Topological Fulde–Ferrell and Larkin–Ovchinnikov states in spin-orbit-coupled lattice system

The spin-orbit coupled lattice system under Zeeman fields provides an ideal platform to realize exotic pairing states. Notable examples range from the topological superfluid/superconducting (tSC) state, which is gapped in the bulk but metallic at the edge, to the Fulde–Ferrell (FF) state (having a phase-modulated order parameter with a uniform amplitude) and the Larkin–Ovchinnikov (LO) state (having a spatially varying order parameter amplitude). Here, we show that the topological FF state with Chern number (C=−1) (tFF₁) and topological LO state with C= 2 (tLO₂) can be stabilized in Rashba spin-orbit coupled lattice systems in the presence of both in-plane and out-of-plane Zeeman fields. Besides the inhomogeneous tSC states, in the presence of a weak in-plane Zeeman field, two topological BCS phases may emerge with C=−1 (tBCS₁) far from half filling and C= 2 (tBCS₂) near half filling. We show intriguing effects such as different spatial profiles of order parameters for FF and LO states, the topological evolution among inhomogeneous tSC states, and different non-trivial Chern numbers for the tFF₁ and tLO_1,2 states, which are peculiar to the lattice system. Global phase diagrams for various topological phases are presented for both half-filling and doped cases. The edge states as well as local density of states spectra are calculated for tSC states in a 2D strip.     

Magnon-mediated binding between holes in an antiferromagnet

The long-range forces between holes in an antiferromagnet are due to magnon exchange. The one-magnon exchange potential between two holes is proportional to cos(2 ϕ)/r ² where r is the distance vector of the holes and ϕ is the angle between r and an axis of the square crystal lattice. One-magnon exchange leads to bound states of holes with antiparallel spins resembling d-wave symmetry.     

Generation, dynamics, and collisions of bending waves at domain boundaries in yttrium orthoferrite

Solitary bending waves have been observed on domain boundaries of Néel type in wafers of yttrium orthoferrite, having a very sharp leading edge and an extended trailing edge and offset as a whole from the domain boundary and moving with high speeds close to the limiting velocity. Head-on collisions of two such waves of the same amplitude lead to their complete annihilation. Analogous collisions of two such waves, but of different amplitudes, lead to the appearance of a wave with the difference amplitude moving in the same direction as the wave of larger amplitude. The solitary bending waves investigated in this study appear to move under the action of gyroscopic forces acting on magnetic vortices on domain boundaries in yttrium orthoferrite, analogous to vertical Bloch lines with departure of the magnetization vector from the ac plane. From equality of the gyroscopic force with the friction force acting on the leading edge of the solitary bending wave we have estimated the amplitudes of these waves and the magnitudes of the topological charges of the magnetic vortices. Zh. éksp. Teor. Fiz. 115, 2160–2169 (June 1999)     

Theoretical investigation of the local lattice structure of Mn 2+ ion doped in tetragonal K 2ZnF 4 crystal

The complete energy matrices for a d⁵configuration ion in a tetragonal ligand-field has been constructed on the basis of the complete set of basis of d⁵configuration (252 dimension), and the relationship between the low-symmetry EPR parameters b₂ ⁰ ,b₄ ⁰ and the local distortion parameters has been established based on the complete energy matrices. As an application, we have studied the EPR parameters and the local lattice structure of Mn²⁺ ion doped in tetragonal K₂ZnF₄ system. The calculation indicated that the local lattice structure around a tetragonal Mn²⁺ ion center has an expansion distortion. Simultaneously, the local lattice structure parameters R₁ =2.0727 ?, R₂ =2.0801 ? at room temperature (295 K) and R₁ ^′ = 2.0439 ?, R₂ ^′ =2.05478 ? at low temperature (4.2 K) are determined.     

Structure and electrical behavior in air of TiO2-doped stabilized tetragonal zirconia ceramics

2 -doped YTZP ([%mol]3 Y₂O₃) compositions sintered in the temperature range of 1300 to 1450 °C, the tetragonal zirconia solid solutions field for the ZrO₂-Y₂O₃-TiO₂ system was established. The solubility of TiO₂ in YTZP was found to be about 12–[%mol]14 at 1450 °C. Structural characterization of the Ti-YTZP tetragonal zirconia solid solutions was carried out using X-ray absorption spectroscopy (EXAFS and XANES) to provide information on the environment of Ti atoms. The electrical behavior in air of the TiO₂-doped tetragonal zirconia solid solutions was studied by impedance spectroscopy in the temperature range of 300 to 800 °C, and it was found that the ionic conductivity decreases with increasing titania content. EXAFS and XANES results show that as the Ti⁴⁺ ions dissolve into the tetragonal zirconia YTZP matrix, a displacement of Ti ions from the center of symmetry takes place, leading to a non-random substitution of Ti⁴⁺ ions on Zr⁴⁺ lattice sites. Ti-O bond distances derived from EXAFS indicate that the Ti ion can be in a square-pyramidal arrangement, i.e., fivefold oxygen-coordinated. As a consequence two kinds of cation–oxygen vacancy associations are created; the high-mobility oxygen-vacancy–eightfold-coordinated cation (Zr⁴⁺) and the low-mobility oxygen-vacancy–fivefold-coordinated cation (Ti⁴⁺). This results in a decrease in the global concentration of moving oxygen vacancies and, therefore, in a decrease of the electrical conductivity. Received: 1 April 1998/Accepted: 28 September 1998     

