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.     

Magnetotransport through ac driven ferromagnetic graphene nanoribbons

We present a theoretical study on the spin-dependent transport through the ferromagnetic graphene nanoribbons in the presence of a magnetic and an in-plane ac electric field, and find that when the ac field is applied, in the two-terminal ferromagnetic graphene device, for the parallel configurations of the electrodes' magnetizations, the width of the even-number conductance plateaus decrease, the new conductance plateaus appear at the odd-number positions, and the even-number conductance plateaus at the high energy are quenched under the sufficiently strong ac field. In contrast, for the antiparallel configuration of the electrodes' magnetizations, the odd-plateaus of the conductance shrink, and the new plateaus developed at the even-number positions. The magnetic resistance exhibits a successive rectangular-like oscillation structure close to the band edge, whereas experiences an alternative transition between the sharp peak and dip near the zero energy with increasing the ac field strength. In the six-terminal ferromagnetic graphene device, the variations of the longitudinal and Hall resistances' plateaus as well as the addition of the new quantized plateaus with the rise of the ac field strength are also revealed.     

Quantum Hall effect of massless dirac fermions in a vanishing magnetic field

The effect of strong long-range disorder on the quantization of the Hall conductivity sigma{xy} in graphene is studied numerically. It is shown that increasing Landau-level mixing progressively destroys all plateaus in sigma{xy} except the plateaus at sigma{xy}=-/+e{2}/2h (per valley and per spin). The critical state at the Dirac point is robust to strong disorder and belongs to the universality class of the conventional plateau transitions in the integer quantum Hall effect. We propose that the breaking of time-reversal symmetry by ripples in graphene can realize this quantum critical point in a vanishing magnetic field.     

Charge density wave in graphene: Magnetic-field-induced Peierls instability

We suggest that a magnetic-field-induced Peierls instability accounts for the recent experiment of Zhang et al. in which unexpected quantum Hall plateaus were observed at high magnetic fields in graphene on a substrate. This Peierls instability leads to an out-of-plane lattice distortion resulting in a charge density wave (CDW) on sublattices A and B of the graphene honeycomb lattice. We also discuss alternative microscopic scenarios proposed in the literature and leading to a similar CDW ground state in graphene.     

Simulation of Electronic Total-Reflection Effect in a Graphene Junction

We investigate theoretically the electron-reflection phenomenon in a graphene n＋n junction based on electron optics, where the local potential in the left n ＋ region is higher than that in the right n region. It is demonstrated numerically that electrons emitting from a point source in the n ＋ region will experience total internal reflection through the interface of the junction. The reflection becomes stronger and the transmission becomes weaker with decrease of the local potential in the right graphene ribbon. It is also found that when a nonideal interface is considered in the junction, the electron-reflection effect is enhanced due to interracial backseattering.     

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.     

Wave-vector filtering effect of the electric-magnetic barrier in HgTe quantum wells

Because of the helicity of electrons in HgTe quantum wells(QWs) with inverted band structures,the electrons cannot be confined by electric barriers since electrons can tunnel the barriers perfectly without backscattering in the HgTe QWs.This behavior is similar to Dirac electrons in graphene.In this paper,we propose a scheme to confine carriers in HgTe QWs using an electric-magnetic barrier.We calculate the transmission of carriers in 2-dimensional HgTe QWs and find that the wave-vector filtering effect of local magnetic fields can confine the carriers.The confining effect will have a potential application in nanodevices based on HgTe QWs.     

Wave-vector filtering effect of electric–magnetic barrier in HgTe quantum wells

Because of helicity of electrons in HgTe quantum wells (QWs) with inverted band structure, the electrons cannot be confined by electric barriers since electrons can tunnel the barriers perfectly without backscattering in HgTe QWs. This behavior is similar to Dirac electrons in graphene. In this paper, we propose a scheme to confine carriers in HgTe QWs using an electric-magnetic barrier. We calculate the transmission of carriers in 2-dimensional HgTe QWs and find that the wave-vector filtering effect of local magnetic fields can confine the carriers. The confining effect will have potential application in nanodevices based on HgTe QWs.     

