Crossover from weak localization to Shubnikov-de Haas oscillations in a high-mobility 2D electron gas

We study the magnetoresistance deltarho(xx)(B)/rho(0) of a high-mobility 2D electron gas in the domain of magnetic fields B, intermediate between the weak localization and the Shubnikov-de Haas oscillations, where deltarho(xx)(B)/rho(0) is governed by the interaction effects. Assuming short-range impurity scattering, we demonstrate that in the second order in the interaction parameter lambda a linear B dependence, deltarho(xx)(B)/rho(0) approximately lambda(2)omega(c)/E(F) with a temperature-independent slope, emerges in this domain of B (here omega(c) and E(F) are the cyclotron frequency and the Fermi energy, respectively). Unlike previous mechanisms, the linear magnetoresistance is unrelated to the electron executing the full Larmour circle, but rather originates from the impurity scattering via the B dependence of the phase of the impurity-induced Friedel oscillations.     

Quantum interference phenomena between impurity states in d-wave superconductors

We investigate the mutual influence of impurities in two-dimensional d-wave superconductors involving self-consistent solutions of the Bogoliubov-de Gennes equations. The local order parameter suppression, the local density of states as well as the interference of impurity-induced structures are analyzed. We employ an impurity position averaging scheme for the density of states that does not neglect these interference effects, as the commonly used T-matrix approaches do.     

Hall resistivity of granular metals

We calculate the Hall conductivity sigma(xy) and resistivity rho(xy) of a granular system at large tunneling conductance g(T)>1. We show that in the absence of Coulomb interaction the Hall resistivity depends neither on the tunneling conductance nor on the intragrain disorder and is given by the classical formula rho(xy)=H/(n*ec), where n* differs from the carrier density n inside the grains by a numerical coefficient determined by the shape of the grains. The Coulomb interaction gives rise to logarithmic in temperature T correction to rho(xy) in the range Gamma less or similar T less or similar min(g(T)E(c), E(Th)), where Gamma is the tunneling escape rate, E(c) is the charging energy, and E(Th) is the Thouless energy of the grain.     

Broken symmetries and directed collective energy transport in spatially extended systems

We study the appearance of directed energy current in homogeneous spatially extended systems coupled to a heat bath in the presence of an external ac field E(t). The systems are described by nonlinear field equations. By making use of a symmetry analysis, we predict the right choice of E(t) and obtain directed energy transport for systems with a nonzero topological charge Q. We demonstrate that the symmetry properties of motion of topological solitons (kinks and antikinks) are equivalent to the ones for the energy current. Numerical simulations confirm the predictions of the symmetry analysis and, moreover, show that the directed energy current drastically increases as the dissipation parameter alpha reduces.     

Local density of states of vortex state in mesoscopic superconductors

We study local density of states (LDOS) of vortex state in mesoscopic square superconductors with Bogoliubov-de Gennes (BdG) equation. We develop one effective numerical method based on the finite element method to self-consistently solve the BdG equation. The LDOS for various vortex states is obtained. Our results about the single vortex show that the LDOS has the particle-hole asymmetry and the results for one- and two-vortex state agree very well with the experimental observation. Besides, we predict the LDOS of multi-vortex states, which is crucial for the further STM/STS experimental study of vortex state in mesoscopic superconducting system.     

Effect of magnetic impurities in chiral <Emphasis Type="Italic">p</Emphasis>-wave superconducting nanoloops

The effect of many magnetic impurities in symmetric chiral p-wave superconducting nanoloops is investigated by numerically solving the BdG equations self-consistently. Two magnetic impurities can lead to the appearance of two impurity bound levels close to the Fermi level. The arising bound states can cross the Fermi level at the same impurity strength for the case of two independent midway impurities, while multiple zero-energy states can be obtained at two separated values of impurity strength when two independent edge impurities are present. Moreover, the multiple zero modes can only show up for appropriate relative positions between two edge impurities due to the quantum interference effect. Particularly, for some appropriate strength of two independent midway impurities, the impurity bound levels cross the Fermi level twice with increasing threaded flux, while the multiple zero modes can not emerge in the flux evolution.     

Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography

We consider the shallow water equations with non-flat bottom topography. The smooth solutions of these equations are energy conservative, whereas weak solutions are energy stable. The equations possess interesting steady states of lake at rest as well as moving equilibrium states. We design energy conservative finite volume schemes which preserve (i) the lake at rest steady state in both one and two space dimensions, and (ii) one-dimensional moving equilibrium states. Suitable energy stable numerical diffusion operators, based on energy and equilibrium variables, are designed to preserve these two types of steady states. Several numerical experiments illustrating the robustness of the energy preserving and energy stable well-balanced schemes are presented.     

