Manifestation of the bulk phase transition in the edge energy spectrum in a two-dimensional bilayer electron system

We use a quasi-Corbino sample geometry with independent contacts to different edge states in the quantum Hall effect regime to investigate the edge energy spectrum of a bilayer electron system at a total filling factor of ν=2. By analyzing nonlinear I–V curves in normal and tilted magnetic fields, we conclude that the edge energy spectrum is in a close connection with the bulk one. At the bulk phase transition spin-singlet-canted antiferromagnetic phase, the I–V curve becomes linear, indicating the disappearance or strong narrowing of the ν=1 incompressible strip at the edge of the sample.     

Effective field theory and tunneling currents in the fractional quantum Hall effect

We review the construction of a low-energy effective field theory and its state space for “abelian” quantum Hall fluids. The scaling limit of the incompressible fluid is described by a Chern–Simons theory in 2+1 dimensions on a manifold with boundary. In such a field theory, gauge invariance implies the presence of anomalous chiral modes localized on the edge of the sample. We assume a simple boundary structure, i.e., the absence of a reconstructed edge. For the bulk, we consider a multiply connected planar geometry. We study tunneling processes between two boundary components of the fluid and calculate the tunneling current to lowest order in perturbation theory as a function of dc bias voltage. Particular attention is paid to the special cases when the edge modes propagate at the same speed, and when they exhibit two significantly distinct propagation speeds. We distinguish between two “geometries” of interference contours corresponding to the (electronic) Fabry–Perot and Mach–Zehnder interferometers, respectively. We find that the interference term in the current is absent when exactly one hole in the fluid corresponding to one of the two edge components involved in the tunneling processes lies inside the interference contour (i.e., in the case of a Mach–Zehnder interferometer). We analyze the dependence of the tunneling current on the state of the quantum Hall fluid and on the external magnetic flux through the sample.     

Ettingshausen effect around a Landau level filling factor nu = 3 studied by dynamic nuclear polarization

A spin current perpendicular to the electric current is investigated around a Landau level filling factor nu=3 in a GaAs/AlGaAs two-dimensional electron system. Measurements of dynamic nuclear polarization in the vicinity of the edge of a specially designed Hall bar sample indicate that the direction of the spin current with respect to the Hall electric field reverses its polarity at nu=3, where the dissipative current carried by holes in the spin up Landau level is replaced with that by electrons in the spin down Landau level.     

Effects of electric and magnetic fields on electronic states and transport of a Hall bar

We study the edge-state band and transport property for a HgTe/CdTe quantum well Hall bar under the combined coupling of a transverse electric field and a perpendicular magnetic field. It is demonstrated that a weak magnetic field can protect one of the two edge states, open or enlarge a gap of the other edge state in the Hall bar. However, an appropriate electric field can remove the gap, restoring the quantum spin Hall effect. Using the scattering matrix method, we study the electronic transport of the system. We find that the electric field can not only make the switch from pure spin-up to spin-down current, but also open or close the edge-state channels in a narrow Hall bar under a weak magnetic field, which provides us with a new way to construct a topological insulator-based spin switch and charge switch.     

Quench dynamics of edge states in 2-D topological insulator ribbons

We study the dynamics of edge states of the two dimensional BHZ Hamiltonian in a ribbon geometry following a sudden quench to the quantum critical point separating the topological insulator phase from the trivial insulator phase. The effective edge state Hamiltonian is a collection of decoupled qubit-like two-level systems which get coupled to bulk states following the quench. We notice a pronounced collapse and revival of the Lochschmidt echo for low-energy edge states illustrating the oscillation of the state between the two edges. We also observe a similar collapse and revival in the spin Hall current carried by these edge states, leading to a persistence of its time-averaged value.     

"Wormhole" geometry for entrapping topologically protected qubits in non-abelian quantum hall states and probing them with voltage and noise measurements

We study a tunneling geometry defined by a single point-contact constriction that brings to close vicinity two points sitting at the same edge of a quantum Hall liquid, shortening the trip between the otherwise spatially separated points along the normal chiral edge path. This wormhole-like geometry allows for entrapping bulk quasiparticles between the edge path and the tunnel junction, possibly realizing a topologically protected qubit if the quasiparticles have non-Abelian statistics. We show how either noise or simpler voltage measurements along the edge can probe the non-Abelian nature of the trapped quasiparticles.     

