Spin polarization of two-dimensional electron system in different Laughlin states and around filling factor

The spin configuration of the ground state of a two-dimensional electron system is investigated for different FQHE states from an analysis of circular polarization of time-resolved luminescence. The method clearly distinguishes between fully spin polarized, partially spin polarized and spin unpolarized FQHE ground states. We demonstrate that FQHE states which are spin unpolarized or partially polarized at low magnetic fields become fully spin polarized at high fields. Temperature dependence of the spin polarization reveals a nonmonotonic behavior at . At and the electron system is found to be fully spin polarized. This result does not indicate the existence of any skyrmionic excitations in high magnetic field limit. However, at the observed spin depolarization of electron system at and becomes broader for lower magnetic fields, so that full spin polarization remains only in a small vicinity of . Such a behavior could be considered as a precursor of skirmionic depolarization, which would dominate for smaller ratios between Zeeman and Coulomb energies.We demonstrate that the spin polarization of 2D-electron system at and can be strongly affected by hyperfine interaction between electrons and optically spin-oriented nuclears. This result is due to the fact that hyperfine interaction can both enhance and suppress effective Zeeman splitting in fixed external magnetic field.     

Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

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.     

Competition between Abelian and Zeeman magnetic field effects in a two dimensional ultracold gas of fermions

The ground state of ultracold fermions in the presence of effects of orbital and Zeeman magnetic fields is analyzed. Five different states are found: unpolarized superconducting state, partially and fully polarized normal states and phase separated regions, partially or fully polarized. The system, in the presence of orbital synthetic magnetic field effects, shows non-monotonous changes of the phase boundaries when electron concentration is varied. We observe not only reentrant phenomena, but also density dependent oscillations of different areas of the phase diagram. Moreover the chemical potential shows oscillatory behavior and discontinuities with respect to changes in the number of fermions.     

Ultra-low temperature study of the even-denominator FQHE state

We present experimental data showing unambiguously an even-denominator fractional quantum Hall effect (FQHE) state at . At a bath temperature T_b=8 mK, we observe a Hall plateau quantized to a value of 2h/5e² with an uncertainty smaller than 2 parts in 10⁶ and a vanishing R_xx (R_xx=1.7±1.7 Ω). The thermal activation energy gaps Δ at Landau level filling factors , and are 0.11, 0.10, and 0.055 K, respectively. Adding a disorder broadening (typically 2 K) to these values, we deduce that all three FQHE states have probably very similar energy gaps. The electron heating experiment shows that the 2D electrons are efficiently cooled to the bath temperature for T_b8 mK. We also explore the density dependence of the activation gap at . Preliminary results at T_b25 mK show that the state is very sensitive to disorder.     

Classification of Topological Insulators with Time-Reversal and Inversion Symmetry

In this paper, we find that topological insulators with time-reversal symmetryand inversion symmetry featuring two-dimensional quantum spin Hall (QSH) state can be divided into 16 classes, which are characterized by four Z₂topological variables ζ_k=0,1 at four points with high symmetry in the Brillouin zone. We obtain the corresponding edge states for each one of these sixteen classes of QSHs. In addition, it is predicted that massless fermionic excitations appear at the quantum phase transition between different QSH states. In the end, we also briefly discuss the three-dimensional case.     

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number C_s for energy-bands of trilayer graphene having the essence of intrinsic spin–orbit coupling is analytically calculated. We find that for each valley and spin, C_s is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states,consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin–orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin–orbit(RSO) interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin–orbit coupling, while the other two layers have zero intrinsic spin–orbit coupling.Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.     

Magnetocapacitance study of the fractional-quantum-Hall effect: Quasiparticle charge and spin polarization

By the method of capacitance spectroscopy and of magnetotransport we have investigated the and fractional-quantum-Hall-effect (FQHE) states in gated GaAs AlGaAs heterojunctions with tuned electron areal density. Our experimental results confirm the theoretical prediction of the fractional quasiparticle charge in the FQHE state and of the existence of spin-aligned quasiholes and spin-reversed quasielectrons in the fully spin-polarized FQHE state.     

Dirac光子晶体

Dirac费米子作为粒子物理中的基本粒子之一,其理论在近年来蓬勃发展的拓扑电子理论领域中被广泛提及并用来刻画具有Dirac费米子性质的电子态.这种特殊的能态通常被称为Dirac点,在能谱上表现为两条不同能带之间的线性交叉点.由于Dirac点往往是发生拓扑相变的转变点,因而也被视为实现各种拓扑态的重要母态.作为可与拓扑电子体系类比的拓扑光子晶体因其独特的潜在应用价值也受到人们的广泛关注,实现包含Dirac点的光子能带已成为研究拓扑光子晶体的核心课题.本文基于电子的拓扑理论,简要地回顾了Dirac点在光子系统中的研究进展,特别介绍了如何在光子晶体中利用不同晶格对称性实现在高对称点/线上的Dirac点,以及由Dirac点衍生的Weyl点.     

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 .     

