Comparison of calculation methods for the tunnel splitting at excited states of biaxial spin models

We present the calculation and comparison of tunnel splitting at excited levels of biaxial spin models by various methods, including the generalized instanton method, the generalized path integral method for coherent spin states, the perturbation method, and the exact method by numerical diagonalization of the Hamiltonian. It is found that, for integer spin with spin number around 10, tunnel splitting predicted by the generalized path integral for coherent spin states is about 10^{-n} times of the exact numerical result for the nth excited level, while the ratio of the results of the perturbation method and the exact numerical method diverges in the large spin limit. We thus conclude that the generalized instanton method is the best approximate way for calculating tunnel splitting in spin models.     

Macroscopic quantum coherence of the Neel vector in antiferromagnetic system without Kramers' degeneracy

At low temperatures the Neel vector in a small antiferromagnetic particle can possess quantum coherence between the classically degenerate minima. In some cases, the topological term in the magnetic action can lead to destructive interference between the symmetry-related trajectories for the half-integer excess spin antiferromagnetic particle. By studying a macroscopic quantum coherence problem of the Neel vector with biaxial crystal symmetry and a weak magnetic field applied along the hard axis, we find that the quenching of tunnel splitting could take place in the system without Kramers' degeneracy. Both the Wentzel-Kramers-Brillouin exponent and the pre-exponential factors are found exactly for the tunnel splitting. Results show that the tunnel splitting oscillates with the weak applied magnetic field for both the integer and half-integer excess spin antiferromagnetic particles, and vanishes at certain values of the field. All the calculations are performed based on the two sublattices model and the instanton method in spin-coherent-state path integral. Received: 24 July 1997 / Accepted: 30 September 1997     

Effects of Arbitrarily Directed Field on Spin Phase Oscillations in Biaxial Molecular Magnets

Quantum phase interference and spin-parity effects are studied in biaxial molecular magnets in a magnetic field at an arbitrarily directed angle.The calculations of the ground-state tunnel splitting are performed on the basis of the instanton technique in the spin-coherent-state path-integral representation,and complemented by exactly numerical diagonalization.Both the Wentzel-Kramers-Brillouin exponent and the pre-exponential factor are obtained for the entire region of the direction of the field.Our results show that the tunnel splitting oscillates with the field for the small field angle,while for the large field angle the oscillation is completely suppressed.This distinct angular dependence,together with the dependence of the tunnel splitting on the field strength,provides an independent test for spin-parity effects in biaxial molexular magnets.The analytical results for the molecular Fes magnet are found to be in good agreement with the numerical simulations,which suggests that even the molecular magnet with total spin S=10 is large enough to be treated as a giant spin system.     

Application of the instanton method for analyzing tunneling splitting spectra of nonrigid molecular systems

General formalism and basic ideas of the instanton method are described. The potentialities of the method are demonstrated by calculating the tunneling splitting of the ground vibrational level for nonrigid molecules with two and three equivalent minima on their potential-energy surface. Some advantages of the application of the instanton method as compared to the well-known semiclassical approximation for describing the spectra of tunneling splitting of a nonrigid molecular system are proved.     

Numerical simulation on tunnel splitting of Bose-Einstein condensate in multi-well potentials

The low-energy-level macroscopic wave functions of the Bose-Einstein condensate (BEC) trapped in a symmetric double-well and a periodic potential are obtained by solving the Gross-Pitaevskii equation numerically. The ground state tunnel splitting is evaluated in terms of the even and odd wave functions corresponding to the global ground and excited states respectively. We show that the numerical result is in good agreement with the analytic level splitting obtained by means of the periodic instanton method.     

双组分玻色-爱因斯坦凝聚体中亚稳态存在条件及其寿命

本文对双势阱中凝聚的冷原子通过约瑟夫森结隧穿时所形成的亚稳态进行研究.通过介观自旋算符建立了体系的精确量子相位模型,利用对量子自旋的势场描述给出了在两阱中振荡的原子之间相位差为时,即亚稳态时所要满足的物理条件,并用瞬子方法计算了该亚稳态存在的寿命.     