Switching noise as a probe of statistics in the fractional quantum Hall effect

We propose an experiment to probe the unconventional quantum statistics of quasiparticles in fractional quantum Hall states by measurement of current noise. The geometry we consider is that of a Hall bar where two quantum point contacts introduce two interfering amplitudes for backscattering. Thermal fluctuations of the number of quasiparticles enclosed between the two point contacts introduce current noise, which reflects the statistics of the quasiparticles. We analyze Abelian nu=1/q states and the non-Abelian nu=5/2 state.     

Spontaneous Edge Currents for the Dirac Equation in Two Space Dimensions

Spontaneous edge currents are known to occur in systems of two space dimensions in a strong magnetic field. The latter creates chirality and determines the direction of the currents. Here we show that an analogous effect occurs in a field-free situation when time reversal symmetry is broken by the mass term of the Dirac equation in two space dimensions. On a half plane, one sees explicitly that the strength of the edge current is proportional to the difference between the chemical potentials at the edge and in the bulk, so that the effect is analogous to the Hall effect, but with an internal potential. The edge conductivity differs from the bulk (Hall) conductivity on the whole plane. This results from the dependence of the edge conductivity on the choice of a selfadjoint extension of the Dirac Hamiltonian. The invariance of the edge conductivity with respect to small perturbations is studied in this example by topological techniques Mathematics Subject Classification (2000). 81Q10, 58J32     

Quantum hall effect in Ge1-XSiX/(111)Ge MQW samples of non-standard six-point contact geometry

We investigate the Quantum Hall Effect (QHE) in selectively boron-doped GeSi/(111)Ge multi-quantum well (MQW) samples of non standard geometry with six-point contacts disconnected from the sample edges. The Hall resistance shows a well-pronounced quantisation that is consistent with integral QHE (IQHE) value (h/ve²) at temperature T = 4.2K. When the temperature was lower than 2.5K, unusual peaks on the R_xy QHE plateaux were observed. We explain this behaviour by non-equilibrium population of Landau levels that results from the separation of current contacts from the edge of the sample.     

Electrical readout of the local nuclear polarization in the quantum Hall effect: a hyperfine battery

It is demonstrated that the now well-established "flip-flop" mechanism of spin exchange between electrons and nuclei in the quantum Hall effect can be reversed. We use a sample geometry which utilizes separately contacted edge states to establish a local nuclear spin polarization--close to the maximum value achievable--by driving a current between electron states of different spin orientation. When the externally applied current is switched off, the sample exhibits an output voltage of up to a few tenths of a mV, which decays with a time constant typical for the nuclear spin relaxation. The surprising fact that a sample with a local nuclear spin polarization can act as a source of energy and that this energy is well above the nuclear Zeeman splitting is explained by a simple model which takes into account the effect of a local Overhauser shift on the edge state reconstruction.     

Charge redistribution between cyclotron-resolved edge states at high imbalance

We use a quasi-Corbino sample geometry with independent contacts to different edge states in the quantum Hall effect regime to investigate a charge redistribution between cyclotron-split edge states at high imbalance. We also modify the Büttiker formalism by introducing local transport characteristics in it and use this modified Büttiker picture to describe the experimental results. We find that charge transfer between cyclotron-split edge states at high imbalance can be described by a single parameter, which is a transferred between edge states portion of the available for transfer part of the electrochemical potential imbalance. This parameter is found to be independent of the particular sample characteristics, describing fundamental properties of the interedge-state scattering. From the experiment we obtain it in the dependence on the voltage imbalance between edge states and propose a qualitative explanation to the experimental findings.     

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.     

Current filamentation in GaAs/AlGaAs heterojunctions preceding quantum-Hall-effect breakdown

Self-induced filamentation of the current near the edges of a sample in the Hall geometry has been observed in the quantum-Hall-effect regime in a two-dimensional electronic system arising near a GaAs/AlGaAs heterojunction. If in the case of integer values of the filling factor ν averaged over the sample the currents flowing along opposite edges are approximately the same, then away from such a value within the quantum plateau the current is increasingly concentrated near that edge of the sample where the local value of ν is closer to being an integer. When the direction of the magnetic field or of the current changes, the filament switches to the opposite edge of the sample. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 9, 700–704 (10 November 1998)     