Low-energy electronic spin excitations between filling factors ν=1 and studied by optically detected nuclear magnetic resonance

We report measurements of the spin relaxation time (T_1n) for nuclei in the potential well confining a high-mobility two-dimensional electron system at a single GaAs–GaAlAs heterojunction. At low temperatures nuclear spin relaxation is dominated by electron–nuclear spin scattering: we find that T_1n displays sharp maxima at incompressible states throughout the hierarchy of the fractional quantum Hall effect. This behaviour is consistent with the existence of low-energy spin excitations only where the electron system is compressible. Our measurements also provide evidence for a gap in the spin excitation spectrum at .     

Particle–hole symmetric Luttinger liquids in a quantum Hall circuit

We report finite-bias differential conductance measurements through a split-gate constriction in the integer quantum Hall regime at ν=1. Both enhanced and suppressed zero-bias inter-edge backscattering can be obtained in a controllable way by changing the split-gate voltage. This behavior is interpreted in terms of local charge depletion and particle–hole symmetry. We discuss the relevance of particle–hole symmetry in connection with the chiral Luttinger model of edge states.     

Limits to Perception by Quantum Monitoring with Finite Efficiency

We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the relative entropy between the assigned state and the actual state of the system. These bounds are expressed solely in terms of the purity and von Neumann entropy of the state assigned by the agent, and are shown to characterize how an agent’s perception of the system is altered by access to additional information. We apply our results to Gaussian states and to the dynamics of a system embedded in an environment illustrated on a quantum Ising chain.     

Phase separation in a polarized Fermi gas at zero temperature

We investigate the phase diagram of asymmetric two-component Fermi gases at zero temperature as a function of polarization and interaction strength. The equations of state of the uniform superfluid and normal phase are determined using quantum Monte Carlo simulations. We find three different mixed states, where the superfluid and the normal phase coexist in equilibrium, corresponding to phase separation between (a) the polarized superfluid and the fully polarized normal gas, (b) the polarized superfluid and the partially polarized normal gas, and (c) the unpolarized superfluid and the partially polarized normal gas.     

Inelastic light scattering by collective excitations in the fractional quantum Hall regime

We report an inelastic light scattering study of long wavelength collective gap excitations of fractional quantum Hall (FQH) states at ν=p/(2p+1) for . The ν-dependence of the gap energy suggests a collapse of the collective excitation gap near . In a range of filling factors close to , where the FQH gap is believed to collapse, we observe a collective excitation mode that exists only at temperatures below 150 mK.     

Non-Abelian Quantum Hall States—Exclusion Statistics, K-Matrices, and Duality

We study excitations in edge theories for non-abelian quantum Hall states, focussing on the spin polarized states proposed by Read and Rezayi and on the spin singlet states proposed by two of the authors. By studying the exclusion statistics properties of edge-electrons and edge-quasiholes, we arrive at a novel K-matrix structure. Interestingly, the duality between the electron and quasihole sectors links the pseudoparticles that are characteristic for non-abelian statistics with composite particles that are associated to the pairing physics of the non-abelian quantum Hall states.     

基于Pancharatnam-Berry相位和动力学相位调控纵向光子自旋霍尔效应

提出了一种基于Pancharatnam-Berry相位和动力学相位操控纵向光子自旋霍尔效应的方法.理论分析表明:当光场通过一个由Pancharatnam-Berry相位透镜和动力学相位透镜构成的透镜组时,透镜组会存在两个自旋相关的焦点.首先,当左旋和右旋圆偏振光通过微结构相位延迟为π的Pancharatnam-Berry相位透镜时,由于Pancharatnam-Berry相位的自旋相关性,两个圆偏振分量会获得符号相反的Pancharatnam-Berry相位而导致其中一个被聚焦而另一个发散.然后,在Pancharatnam-Berry相位透镜后再插入普通透镜引入动力学相位调制,由于动力学相位是自旋无关,使得这一透镜组,可以在合适的条件下使不同自旋态的光子分别聚焦于纵向上不同焦点处.纵向自旋分裂由两透镜焦距及间距共同决定,因此可以通过改变两个透镜的焦距及其间距获得任意的纵向自旋分裂值.最后,搭建了一套实验装置,所得实验结果与理论结果一致.     

Transport through a constriction in a FQH-annulus

The flux periodicity of thermodynamic properties of an annulus in the fractional quantum Hall state with a constriction is considered. It is found that -periodicity is obtained due to transfer of fractionally charged particles or composite fermions between the edges of the annulus, respectively. The result for the finite magnitude of the persistent current across a very strong constriction is presented, as obtained with an extension of Wen’s edge state theory.     

The enigma of the quantum Hall effect in graphene

We apply Laughlin’s gauge argument to analyze the ν=0 quantum Hall effect observed in graphene when the Fermi energy lies near the Dirac point, and conclude that this necessarily leads to divergent bulk longitudinal resistivity in the zero temperature thermodynamic limit. We further predict that in a Corbino geometry measurement, where edge transport and other mesoscopic effects are unimportant, one should find the longitudinal conductivity vanishing in all graphene samples which have an underlying ν=0 quantized Hall effect. We argue that this ν=0 graphene quantum Hall state is qualitatively similar to the high field insulating phase (also known as the Hall insulator) in the lowest Landau level of ordinary semiconductor two-dimensional electron systems. We establish the necessity of having a high magnetic field and high mobility samples for the observation of the divergent resistivity as arising from the existence of disorder-induced density inhomogeneity at the graphene Dirac point.