Particle-hole symmetric Luttinger liquids in a quantum Hall circuit

We report current transmission data through a split-gate constriction fabricated onto a two-dimensional electron system in the integer quantum Hall (QH) regime. Split-gate biasing drives interedge backscattering and is shown to lead to suppressed or enhanced transmission, in marked contrast to the expected linear Fermi-liquid behavior. This evolution is described in terms of particle-hole symmetry and allows us to conclude that an unexpected class of gate-controlled particle-hole-symmetric chiral Luttinger liquids (CLLs) can exist at the edges of our QH circuit. These results highlight the role of particle-hole symmetry on the properties of CLL edge states.     

Quantum Hall ferromagnetism in a two-valley strained Si quantum well

Tilted field magnetotransport study was performed in a two-valley strained Si quantum well and hysteretic diagonal resistance spikes were observed near the coincidence angles. The spike around filling factor ν=3 develops into a giant feature when it moves to the high-field edge of the quantum Hall (QH) state and quenches for higher tilt angles. When the spike is most prominent, its peak resistance is temperature independent from T20 mK up to 0.3 K, which is different from the critical behavior previously reported near the Curie temperature of the QH ferromagnet in AlAs quantum wells. Our data suggest a strong interplay between spins and valleys near the coincidence.     

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.     

Quantum antidot as an electrometer:Observation of fractional charge

In experiments on resonant tunneling through a quantum antidot in the quantum Hall (QH) regime, we observe periodic conductance peaks both versus magnetic field and a global gate voltage, i.e., electric field. Each conductance peak can be attributed to tunneling through a quantized antidot-bound state. The fact that the variation of the uniform electric field produces conductance peaks implies that the deficiency of the electrical charge on the antidot is quantized in units of charge of quasiparticles of surrounding QH condensate. The period in magnetic field gives the effective area of the antidot state through which tunneling occurs, the period in electric field (obtained from the global gate voltage) then constitutes a direct measurement of the charge of the tunneling particles. We obtain electron charge C in the integer QH regime, and quasiparticle charge C for the QH state.     

Multi-types of Skyrmions in SU（N） Quantum Hall System

The skyrmions in SU（N） quantum Hall （QH） system are discussed. By analyzing the gauge field structure and the topological properties of this QH system it is pointed out that in the SU（N） QH system there can exist （N-1） types of skyrmion structures, instead of only one type of skyrmions. In this paper, by means of the Abelian projections according to the （N - 1） Cartan subalgebra local bases, we obtain the （N - 1） U（1） electromagnetic field tensors in the SU（N） gauge field of the QH system, and then derive （N - 1） types of skyrmion structures from these U（1） sub-field tensors. Furthermore, in light of the C-mapping topological current method, the topological charges and the motion of these skyrmions are also discussed.     

原子霍尔效应中复合粒子和场描述

研究了原子霍尔效应中复合粒子描述方法，并进一步给出Chern－Simon－Gross－Pitaevskii(CSGP)有效场描述。研究结果表明从平均场和复合粒子的角度来看原子霍尔效应和电子霍尔效应是一致的。     

Masses of colored vector mesons

Mass formulas for colored vector mesons are derived under the assumption of one common mixing angle forSU(3), independent of the color quantum numbers, and correspondingly one common mixing angle () forSU(3). This a priori plausible assumption turns out to have strong implications and thus might be too restrictive. We allow for a non-trivial spatial overlap integral between color-singlet and color-octet states. Various cases are treated and physical possibilities are identified. The best agreement is obtained for = 0. There are two models of this type with and without a part of the symmetry breaking Hamiltonian density transforming as (Y, Y) underSU(3)SU(3). Models with 0 are also possible. They cannot have a (Y, Y) and predict 3.34 GeV as the mass of the (3.7). This error of 10% may however be used to reject this possibility. Masses of colored vector mesons are predicted in the various models. If a (Y, Y) is present, ideal mixing inSU (3) is implied by the general formalism of the model.     

