Imaging of Coulomb-driven quantum Hall edge states

The edges of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime are divided into alternating metallic and insulating strips, with their widths determined by the energy gaps of the QHE states and the electrostatic Coulomb interaction. Local probing of these submicrometer features, however, is challenging due to the buried 2DEG structures. Using a newly developed microwave impedance microscope, we demonstrate the real-space conductivity mapping of the edge and bulk states. The sizes, positions, and field dependence of the edge strips around the sample perimeter agree quantitatively with the self-consistent electrostatic picture. The evolution of microwave images as a function of magnetic fields provides rich microscopic information around the ν=2 QHE state.     

Magnetic quantum ring in two-dimensional topological insulators

The quantum properties of topological insulator magnetic quantum rings formed by inhomogeneous magnetic fields are investigated using a series expansion method for the modified Dirac equation. Cycloid-like and snake-like magnetic edge states are respectively found in the bulk gap for the normal and inverted magnetic field profiles. The energy spectra, current densities and classical trajectories of the magnetic edge states are discussed in detail. The bulk band inversion is found to manifest itself through the angular momentum transition in the ground state for the cycloid-like states and the resonance tunneling effect for the snake-like states.     

Electron structure of a 2D crystalline stripe in magnetic fields

Edge states in the 2DEG systems play an important role in magnetotransport phenomena in strong magnetic fields. Even in the strongest magnetic field available, spacing of discrete Landau levels cannot be considered large in comparison with the crystalline potential. A treatment considering both the crystalline and magnetic field effects on the same level is presented by means of the surface Green function formalism complemented by the transfer matrix method. Formation of the electron band structure of a stripe of finite width is evaluated as a function of the stripe width especially with respect to localized edge states. Influence of perpendicular magnetic fieds on energy spectrum is displayed.     

Edge state propagation direction in the fractional quantum Hall regime: multi-terminal magnetocapacitance experiment

The propagation direction of fractional quantum Hall effect (FQHE) edge states has been investigated experimentally via the symmetry properties of the multi-terminal capacitances of a two-dimensional electron gas. Although strong asymmetries with respect to zero magnetic field appear, no asymmetries with respect to even denominator Landau level filling factor ν are seen. This indicates that current-carrying FQHE edge states propagate in the same direction as integer QHE edge states. In addition, anomalous capacitance features, indicative of enhanced bulk conduction, are observed at and .     

Spin edge helices in a perpendicular magnetic field

We present an exact solution to the problem of the spin edge states in the presence of equal Bychkov-Rashba and Dresselhaus spin-orbit fields in a two-dimensional electron system, restricted by a hard-wall confining potential and exposed to a perpendicular magnetic field. We find that the spectrum of the spin edge states depends critically on the orientation of the sample edges with respect to the crystallographic axes. Such a strikingly different spectral behavior generates new modes of the persistent spin helix-spin edge helices with novel properties, which can be tuned by the applied electric and magnetic fields.     

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.     

Evidence for a new dissipationless effect in 2D electronic transport

In an ultraclean 2D electron system (2DES) subjected to crossed millimeterwave (30-150 GHz) and weak (B<2 kG) magnetic fields, a series of apparently dissipationless states emerges as the system is detuned from cyclotron resonances. Such states are characterized by an exponentially vanishing low-temperature diagonal resistance and a classical Hall resistance. The activation energies associated with such states exceed the Landau level spacing by an order of magnitude. Our findings are likely indicative of a collective ground state previously unknown for 2DES.     

Pseudomagnetic fields and Landau levels for out-of-plane elastic waves in gradient snowflake-shaped crystals

The study of pseudomagnetic fields (PMF) in classical waves draws a growing attention due to the strength of PMF far higher than real magnetic fields. Here, we show that a giant PMF for out-of-plane elastic waves can be created in the snowflake-shaped crystals by introducing a gradient angle modulation along one direction. In particular, we demonstrate that the Landau energy levels for out-of-plane elastic waves can be formed near the Dirac cone region, as a hallmark of high-field physics induced by PMF. Moreover, the sublattice polarized bulk states similar to the behavior of graphene electron in magnetic fields are achieved in our elastic systems. Furthermore, the magnetic-induced edge state propagation along bend pathway is also demonstrated. Our study provides a new paradigm for manipulating the elastic waves in aspects of information processing and energy transport.     

Notes on infinite layer quantum Hall systems

We study the fractional quantum Hall effect in three-dimensional systems consisting of infinitely many stacked two-dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics such as quasiparticles with non-trivial internal structure, irrational braiding phases, and the necessity of a boundary hierarchy construction for interlayer correlated states. The bulk states host a family of surface phases obtained by hybridizing the edge states in each layer. We analyze the surface conduction in these phases by means of sum rule and renormalization group arguments and by explicit computations at weak tunneling in the presence of disorder. We find that in cases where the interlayer electron tunneling is not relevant in the clean limit, the surface phases are chiral semi-metals that conduct only in the presence of disorder or at finite temperature. We show that this class of problems which are naturally formulated as interacting bosonic theories can be fermionized by a general technique that could prove useful in the solution of such “one and a half” dimensional problems.     

