Cooper-pair injection into quantum spin Hall insulators

We theoretically study tunneling of Cooper pairs from a superconductor spanning a two-dimensional topological insulator strip into its helical edge states. The coherent low-energy electron-pair tunneling sets off positive current cross correlations along the edges, which reflect an interplay of two quantum-entanglement processes. Most importantly, superconducting spin pairing dictates a Cooper pair partitioning into the helical edge liquids, which transport electrons in opposite directions for opposite spin orientations. At the same time, Luttinger-liquid correlations fractionalize electrons injected at a given edge into counterpropagating charge pulses carrying definite fractions of the elementary electron charge.     

Effects of interaction on quantum spin Hall insulators

We study the S(z)-conserving quantum spin Hall insulator in the presence of Hubbard U from a field theory point of view. The main findings are the following. (1) For arbitrarily small U the edges possess power-law correlated antiferromagnetic XY local moments. Gapless charge excitations arise from the Goldstone-Wilczek mechanism. (2) Electron tunneling between opposite edges allows vortex instantons to proliferate when K, the XY stiffness constant, satisfies 4πK+(4πK)(-1)<4. When the preceding inequality is violated, the edge modes remain gapless despite the sample width being finite. (3) The phase transition from the topological insulator to the large U antiferromagnetic insulator is triggered by the condensation of magnetic excitons. (4) In the large U antiferromagnetic insulating phase the magnetic vortices carry charges proportional to the square magnitude of the antiferromagnetic order parameter.     

Probing spin entanglement by gate-voltage-controlled interference of current correlation in quantum spin Hall insulators

We propose an entanglement detector composed of two quantum spin Hall insulators and a side gate deposited on one of the edge channels. For an ac gate voltage, the differential noise contributed from the entangled electron pairs exhibits the nontrivial step structures, from which the spin entanglement concurrence can be easily obtained. The possible spin dephasing effects in the quantum spin Hall insulators are also included.     

Time-reversal-symmetry-broken quantum spin Hall effect

The quantum spin Hall (QSH) state of matter is usually considered to be protected by time-reversal (TR) symmetry. We investigate the fate of the QSH effect in the presence of the Rashba spin-orbit coupling and an exchange field, which break both inversion and TR symmetries. It is found that the QSH state characterized by nonzero spin Chern numbers C(±) = ±1 persists when the TR symmetry is broken. A topological phase transition from the TR-symmetry-broken QSH phase to a quantum anomalous Hall phase occurs at a critical exchange field, where the bulk band gap just closes. It is also shown that the transition from the TR-symmetry-broken QSH phase to an ordinary insulator state cannot happen without closing the band gap.     

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.     

Strong quantum spin correlations observed in atomic spin mixing

We have observed sub-Poissonian spin correlations generated by collisionally induced spin mixing in a spin-1 Bose-Einstein condensate. We measure a quantum noise reduction of -7 dB (-10 dB corrected for detection noise) below the standard quantum limit for the corresponding coherent spin states. The spin fluctuations are detected as atom number differences in the spin states using fluorescent imaging that achieves a detection noise floor of 8 atoms per spin component for a probe time of 100 μs.     

Localization in a quantum spin Hall system

The localization problem of electronic states in a two-dimensional quantum spin Hall system (that is, a symplectic ensemble with topological term) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent nu for the divergence of the localization length is estimated as nu congruent with 1.6, which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. Our analysis strongly suggests a different universality class related to the topology of the pertinent system.     

Electron spin transitions in quantum Hall systems

A system of two-dimensional electron gas in a strong magnetic field exhibits a remarkable phenomenon known as the fractional quantum Hall effect. Rapid advances in experimental techniques and intense theoretical work for well over a decade have significantly contributed to our understanding of the mechanism behind the effect. It is now a well established fact that electron correlations are largely responsible for the occurrence of this phenomenon. In recent years, theoretical and experimental investigations have revealed that those electron correlations, which are responsible for the quantum Hall effect, are also the reason for various spin transitions in the system. In this review, we systematically follow the theoretical studies of the role spin degree of freedom play in the quantum Hall effect regime and also describe several ingenious experiments reported in recent years which are in good agreement with the emerging theoretical picture.     

Determining spin through quantum azimuthal-angle correlations

Determining the spin of new particles is critical in identifying the true theory among various extensions of the Standard Model at the next generation of colliders. Quantum interference between different helicity amplitudes was shown to be effective when the final state is fully reconstructible. However, many interesting new physics processes allow only for partial reconstruction. In this Letter, we show how the interference effect can be unambiguously extracted even in processes that have two-fold ambiguity, by considering the correlation between two decay planes in e⁺e⁻$e^{+}{e}^{-}$ collisions.     

The stability of the fractional quantum Hall effect in topological insulators

With the recent observation of graphene-like Landau levels at the surface of topological insulators, the possibility of fractional quantum Hall effect, which is a fundamental signature of strong correlations, has become of interest. Some experiments have reported intra-Landau level structure that is suggestive of fractional quantum Hall effect. This paper discusses the feasibility of fractional quantum Hall effect from a theoretical perspective, and argues that while this effect should occur, ideally, in the n=0 and |n|=1 Landau levels, it is ruled out in higher |n| Landau levels. Unlike graphene, the fractional quantum Hall effect in topological insulators is predicted to show an interesting asymmetry between n=1 and n=−1 Landau levels due to spin-orbit coupling.     

