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.     

Integer quantum Hall effect in trilayer graphene

By using high-magnetic fields (up to 60 T), we observe compelling evidence of the integer quantum Hall effect in trilayer graphene. The magnetotransport fingerprints are similar to those of the graphene monolayer, except for the absence of a plateau at a filling factor of ν=2. At a very low filling factor, the Hall resistance vanishes due to the presence of mixed electron and hole carriers induced by disorder. The measured Hall resistivity plateaus are well reproduced theoretically, using a self-consistent Hartree calculations of the Landau levels and assuming an ABC stacking order of the three layers.     

Correlated electron states at level crossings of bilayer two-dimensional electron systems in tilted magnetic fields

We have measured the energy-level structure of high mobility, strongly coupled bilayer two-dimensional electron systems in tilted magnetic fields by means of magnetotransport experiments. At tilt angles where single-particle levels with opposite spin and symmetry cross, we observe a surprising sudden broadening of the quantum Hall plateaus and a deepening of the Shubnikov–de Haas minima. This observation is explained by an interaction-induced rearrangement of the energy level structure which strongly increases the energetic splitting of two (anti-)crossing levels.     

Fractional Quantum Conductance Plateaus in Mosaic‐Like Conductors and Their Similarities to the Fractional Quantum Hall Effect

A simple route to generate magnetotransport data is reported that results in fractional quantum Hall plateaus in the conductance without invoking strongly correlated physics. Ingredients to the generating model are conducting tiles with integer quantum Hall effect and metallic linkers, further Kirchhoff rules. When connecting few identical tiles in a mosaic, fractional steps occur in the conductance values. Richer spectra representing several fractions occur when the tiles are parametrically varied. Parts of the simulation data are supported with purposefully designed graphene mosaics in high magnetic fields. The findings emphasize that the occurrence of fractional conductance values, in particular in two‐terminal measurements, does not necessarily indicate interaction‐driven physics. The importance of an independent determination of charge densities is underscored and similarities with and differences to the fractional quantum Hall effect are critically discussed.     

Universal behaviour of metal–insulator transitions in the p-SiGe system

Magnetoresistance measurements are presented for a strained p-SiGe quantum well sample where the density is varied through the B=0 metal–insulator transition. The close relationship between this transition, the high-field Hall insulator transition and the filling factor insulating state is demonstrated.     

Spin-dependent electron transport in a type II GaInAsSb/p-InAs heterojunction doped with Mn in quantized magnetic fields

We report a study of spin-related magnetotransport properties of a type II broken-gap heterostructure formed by InAs substrate bulky doped with Mn and δ-Mn-doped GaInAsSb epilayer. Planar and vertical quantum magnetotransport in a 2D-electron-hole system at the single type II broken-gap InAs/GaInAsSb heterointerface was investigated in high magnetic fields under the quantum Hall regime up to 15 T at low temperature (T=1.5 K). The I-V characteristics near the dielectric phase boundary show the step-like behavior that corresponds to the quantum conductance in a disordered 2D structure through the extended edge states of the nearest Landau level closest to the Fermi level. The value of these steps is determined by the orientation of the 2D-electron spin at the Landau level and the magnetic moment of Mn in the δ-layer.     

Magnetic field induced transitions between quantized hall and insulator states in a dilute 2D electron gas

We report on the observation of a new phenomenon: a sequence of magnetic field induced transitions between well defined quantum Hall effect states, with a Hall resistance quantized as integer fractions of h/e² and a vanishingly small longitudinal resistance, and insulator states with longitudinal resistance exceeding 2×10⁹ Ω. This phenomenon is observed in extremely high mobility Si MOSFETs, in a range of electron concentrations corresponding to a dilute 2D electron gas in or near an activated electronic transport regime. We attribute this effect to a modulation of the metal-insulator transition by the quantum Hall effect or to the formation of a pinned Wigner solid.     

