Algorithm for constructing customized quantized resistances in graphene $p-n$ junctions
Albert F. Rigosi, Martina Marzano, Antonio Levy, Heather M. Hill, Dinesh K. Patel, Mattias Kruskopf, Hanbyul Jin, Randolph E. Elmquist, David B. Newell
An algorithm is introduced for predicting quantized resistances in graphene p-n junction devices that utilize more than a single entry and exit point for electron flow. Depending on the configuration of an arbitrary number of terminals, electrical measurements yield fractional multiples of the typical quantized Hall resistance at the $ν=2$ plateau $R_H \approx 12906 Ω$ and take the form: $\frac{a}{b}R_H$. This theoretical formulation is independent of material, and applications to other material systems that exhibit quantum Hall behaviors are to be expected. Furthermore, this formulation is supported with experimental data from graphene-based devices with multiple source and drain terminals.
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 unconventional transport properties of HgTe wells with inverted band structure: the resistance does not show insulating behavior even when it is of the order of $10^2\times h/2e^{2}$. The system is expected to be a two-dimensional topological insulator with a dominant edge state contribution. The results are inconsistent with theoretical models developed within the framework of the helical Luttinger liquid.
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…
In this work, limiting factors for developing metrologically useful arrays from epitaxial graphene on SiC are lifted with a combination of centimeter-scale, high-quality material growth and the implementation of superconducting contacts. Standard devices for metrology have been restricted to having a single quantized value output based on the $ν$ = 2 Landau level. With the demonstrations herein of devices having multiple outputs of quantized values available simultaneously, these versatile devices can be used to disseminate the ohm globally. Such devices are designed to give access to quantize…
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…
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 $R_{xx}$.
We have demonstrated the millimeter-scale fabrication of monolayer epitaxial graphene $p-n$ junction devices using simple ultraviolet photolithography, thereby significantly reducing device processing time compared to that of electron beam lithography typically used for obtaining sharp junctions. This work presents measurements yielding nonconventional, fractional multiples of the typical quantized Hall resistance at $ν=2$ ($R_H\approx 12906 Ω$) that take the form: $\frac{a}{b}R_H$. Here, $a$ and $b$ have been observed to take on values such 1, 2, 3, and 5 to form various coefficients of $R_H$…
The quantum Hall and longitudinal resistances in multi-terminal ferromagnetic graphene p-n junctions under a perpendicular magnetic field are investigated. In the Hall measurements, the transverse contacts are assumed to be located at p-n interface to avoid the mixing of edge states at the interface and the resulting quantized resistances are then topologically protected. According to the charge carrier type, the resistances in four-terminal p-n junction can be naturally divided into nine different regimes. The symmetric Hall and longitudinal resistances are observed, with lots of new robust q…
An unusually wide plateau in the quantized Hall resistance has been revealed for a MQW heterostructure of wide p-GeSi / Ge / p-GeSi quantum wells with the Fermi energy comparable to the well bottom bending amplitude. This plateau exists in one of two metastable states of the sample, for which a symmetric quasi-double-quantum-well system is formed inside the Ge layer, and corresponds to the filling factor nu = 1 for each of two sublayers in the Ge layer. The plateau exists not only within a magnetic field range related to the quantum-Hall liquid, but extends beyond it into a so-called quantized…
In this work we investigate an unusual transport phenomenon observed in two-dimensional electron gas under integer quantum Hall effect conditions. Our calculations are based on the screening theory, using a semi-analytical model. The transport anomalies are \emph{dip} and overshoot effects, where the Hall resistance decreases (or increases) unexpectedly at the quantized resistance plateaus intervals. We report on our numerical findings of the \emph{dip} effect in the Hall resistance, considering GaAs/AlGaAs heterostructures in which we investigated the effect under different experimental condi…
We report on our theoretical investigation considering the widths of quantized Hall plateaus (QHPs) depending on the density asymmetry induced by the large current within the out-of-linear response regime. We solve the Schrodinger equation within the Hartree type mean field approximation using Thomas Fermi Poisson nonlinear screening theory. We observe that the two dimensional electron system splits into compressible and incompressible regions for certain magnetic field intervals, where the Hall resistance is quantized and the longitudinal resistance vanishes, if an external current is imposed…
We present nonlocal resistance measurements in an ultra high mobility two dimensional electron gas. Our experiments show that even at weak magnetic fields classical guiding along edges leads to a strong non local resistance on macroscopic distances. In this high Landau level regime the transport along edges is dissipative and can be controlled by the amplitude of the voltage drop along the edge. We report resonances in the nonlocal transport as a function of this voltage that are interpreted as escape and formation of edge channels.