Unusual behaviour of chemical waves in the NO + H2 reaction on Rh(111): long-range diffusion and formation of patches with reduced work function

Pattern formation in the NO + H₂ reaction on Rh(111) has been investigated in the 10⁻⁶ mbar range using photoelectron emission microscopy (PEEM) as a spatially resolving method. Target patterns, spiral waves and irregular patterns are observed in a T-window of ∼20 K width at around 460 K, located in the transition range between the reactive and unreactive states of the surface. A new species characterized by a work function below that of the clean surface forms upon collision of two wave fronts. This new species is tentatively assigned to subsurface oxygen. The colliding wave fronts start to interact when they are still more than 100 μm apart, thus demonstrating the presence of a long-range diffusional coupling.     

KMS States, Entropy and the Variational Principle¶in Full C*-Dynamical Systems

To any periodic and full C ^*-dynamical system , an invertible operator s acting on the Banach space of trace functionals of the fixed point algebra is canonically associated. KMS states correspond to positive eigenvectors of s. A Perron–Frobenius type theorem asserts the existence of KMS states at inverse temperatures equals the logarithms of the inner and outer spectral radii of s (extremal KMS states). Examples arising from subshifts in symbolic dynamics, self-similar sets in fractal geometry and noncommutative metric spaces are discussed. Certain subshifts are naturally associated to the system, and criteria for the equality of their topological entropy and inverse temperatures of extremal KMS states are given. Unital completely positive maps implemented by partitions of unity {x _j } of grade 1 are considered, resembling the “canonical endomorphism” of the Cuntz algebras. The relationship between the Voiculescu topological entropy of and the topological entropy of the associated subshift is studied. Examples where the equality holds are discussed among Matsumoto algebras associated to non finite type subshifts. In the general case is bounded by the sum of the entropy of the subshift and a suitable entropic quantity of the homogeneous subalgebra. Both summands are necessary. The measure-theoretic entropy of , in the sense of Connes–Narnhofer–Thirring, is compared to the classical measure-theoretic entropy of the subshift. A noncommutative analogue of the classical variational principle for the entropy is obtained for the “canonical endomorphism” of certain Matsumoto algebras. More generally, a necessary condition is discussed. In the case of Cuntz–Krieger algebras an explicit construction of the state with maximal entropy from the unique KMS state is done. Received: 1 February 2000 / Accepted: 23 February 2000     

Three-body structure of low-lying <Superscript>18</Superscript>Ne states

We investigate to what extent ¹⁸Ne can be descibed as a three-body system made of an inert ¹⁶O core and two protons. We compare to experimental data and occasionally to shell model results. We obtain three-body wave functions with the hyperspherical adiabatic expansion method. We study the spectrum of ¹⁸Ne , the structure of the different states and the predominant transition strengths. Two 0⁺, two 2⁺, and one 4⁺ bound states are found where they are all known experimentally. Also one 3⁺ close to threshold is found and several negative-parity states, 1^-, 3^-, 0^-, 2^-, most of them bound with respect to the ¹⁶O excited 3^- state. The structures are extracted as partial-wave components, as spatial sizes of matter and charge, and as probability distributions. Electromagnetic decay rates are calculated for these states. The dominating decay mode for the bound states is E2 and occasionally also M1 .     

On Algebraic Integrability of the Deformed Elliptic Calogero-Moser Problem

Abstract

We discuss stationary solutions of the discrete nonlinear Schrödinger equation (DNSE) with a potential of the ? ⁴ type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that there may arise chaotic spatial structures in the form of incommensurate or irregular quantum states. As a first (typical) example we consider a single electron which is strongly coupled with phonons on a 1D chain of atoms — the (Rashba)–Holstein polaron model. In the adiabatic approximation this system is conventionally described by the DNSE. Another relevant example is that of superconducting states in layered superconductors described by the same DNSE. Amongst many other applications the typical example for a classical lattice is a system of coupled nonlinear oscillators. We present the exact energy spectrum of this model in the strong coupling limit and the corresponding wave function. Using this as a starting point we go on to calculate the wave function for moderate coupling and find that the energy eigenvalue of these structures of the wave function is in exquisite agreement with the exact strong coupling result. This procedure allows us to obtain (numerically) exact solutions of the DNSE directly. When applied to our typical example we find that the wave function of an electron on a deformable lattice (and other quantum or classical discrete systems) may exhibit incommensurate and irregular structures. These states are analogous to the periodic, quasiperiodic and chaotic structures found in classical chaotic dynamics.     