Renormalized quasiparticles in antiferromagnetic states of the Hubbard model

We analyze the properties of the quasiparticle excitations of metallic antiferromagnetic states in a strongly correlated electron system. The study is based on dynamical mean field theory (DMFT) for the infinite dimensional Hubbard model with antiferromagnetic symmetry breaking. Self-consistent solutions of the DMFT equations are calculated using the numerical renormalization group (NRG). The low energy behavior in these results is then analyzed in terms of renormalized quasiparticles. The parameters for these quasiparticles are calculated directly from the NRG derived self-energy, and also from the low energy fixed point of the effective impurity model. From these the quasiparticle weight and the effective mass are deduced. We show that the main low energy features of the k-resolved spectral density can be understood in terms of the quasiparticle picture. We also find that Luttinger's theorem is satisfied for the total electron number in the doped antiferromagnetic state.     

Periodic Sturm-Liouville problems related to two Riccati equations of constant coefficients

We consider two closely related Riccati equations of constant parameters whose particular solutions are used to construct the corresponding class of supersymmetrically coupled second-order differential equations. We solve analytically these parametric periodic problems along the whole real axis. Next, the analytically solved model is used as a case study for a powerful numerical approach that is employed here for the first time in the investigation of the energy band structure of periodic not necessarily regular potentials. The approach is based on the well-known self-matching procedure of James (1949) [9] and implements the spectral parameter power series solutions introduced by Kravchenko (2008) [10]. We obtain additionally an efficient series representation of the Hill discriminant based on Kravchenko’s series.     

Quantum phase transition of the Fulde–Ferrell–Larkin–Ovchinnikov states in two-dimensional anisotropic triangular system

Based on the Bogoliubov de Gennes (BdG) equations, we study the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) states for d-wave superconductor in anisotropic triangular system self-consistently with a strong magnetic field applied parallel to its conducting planes. We find that the two-dimensional FFLO state transforms to one-dimensional FFLO state as the system frustrated. The calculated local density of states are suggested to distinguish these states.     

Shot Noise in Ferromagnetic Superconductor Tunnel Junctions

In this paper, the superconducting order parameter and the energy spectrum of the Bogoliubov excitations are obtained from the Bogoliubov-de Gennes (BdG) equation for a ferromagnetic superconductor (FS). Taking into account the rough interface scattering effect, we calculate the shot noise and the differential conductance of the normal-metal insulator ferromagnetic superconductor junction. It is shown that the exchange energy E_h in FS can lead to splitting of the differential shot noise peaks and the conductance peaks. The energy difference between the two splitting peaks is equal to 2E_h. The rough interface scattering strength results in descent of conductance peaks and the shot noise-to-current ratio but increases the shot noise.     

基于广义交替数值通量的局部间断Galerkin方法求解二维波动方程

波的传播往往在复杂的地质结构中进行,如何有效地求解非均匀介质中的波动方程一直是研究的热点.本文将局部间断Galekin(local discontinuous Galerkin, LDG)方法引入到数值求解波动方程中.首先引入辅助变量,将二阶波动方程写成一阶偏微分方程组,然后对相应的线性化波动方程和伴随方程构造间断Galerkin格式;为了保证离散格式满足能量守恒,在单元边界上选取广义交替数值通量,理论证明该方法满足能量守恒性.在时间离散上,采用指数积分因子方法,为了提高计算效率,应用Krylov子空间方法近似指数矩阵与向量的乘积.数值实验中给出了带有精确解的算例,验证了LDG方法的数值精度和能量守恒性;此外,也考虑了非均匀介质和复杂计算区域的计算,结果表明LDG方法适合模拟具有复杂结构和多尺度结构介质中的传播.     

Screening of Local Magnetic Moment by Electrons of Disordered Graphene

Based on the Anderson impurity model and self-consistent approach, we investigate the condition for the screening of a local magnetic moment by electrons in graphene and the influence of the moment on electronic properties of the system. The results of numerical calculations carried out on a finite sheet of graphene show that when the Fermi energy is above the single occupancy energy and below the double occupancy energy of the local impurity, a magnetic state is possible. A phase diagram in a parameter space spanned by the Coulomb energy U and the Fermi energy is obtained to distinguish the parameter regions for the magnetic and nonmagnetic states of the impurity. We find that the combined effect of the impurity and finite size effect results in a large charge density near the edges of the finite graphene sheet. The density of states exhibits a peak at the Dirac point which is caused by the appearance of the edge states localized at the zigzag edges of the sheet.     

Quantum correction to conductivity close to a ferromagnetic quantum critical point in two dimensions

We study the temperature dependence of the conductivity due to quantum interference processes for a two-dimensional disordered itinerant electron system close to a ferromagnetic quantum critical point. Near the quantum critical point, the crossover between diffusive and ballistic regimes of quantum interference effects occurs at a temperature T*=1/taugamma(E(F)tau)2, where gamma is the parameter associated with the Landau damping of the spin fluctuations, tau is the impurity scattering time, and E(F) is the Fermi energy. For a generic choice of parameters, T* is smaller than the nominal crossover scale 1/tau. In the ballistic quantum critical regime, the conductivity behaves as T1/3.     