Instantons and Asymmetric Vacua

It is shown that with asymmetric classical vacua the quantum mechanical instanton approach to the energy splitting of degenerate states applies even though the degenerate state in one well is not the quantum mechanical ground state of that well. The instanton approach leads to the correct leading exponential behavior of the energy splitting E, but the prefactor is much more difficult to compute due to the asymmetric nature of the fluctuation potential V(_c(t)), which is in turn a direct consequence of the asymmetry of the two classical minima between which the instanton interpolates.     

HgMnTe磁性二维电子气自旋-轨道和交换相互作用研究

通过分析不同温度下HgMnTe磁性二维电子气Shubnikov-de Hass（SdH）振荡的拍频现象，研究了量子阱中电子自旋 轨道相互作用和spd交换相互作用.结果表明：（1）在零磁场下，电子的自旋 轨道相互作用导致电子发生零场自旋分裂；（2）在弱磁场下，电子的自旋-轨道相互作用占主导地位，并受Landau分裂和Zeeman分裂的影响，电子的自旋分裂随磁场增加而减小；（3）在高磁场下，电子的spd交换相互作用达到饱和，电子的自旋分裂主要表现为Zeeman分裂.实验证明了当电子的Zeeman分裂能量与零场 关键词： 磁性二维电子气 Zeeman分裂 Rashba自旋分裂     

外磁场中单畴反铁磁颗粒的宏观量子效应

用瞬子方法研究了外加磁场对单畴双轴反铁磁颗粒宏观量子效应的影响. 当外磁场沿易磁化方向时,简并基态中的一个能量抬高,变为亚稳态,其隧穿衰变率随外磁场增大;当外磁场沿中间磁化方向时,能级的隧穿劈裂随外磁场的变化而振荡.从而提出一种观察单畴反铁磁颗粒中宏观量子相干和隧穿现象的实验方法.     

拓扑绝缘体Bi_2Se_3中层堆垛效应的第一性原理研究

运用第一性原理方法,研究了拓扑绝缘体Bi_2Se_3块体和薄膜中的层堆垛对其结构、电子态、拓扑态和自旋劈裂的影响.发现不同的堆垛会引起Bi_2Se_3层间的相互作用,改变系统的中心对称性.块体的ABC和AAA堆垛都具有中心对称性和相似的能带结构.ABA堆垛破坏了体系的中心对称性,能带发生很大改变,并且产生了很大的能带自旋劈裂.用能带反转的方法判定体系的拓扑相,在不同堆垛的Bi_2Se_3块体中,考虑自旋轨道耦合时都发生了能带反转,因而具有不同堆垛的Bi2Se3仍是拓扑绝缘体.进一步研究了Bi_2Se_3薄膜中的堆垛效应,发现非中心对称的ABA堆垛在Bi_2Se_3薄膜中引起明显的自旋劈裂,并且提出和验证了用应变调控自旋劈裂的方法.     

Spin-filtered edge states and quantum Hall effect in graphene

Electron edge states in graphene in the quantum Hall effect regime can carry both charge and spin. We show that spin splitting of the zeroth Landau level gives rise to counterpropagating modes with opposite spin polarization. These chiral spin modes lead to a rich variety of spin current states, depending on the spin-flip rate. A method to control the latter locally is proposed. We estimate Zeeman spin splitting enhanced by exchange, and obtain a spin gap of a few hundred Kelvin.     

Implications of the ALEPH tau-lepton decay data for perturbative and nonperturbative QCD

We use ALEPH data on hadronic tau decays in order to calculate Euclidean coordinate space correlation functions in the vector and axial-vector channels. The linear combination V-A receives no perturbative contribution and is quantitatively reproduced by the instanton liquid model. In the case of V+A the instanton calculation is in good agreement with the data once perturbative corrections are included. These corrections clearly show the evolution of alpha(s). We also analyze the range of validity of the operator product expansion (OPE). We conclude that the range of validity of the OPE is limited to x less, similar 0.3 fm, whereas the instanton model describes the data over the entire range.     

