a simple s…
A quantum Hall line junction system consists of a one-dimensional Luttinger liquid (LL) and two chiral channels that allow density waves incident upon and reflected by the LL to be measured separately. We demonstrate that interactions in a quantum Hall line junction system can be probed by studying edge magnetoplasmon absorption spectra and their polarization dependences. Strong interactions in the junction lead to collective modes that are isolated in either Luttinger liquid or contact subsystems.
Mechanical deformations of graphene induce a term in the Dirac Hamiltonian which is reminiscent of an electromagnetic vector potential. Strain gradients along particular lattice directions induce local pseudomagnetic fields and substantial energy gaps as indeed observed experimentally. Expanding this analogy, we propose to complement the pseudomagnetic field by a pseudoelectric field, generated by a time dependent oscillating stress applied to a graphene ribbon. The joint Hall-like response to these crossed fields results in a strain-induced charge current along the ribbon. We analyze in detai…
We have studied the tachyonic excitations in the junction of two topological insulators in the presence of an external magnetic field. The Landau levels, evaluated from an effective two-dimensional model for tachyons, and from the junction states of two topological insulators, show some unique properties not seen in conventional electrons systems or in graphene. The $ν=1/3$ fractional quantum Hall effect has also a strong presence in the tachyon system.
Here we comprehensively investigate Landau levels, Hofstadter butterfly and transport properties of a semi-Dirac nanoribbon in a perpendicular magnetic field using a recently developed real-space implementation of the Kubo formula based on Kernel Polynomial Method. A Dirac ribbon is considered to compare and contrast our results for a semi-Dirac system. We find that the Landau levels being non-equidistant from each other for the semi-Dirac case (true for a Dirac as well), the flatness of the energy bands vanishes in the bulk and becomes dispersive for a semi-Dirac ribbon in contrast to a Dirac…
We demonstrate that the phenomenon of current confinement along graphene n-p junctions at high magnetic fields can be used to form an Aharonov-Bohm interferometer. The interference system exploits a closed n-p junction that can be induced by a floating gate within the sample, and coupling of the junction currents with the edge currents in the quantum Hall regime. Operation of the device requires current splitting at the edge and the n-p junction contacts which is found for armchair ribbons at low Fermi energy.
We present a microscopic theory of the chiral one-dimensional electron gas system localized on the sidewalls of magnetically-doped Bi$_2$Se$_3$-family topological insulator nanoribbons in the quantum anomalous Hall effect (QAHE) regime. Our theory is based on a simple continuum model of sidewall states whose parameters are extracted from detailed ribbon and film geometry tight-binding model calculations. In contrast to the familiar case of the quantum Hall effect in semiconductor quantum wells, the number of microscopic chiral channels depends simply and systematically on the ribbon thickness …
We propose tunnel junctions of a Hall bar and a superconducting lead, for observing Cooper-pair tunneling into singlet fractional quantum Hall edge states. These tunnel junctions provide a natural means of extracting precise information of the spin polarization and the filling factor of the state. The low energy regime of one of the set-ups is governed by a novel quantum entangled fixed point.
The ferromagnet-topological insulator-ferromagnet (FM-TI-FM) junction exhibits thermal and electrical quantum Hall effects. The generated Hall voltage and transverse temperature gradient can be controlled by the directions of magnetizations in the FM leads, which inspires the use of FM-TI-FM junctions as electrical and as heat switches in spintronic devices. Thermal and electrical Hall coefficients are calculated as functions of the magnetization directions in ferromagnets and the spin-relaxation time in TI. Both the Hall voltage and the transverse temperature gradient decrease but are not com…
We investigate the magnetic field dependence of the Hall and the bend resistances for a ballistic Hall bar structure containing a pn-junction sculptured from a bilayer of graphene. The electric response is obtained using the billiard model and we investigate the cases of bilayer graphene with and without a band gap. Two different conduction regimes are possible: $i$) both sides of the junction have the same carrier type, and $ii$) one side of the junction is n-type while the other one is p-type. The first case shows Hall plateau-like features in the Hall resistance that fade away as the band g…
In two recent articles [PRL 90, 026802 (2003); PRB 69, 085307 (2004)], we developed a transport theory for an extended tunnel junction between two interacting fractional-quantum-Hall edge channels, obtaining analytical results for the conductance. Ponomarenko and Averin (PA) have expressed disagreement with our theoretical approach and question the validity of our results (cond-mat/0602532). Here we show why PA's critique is unwarranted.
