We calculate the tunneling current through long line junctions of a $ν=5/2$ quantum Hall liquid and i) another $ν=5/2$ liquid, ii) an integer quantum Hall liquid and iii) a quantum wire. Momentum resolved tunneling provides information about the number, propagation directions and other features of the edge modes and thus helps distinguish several competing models of the 5/2 state. We investigate transport properties of two proposed Abelian states: $K=8 state and 331 state, and four possible non-Abelian states: Pfaffian, edge-reconstructed Pfaffian, and two versions of the anti-Pfaffian state. We also show that the non-equilibrated anti-Pfaffian state has a different resistance from other proposed states in the bar geometry.
A non-planar geometry for the quantum Hall (QH) effect is studied, whereby two quantum Hall (QH) systems are joined at a sharp right angle. When both facets are at equal filling factor nu the junction hosts a channel with non-quantized conductance, dependent on nu. The state is metallic at nu = 1/3, with conductance along the junction increasing as the temperature T drops. At nu = 1, 2 it is strongly insulating, and at nu = 3, 4 shows only weak T dependence. Upon applying a dc voltage bias along the junction, the differential conductance again shows three different behaviors. Hartree calculati…
$\mathbb{Z}_4$ parafermions can be realized in a strongly interacting quantum spin Hall Josephson junction or in a spin Hall Josephson junction strongly coupled to an impurity spin. In this paper we study a system that has both features, but with weak (repulsive) interactions and a weakly coupled spin. We show that for a strongly anisotropic exchange interaction, at low temperatures the system enters a strong coupling limit in which it hosts two $\mathbb{Z}_4$ parafermions, characterizing a fourfold degeneracy of the ground state. We construct the parafermion operators explicitly, and show tha…
Physical Review Letter {\bf 90}, 026802 (2003) by U. Zülicke and E. Shimshoni and subsequent extended paper proposed an ``exact solution'' of the problem of a tunnel junction of length $L$ between two single-mode edges of the Fractional Quantum Hall Liquids with different filling factors $ν_{j}=1/(2m_j+1)$, $j=1,2$; $m_j=0,1,...$. The purpose of this comment is to point out that the solution found in these papers is not correct and to present correct solution of a particular instance of this model.
Using high quality graphene pnp junctions, we observe prominent conductance fluctuations on transitions between quantum Hall (QH) plateaus as the top gate voltage Vtg is varied. In the Vtg-B plane, the fluctuations form crisscrossing lines that are parallel to those of the adjacent plateaus, with different temperature dependences for the conductance peaks and valleys. These fluctuations arise from Coulomb-induced charging of electron- or hole-doped localized states when the device bulk is delocalized, underscoring the importance of electronic interactions in graphene in the QH regime.
In this paper we address some of the properties of quantum Hall line junctions (QHLJ) that occur near barriers separating electron gases on quantum Hall plateaus.In narrow barriers where electron tunneling can occur, the low energy physics of the QHLJ is described by the quantum sine-Gordon model. We propose procedures to study a sort of properties of these systems in relation with recent experimental studies of Kang {\it et al.}, Nature {\bf 403}, 59 (2000). We propose experimental ways of measuring the values of the dimensionless coupling constant characteristic for the Sine-Gordon model as …
We study the tunneling density of states (TDOS) for a junction of three Tomonaga-Luttinger liquid wires. We show that there are fixed points which allow for the enhancement of the TDOS, which is unusual for Luttinger liquids. The distance from the junction over which this enhancement occurs is of the order of x = v/(2 ω), where v is the plasmon velocity and ωis the bias frequency. Beyond this distance, the TDOS crosses over to the standard bulk value independent of the fixed point describing the junction. This finite range of distances opens up the possibility of experimentally probing the enh…
We report on quantum interference between a pair of counterpropagating quantum Hall edge states that are separated by a high quality tunnel barrier. Observed Aharonov-Bohm oscillations are analyzed in terms of resonant tunneling between coupled Luttinger liquids that creates bound electronic states between pairs of tunnel centers that act like interference slits. We place a lower bound in the range of 20-40 $μ$m for the phase coherence length and directly confirm the extended phase coherence of quantum Hall edge states.
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.
Motivated by recent non-local transport studies of quantum-Hall-magnet (QHM) states formed in monolayer graphene's $N=0$ Landau level, we study the scattering of QHM magnons by gate-controlled junctions between states with different integer filling factors $ν$. For the $ν=1|-1|1$ geometry we find magnons are weakly scattered by electric potential variation in the junction region, and that the scattering is chiral when the junction lacks a mirror symmetry. For the $ν=1|0|1$ geometry, %in which the scattering region contains a $ν=0$ canted antiferromagnet, we find that kinematic constraints comp…
We study a system of an impurity spin coupled to a junction of several Tomonaga-Luttinger liquids using a renormalization group scheme. For the decoupled S-matrix at the junction, there is a range of Kondo couplings which flow to a multi-channel fixed point for repulsive inter-electron interactions; this is associated with a characteristic temperature dependence of the spin-flip scatterings. If the junction is governed by the Griffiths S-matrix, the Kondo couplings flow to a strong coupling fixed point where all the wires are decoupled.
