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 θ^-, respectively. In our calculation, we assume that these parameters vary from laver to laver.     

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.     

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。     

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.     

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.     

Quantum coherence and W∞ × SU(2) algebra in bilayer quantum Hall systems

We analyze the bilayer quantum Hall (QH) system by mapping it to the monolayer QH system with spin degrees of freedom. By this mapping the tunneling interaction term is identified with the Zeeman term. We clarify the mechanism of a spontaneous development of quantum coherence based on the Chern-Simons gauge theory with the lowest-Landau-level projection taken into account. The symmetry group is found to be W_∞ × SU(2), which says that the spin rotation affects the total electron density nearby. Using it extensively we construct the Landau-Ginzburg theory of the coherent mode. Skyrmion excitations are topological solitions in this coherent mode. We point out that they are detectable by measuring the Hall current distribution.     

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.     

Interlayer phase coherence and Josephson effects in bilayer quantum Hall systems

When an electron is confined within the lowest Landau level, its position is described solely by the guiding center, whose X and Y coordinates do not commute with one another. The equations of motion do not follow from the kinetic Hamiltonian but from the noncommutative property of the space. Based on this microscopic theory, we analyze the bilayer QH system at the filling factor ?? = 1, and show that there develops an interlayer phase coherence. It is interpreted that the phase coherence occurs due to the Bose-Einstein condensation of composite bosons, which are single electrons bound to magnetic flux quanta. The phase coherence can induce the Josephson inplane current as well as the Josephson tunneling current, which are dissipationless as in superconductor. We demonstrate that the Josephson inplane current provokes anomalous behaviors in the Hall resistance in counterflow and drag experiments. Furthermore, we investigate the condition on the input current for the tunneling current to be coherent and dissipationless. We predict also how the condition changes when the sample is tilted in the magnetic field.     

Improved composite-boson theory of monolayer and bilayer quantum Hall ferromagnets

An improved composite-boson theory of quantum Hall ferromagnets is formulated both for the monolayer and bilayer systems. In this scheme the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. Skyrmions are charged excitations confined to the lowest Landau level. By evaluating the excitation energy of one skyrmion in the interlayer-coherent phase it is shown that the bilayer QH state becomes stabler as the interlayer density difference becomes larger.     

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.     

Phase diagram of interacting composite fermions in the bilayer nu=2/3 quantum hall effect

We study the phase diagram of composite fermions (CFs) in the presence of spin and pseudospin degrees of freedom in the bilayer nu=2/3 quantum Hall (QH) state. Activation studies elucidate the existence of three different QH states with two different types of hysteresis in the magnetotransport. While a noninteracting CF model provides a qualitative account of the phase diagram, the observed renormalization of tunneling gap and a non-QH state at high densities are not explained in the noninteracting CF model, and are suggested to be manifestations of interactions between CFs.     

二维模糊球上的量子霍尔流体

在回顾了Haldane对量子Hall效应在二维球面S2上的描述后,本文构造了二维模糊球S2上的非对易代数及其Hilbert空间的Moyal结构.通过构造模糊球上不可压缩量子霍尔流体的非对易Chern-Simons理论,求解具有准粒子源的Gaussian约束,找出模糊球上的Calogero矩阵及最低Landau能级Laughlin波函数的完全集,此Laughlin波函数由旋量坐标推广的Jack多项式表示.     

Assessment of bilayer silicene to probe as quantum spin and valley Hall effect

Silicene takes precedence over graphene due to its buckling type structure and strong spin orbit coupling. Motivated by these properties, we study the silicene bilayer in the presence of applied perpendicular electric field and intrinsic spin orbit coupling to probe as quantum spin/valley Hall effect. Using analytical approach, we calculate the spin Chern-number of bilayer silicene and then compare it with monolayer silicene. We reveal that bilayer silicene hosts double spin Chern-number as compared to single layer silicene and therefore accordingly has twice as many edge states in contrast to single layer silicene. In addition, we investigate the combined effect of intrinsic spin orbit coupling and the external electric field, we find that bilayer silicene, likewise single layer silicene, goes through a phase transitions from a quantum spin Hall state to a quantum valley Hall state when the strength of the applied electric field exceeds the intrinsic spin orbit coupling strength. We believe that the results and outcomes obtained for bilayer silicene are experimentally more accessible as compared to bilayer graphene, because of strong SO coupling in bilayer silicene.     

Nuclear-spin-lattice relaxation in a bilayer quantum Hall system

We examined the electron spin degree of freedom around the total Landau-level filling factor ν=1 in a bilayer system via nuclear spins. In a balanced bilayer system, nuclear-spin-lattice relaxation rate 1/T₁, which probes low-energy electron spin fluctuations, increases gradually as the system is driven from the quantum Hall (QH) state through a phase transition to the compressible state. This result demonstrates that the electron spin degree of freedom is not frozen either in the QH or compressible states. Furthermore, as the density difference between the two layers is increased from balanced bilayer to monolayer configurations, 1/T₁ around ν=1 shows a rapid yet smooth increase. This suggests that pseudospin textures around the bilayer ν=1 system evolves continuously into the spin texture for the monolayer system.     

Quantum transport study of canted antiferromagnetic phase in the bilayer quantum Hall state

We examine the ν=2 bilayer quantum Hall (QH) state in clean two-dimensional electron systems (2DESs) to study effects due to not only the layer degree of freedom called pseudospin but also the real spin degree of freedom. The novel canted antiferromagnetic phase (CAF phase) has been predicted to emerge from subtle many-body electron interactions between the singlet (S) and ferromagnet (F) phases. Though several experiments indicate an onset of the CAF phase, a systematic transport study is not yet to be demonstrated. We have carried out magnetotransport measurements of the ν=2 bilayer QH state using a sample with tunneling energy . Activation energy was precisely measured as a function of the total density of the 2DES and the density difference between the two layers. Results support an appearance of the CAF phase between the S and F phases.     

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.     

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.     

Constraints in Noncommutative Chern-Simons Mechanics and Hall Effect

We study noncommutative Chern-Simons mechanics and noncommutative Hall effect by Dirac theory in this paper. The magnetic field is introduced by means of minimal coupling. We show that the constraint set will enlarge when a dimensionless parameter takes zero value. In order to illustrate our idea, we study two specific models. One is noncommutative Chern-Simons mechanics which describes a charged particle on a noncommutative plane interacting with a perpendicular uniform magnetic field. The other is a charged particle on a noncommutative plane with a background uniform electromagnetic field. We show that when the dimensionless parameter tends to zero, the particle will live in a lower dimensional space in both models. Noncommutative Chern-Simons mechanics will reduce to a harmonic oscillator and the classical equations of motion of a charged particle in the background of a uniform electromagnetic field are governed by classical Hall law when the dimensionless parameter tends to zero.     

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.     

Unusual Anomalous Hall Effect in a Co_2MnSi/MnGa/Pt Trilayer

An ultra-thin Co_2MnSi(0.5 nm)/Mn Ga(1.5 nm) bilayer capped with Pt(5 nm) has been successfully grown by molecular-beam epitaxy.It is a potential candidate of synthetic antiferromagnets due to antiferromagnetic coupling between Co_2MnSi and MnGa,which is a promising skyrmion-racetrack-memory medium without skyrmion Hall effect after capping with a Pt layer.Unusual humps in transverse Hall resistance loops are clearly observed in the temperature range from 260 to 400 K.This anomaly is generally attributed to topological Hall effect,but other than that,we prove that non-uniform rotation of magnetic moments in the bilayer with magnetic field sweeping is also a possible mechanism contributed to the unusual hump.