Quantum Anomalous Hall Multilayers Grown by Molecular Beam Epitaxy

Quantum anomalous Hall(QAH) effect is a quantum Hall effect that occurs without the need of external magnetic field. A system composed of multiple parallel QAH layers is an effective high Chern number QAH insulator and the key to the applications of the dissipationless chiral edge channels in low energy consumption electronics. Such a QAH multilayer can also be engineered into other exotic topological phases such as a magnetic Weyl semimetal with only one pair of Weyl points. This work reports the first experimental realization of QAH multilayers in the superlattices composed of magnetically doped(Bi,Sb)_2Te_3 topological insulator and Cd Se normal insulator layers grown by molecular beam epitaxy. The obtained multilayer samples show quantized Hall resistance h/N_e~2, where h is Planck's constant, e is the elementary charge and N is the number of the magnetic topological insulator layers, resembling a high Chern number QAH insulator. The QAH multilayers provide an excellent platform to study various topological states of matter.     

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.     

Landau-level splitting in graphene in high magnetic fields

The quantum Hall (QH) effect in two-dimensional electrons and holes in high quality graphene samples is studied in strong magnetic fields up to 45 T. QH plateaus at filling factors nu = 0, +/-1, +/-4 are discovered at magnetic fields B > 20 T, indicating the lifting of the fourfold degeneracy of the previously observed QH states at nu = +/-4(absolute value(n) + 1/2), where n is the Landau-level index. In particular, the presence of the nu = 0, +/-1 QH plateaus indicates that the Landau level at the charge neutral Dirac point splits into four sublevels, lifting sublattice and spin degeneracy. The QH effect at nu = +/-4 is investigated in a tilted magnetic field and can be attributed to lifting of the spin degeneracy of the n = 1 Landau level.     

Unveiling the magnetic structure of graphene nanoribbons

We perform magnetotransport measurements in lithographically patterned graphene nanoribbons down to a 70 nm width. The electronic spectrum fragments into an unusual Landau levels pattern, characteristic of Dirac fermion confinement. The two-terminal magnetoresistance reveals the onset of magnetoelectronic subbands, edge currents and quantized Hall conductance. We bring evidence that the magnetic confinement at the edges unveils the valley degeneracy lifting originating from the electronic confinement. Quantum simulations suggest some disorder threshold at the origin of mixing between chiral magnetic edge states and disappearance of quantum Hall effect.     

Semi‐Classical Model of Strongly Correlated Coulomb Systems in Weak Magnetic Field

The integer and fractional quantum Hall effects are two remarkable macroscopic quantum phenomena occurring in two‐dimensional strongly correlated electronic systems at high magnetic fields and low temperatures. Quantization of Hall resistivity in the very high magnetic field regime at partial filling of the lowest Landau level indicates the stabilization of an electronic liquid quantum Hall phase of matter. Other interesting phases that differ from the quantum Hall phases take prominence in weaker magnetic fields when many more Landau levels are filled. These states manifest anisotropic magneto‐transport properties and, under certain conditions, appear to mimic charge density waves and/or liquid crystalline phases. One way to understand such a behavior has been in terms of effective interaction potentials confined to the highest Landau level partially filled with electrons. In this work we show that, for weak magnetic fields, such a quantum treatment of these strongly correlated Coulomb systems resembles a semi‐classical model of rotating electrons in which the time‐averaged interaction potential can be expressed solely in terms of guiding center coordinates. We discuss how the features of this semi‐classical effective potential may affect the stability of various strongly correlated electronic phases in the weak magnetic field regime (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Scattering mechanism of integer quantum Hall conductance in a model system

We consider a large class of two-dimensional systems of charged particles in crossed electric and strong magnetic fields in the presence of a static substrate potentialV(x,y), which contains disorder. The time dependence of the single-particle Schroedinger functions are investigated. It is found on general grounds, that adiabatic states are dc-insulating and, that the macroscopic Hall current is carried by the non-adiabatic states. Hall conductance plateaus correspond to spectral domains, which contain only adiabatic states. The plateaus disappear, when these states become non-adiabatic at sufficiently high electric fields, i.e., at sufficiently large Hall currents. An explicit model system is investigated with a substrate potential composed of disorder and of a sequence of smooth barriers and wells. Here the non-adiabatic states can be calculated in a weak-disorder approximation, whenever the electric field (and hence the Hall current) is sufficiently low. In this case the quantum mechanical scattering process leading, to the quantisation of the Hall conductance can be understood in detail. Non-classical particle propagation plays a crucial role in this process. Our analysis opens new perspectives for the theory of the integer quantum Hall effect.     