Using the Chalker-Coddington network model as a drastically simplified, but universal model of integer quantum Hall physics, we investigate the plateau-to-insulator transition at strong magnetic field by means of a real-space renormalization approach. Our results suggest that for a fully quantum coherent situation, the quantized Hall insulator with R_H approx. h/e^2 is observed up to R_L ~25 h/e^2 when studying the most probable value of the distribution function P(R_H). Upon further increasing R_L ->\infty the Hall insulator with diverging Hall resistance R_H \propto R_L^kappa is seen. The cr…
We have investigated the Hall resistance $R_H$ near the plateau-insulator transition of a two-dimensional electron gas in the quantum critical regime. High-field magnetotransport data taken on a low-mobility InGaAs/InP heterostructure with the plateau-insulator transition at a critical field $B_c$ of 17.2 T show that the Hall resistance $R_H$ is quantized at $h/e^2$ near the critical filling fraction ($ν_c$ = 0.55) when $T \to 0$. By making use of universal scaling functions extracted from the magnetotransport data we show that $R_H$ in the insulating phase in the limit $T \to 0$ is quantized …
The quantized version of the anomalous Hall effect has been predicted to occur in magnetic topological insulators, but the experimental realization has been challenging. Here, we report the observation of the quantum anomalous Hall (QAH) effect in thin films of Cr-doped (Bi,Sb)2Te3, a magnetic topological insulator. At zero magnetic field, the gate-tuned anomalous Hall resistance reaches the predicted quantized value of h/e^2,accompanied by a considerable drop of the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes whereas the Hall resistance remains…
Quite generally, an insulator is theoretically defined by a vanishing conductivity tensor at the absolute zero of temperature. In classical insulators, such as band insulators, vanishing conductivities lead to diverging resistivities. In other insulators, in particular when a high magnetic field (B) is added, it is possible that while the magneto-resistance diverges, the Hall resistance remains finite, which is known as a Hall insulator. In this letter we demonstrate experimentally the existence of another, more exotic, insulator. This insulator, which terminates the quantum Hall effect series…
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 …
The quantization of resistances in the quantum Hall effect and ballistic transport through quantum point contacts is compared with the quantization of the charge relaxation resistance of a coherent mesoscopic capacitor. While the former two require the existence of a perfectly transmitting channel, the charge relaxation resistance remains quantized for arbitrary backscattering. The quantum Hall effect and the quantum point contact require only local phase coherence. In contrast quantization of the charge relaxation resistance requires global phase coherence.
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…
Just a few of the promising applications of graphene Corbino pnJ devices include two-dimensional Dirac fermion microscopes, custom programmable quantized resistors, and mesoscopic valley filters. In some cases, device scalability is crucial, as seen in fields like resistance metrology, where graphene devices are required to accommodate currents of the order 100 μA to be compatible with existing infrastructure. However, fabrication of these devices still poses many difficulties. In this work, unusual quantized resistances are observed in epitaxial graphene Corbino p-n junction devices held at t…
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 …
The quantum Hall effect (QHE) is a topologically protected phenomenon which has been observed in various systems. In experiments, the size of Hall bar device to realize the QHE is generally much larger than the phase coherence length, in which the quantum coherence of electrons is destroyed. Here, we theoretically study the influence of dephasing effect on the quantized Hall (QH) plateaus. We find that the QH plateau disappears in perfectly quantum coherent systems if the coupling between leads and central region is imperfect. The Hall resistance is very large and strongly oscillates instead o…
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.