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…
Coupling superconductors to quantum Hall edge states is the subject of intense investigation as part of the ongoing search for non-abelian excitations. Our group has previously observed supercurrents of hundreds of picoamperes in graphene Josephson junctions in the quantum Hall regime. One of the explanations of this phenomenon involves the coupling of an electron edge state on one side of the junction to a hole edge state on the opposite side. In our previous samples, these states are separated by several microns. Here, a narrow trench perpendicular to the contacts creates counterpropagating …
We present a microscopic model for a line junction formed by counter or co-propagating single mode quantum Hall edges corresponding to different filling factors. The ends of the line junction can be described by two possible current splitting matrices which are dictated by the conditions of both lack of dissipation and the existence of a linear relation between the bosonic fields. Tunneling between the two edges of the line junction then leads to a microscopic understanding of a phenomenological description of line junctions introduced some time ago. The effect of density-density interactions …
We study the electronic properties of electrons in flat and curved zigzag graphene ribbons using a tight-binding model within the Slater Koster approximation. We find that curvature dramatically enhances the action of spin orbit effects in graphene ribbons and has a strong effect on the spin orientation of the edge states: whereas spins are normal to the surface in the case of flat ribbons, this is no longer the case in the case of curved ribbons. We find that for the edge states, the spin density lies always in the plane perpendicular to the ribbon axis, and deviate strongly from the normal t…
Anomalous and spin Hall effects are investigated theoretically for a magnetic tunnel junction where the applied voltage produces a Rashba spin-or bit coupling within the tunneling barrier layer. The ferromagnetic electrodes are the source of the spin-polarized current. The tunneling electrons experience a spin-orbit coupling inside the barrier due to the applied electrical field. Charge and spin Hall currents are calculated as functions of the position inside the barrier and the angle between the magnetizations of the electrodes. We find that both charge and spin Hall currents are located insi…
We present the theoretical description for a class of experimental setups that measure quantum Hall coefficients in ferromagnet-topological insulator-ferromagnet (FM-TI-FM) junctions. We predict that varying the magnetization direction in ferromagnets, one can change the induced Hall voltage and transverse temperature gradient from the maximal values, corresponding to the quantized Hall coefficients, down to their complete suppression to zero. We provide detailed analysis of thermal and electrical Hall resistances as functions of the magnetization directions in ferromagnets, the spin-scatterin…
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…
We have studied a clean finite-length line junction between interacting counterpropagating single-branch fractional-quantum-Hall edge channels. Exact solutions for low-lying excitations and transport properties are obtained when the two edges belong to quantum Hall systems with different filling factors and interact via the long-range Coulomb interaction. Charging effects due to the coupling to external edge-channel leads are fully taken into account. Conductances and power laws in the current-voltage characteristics of tunneling are strongly affected by inter-edge correlations.
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…
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.
We show that a nanometric four-probe ballistic junction can be used to check the presence of a transverse spin Hall current in a system with a Spin Orbit coupling not of the Rashba type, but rather due to the in-plane electric field. Indeed, the spin Hall effect is due to the presence of an effective small transverse magnetic field corresponding to the Spin Orbit coupling generated by the confining potential. The strength of the field and the junction shape characterize the quenching Hall regime, usually studied by applying semi-classical approaches. We discuss how a quantum mechanical relativ…
The quantum Hall effect in graphene p-n junctions is studied numerically with emphasis on the effect of disorder at the interface of two adjacent regions. Conductance plateaus are found to be attached to the intensity of the disorder, and are accompanied by universal conductance fluctuations in the bipolar regime, which is in good agreement with theoretical predictions of the random matrix theory on quantum chaotic cavities. The calculated Fano factors can be used in an experimental identification of the underlying transport character.