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 …
We investigate rectification of a low-frequency ac bias in Y-junctions of one-channel Luttinger liquid wires with repulsive electron interaction. Rectification emerges due to three scatterers in the wires. We find that it is possible to achieve a higher rectification current in a Y-junction than in a single wire with an asymmetric scatterer at the same interaction strength and voltage bias. The rectification effect is the strongest in the absence of the time-reversal symmetry. In that case, the maximal rectification current can be comparable with the total current $\sim e^2V/h$ even for low vo…
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.
We show that multiple point contacts on a barrier separating two laterally coupled quantum Hall fluids induce Aharonov-Bohm (AB) oscillations in the tunneling conductance. These quantum coherence effects provide new evidence for the Luttinger liquid behavior of the edge states of quantum Hall fluids. For a two point contact, we identify coherent and incoherent regimes determined by the relative magnitude of their separation and the temperature. We analyze both regimes in the strong and weak tunneling amplitude limits as well as their temperature dependence. We find that the tunneling conductan…
A mapping between fractional quantum Hall (FQH) junctions and the two-channel Kondo model is presented. We discuss in detail this relation for the particular case of a junction of a FQH state at $ν= 1/3$ and a normal metal. We show that in the strong coupling regime this junction has a non-Fermi liquid fixed point. At this fixed point the electron Green's function has a branch cut, and the entropy has a non-zero value equal to $S={1/2} \ln{2}$. We construct the space of perturbations at the strong coupling fixed point and find that the dimensions of the tunneling operator is 1/2. These behavio…
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.
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.
We construct a generalization of the Chalker-Coddington network model to the case of fractional quantum Hall effect, which describes the tunneling between multiple chiral edges. We derive exact local and global duality symmetries of this model, and show that its infrared properties are identical to those of disordered planar Josephson junction array (JJA) in a weak magnetic field, which implies the same universality class. The zero frequency Hall resistance of the system, which was expressed through exact correlators of the tunneling fields, is shown to be quantized both in the quantum Hall li…
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 consider a honeycomb network built of quantum wires, with each node of the network having a Y-junction of three wires with a ring through which flux can be inserted. The junctions are the basic circuit elements for the network, and they are characterized by 3 x 3 conductance tensors. The low energy stable fixed point tensor conductances result from quantum effects, and are determined by the strength of the interactions in each wire and the magnetic flux through the ring. We consider the limit where there is decoherence in the wires between any two nodes, and study the array as a network of …
Owing to a linear and gapless band structure and a tunability of the charge carrier type, graphene offers a unique system to investigate transport of Dirac Fermions at p-n junctions (PNJs). In a magnetic field, combination of quantum Hall physics and the characteristic transport across PNJs leads to a fractionally quantized conductance associated with the mixing of electron-like and hole-like modes and their subsequent partitioning. The mixing and partitioning suggest that a PNJ could be used as an electronic beam-splitter. Here we report the shot noise study of the mode mixing process and dem…
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 …
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…
Transport through a superconductor-Luttinger liquid junction is considered. When the interaction in the Luttinger liquid is repulsive, the resistance of the junction with a sufficiently clean interface shows nonmonotonic temperature- or voltage-dependence due to the competition between the superconductivity and the repulsive interaction. The result is discussed in connection with recent experiments on single-wall carbon nanotubes in contact with superconducting leads.
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…
We study charge transport through $N$-lead junctions ($N\geq 3$) of spinless Luttinger liquid wires with bias voltages applied to Fermi-liquid reservoirs. In particular, we consider a Y junction, which is a setup characteristic of the tunneling experiment. In this setup, the strength of electron-electron interactions in one of the arms ("tunneling tip") is different from that in the other two arms (which form together the "main wire"). For a generic single-particle $S$ matrix of the junction, we find that the bias voltage $V$ applied---even symmetrically---to the main wire generates a current …
We present electronic transport measurements through thiolated C$_{60}$ molecules in liquid environment. The molecules were placed within a mechanically controllable break junction using a single anchoring group per molecule. When varying the electrode separation of the C$_{60}$-modified junctions, we observed a peak in the conductance traces. The shape of the curves is strongly influenced by the environment of the junction as shown by measurements in two distinct solvents. In the framework of a simple resonant tunneling model, we can extract the electronic tunneling rates governing the transp…
We theoretically study the Josephson current in a superconductor/quantum anomalous Hall insulator/superconductor junction by using the lattice Green function technique. When an in-plane external Zeeman field is applied to the quantum anomalous Hall insulator, the Josephson current $J$ flows without a phase difference across the junction $θ$. The phase shift $φ$ appealing in the current-phase relationship $J\propto \sin(θ-φ$) is proportional to the amplitude of Zeeman fields and depends on the direction of Zeeman fields. A phenomenological analysis of the Andreev reflection processes explains t…
We study time resolved transport properties of a $Y$-junction composed of interacting one-dimensional quantum wires using a bosonization approach. In particular, we investigate the AC conductivity of the $Y$-junction formed from finite length Tomonaga-Luttinger liquid wires based on a plasmon scattering approach for injected charge pulses of arbitrary shapes. In addition, we calculate the tunneling current and quantum noise of the $Y$-junction arising from point-like tunneling impurities at the junction, including finite temperature effects. Our results will be useful for designing nano-electr…
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…
We elucidate the nature of neutral collective excitations of fractional quantum Hall liquids in the long-wavelength limit. We demonstrate that they are chiral gravitons carrying angular momentum - 2, which are quanta of quantum motion of an internal metric, and show up as resonance peaks in the systems response to what is the fractional Hall analog of gravitational waves. Relation with existing and possible future experimental work that can detect these fractional quantum Hall gravitons and reveal their chirality are discussed.