Linewidth Analysis of Spin Labels in Liquids: II. Experimental

This work demonstrates that homogeneous linewidths can be extracted from continuous wave electron paramagnetic resonance spectra and that they quantitatively agree with the predictions of existing relaxation theory. We suggest that relaxation theory can be used to predict experimental lineshapes provided that the simulations properly include sources of broadening. We have found that the rotational correlation times for spin labels in different percentages of glycerol/water mixtures are best modeled by a power law treatment for the viscosity, similar to that for translational diffusion. The translational diffusion coefficients themselves also have a power law dependence on the viscosity for glycerol/water mixtures. The linewidths were linearly dependent upon both the oxygen and the spin label concentration. The hyperfine splittings of all nuclei were observed to decrease linearly with increasing spin label concentration, completely at odds with existing theory which predicts a quadratic dependence upon concentration. The linear dependence was independent of hyperfine splitting until the magnitude of the hyperfine splitting was less than the homogeneous linewidth.     

Anisotropic Spin Splitting in Step Quantum Wells

By the method of finite difference, the anisotropic spin splitting of the AlxGa1-xAs/GaAs/Aly Ga1-yAs/AlxGal-xAs step quantum wells （QWs） are theoretically investigated considering the interplay of the bulk inversion asymmetry and structure inversion asymmetry induced by step quantum well structure and external electric field. We demonstrate that the anisotropy of the total spin splitting can be controlled by the shape of the QWs and the external electric field. The interface related Rashba effect plays an important effect on the anisotropic spin splitting by influencing the magnitude of the spin splitting and the direction of electron spin. The Rashba spin splitting presents in the step quantum wells due to the interface related Rashba effect even without external electric field or magnetic field.     

Spin-orbit interactions in semiconductor superlattice

The purpose of this paper is to theoretically investigate the spin-orbit interactions of common semiconductor superlattices. Spin splitting and spin-orbit interaction coefficients are calculated based on interactions between the interface-related-Rashba effect and Dresselhaus effect. Semiconductor superlattice shows a series of specific characteristics in spin splitting as follows. The spin splitting of the superlattice structure is greater than that of a single quantum well, contributing to significant spin polarization, spin filtering, and convenient manipulation of spintronic devices. The spin splitting of some superlattice structures does not change with variation of the size of some constituent quantum wells, reducing the requirements for accuracy in the size of quantum wells. The total spin splitting of lower sub-levels of some superlattice can be designed to be zero, realizing a persistent spin helix effect and long spin relaxation time, however, the total spin splitting of higher sub-levels is still appreciable, contributing to desirable spin polarization. These results demonstrate that one superlattice structure can realize two functions, acting as a spin field effect transistor and a spin filter.     

Instanton zero modes and β-functions in gauged supergravity

We prove that one loop infinities in N?3 gauged O(N) supergravities are produced only by zero modes both on de Sitter and gauge instanton backgrounds. This strongly suggests (in analogy with the super Yang-Mills case) that instantons may be used for establishing exact β-functions in supergravities. We also derive the general formula for the number of gauge instanton zero modes for arbitrary spin and find that the “magnetic moment” part of the contribution in the gauge β-function is completely due to zero modes.     

Quantum tunneling between paramagnetic and superconducting states of a nanometer-scale superconducting grain placed in a magnetic field

We consider the process of quantum tunneling between the superconducting and paramagnetic states of a nanometer-scale superconducting grain placed in a magnetic field. The grain is supposed to be weakly coupled to a normal metallic contact that plays the role of the spin reservoir. Using the instanton method, we find the probability of the quantum tunneling process and express it in terms of the applied magnetic field, order parameter of the superconducting grain, and conductance of the tunneling junction between the grain and metallic contact.