Spin-charge separation in the quantum spin Hall state

The quantum spin Hall state is a topologically nontrivial insulator state protected by the time-reversal symmetry. We show that such a state always leads to spin-charge separation in the presence of a pi flux. Our result is generally valid for any interacting system. We present a proposal to experimentally observe the phenomenon of spin-charge separation in the recently discovered quantum spin Hall system.     

缀饰格子中时间反演对称破缺的量子自旋霍尔效应

<正>研究了缀饰格子中的量子自旋霍尔效应,模型中同时考虑了Rashba自旋轨道耦合和交换场的作用.缀饰格子具有简立方对称性,以零能平带和单狄拉克锥结构为主要特点.在缀饰格子中,不论是实现量子自旋霍尔效应还是量子反常霍尔效应,都需要一个不为零的内禀自旋轨道耦合作用来打开一个完全的体能隙,这与石墨烯等六角格子模型有着很大的不同.在交换场破坏了时间反演对称性的情况下,以自旋陈数为标志的量子自旋霍尔效应仍然能够存在,边缘态和极化率的相关结果也证明了这一结论.结果表明自旋陈数比z2拓扑数在表征量子自旋霍尔效应方面有着更广泛的适用范围,相应的结论为利用磁场控制量子自旋霍尔效应提出了一个理论模型和依据.     

Anisotropic intrinsic spin Hall effect in quantum wires

We use numerical simulations to investigate the spin Hall effect in quantum wires in the presence of both Rashba and Dresselhaus spin-orbit coupling. We find that the intrinsic spin Hall effect is highly anisotropic with respect to the orientation of the wire, and that the nature of this anisotropy depends strongly on the electron density and the relative strengths of the Rashba and Dresselhaus spin-orbit couplings. In particular, at low densities, when only one subband of the quantum wire is occupied, the spin Hall effect is strongest for electron momentum along the [N110] axis, which is the opposite of what is expected for the purely 2D case. In addition, when more than one subband is occupied, the strength and anisotropy of the spin Hall effect can vary greatly over relatively small changes in electron density, which makes it difficult to predict which wire orientation will maximize the strength of the spin Hall effect. These results help to illuminate the role of quantum confinement in spin-orbit-coupled systems, and can serve as a guide for future experimental work on the use of quantum wires for spin-Hall-based spintronic applications.     

Spin-orbit gauge and quantum spin Hall effect

We have shown that the non-Abelian spin-orbit gauge field strength of the Rashba and Dresselhaus interactions, when split into two Abelian field strengths, the Hamiltonian of the system can be re-expressed as a Landau level problem with a particular relation between the two coupling parameters. The quantum levels are created with up and down spins with opposite chirality and leads to the quantum spin Hall effect.     

Transverse spin and momentum correlations in quantum chromodynamics

The naive time reversal odd (‘T-odd’) parton distribution and fragmentation functions are explored. We use the spectator model framework to study flavour dependence of the Boer-Mulders (h ₁^⊥ ) and Sivers (f _1T^⊥) functions as well as the ‘T-even’ but chiral odd function h _1L^⊥. These transverse momentum-dependent parton distribution functions are of significance for the analysis of azimuthal asymmetries in semi-inclusive deep inelastic scattering, as well as for the overall physical understanding of the distribution of transversely polarized quarks in unpolarized hadrons. In this context we also consider the Collins mechanism and the fragmentation function H ₁^⊥. As a by-product of this analysis we calculate the leading twist unpolarized cos(2ϕ) asymmetry, and sin(2ϕ) single spin asymmetry for a longitudinally polarized target in semi-inclusive deep inelastic scattering.      

Electron correlations at the fractional quantum Hall edge

This paper reviews tunnel spectroscopy of fractional quantum Hall edges using cleaved-edge overgrown devices. Beginning with an intuitive introduction to various experimental and theoretical aspects, the device structure is reviewed, and the experimental result of a continuum of power-law tunneling exponents is revisited. The unanticipated behavior of the exponent with fractional filling factor is described, and all subsequent theoretical explanations for these results are laid out for comparison. Finally, we propose new directions for experimentally resolving the remaining questions.     

铁磁石墨烯体系的CT不变量子自旋霍尔效应

文章作者在垂直磁场作用下的铁磁石墨烯体系里预言了一种新类型的量子自旋霍尔效应.这量子自旋霍尔效应与自旋轨道耦合无关,体系也不具有时间反演不变性;但是有CT不变（C为电子-空穴变换、T为时间反演变换）.由于量子自旋霍尔效应,体系的纵向电阻和自旋霍尔阻出现量子化平台.特别是,自旋霍尔阻的量子化平台有很强的抗杂质干扰能力.     

铁磁石墨烯体系的CT不变量子自旋霍尔效应

文章作者在垂直磁场作用下的铁磁石墨烯体系里预言了一种新类型的量子自旋霍尔效应.这量子自旋霍尔效应与自旋轨道耦合无关,体系也不具有时间反演不变性;但是有CT不变(C为电子-空穴变换、T为时间反演变换).由于量子自旋霍尔效应,体系的纵向电阻和自旋霍尔阻出现量子化平台.特别是,自旋霍尔阻的量子化平台有很强的抗杂质干扰能力.