Quantization of the diagonal resistance: density gradients and the empirical resistance rule in a 2D system

We have observed quantization of the diagonal resistance, R(xx), at the edges of several quantum Hall states. Each quantized R(xx) value is close to the difference between the two adjacent Hall plateaus in the off-diagonal resistance, R(xy). Peaks in R(xx) occur at different positions in positive and negative magnetic fields. Practically all R(xx) features can be explained quantitatively by a 1%/cm electron density gradient. Therefore, R(xx) is determined by R(xy) and unrelated to the diagonal resistivity rho(xx). Our findings throw an unexpected light on the empirical resistivity rule for 2D systems.     

Quantum transport in an H shaped wire and a ring structure

We have numerically studied the transport properties of an H shaped quantum wire structure and a circular quantum ring structure by using the mode matching technique. We have observed that for the H structure, anomalous Hall resistance plateaus exist in relatively low magnetic fields as precursors of integer Hall plateaus. We have found that the resonance patterns of the nonlocal resistance are mainly caused by inter-mode transitions between two highest modes in the system, yielding large oscillations with a mixing frequency in the resistance curve with respect to the width of the bridge-like part of the H structure. For the ring structure, we have found that two oppositely circulating internal waves contribute to the Aharonov-Bohm oscillations, producing beating in the transmission amplitudes.     

Helical-edge transport near ν = 0 of monolayer graphene

The complex nature of filling factor ν = 0 of monolayer graphene is studied in magnetotransport experiments. As a function of perpendicular magnetic field a metal-insulator transition is observed, which is attributed to disorder-induced Landau level broadening in the canted antiferromagnetic phase. In the metallic regime a separation of the zeroth Landau level appears and signs of the quantum spin Hall effect are seen near ν = 0. In addition to local transport, nonlocal transport experiments show results being consistent with helical edge transport.     

Local density of states of a three-dimensional conductor in the extreme quantum limit

The electronic structure of the narrow gap semiconductor InAs is investigated by scanning tunneling spectroscopy and magnetotransport measurements in the extreme quantum limit. The well-known oscillations of the Hall coefficient are reproduced and the last, most pronounced oscillation is shown to be correlated with the appearance of corrugations in the local density of states. While the increasing part of the Hall constant corresponds to the existence of isolated patterns indicating magnetic field induced localization, the decreasing part correlates with the development of a network which most likely consists of one-dimensional channels. We conclude that the decrease of the Hall constant in the extreme quantum limit is caused by a transition from a purely three-dimensional to a partly one-dimensional transport regime.     

Magnetic field induced metal-insulator transitions in p-SiGe

Low density modulation doped p-SiGe, where the holes lie in a strained SiGe quantum well, frequently exhibits anomalous insulating behaviour between filling factors ν=2 and 1. There is also anomalous metallic behavior with a metal-insulator transition between the two. It is shown that in these samples exchange effects are sufficiently large to induce the paramagnetic-ferromagnetic phase transition predicted by Giuliani and Quinn in 1985, also that the metallic and insulating behavior is associated with the coincidence of two Landau levels of opposite spin. A model calculation shows that while a ferromagnetic polarization may occur at integer filling factors screening suppresses it for non-integer filling factors. It is argued the Landau levels then stick-together and allow a spin-density instability to form. Because of the strong spin-orbit coupling in p-SiGe the transport properties of this state differ from those of other systems where a similar quantum Hall ferromagnet probably forms.     

Tunable topological quantum states in three- and two-dimensional materials

We review our theoretical advances in tunable topological quantum states in three- and twodimensional materials with strong spin–orbital couplings. In three-dimensional systems, we propose a new tunable topological insulator, bismuth-based skutterudites in which topological insulating states can be induced by external strains. The orbitals involved in the topological band-inversion process are the d- and p-orbitals, unlike typical topological insulators such as Bi₂Se₃and BiTeI, where only the p-orbitals are involved in the band-inversion process. Owing to the presence of large d-electronic states, the electronic interaction in our proposed topological insulator is much stronger than that in other conventional topological insulators. In two-dimensional systems, we investigated 3d-transition-metal-doped silicene. Using both an analytical model and first-principles Wannier interpolation, we demonstrate that silicene decorated with certain 3d transition metals such as vanadium can sustain a stable quantum anomalous Hall effect. We also predict that the quantum valley Hall effect and electrically tunable topological states could be realized in certain transition-metal-doped silicenes where the energy band inversion occurs. These findings provide realistic materials in which topological states could be arbitrarily controlled.