Spontaneous parity breaking of graphene in the Quantum Hall regime

We propose that the inversion symmetry of the graphene honeycomb lattice is spontaneously broken via a magnetic-field-dependent Peierls distortion. This leads to valley splitting of the n=0 Landau level but not of the other Landau levels. Compared to Quantum Hall valley ferromagnetism recently discussed in the literature, lattice distortion provides an alternative explanation to all of the currently observed Quantum Hall plateaus in graphene.     

Interedge strong-to-weak scattering evolution at a constriction in the fractional quantum Hall regime

Gate-voltage control of interedge tunneling at a split-gate constriction in the fractional quantum Hall regime is reported. Quantitative agreement with the behavior predicted for out-of-equilibrium quasiparticle transport between chiral Luttinger liquids is shown at low temperatures at specific values of the backscattering strength. When the latter is lowered by changing the gate voltage, the zero-bias peak of the tunneling conductance evolves into a minimum, and a nonlinear quasiholelike characteristic emerges. Our analysis emphasizes the role of the local filling factor in the split-gate constriction region.     

Disorder-induced enhancement of transport through graphene p-n junctions

We investigate the electron transport through a graphene p-n junction under a perpendicular magnetic field. By using the Landauer-Büttiker formalism combined with the nonequilibrium Green function method, the conductance is studied for clean and disordered samples. For the clean p-n junction, the conductance is quite small. In the presence of disorders, it is strongly enhanced and exhibits a plateau structure at a suitable range of disorders. Our numerical results show that the lowest plateau can survive for a very broad range of disorder strength, but the existence of high plateaus depends on system parameters and sometimes cannot be formed at all. When the disorder is slightly outside of this disorder range, some conductance plateaus can still emerge with its value lower than the ideal value. These results are in excellent agreement with a recent experiment.     

Quantized four-terminal resistances in a ferromagnetic graphene p-n junction

The quantum Hall and longitudinal resistances in four-terminal ferromagnetic graphene p-n junctions under a perpendicular magnetic field are investigated. In the Hall measurement, the transverse contacts are assumed to be located at the 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 a four-terminal p-n junction can be naturally divided into nine different regimes. The symmetric Hall and longitudinal resistances are observed, with many new robust quantum plateaus revealed due to the competition between spin splitting and local potentials.     

石墨烯中新奇量子物态的研究

石墨烯特殊的晶格结构和能带结构赋予了它独特的电学性质. 近年来, 分数量子霍尔态、 魔角石墨烯中的 关联绝缘体态和超导态等现象的发现不断证明着石墨烯是一种理想的二维模型体系, 可用于实现一系列新奇的量子物态, 对石墨烯中新奇量子物态的探测和调控也一直是凝聚态物理领域的前沿研究热点之一. 本文将系统地介绍近年来石墨烯中对称性破缺量子物态的研究进展, 包括平带中强关联量子物态的研究以及谷赝自旋调控的研究, 并介绍一种在纳米尺度、 单电子精度上探测二维材料体系简并度及对称性破缺态的普适方法, 希望为相关领域的研究人员提供参考和借鉴.     

Magnetization plateaus and supersolid phases in an extended Shastry–Sutherland model

New magnetization plateaus and supersolid phases are identified in an extended Shastry–Sutherland model – with additional longer range interactions and exchange anisotropy – over a wide range of interaction parameters and an applied magnetic field. The model is appropriate for describing the low energy properties of some members of the rare earth tetraborides. Using a plaquette representation and exact mapping of ground state configurations in the Ising limit, supplemented by large scale quantum Monte Carlo simulations to include the effects of exchange interactions, we have identified several magnetization plateaus and associated spin supersolid phases. Our methods enable us to elucidate the underlying structure and mechanism of formation of the supersolid phases, thus gaining deeper understanding into their emergence from competing interactions. Additionally, in this regime we find evidence of a fractional plateau at 1∕9 saturation magnetization, which may hold the clue to understanding the fractional plateau in TmB₄ that exhibits magnetic hysteresis.     