Quantum spin Hall-superconductor hybrids are promising sources of topological superconductivity and Majorana modes, particularly given recent progress on HgTe and InAs/GaSb. We propose a new method of revealing topological superconductivity in extended quantum spin Hall Josephson junctions supporting `fractional Josephson currents'. Specifically, we show that as one threads magnetic flux between the superconductors, the critical current traces an interference pattern featuring sharp fingerprints of topological superconductivity---even when noise spoils parity conservation.
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 $\mathbb{Z}_4$)…
Recent experimental work on locally gated graphene layers resulting in p-n junctions have revealed quantum Hall effect in their transport behavior. We explain the observed conductance quantization which is fractional in the bipolar regime and integer in the unipolar regime in terms of quantum Hall edge modes propagating along and across the p-n interface. In the bipolar regime the electron and hole modes can mix at the p-n boundary, leading to current partition and quantized shot noise plateaus similar to those of conductance, while in the unipolar regime transport is noiseless. These quantum …
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 propose a spin Hall device to induce a large spin Hall effect in a superconductor/normal metal (SN) junction. The side jump and skew scattering mechanisms are both taken into account to calculate the extrinsic spin Hall conductivity in the normal metal. We find that both contributions are anomalously enhanced when the voltage between the superconductor and the normal metal approaches to the superconducting gap. This enhancement is attributed to the resonant increase of the density of states in the normal metal at the Fermi level. Our results demonstrate a novel way to control and amplify th…
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…
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…
We present a study of a graphene-based Josephson junction with dedicated side gates carved from the same sheet of graphene as the junction itself. These side gates are highly efficient, and allow us to modulate carrier density along either edge of the junction in a wide range. In particular, in magnetic fields in the $1-2$ Tesla range, we are able to populate the next Landau level, resulting in Hall plateaus with conductance that differs from the bulk filling factor. When counter-propagating quantum Hall edge states are introduced along either edge, we observe supercurrent localized along that…
We report on low-temperature transport study of a single layer graphene (SLG)-twisted bilayer graphene (tBLG) junction device. The SLG-tBLG junction in the device is grown by chemical vapor deposition and the device is fabricated in a Hall-bar configuration on Si/SiO$_2$ substrate. The longitudinal resistances across the SLG-tBLG junction (cross-junction resistances) on the two sides of the Hall bar and the Hall resistances of SLG and tBLG in the device are measured. In the quantum Hall regime, the measurements show that the measured cross-junction resistances exhibit a series of new quantized…
We study junctions between superconductors mediated by the edge states of a quantum spin Hall insulator. We show that such junctions exhibit a fractional Josephson effect, in which the current phase relation has a 4π, rather than a 2πperiodicity. This effect is a consequence of the conservation of fermion parity - the number of electrons modulo 2 - in a superconducting junction, and is closely related to the Z_2 topological structure of the quantum spin Hall insulator. Inelastic processes, which violate the conservation of fermion parity, lead to telegraph noise in the equilibrium supercurrent…
In this study, we examine multiple encapsulated graphene Josephson junctions to determine which mechanisms may be responsible for the supercurrent observed in the quantum Hall (QH) regime. Rectangular junctions with various widths and lengths were studied to identify which parameters affect the occurrence of QH supercurrent. We also studied additional samples where the graphene region is extended beyond the contacts on one side, making that edge of the mesa significantly longer than the opposite edge. This is done in order to distinguish two potential mechanisms: a) supercurrents independently…
We investigate anomalous Hall effect in a magnet coupled to a triplet superconductor under phase gradient. It is found that the anomalous Hall supercurrent arises from non-trivial structure of the magnetization. The magnetic structure manifested in the Hall supercurrent is characterized by even order terms of the exchange coupling, essentially different from that discussed in the context of anomalous Hall effect, reflecting the disspationless nature of supercurrent. We also discuss a possible candidate for magnetic structure to verify our prediction.