Edge and Impurity Effects on Quantization of Hall Currents

We consider the edge Hall conductance and show it is invariant under perturbations located in a strip along the edge (decaying perturbations far from the edge are also allowed). This enables us to prove for the edge conductances a general sum rule relating currents due to the presence of two different media located respectively on the left and on the right half plane. As a particular interesting case we put forward a general quantization formula for the difference of edge Hall conductances in semi-infinite samples with and without a confining wall. It implies in particular that the edge Hall conductance takes its ideal quantized value under a gap condition for the bulk Hamiltonian, or under some localization properties for a random bulk Hamiltonian (provided one first regularizes the conductance; we shall discuss this regularization issue). Our quantization formula also shows that deviations from the ideal value occurs if a semi-infinite distribution of impurity potentials is repulsive enough to produce current-carrying surface states on its boundary.UPR 7061 au CNRSUMR 8088 au CNRS     

磁场中的拓扑绝缘体边缘态性质

用数值方法研究了拓扑绝缘体薄膜体系在外加垂直磁场 作用下其边缘态的性质. 磁场的加入通过耦合k+eA, 即Peierls势替换关系和 该作用导致的Zeeman交换场体现在哈密顿量中. 考虑窄条圆环状结构的二维InAs/GaSb/AlSb薄膜量子阱材料, 当其处于拓扑非平庸状态, 即量子自旋霍尔态时, 会出现受时间反演对称性保护的两支简并边缘态, 而在垂直磁场的作用下, 时间反演对称性被破坏, 这时能带将形成一条条的朗道能级, 原来简并的两支边缘态也会分开到朗道能级谱线的两侧, 从电子态密度的空间分布情况则可以看到边缘态分别局域在材料的两个边界. 随着磁场的增大, 位于同一边界上的不同 自旋极化的边缘态将出现分离: 一支仍然局域在边缘, 另一支则随外加磁场的增加而有逐渐演化到材料内部的趋势. 文中还计算了同一边界上的两支边缘态之间的散射, 结果表明由于两个边缘态在空间发生分离, 相互之间的散射被很大的压制, 得到了其散射随磁场增加没有明显变化的结论, 所以磁场并不会增强散射过程, 也没有破坏体拓扑材料的性质, 说明了量子自旋霍尔态在没有时间反演对称的情况下也可以有较强的稳定性.     

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.     

Neutral excitation and bulk gap of fractional quantum Hall liquids in disk geometry

For the numerical simulation of the fractional quantum Hall(FQH) effects on a finite disk, the rotational symmetry is the only symmetry that is used in diagonalizing the Hamiltonian. In this work, we propose a method of using the weak translational symmetry for the center of mass of the many-body system. With this approach, the bulk properties, such as the energy gap and the magneto-roton excitation are consistent with those in the closed manifolds like the sphere and torus. As an application, we consider the FQH phase and its phase transition in the fast rotated dipolar fermions. We thus demonstrate the disk geometry having versatility in analyzing the bulk properties beside the usual edge physics.     

Intrinsic spin and orbital angular momentum Hall effect

A generalized definition of intrinsic and extrinsic transport coefficients is introduced. We show that transport coefficients from the intrinsic origin are solely determined by local electronic structure, and thus the intrinsic spin Hall effect is not a transport phenomenon. The intrinsic spin Hall current is always accompanied by an equal but opposite intrinsic orbital angular momentum Hall current. We prove that the intrinsic spin Hall effect does not induce a spin accumulation at the edge of the sample or near the interface.     

Generating spin currents in semiconductors with the spin Hall effect

We investigate electrically induced spin currents generated by the spin Hall effect in GaAs structures that distinguish edge effects from spin transport. Using Kerr rotation microscopy to image the spin polarization, we demonstrate that the observed spin accumulation is due to a transverse bulk electron spin current, which can drive spin polarization nearly 40 microns into a region in which there is minimal electric field. Using a model that incorporates the effects of spin drift, we determine the transverse spin drift velocity from the magnetic field dependence of the spin polarization.     

Observation of an interedge magnetoplasmon mode in a degenerate two-dimensional electron gas

We study the propagation of edge magnetoplasmons by time-resolved current measurements in a sample which allows for selective detection of edge states in the quantum Hall regime. At filling factors close to nu=3 we observe two decoupled modes of edge excitations, one of which is related to the innermost compressible strip and is identified as an interedge magnetoplasmon mode. From the analysis of the propagation velocities of each mode the internal spatial parameters of the edge structure are derived.