Gate-voltage-induced realization of different rational fractions ofh/e2at fixed values of current and magnetic field

We present magnetotransport measurement results obtained on samples with a window-shaped geometry and Schottky gates in the quantum Hall regime. The investigated samples consist of two Hall bars shorted by wide regions of 2DEG. With Schottky gates across each of the Hall bars electron densities and hence filling factors within the two arms of the structures can individually be tuned.We show that by applying appropriate gate voltages to the samples four-terminal resistances equal to different rational fractions ofh/e²can be realized at fixed magnetic field. The measurement results can be explained in the edge channel picture of the quantum Hall effect as well as in a local transport model. In both models it is the interplay between the gate-voltage-induced sub-gate filling factors and the resulting partition of the total current onto the two sample arms that leads to the observed phenomena.     

Near-perfect correlation of the resistance components of mesoscopic samples at the quantum Hall regime

We study the four-terminal resistance fluctuations of mesoscopic samples near the transition between the nu=2 and the nu=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 transitions.     

Counterflow measurements in strongly correlated GaAs hole bilayers: evidence for electron-hole pairing

We study interacting GaAs bilayer hole systems, with very small interlayer tunneling, in a counterflow geometry where equal currents are passed in opposite directions in the two, independently contacted layers. At low temperatures, both the longitudinal and Hall counterflow resistances tend to vanish in the quantum Hall state at total bilayer filling nu=1, demonstrating the pairing of oppositely charged carriers in opposite layers. The counterflow Hall resistance decreases much more strongly than the longitudinal resistances as the temperature is reduced.     

Integer quantum Hall effect in a PbTe quantum well

Transport measurements have been carried out on a 10 nm n-type PbTe/Pb_0.9Eu_0.1Te quantum well at millikelvin temperatures. The Hall and longitudinal resistances are measured in a Van der Pauw geometry under high magnetic fields up to 23 T. A robust signature of the integer quantum Hall effect is observed without any sign of parasitic parallel conduction. The unconventional sequence of filling factors associated with the integer quantum Hall effect is discussed in terms of the occupancy of multiple valleys.     

The effect of carrier density gradients on magnetotransport data measured in Hall bar geometry

We have measured magnetotransport of the two-dimensional electron gas in a Hall bar geometry in the presence of small carrier density gradients. We find that the longitudinal resistances measured at both sides of the Hall bar interchange by reversing the polarity of the magnetic field. We offer a simple explanation for this effect and discuss implications for extracting conductivity flow diagrams of the integer quantum Hall effect.     

Edge current switch of two-dimensional electron gas using carrier density control

We have investigated the effects of electron density discontinuity on the transports of edge currents of two-dimensional electron gas (2DEG). The electric field applied to a gate, which covers the 2DEG partially, gives rise to change in the carrier density and results in a density gradient, which deforms the edge currents. The transverse and longitudinal resistances were measured as functions of gate voltage V_G in the quantum Hall regime. The deviations of the longitudinal resistances from the normal quantum Hall resistances are attributed to the reflections of the edge currents under the influence of the abrupt density discontinuity. A switching behavior of the transverse resistance by controlling the gate voltage was observed when V_G=−2.2 and −2.0 V for magnetic field H=5 and 7.2 T, respectively.     

Current correlations in quantum spin Hall insulators

We consider a four-terminal setup of a two-dimensional topological insulator (quantum spin Hall insulator) with local tunneling between the upper and lower edges. The edge modes are modeled as helical Luttinger liquids and the electron-electron interactions are taken into account exactly. Using perturbation theory in the tunneling, we derive the cumulant generating function for the interedge current. We show that different possible transport channels give rise to different signatures in the current noise and current cross correlations, which could be exploited in experiments to elucidate the interplay between electron-electron interactions and the helical nature of the edge states.     

Quantum hall effect in an antidot lattice: Macroscopic limit

The quantum Hall effect in a 2D system with antidots is studied. The antidots are assumed to be large compared with the quantum and relaxation lengths. In this approximation the electric field in the system can be described by the continuity equation. It is found that the electric field in a system without conducting boundaries can be expressed in terms of the same system without a magnetic field. Specific problems of the electric field and current in structures containing one or two antidots and in a circular disk with point contacts are solved. The effective Hall and longitudinal conductivities in a sample containing a large number of randomly distributed antidots are found. In the limit of zero local longitudinal conductivity, the effective longitudinal conductivity also vanishes, and the Hall conductivity is equal to the local conductivity. The corrections to the conductivity tensor which are due to the finiteness of the local conductivity are obtained. Breakdown of the quantum Hall effect in a lattice of antidots is studied on the basis of the assumption that a high current density in narrow locations of the system results in overheating of the electrons. Local and nonlocal models of over-heating are studied. The high-frequency effective conductivity of a system with antidots and the shift of the cyclotron resonance frequency are found.     

Role of coherence in resistance quantization

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.     

声子晶体中的多重拓扑相

研究了圆环型波导依照蜂窝结构排列的声子晶体系统中的拓扑相变.利用晶格结构的点群对称性实现赝自旋,并在圆环中引入旋转气流来打破时间反演对称性.通过紧束缚近似模型计算的解析结果表明,没有引入气流时,调节几何参数,系统存在普通绝缘体和量子自旋霍尔效应绝缘体两个相;引入气流后,可以实现新的时间反演对称性破缺的量子自旋霍尔效应相,而增大气流强度,则可以实现量子反常霍尔效应相.这三个拓扑相可以通过自旋陈数来分类.通过有限元软件模拟了多个系统中边界态的传播,发现不同于量子自旋霍尔效应相,量子反常霍尔相系统的表面只支持一种自旋的边界态,并且它无需时间反演对称性保护.     