Operation of the Faddeev Kernel in Configuration Space

We present a practical method to solve Faddeev three-body equations at energies above the three-body breakup threshold as integral equations in coordinate space. This is an extension of a previously used method for bound states and scattering states below three-body breakup threshold energy. We show that breakup components in three-body reactions produce long-range effects on Faddeev integral kernels in coordinate space, and propose numerical procedures to treat these effects. Using these techniques, we solve Faddeev equations for neutron-deuteron scattering to compare with benchmark solutions.     

正常金属-铁磁绝缘层-dx2-y2+idxy混合波超导结中的磁散射对隧道谱的影响

在正常金属铁磁绝缘层dx2-y2 idxy混合波超导隧道结中,考虑到铁磁绝缘层的磁散射和界面的粗糙散射效应,运用BogoliubovdeGennes(BdG)方程和BlonderTinkhamKlapwijk(BTK)理论,计算了隧道结中的准粒子传输系数和微分电导.研究表明:(1)磁散射和界面粗糙散射均可以压低电导峰,其中磁散射能使电导峰滑移,而粗糙界面散射却能阻止这种滑移,且两散射的共同作用可抑制由混合波两序参数的幅值比不同所导致的电导峰滑移;(2)随铁磁层离超导表面距离的增加,隧道谱在零偏压处由凹陷变成了零偏压电导峰,继而又演化为凹陷中的中心峰;(3)当铁磁层离开超导表面有若干相干长度时,隧道谱中将呈现一些子能级谐振峰.     

纤锌矿GaN柱形量子点中类氢施主杂质态

在有效质量近似和变分原理的基础上,选取含两个变分参数的波函数,研究了纤锌矿结构的GaN/AlxGa1-xN单量子点中类氢施主杂质体系的结合能随量子点(QD)尺寸以及杂质在量子点中位置的变化,并与以前使用不同尝试波函数的计算结果进行了比较。结果表明:由我们选取的两变分参数波函数得到的结果与前人选取的两变分参数波函数得到的结果相比有所改进,而与选取一个变分参数波函数得到的结果一致。同时我们还计算了体系的维里定理值随量子点半径的变化情况,所得结果与前人工作结果一致,说明本文选取的两变分参数波函数能很好地描述柱形量子点中施主杂质态的运动。     

Surface Majorana flat bands in j=3/2 superconductors with singlet-quintet mixing

Recent experiments [Science Advances 4 eaao4513(2018)] have revealed the evidence of nodal-line superconductivity in half-Heusler superconductors, e.g., YPt Bi. Theories have suggested the topological nature of such nodal-line superconductivity and proposed the existence of surface Majorana flat bands on the(111) surface of half-Heusler superconductors.Due to the divergent density of states of the surface Majorana flat bands, the surface order parameter and the surface impurity play essential roles in determining the surface properties. We study the effect of the surface order parameter and the surface impurity on the surface Majorana flat bands of half-Heusler superconductors based on the Luttinger model. To be specific, we consider the topological nodal-line superconducting phase induced by the singlet-quintet pairing mixing, classify all the possible translationally invariant order parameters for the surface states according to irreducible representations of C_(3v)point group, and demonstrate that any energetically favorable order parameter needs to break the time-reversal symmetry. We further discuss the energy splitting in the energy spectrum of surface Majorana flat bands induced by different order parameters and non-magnetic or magnetic impurities. We propose that the splitting in the energy spectrum can serve as the fingerprint of the pairing symmetry and mean-field order parameters. Our theoretical prediction can be examined in the future scanning tunneling microscopy experiments.     

Numerical study of magneto-convective heat and mass transfer from inclined surface with Soret diffusion and heat generation effects: A model for ocean magnetic energy generator fluid dynamics

A mathematical model is developed for steady state magnetohydrodynamic (MHD) heat and mass transfer flow along an inclined surface in an ocean MHD energy generator device with heat generation and thermo-diffusive (Soret) effects. The governing equations are transformed into nonlinear ordinary differential equations with appropriate similarity variables. The emerging two-point boundary value problem is shown to depend on six dimensionless thermophysical parameters - magnetic parameter, Grashof number, Prandtl number, modified Prandtl number, heat source parameter and Soret number in addition to plate inclination. Numerical solutions are obtained for the nonlinear coupled ordinary differential equations for momentum, energy and salinity (species) conservation, numerically, using the Nachtsheim–Swigert shooting iteration technique in conjunction with the Runge–Kutta sixth order iteration scheme. Validation is achieved with Nakamura's implicit finite difference method. Further verification is obtained via the semi-numerical Homotopy analysis method (HAM). With an increase in magnetic parameter, skin friction is depressed whereas it generally increases with heat source parameter. Salinity magnitudes are significantly reduced with increasing heat source parameter. Temperature gradient is decreased with Prandtl number and salinity gradient (mass transfer rate) is also reduced with modified Prandtl number. Furthermore, the flow is decelerated with increasing plate inclinations and temperature also depressed with increasing thermal Grashof number.