THz imaging of cyclotron emission in quantum Hall conductors

Recent studies of cyclotron emission microscopy on quantum Hall related states are reported. The topics include non-equilibrium between edge and bulk states, current-induced breakdown of the quantum Hall effect, and the emission threshold at hot spots. Experimental method of scanning-type terahertz microscopes developed towards photon-counting level sensitivity is also described.     

Strong coupling between a permalloy ferromagnetic contact and helical edge channel in a narrow HgTe quantum well

We experimentally investigate spin-polarized electron transport between a permalloy ferromagnet and the edge of a two-dimensional electron system with band inversion, realized in a narrow, 8 nm wide, HgTe quantum well. In zero magnetic field, we observe strong asymmetry of the edge potential distribution with respect to the ferromagnetic ground lead. This result indicates that the helical edge channel, specific for the structures with band inversion even at the conductive bulk, is strongly coupled to the ferromagnetic side contact, possibly due to the effects of proximity magnetization. This allows selective and spin-sensitive contacting of helical edge states.     

Spontaneously gapped ground state in suspended bilayer graphene

Bilayer graphene bears an eightfold degeneracy due to spin, valley, and layer symmetry, allowing for a wealth of broken symmetry states induced by magnetic or electric fields, by strain, or even spontaneously by interaction. We study the electrical transport in clean current annealed suspended bilayer graphene. We find two kinds of devices. In bilayers of type B1 the eightfold zero-energy Landau level is partially lifted above a threshold field revealing an insulating ν=0 quantum-Hall state at the charge neutrality point. In bilayers of type B2 the Landau level lifting is full and a gap appears in the differential conductance even at zero magnetic field, suggesting an insulating spontaneously broken symmetry state. Unlike B1, the minimum conductance in B2 is not exponentially suppressed, but remains finite with a value G is < or approximately equall to e(2)/h even in a large magnetic field. We suggest that this phase of B2 is insulating in the bulk and bound by compressible edge states.     

Electrical manipulation and measurement of spin properties of quantum spin Hall edge states

We study the effects of a gate-controlled Rashba spin-orbit coupling to quantum spin Hall edge states in HgTe quantum wells. A uniform Rashba coupling can be employed in tuning the spin orientation of the edge states while preserving the time-reversal symmetry. We introduce a sample geometry where the Rashba coupling can be used in probing helicity by purely electrical means without requiring spin detection, application of magnetic materials or magnetic fields. In the considered setup a tilt of the spin orientation with respect to the normal of the sample leads to a reduction in the two-terminal conductance with current-voltage characteristics and temperature dependence typical of Luttinger liquid constrictions.     

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.     

Novel optical probe for quantum Hall system

Surface photovoltage (SPV) spectroscopy has been used for the first time to explore Landau levels of a two-dimensional electron gas (2DEG) in modulation doped InP/InGaAs/InP QW in the quantum Hall regime. The technique gives spectroscopically distinct signals from the bulk Landau levels and the edge states. Evolution of the bulk Landau levels and the edge electronic states is investigated at 2.0 K for magnetic field up to 8 T using SPV spectroscopy.     

Electron transport in magnetic-field-induced quasi-one-dimensional electron systems in semiconductor nanowhiskers

Many-body effects on tunneling of electrons in semiconductor nanowhiskers are investigated in a magnetic quantum limit. We consider the system with which bulk and edge states coexist. We show that interaction parameters of edge states are much smaller than those of bulk states and the tunneling conductance of edge states hardly depends on temperature and the singular behavior of tunneling conductance of bulk states can be observed.     

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     

Criticality in a non-equilibrium,driven system: Charged colloidal rods (fd-viruses) in electric fields

Experiments on suspensions of charged colloidal rods (fd-virus particles) in external electric fields are performed, which show that a non-equilibrium critical point can be identified. Several transition lines of field-induced phases and states meet at this point and it is shown that there is a length- and time-scale which diverge at the non-equilibrium critical point. The off-critical and critical behavior is characterized, with both power law and logarithmic divergencies. These experiments show that analogous features of the classical, critical divergence of correlation lengths and relaxation times in equilibrium systems are also exhibited by driven systems that are far out of equilibrium, related to phases/states that do not exist in the absence of the external field.     

New type of conductivity?

Experiments yielded rapid rise in the Hall gr_xy and magnetoresistance ρ_xx, ρ_zz in Hg_0.76Cd_0.24Te to almost linear dependence in strong magnetic fields. This paper relates it to the states, which are extended at the Hall edge for ρ_xy and between the Hall edges for ρ_xx, ρ_zz, while bulk states are localized. Theory agrees with experiments, and suggests that thin enough samples may have zero magnetoresistance in strong enough magnetic fields.