Ballistic transport in InSb quantum wells at high temperature

Measurements were made on a 0.2 μm four-terminal device, fabricated from an InSb/Al_0.15In_0.85Sb quantum well structure, at temperatures from 1.5 to 300 K. Negative bend resistance, a signature of ballistic transport, was observed at temperatures up to 205 K. The disappearance of the negative bend resistance at higher temperatures was accompanied by a non-linear dependence of the Hall voltage on magnetic field. The non-linearity indicates multiple-carrier conduction, which we characterize using quantitative mobility spectrum analysis.     

Measurement of the ν=1/3 fractional quantum hall energy gap in suspended graphene

We report on magnetotransport measurements of multiterminal suspended graphene devices. Fully developed integer quantum Hall states appear in magnetic fields as low as 2 T. At higher fields the formation of longitudinal resistance minima and transverse resistance plateaus are seen corresponding to fractional quantum Hall states, most strongly for ν=1/3. By measuring the temperature dependence of these resistance minima, the energy gap for the 1/3 fractional state in graphene is determined to be at ～20 K at 14 T.     

From magnetically doped topological insulator to the quantum anomalous Hall effect

Quantum Hall effect （QHE）, as a class of quantum phenomena that occur in macroscopic scale, is one of the most important topics in condensed matter physics. It has long been expected that QHE may occur without Landau levels so that neither external magnetic field nor high sample mobility is required for its study and application, Such a QHE free of Landau levels, can appear in topological insulators （TIs） with ferromagnetism as the quantized version of the anomalous Hall effect, i.e., quantum anomalous Hall （QAH） effect. Here we review our recent work on experimental realization of the QAH effect in magnetically doped TIs. With molecular beam epitaxy, we prepare thin films of Cr-doped （Bi,Sb）2Te3 TIs with well- controlled chemical potential and long-range ferromagnetic order that can survive the insulating phase. In such thin films, we eventually observed the quantization of the Hall resistance at h/e2 at zero field, accompanied by a considerable drop in the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes, whereas the Hall resistance remains at the quantized value. The realization of the QAH effect provides a foundation for many other novel quantum phenomena predicted in TIs, and opens a route to practical applications of quantum Hall physics in low-power-consumption electronics.     

Bilayer counterflow transport at filling factor 1 in the strong interacting regime

We review magneto-transport properties of interacting GaAs bilayer hole systems, with very small inter-layer tunneling, in a geometry where equal currents are passed in opposite directions in the two, independently contacted layers (counterflow). In the quantum Hall state at total bilayer filling ν=1 both the longitudinal and Hall counterflow resistances tend to vanish in the limit of zero temperature, suggesting the existence of a superfluid transport mode in the counterflow geometry. As the density of the two layers is reduced, making the bilayer more interacting, the counterflow Hall resistivity (ρ_xy) decreases at a given temperature while the counterflow longitudinal resistivity (ρ_xx), which is much larger than ρ_xy, hardly depends on density. Our data suggest that the counterflow dissipation present at any finite temperature is a result of mobile vortices in the superfluid created by the ubiquitous disorder in this system.     

Fractional Quantum Hall Effect in SiGe/Si/SiGe Quantum Wells in Weak Quantizing Magnetic Fields

We have experimentally studied the fractional quantum Hall effect in SiGe/Si/SiGe quantum wells in relatively weak magnetic fields, where the Coulomb interaction between electrons exceeds the cyclotron splitting by a factor of a few XX. Minima of the longitudinal resistance have been observed corresponding to the quantum Hall effect of composite fermions with quantum numbers p = 1, 2, 3, and 4. Minima with p = 3 disappear in magnetic fields below 7 T, which may be a consequence of the intersection or even merging of the quantum levels of the composite fermions with different orientations of the pseudo-spin, i.e., those belonging to different valleys. We have also observed minima of the longitudinal resistance at filling factors ν = 4/5 and 4/11, which may be due to the formation of the second generation of the composite fermions.     

Gate-defined graphene quantum point contact in the quantum Hall regime

We investigate transport in a gate-defined graphene quantum point contact in the quantum Hall regime. Edge states confined to the interface of p and n regions in the graphene sheet are controllably brought together from opposite sides of the sample and allowed to mix in this split-gate geometry. Among the expected quantum Hall features, an unexpected additional plateau at 0.5h/e2 is observed. We propose that chaotic mixing of edge channels gives rise to the extra plateau.     

Vanishing Hall resistance at high magnetic field in a double-layer two-dimensional electron system

At total Landau level filling factor nu(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 nu(tot)=1 is an excitonic superfluid.     

Rashba-induced transverse pure spin currents in a four-terminal quantum dot ring

By applying a local Rashba spin–orbit interaction to an individual quantum dot of a four-terminal four-quantum-dot ring and introducing a finite bias between the longitudinal terminals, we theoretically investigate the charge and spin currents in the transverse terminals. It is found that when the quantum dot levels are separate from the chemical potentials of the transverse terminals, notable pure spin currents appear in the transverse terminals with the same amplitude but opposite polarization directions. In addition, the polarization directions of such pure spin currents can be inverted by altering the structure parameters, i.e., the magnetic flux, the bias voltage, and the values of quantum dot levels with respect to the chemical potentials of the transverse terminals.