Spin degree of freedom in the nu=1 bilayer electron system investigated by nuclear spin relaxation

The nuclear-spin-relaxation rate 1/T(1) has been measured in a bilayer electron system at and around total Landau level filling factor nu=1. The measured 1/T(1), which probes electron spin fluctuations, is found to increase gradually from the quantum Hall (QH) state at low fields through a phase transition to the compressible state at high fields. Furthermore, 1/T(1) in the QH state shows a noticeable increase away from nu=1. These results demonstrate that, as opposed to common assumption, the electron spin degree of freedom is not completely frozen either in the QH or the compressible states.     

Topological entanglement in Abelian and non-Abelian excitation eigenstates

Entanglement in topological phases of matter has so far been investigated through the perspective of their ground-state wave functions. In contrast, we demonstrate that the excitations of fractional quantum Hall (FQH) systems also contain information to identify the system's topological order. Entanglement spectrum of the FQH quasihole (QH) excitations is shown to differentiate between the conformal field theory (CFT) sectors, based on the relative position of the QH with respect to the entanglement cut. For Read-Rezayi model states, as well as Coulomb interaction eigenstates, the counting of the QH entanglement levels in the thermodynamic limit matches exactly the CFT counting, and sector changes occur as non-Abelian quasiholes successively cross the entanglement cut.     

Integer and fractional quantum Hall effects in bilayer electron systems

Integer and fractional quantum Hall (QH) effects are studied in bilayer electron systems both theoretically and experimentally, especially, at ν=2 and 2/3. Due to the spin and layer degrees of freedom, the SU(4) symmetry underlies the integer QH states, where quantum coherence develops spontaneously and quasiparticles are coherent excitations. It is intriguing that a pair of skyrmions makes one quasiparticle at ν=2. In the fractional QH regime, on the other hand, the composite-fermion cyclotron gap competes with the Zeeman and tunneling gaps, bringing in new phases and excitations. At ν=2/3 our experimental data suggest that a quasiparticle is not a coherent excitation but simply a composite fermion.     

Multiprobe quantum spin Hall bars

We analyze electron transport in multiprobe quantum spin Hall (QSH) bars using the Büttiker formalism and draw parallels with their quantum Hall (QH) counterparts. We find that in a QSH bar the measured resistance changes upon introducing side voltage probes, in contrast to the QH case. We also study four- and six-terminal geometries and derive the expressions for the resistances. For these our analysis is generalized from the single-channel to the multi-channel case and to the inclusion of backscattering originating from a constriction placed within the bar.     

Quantum oscillation of Hall resistance in the extreme quantum limit of an organic conductor (TMTSF)2ClO4

We report resistance and magnetic torque experiments under a high magnetic field up to 45 T in a three dimensional quantum Hall (QH) system (TMTSF)(2)ClO(4), where TMTSF = tetramethyltetraselenafulvalene. The Hall resistance shows huge oscillations accompanied with sign reversal after the final QH state, where the Landau level filling factor is unity, is removed above 26 T. The magnetic torque also oscillates with the field. The results suggest that a novel quantum state, where the character of the carriers periodically changes with the field, is stabilized in the extreme quantum limit.     

Insulator, semiclassical oscillations and quantum Hall liquids at low magnetic fields

Magneto-transport measurements are performed on two-dimensional GaAs electron systems to probe the quantum Hall (QH) effect at low magnetic fields. Oscillations following the Shubnikov-de Haas (SdH) formula are observed in the transition from the insulator to QH liquid when the observed almost temperature-independent Hall slope indicates insignificant interaction correction. Our study shows that the existence of SdH oscillations in such a transition can be understood based on the non-interacting model.     

Noncommutative Quantum Hall Effect of Bilayer Systems

In this paper we study the bilayer quantum Hall (QH) effect on a noncommutative phase space (NCPS). By using perturbation theory, we calculate the energy spectrum, eigenfunction, Hall current, and Hall conductivity of the bilayer QH system, and express them in terms of noncommutative parameters θ and \bar{θ}, respectively. In our calculation, we assume that these parameters vary from layer to layer.     