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…
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…
We have analyzed the breakdown of the quantum Hall effect in 1 micrometer wide Hall devices fabricated from an exfoliated monolayer graphene transferred on SiOx. We have observed that the deviation of the Hall resistance from its quantized value is weakly dependent on the longitudinal resistivity up to current density of 5 A/m, where the Hall resistance remains quantized even when the longitudinal resistance increases monotonously with the current. Then a collapse in the quantized resistance occurs while longitudinal resistance keeps its gradual increase. The exponential increase of the conduc…
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…
We predict by first-principles calculations that thin films of Cr-doped (Bi,Sb)$_2$Te$_3$ magnetic topological insulator have gapless non-chiral edge states coexisting with the chiral edge state. Such gapless non-chiral states are not immune to backscattering, which would explain dissipative transport in the quantum anomalous Hall (QAH) state observed in this system experimentally. Here we study the edge transport with both chiral and non-chiral states by Landaur-Büttiker formalism, and find that the longitudinal resistance is nonzero whereas Hall resistance is quantized to $h/e^2$. In particu…
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 study the current and charge distribution of a two dimensional electron gas under strong perpendicular magnetic fields within the linear response regime. We show within a self-consistent screening theory that incompressible strips with integer values of local Landau-level filling factor exist for finite intervals of the magnetic field strength $B$. Within an essentially local conductivity model, we find that the current density in these $B$ intervals is confined to the incompressible strips of vanishing local longitudinal resistivity. This leads to vanishing longitudinal and exactly quantiz…
We summarize the screening theory of the integer quantized Hall effect (IQHE) and emphasize its two key mechanisms: first, the existence, in certain magnetic field intervals, of incompressible strips, with integer values of the local filling factor and quantized values of longitudinal and Hall resistivity, and second, the confinement of an imposed dissipative current to these strips, leading to the quantization of the global resistances. We demonstrate that, without any localization assumption, this theory explains the enormous experimental reproducibility of the quantized resistance values, a…
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…
Quantum Resistance in Multilayer Graphene-BiFeO3 Memristor for Brain-Inspired Computing
Institute of Physics（印度物理研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Sambalpur University（桑巴尔普尔大学）；Chalmers University of Technology（查尔姆斯理工大学）；Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay（巴黎萨克雷大学纳米科学和纳米技术中心，法国国家科学研究中心）；Institute of Nano Science and Technology（纳米科学与技术研究所）；Indian Institute of Technology Madras（马德拉斯印度理工学院）
We report development of a quantum Hall resistance standard accurate to a few parts in a billion at 300 mK and based on large area epitaxial graphene. The remarkable precision constitutes an improvement of four orders of magnitude over the best results obtained in exfoliated graphene and is similar to the accuracy achieved in well-established semiconductor standards. Unlike the traditional resistance standards the novel graphene device is still accurately quantized at 4.2 K, vastly simplifying practical metrology. This breakthrough was made possible by exceptional graphene quality achieved wit…
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…
In a GaAs/AlGaAs two-dimensional electron system with two occupied subbands, the experimentally determined phase diagram in the density-magnetic field plane exhibits rich topological features. Ring-like structures are observed at even integer filling factors, in the phase diagram. Even with the identical quantized Hall resistance values as those given rise by the ordinary integer quantum Hall effect due to the Landau level quantization; the activation energies of these states within the rings are much smaller. These ring structures cannot account for by the simple single particle picture. We a…
Experimental and theoretical investigations on the integer quantized Hall effect in gate defined narrow Hall bars are presented. At low electron mobility the classical (high temperature) Hall resistance line RH(B) cuts through the center of all Hall plateaus. In contrast, for our high mobility samples the intersection point, at even filling factors ν= 2; 4 ..., is clearly shifted towards larger magnetic fields B. This asymmetry is in good agreement with predictions of the screening theory, i. e. taking Coulomb interaction into account. The observed effect is directly related to the formation o…
The two-dimensional metal forming at the interface between an oxide insulator and SrTiO3 provides new opportunities for oxide electronics. However, the quantum Hall effect, one of the most fascinating effects of electrons confined in two dimensions, remains underexplored at these complex oxide heterointerfaces. Here, we report the experimental observation of quantized Hall resistance in a SrTiO3 heterointerface based on the modulation-doped amorphous-LaAlO$_{3}$/SrTiO$_{3}$ heterostructure, which exhibits both high electron mobility exceeding 10000 cm$^{2}$/Vs and low carrier density on the or…
The Josephson effect in superconductors links a quantized output voltage Vout = f \cdot(h/2e) to the natural constants of the electron's charge e, Planck's constant h, and to an excitation frequency f with important applications in electrical quantum metrology. Also semiconductors are routinely applied in electrical quantum metrology making use of the quantum Hall effect. However, despite their broad range of further applications e.g. in integrated circuits, quantized voltage generation by a semiconductor device has never been obtained. Here we report a semiconductor quantized voltage source g…
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…
Series connection of four quantum Hall effect (QHE) devices based on epitaxial graphene films was studied for realization of a quantum resistance standard with an up-scaled value. The tested devices showed quantum Hall plateaux RH,2 at filling factor i = 2 starting from relatively low magnetic field (between 4 T and 5 T) when temperature was 1.5 K. Precision measurements of quantized Hall resistance of four QHE devices connected by triple series connections and external bonding wires were done at B = 7 T and T = 1.5 K using a commercial precision resistance bridge with 50 microA current throug…
We study a particle on a ring in presence of a dissipative Caldeira-Leggett environment and derive its response to a DC field. We find, through a 2-loop renormalization group analysis, that a large dissipation parameter $η$ flows to a fixed point $η_R=η_c=\hbar/2π$. We also reexamine the mapping of this problem to that of the Coulomb box and show that the relaxation resistance, of recent interest, is quantized for large $η$. For finite $η>η_c$ we find that a certain average of the relaxation resistance is quantized. We propose a box experiment to measure a quantized noise.