Calculation of Be in an α-α-Λ Three-Body Model Using the Faddeev Equations

 The hypernucleus Be is investigated in an α-α-Λ three-body model using the Faddeev formalism. We use an α-α interaction in which the Pauli-forbidden states are correctly taken into account and we employ some phenomenological potentials between the α and Λ particles. We obtained two bound states for and , and three resonance states of . We studied the properties of these states by calculating the components and the expectation values of the potential for each partial wave. It is found that a few channels dominate in the α (α, Λ) and states, so that the alpha-clusters or the ⁸Be core are still alive in the nucleus. In a case where the two alpha particles are fixed on an axis the contour plots of the distribution of the Λ particle are shown. With the assistance of these plots one can visually understand that some of them are shell-model-like states while others are well developed cluster-model-like states. For the structure of Be, it is concluded that the Λ particle is loosely coupled in S- and P-wave orbits about the ⁸Be(0⁺) and ⁸Be(2⁺) core states. Finally, we discuss a redundant state in the Faddeev amplitude which could arise from the treatment of symmetrization. Received June 25, 1998; revised April 13, 1999; accepted for publication December 29, 1999     

Transport through a quantum dot coupled to two Majorana bound states

We investigate electron transport inside a ring system composed of a quantum dot (QD) coupled to two Majorana bound states confined at the ends of a one-dimensional topological superconductor nanowire. By tuning the magnetic flux threading through the ring, the model system we consider can be switched into states with or without zero-energy modes when the nanowire is in its topological phase. We find that the Fano profile in the conductance spectrum due to the interference between bound and continuum states exhibits markedly different features for these two different situations, which consequently can be used to detect the Majorana zero-energy mode. Most interestingly, as a periodic function of magnetic flux, the conductance shows 2π periodicity when the two Majorana bound states are nonoverlapping (as in an infinitely long nanowire) but displays 4π periodicity when the overlapping becomes nonzero (as in a finite length nanowire). We map the model system into a QD–Kitaev ring in the Majorana fermion representation and affirm these different characteristics by checking the energy spectrum.     

Universality in diffusion front growth dynamics

We have studied the scaling properties of diffusion fronts by numerical calculations based on the mean field approach in the context of a lattice gas model, performed in a triangular lattice. We find that the height-height correlation function scales with time t and length l as C(l, t) ≈l ^α f (t/l ^α/β) with α = 0.62±0.01 and β = 0.39±0.02. These exponent values are identical to those characterising the roughness of the diffusion fronts evolving through a square lattice [1,2], thus confirming their universality. Received 14 November 2001 / Received in final form 20 April 2002 Published online 31 July 2002     

Universal weak coupling limit in (2+1)-dimensionalSU(2) lattice gauge theory

Mass gaps and wave functions in (2+1)-dimensionalSU (2) lattice gauge theory (no quarks) are investigated. Starting with lattice Hamiltonians possessing exactly known ground states and the correct naive continuum limit, it is possible to reach the very deep weak-coupling region. Using variational approximation and rescaling all parameters with the help of the dimensionful coupling constantg ², we gain a formulation that is independent of the special choice of the Hamiltonian in the weak-coupling limit. The mass gap can be calculated and a kind of wave function for excited states obtained.     

Nonlinear excitations and electric transport in dissipative Morse-Toda lattices

We investigate the onset and maintenance of nonlinear soliton-like excitations in chains of atoms with Morse interactions at rather high densities, where the exponential repulsion dominates. First we discuss the atomic interactions and approximate the Morse potential by an effective Toda potential with adapted density-dependent parameters. Then we study several mechanisms to generate and stabilize the soliton-like excitations: (i) External forcing: we shake the masses periodically, mimicking a piezoelectric-like excitation, and delay subsequent damping by thermal excitation; (ii) heating, quenching and active friction: we heat up the system to a relatively high temperature Gaussian distribution, then quench to a low temperature, and subsequently stabilize by active friction. Finally, we assume that the atoms in the chain are ionized with free electrons able to move along the lattice. We show that the nonlinear soliton-like excitations running on the chain interact with the electrons. They influence their motion in the presence of an external field creating dynamic bound states (“solectrons”, etc.). We show that these bound states can move very fast and create extra current. The soliton-induced contribution to the current is constant, field-independent for a significant range of values when approaching the zero-field value.     