Low-energy electron transmission in a partially unzipped zigzag nanotube

Based on the nearest-neighbor tight-binding approximation, we present exact analytical expressions for electron transmission in nanotube/ribbon junctions, generated by incomplete unzipping of zigzag nanotubes. By assuming one-dimer-line difference in the widths of the leads, it is demonstrated that such a contact exhibits zero backscattering of low-energy electrons entering from the graphene side of the junction. We also show that a zigzag nanotube section sandwiched between two armchair graphene ribbons is completely transparent for incident low-energy electrons. Possible application of the results to nanosensor engineering is also included.     

On the Singular Effects in the Relativistic Landau Levels in Graphene with a Disclination

The effect of a pseudo Aharonov-Bohm (AB) magnetic field generated by a disclination on a two-dimensional electron gas in graphene is addressed in the continuum limit within the geometric approach. The influence of the coupling between the spinor fields and the singular conical curvature is investigated, which shows that singularities have pronounced impact in the Hall conductivity. Moreover, the degeneracy related to the Dirac valleys is broken for negative values of the angular momentum quantum numbers, l, includingl ≡ 0. In this case, a Hall plateau develops at the null filling factor. Obtaining the Hall conductivity by summing over the positive and the negative l's, the null Landau level is recovered and the plateau at the null filling factor disappears. In any case, the standard plateaus, which are seen in a flat graphene are not obtained with these curvature and singular effects.     

Edge states and distributions of edge currents in semi-infinite graphene

The distributions of edge currents in semi-infinite graphene under a uniform perpendicular magnetic field are investigated. We show unambiguously that the edge current is finite at the armchair edge but vanishes at the zigzag edge. It is shown that the current density oscillates with the distance away from the boundary and tends to zero deep inside the graphene. The study shows that the total current is independent of edge configurations. The interplay of the bulk and edge contributions to the total current is presented. The quantized plateaus of Hall conductivity at (4e ²/h)(n+1/2) provide a direct evidence of the connection between the edge states and topological properties of relativistic fermions in a magnetic field.     

Detection of hidden localized states by the quantum Hall effect in graphene

We fabricated a monolayer graphene transistor device in the shape of the Hall-bar structure, which produced an exactly symmetric signal following the sample geometry. During electrical characterization, the device showed the standard integer quantum Hall effect of monolayer graphene except for a broader range of several quantum Hall plateaus corresponding to small filling factors in the electron region. We investigated this anomaly on the basis of localized states owing to the presence of possible electron traps, whose energy levels were estimated to be near the Dirac point. In particular, the inequality between the filling of electrons and holes was ascribed to the requirement of excess electrons to fill the trap levels. The relations between the quantum Hall plateau, Landau level, and filling factor were carefully analyzed to reveal the details of the localized states in this graphene device.     

Two-terminal quantized conductance in inhomogeneous graphene

Quantized two-terminal conductance plateaus in graphene were observed and were explained through the mechanism of different Landau level filling factors in inhomogeneous sample. Furthermore, the quantized conductance plateaus are different due to the difference of the carrier exchange through the graphene-substrate interface during the increasing and decreasing gate voltage-sweeps.     

Fractional magnetization plateaus and magnetic order in the Shastry-Sutherland magnet TmB4

We investigate the phase diagram of TmB4, an Ising magnet on a frustrated Shastry-Sutherland lattice, by neutron diffraction and magnetization experiments. At low temperature we find Néel order at low field, ferrimagnetic order at high field, and an intermediate phase with magnetization plateaus at fractional values M/M_(sat)=1/7,1/8,1/9,... and spatial stripe structures. Using an effective S=1/2 model and its equivalent two-dimensional fermion gas we suggest that the magnetic properties of TmB4 are related to the fractional quantum Hall effect of a 2D electron gas.