Recently,a half-quantized Hall conductance (HQHC) plateau is experimentally observed in a semi-magnetic topological insulator heterostructure. However,the heterostructure is metallic with a nonzero longitudinal conductance, which contradicts the common belief that quantized Hall conductance is usually observed in insulators.In this work,we systematically study the surface transport of the semi-magnetic topological insulator with both gapped and gapless Dirac surfaces in the presence of dephasing process.In particular, we reveal that the HQHC is directly related to the half-quantized chiral cur…
A striking prediction in topological insulators is the appearance of the quantized Hall resistance when the surface states are magnetized. The surface Dirac states become gapped everywhere on the surface, but chiral edge states remain on the edges. In an applied current, the edge states produce a quantized Hall resistance that equals the Chern number C = +1 or -1 (in natural units), even in zero magnetic field. This quantum anomalous Hall effect was observed by Chang et al. With reversal of the magnetic field, the system is trapped in a metastable state because of magnetic anisotropy. Here we …
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…
The Hall resistance of a homogeneous electron system is well known to be anti-symmetric with respect to the magnetic field and the sign of charge carriers. We have observed that such symmetries no longer hold in planar hybrid structures consisting of partly single layer graphene (SLG) and partly bilayer graphene (BLG) in the quantum Hall (QH) regime. In particular, the Hall resistance (R12xy) across the SLG and BLG interface is observed to exhibit quantized plateaus that switch between those characteristic of SLG QH states and BLG QH states when either the sign of the charge carriers (controll…
Since 2017, epitaxial graphene has been the base material for the US national standard for resistance. A future avenue of research within electrical metrology is to remove the need for strong magnetic fields, as is currently the case for devices exhibiting the quantum Hall effect. The quantum Hall effect is just one of many research endeavours that revolve around recent quantum physical phenomena like composite fermions, charge density waves, and topological properties [1-2]. New materials, like magnetically doped topological insulators (MTIs), offer access to the quantum anomalous Hall effect…
We investigate the resistance enhancement state (RES) where the magnetoresistance of the $ν= 2/3$ fractional quantum Hall state (FQHS) is increased with dynamic nuclear spin polarization (DNP) induced by a large electric current. After inducing DNP, we measure the temperature dependence of the magnetoresistance by a small current over a short period of time. We find that the FQHS makes a phase transition to an insulating state. By measuring the Hall resistance in the insulating state, we find that the RES exhibits a quantized Hall resistance. We discuss the RES in association with the Anderson…
We study the current and charge distribution in a two dimensional electron system, under the conditions of the integer quantized Hall effect, on the basis of a quasi-local transport model, that includes non-linear screening effects on the conductivity via the self-consistently calculated density profile. The existence of ``incompressible strips'' with integer Landau level filling factor is investigated within a Hartree-type approximation, and non-local effects on the conductivity along those strips are simulated by a suitable averaging procedure. This allows us to calculate the Hall and the lo…
In the quantum anomalous Hall effect, the edge states of a ferromagnetically doped topological insulator exhibit quantized Hall resistance and dissipationless transport at zero magnetic field. Up to now, however, the resistance was experimentally assessed with standard transport measurement techniques which are difficult to trace to the von-Klitzing constant R$_K$ with high precision. Here, we present a metrologically comprehensive measurement, including a full uncertainty budget, of the resistance quantization of V-doped (Bi,Sb)$_2$Te$_3$ devices without external magnetic field. We establishe…
A comprehensive understanding of quantum Hall edge transmission, especially the hole-conjugate of a Laughlin state such as a $2/3$ state, is critical for advancing fundamental quantum Hall physics and enhancing the design of quantum Hall edge interferometry. In this study, we report a robust intermediate $2h/e^2$ resistance quantization in a quantum point contact (QPC) when the bulk is set at the fractional filling $2/3$ quantum Hall state. Our results suggest the occurrence of two equilibration processes. First, the co-propagating $1/3$ edges moving along a soft QPC arm confining potential fu…
We study a particle on a ring in presence of a dissipative Caldeira-Leggett environment and derive its response to a DC field. We show how this non-equilibrium response is related to a flux averaged equilibrium response. We find, through a 2-loop renormalization group analysis, that a large dissipation parameter ηflows to a fixed point η^R=\hbar/2π. We also reexamine the mapping of this problem to that of the Coulomb box and show that the relaxation resistance, of recent interest, is quantized for large η. For finite η>η^R we find that a certain average of the relaxation resistance is quantize…
The quantum Hall effect (QHE) with quantized Hall resistance of h/νe2 starts the research on topological quantum states and lays the foundation of topology in physics. Afterwards, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C|=1, which has been experimentally observed at relatively low temperatures. For emerging physics and low-power-consumption electronics, the key issues are how to increase the working temperature and realize high Chern numbers (C>1). Here, we report the experimental discovery of high-Chern-number QHE (C=2) without Landau levels and C=1 Cher…