Metastable States in Parametrically Excited Multimode Hamiltonian Systems

 Consider a linear autonomous Hamiltonian system with m time periodic bound state solutions. In this paper we study their dynamics under time almost periodic perturbations which are small, localized and Hamiltonian. The analysis proceeds through a reduction of the original infinite dimensional dynamical system to the dynamics of two coupled subsystems: a dominant m-dimensional system of ordinary differential equations (normal form), governing the projections onto the bound states and an infinite dimensional dispersive wave equation. The present work generalizes previous work of the authors, where the case of a single bound state is considered. Here, the interaction picture is considerably more complicated and requires deeper analysis, due to a multiplicity of bound states and the very general nature of the perturbation's time dependence. Parametric forcing induces coupling of bound states to continuum radiation modes, of bound states directly to bound states, as well as coupling among bound states, which is mediated by continuum modes. Our analysis elucidates these interactions and we prove the metastability (long life time) and eventual decay of bound states for a large class of systems. The key hypotheses for the analysis are: appropriate local energy decay estimates for the unperturbed evolution operator, restricted to the continuous spectral part of the Hamiltonian, and a matrix Fermi Golden rule condition, which ensures coupling of bound states to continuum modes. Problems of the type considered arise in many areas of application including ionization physics, quantum molecular theory and the propagation of light in optical fibers in the presence of defects. Received: 13 March 2002 / Accepted: 2 January 2003 Published online: 14 April 2003 Communicated by J.L. Lebowitz     

Nuclear vertex constants for the virtual decay <Superscript>7</Superscript>Be → <Superscript>3</Superscript>He + <Superscript>4</Superscript>He of the 7Be bound states from a phase-shift analysis in the effective-range theory

The phase-shift-analysis data for the ³He⁴He scattering are analyzed using the effective-range theory, with the Coulomb interaction taken into account. We find both the renormalized nuclear vertex constants for the vertex ⁷Be → ³He + ⁴He in the ground (3/2⁻) and in the first excited (1/2⁻) bound states of ⁷Be, and the corresponding asymptotic normalization constants of the radial wave functions in these states. The results obtained can be used in an astrophysical S-factor calculation for radiative capture reaction ⁴He(³He, γ)⁷Be     

类石墨烯复杂晶胞光子晶体中的确定性界面态

拓扑绝缘体是当前凝聚态物理领域研究的热点问题.利用石墨烯材料的特殊能带特性来实现拓扑输运特性在设计下一代电子和能谷电子器件方面具有较广泛的应用前景.基于光子与电子的类比,利用光子拓扑材料实现了确定性界面态;构建了具有C_(6v)。对称性的类似石墨烯结构的的光子晶体复杂晶格;通过多种方式降低晶格对称性来获得具有C_(3v),C_3,C_(2v)和C_2对称的晶体,从而打破能谷简并实现全光子带隙结构;将体拓扑性质不同的两种光子晶体摆放在一起,在此具有反转体能带性质的界面上,实现了具有单向传输特性的拓扑确定性界面态的传输.利用光子晶体结构的容易加工性,可以简便地调控拓扑界面态控制光的传播,可为未来光拓扑绝缘体的研究提供良好的平台.     

Layer construction of topological crystalline insulator LaSbTe

Topological crystalline insulator(TCI) is one of the symmetry-protected topological states. Any TCI can be deformed into a simple product state of several decoupled two-dimensional(2 D) topologically nontrivial layers in its lattice respecting its crystalline symmetries called the layer construction(LC) limit. In this work, based on first-principles calculations we have revealed that both tetragonal LaSbTe(t-LaSbTe) and orthorhombic LaSbTe(o-LaSbTe) can be interpreted as stacking of 2 D topological insulators in each lattice space. The structural phase transition from t-LaSbTe to o-LaSbTe due to soft phonon modes demonstrates how the real space change can lead to the modification of topological states. Their symmetry-based indicators and topological invariants have been analyzed based on LC. We propose that LaSbTe is an ideal example demonstrating the LC paradigm, which bridges the crystal structures in real space to the band topology in momentum space.     

Knotted Wave Dislocation with the Hopf Invariant

We study the wave dislocations with an induced gauge potential. The topological current characterized the wave dislocations is constructed with the dual of Abelian gauge field. And the topological charges and locations of the wave dislocations are determined by the φmapping topological current theory. Furthermore, it is shown that the knotted wave dislocations can be described with a Hopf invariant in the wave field. At last we discussed the evolution of the knotted wave dislocations. PACS 02.10.Kn, 02.40.-k, 11.15.-q