We study theoretically reflection problem in the junction between a normal metal and an insulator characterized by a parameter $M$, which is a usual insulator for $M>0$ or a quantum spin Hall system for $M<0$. The spin rotation angle $α$ at the reflection is obtained in the plane of $M$ and the incident angle $θ$ measured from the normal to the interface. The $α$ shows rich structures around the quantum critical point M=0 and $θ=0$, i.e., $α$ can be as large as $\sim π$ at an incident angle in the quatum spin Hall case $M<0$ because the helical edge modes resonantly enhance the spin rotation, …
The formation of quantum Hall channels inside the bulk of graphene is studied using various contact and gate geometries. p-n junctions are created along the longitudinal direction of samples, and enhanced conductance is observed in the case of bipolar doping due to new conducting channels forming in the bulk, whose position, propagating direction and, in one geometry, coupling to electrodes are determined by the gate-controlled filling factor across the device. This effect could be exploited to probe the behavior and interaction of quantum Hall channels protected against uncontrolled scatterin…
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…
Electronic transport in a graphene-based ferromagnetic/normal/ferromagnetic junction is investigated by means of Landauer-Büttiker formulism and the nonequilibrium Green's function technique. For the zigzag edge case, the results show that the conductance is always larger than $e^{2}/h$ for the parallel configuration of lead magnetizations, but for the antiparallel configuration the conductance becomes zero because of the band-selective rule. So a magnetoresistance (MR) plateau emerges with the value 100% when the Fermi energy is located around the Dirac point. Besides, choosing narrower graph…
We investigate possible phase transitions among the different quantum anomalous Hall (QAH) phases in a zigzag graphene ribbon under the influence of the exchange field. The effective tight-binding Hamiltonian for graphene is made up of the hopping term, the Kane-Mele and Rashba spin-orbit couplings as well as the Haldane orbital term. We find that the variation of the exchange field results in bulk gap-closing phenomena and phase transitions occur in the graphene system. If the Haldane orbital coupling is absent, the phase transition between the chiral (anti-chiral) edge state $ν=+2$ ($ν=-2$) …
Kang et al. have recently observed a remarkable zero-bias anomaly in the spectrum for electron tunneling between two 2D electron gases separated laterally by a narrow but high barrier in the presence of a perpendicular quantising magnetic field. We argue that this is a result of interedge phase coherence analogous to the interlayer phase coherence in quantum Hall (QHE) bilayer systems. The disruption of the QHE by the barrier is 'healed' by strong coulomb exchange enhancement of the weak tunneling through the barrier.
We study the Josephson effect in a quantum spin Hall system coupled to a localized magnetic impurity. As a consequence of the fermion parity anomaly, the spin of the combined system of impurity and spin-Hall edge alternates between half-integer and integer values when the superconducting phase difference across the junction advances by $2π$. This leads to characteristic differences in the splittings of the spin multiplets by exchange coupling and single-ion anisotropy at phase differences, for which time-reserval symmetry is preserved. We discuss the resulting $8π$-periodic (or $\mathbb{Z}_4$)…
Transport studies of a bent quantum Hall junction at integer filling factors show strongly insulating states at higher fields. In this paper we analyze the strongly insulating behavior as a function of temperature T and dc bias V, in order to classify the localization mechanisms responsible for the insulating state. The temperature dependence suggests a crossover from activated nearest-neighbor hopping at higher T to variable-range hopping conduction at lower T. The base temperature electric field dependence is consistent with 1D variable-range hopping conduction. We observe almost identical b…
We present a detailed theory of transport through line junctions formed by counterpropagating single-branch fractional-quantum-Hall edge channels having different filling factors. Intriguing transport properties are exhibited when strong Coulomb interactions between electrons from the two edges are present. Such strongly correlated line junctions can be classified according to the value of an effective line-junction filling factor n that is the inverse of an even integer. Interactions turn out to affect transport most importantly for n=1/2 and n=1/4. A particularly interesting case is n=1/4 co…
We report an experimental demonstration of a local amplification of the spin Hall voltage using an expanding depletion zone at a pn-junction in GaAs/AlGaAs Hall-bar microdevices. It is demonstrated that the depletion zone can be spatially expanded by applying reverse bias by at least 10~$μ$m at low temperature. In the depleted regime, the spin Hall signals reached more than one order of magnitude higher values than in the normal regime at the same electrical current flowing through the micro-device. It is shown that the pn-bias has two distinct effects on the detected spin Hall signal. It cont…