Continuous topological phase transitions between clean quantum hall states

Continuous transitions between states and the same symmetry but different topological orders are studied. Clean quantum Hall (QH) liquids with neutral nonbosonic quasiparticles are shown to have such transitions under the right conditions. For clean bilayer (mmn) states, a continuous transition to other QH states (including non-Abelian states) can be driven by increasing interlayer repulsion/tunneling. The effective theories describing the critical points at some transitions are obtained.     

Quantum anomalous Hall effect in real materials

Under a strong magnetic field,the quantum Hall(QH) effect can be observed in two-dimensional electronic gas systems.If the quantized Hall conductivity is acquired in a system without the need of an external magnetic field,then it will give rise to a new quantum state,the quantum anomalous Hall(QAH) state.The QAH state is a novel quantum state that is insulating in the bulk but exhibits unique conducting edge states topologically protected from backscattering and holds great potential for applications in low-power-consumption electronics.The realization of the QAH effect in real materials is of great significance.In this paper,we systematically review the theoretical proposals that have been brought forward to realize the QAH effect in various real material systems or structures,including magnetically doped topological insulators,graphene-based systems,silicene-based systems,two-dimensional organometallic frameworks,quantum wells,and functionalized Sb(111) monolayers,etc.Our paper can help our readers to quickly grasp the recent developments in this field.     

Three-dimensional topological insulator in a magnetic field: chiral side surface states and quantized Hall conductance

Low energy excitation of surface states of a three-dimensional topological insulator (3DTI) can be described by Dirac fermions. By using a tight-binding model, the transport properties of the surface states in a uniform magnetic field are investigated. It is found that chiral surface states parallel to the magnetic field are responsible for the quantized Hall (QH) conductance (2n + 1)e2/h multiplied by the number of Dirac cones. Due to the two-dimensional nature of the surface states, the robustness of the QH conductance against impurity scattering is determined by the oddness and evenness of the Dirac cone number. An experimental setup for transport measurement is proposed.     

Beam radiated from quasi-homogeneous uniformly polarized electromagnetic source scattering on quasi-homogeneous media

We study the coherence properties of the field generated by beam radiated from quasi-homogeneous (QH) electromagnetic source scattering on QH media. Formulas for the spectral density and spectral degree of coherence of the three dimensional scattered field are derived. The results show under assumption that the diagonal correlation coefficients of the source are proportional to each other, the far field of the scattered light satisfy two reciprocity relations analogous to that in the scalar case, that, the spectral density is proportional to the convolution of the spectral density of the source and the spatial Fourier transform of the correlation coefficient of the scattering potential; the spectral degree of coherence is proportional to the convolution of the diagonal correlation coefficients and the strength of the scattering potential.     

Quantum Hall effect in noncommutative quantum mechanics

We study the quantum Hall (QH) effect for an electron moving in a plane whose coordinates and momenta are noncommuting under the influence of uniform external magnetic and electric fields. After solving the time independent Schrödinger equation both on a noncommutative space (NCS) and a noncommutative phase space (NCPS), we obtain the energy eigenvalues and eigenfunctions of the relevant Hamiltonian. We derive the electric current whose expectation value gives the QH effect both on a NCS and a NCPS.     

Effect of strain on stripe phases in the quantum Hall regime

Preferential orientation of the stripe phases in the quantum Hall (QH) regime has remained a puzzle since its discovery. We show experimentally and theoretically that the direction of high and low resistance of the two-dimensional (2D) hole gas in the QH regime can be controlled by an external strain. Depending on the sign of the in-plane shear strain, the Hartree-Fock energy of holes or electrons is minimized when the charge density wave (CDW) is oriented along the [110] or [110] directions. We suggest that shear strains due to internal electric fields in the growth direction are responsible for the observed orientation of CDW in pristine electron and hole samples.