Wall Excitations Research Articles

Topologically protected steady cycles in an icelike mechanical metamaterial

Competing ground states may lead to topologically constrained excitations such as domain walls or quasiparticles, which govern metastable states and their dynamics. Domain walls and more exotic topological excitations are well studied in magnetic systems such as artificial spin ice, in which nanoscale magnetic dipoles are placed on geometrically frustrated lattices, giving rise to highly degenerate ground states. We propose a mechanical spin-ice constructed from a lattice of floppy, bistable square unit cells. We compare the domain wall excitations that arise in this metamaterial to their magnetic counterparts, finding that new behaviors emerge in this overdamped mechanical system. By tuning the ratios of the internal elements of the unit cell, we control the curvature and propagation speed of internal domain walls. We change the domain wall morphology from a binary, strictly spin-like regime, to a more continuous, elastic regime. In the elastic regime, we inject, manipulate, and expel domain walls via textured forcing at the boundaries. The system exhibits dynamical hysteresis, and we find a first-order dynamical transition as a function of the driving frequency. We demonstrate a forcing protocol that produces multiple, topologically-distinct steady cycles, which are protected by the differences in their internal domain wall arrangements. These distinct steady cycles rapidly proliferate as the complexity of the applied forcing texture is increased, thus suggesting that such mechanical systems could serve as useful model systems to study multistability, glassiness, and memory in materials.

Bénard-Taylor ferroconvection with time-dependent sinusoidal boundary temperatures

The combined effect of centrifugal acceleration and time-varying boundary temperatures on the onset of convective instability of a rotating magnetic fluid layer is investigated by means of the regular perturbation method. A perturbation expansion in terms of the amplitude of applied temperature field is implemented to effectively deal with the effects of temperature modulation. The criterion for the threshold is established based on the condition of stationary instability manifesting prior to oscillatory convection. The modulated critical Rayleigh number is computed in terms of Prandtl number, magnetic parameters, Taylor number and the frequency of thermal modulation. It is shown that subcritical motion exists only for symmetric excitation and the destabilizing effect of magnetic mechanism is perceived only for asymmetric and bottom wall excitations. It is also delineated that, for bottom wall modulation, rotation tends to stabilize the system at low frequencies and the opposite is true for moderate and large frequencies. Furthermore, it is established that, notwithstanding the type of thermal excitation, the modulation mechanism attenuates the influences of both magnetic stresses and rotation for moderate and large frequencies.

Relevance of two- and three-dimensional disturbance field explained with linear stability analysis of Orr-Sommerfeld equation by compound matrix method

Three-dimensional Orr-Sommerfeld equation is analyzed by compound-matrix method to explain the relevance of two- and three-dimensional wall excitations with respect to three-dimensional direct simulation results presented in Sharma and Sengupta, Effect of frequency and wavenumber on the three-dimensional routes of transition by wall excitation, Phys. Fluids, 31 (6), 064107 (2019). Physical variables are considered in a finite spanwise domain which allows us to consider spanwise wavenumber β as the higher harmonics of fundamental spanwise mode β0 defined by the spanwise domain. Linear stability analysis is performed for various cases with different spanwise wavenumber and neutral curves are generated in both spatial and temporal frameworks. Even though the neutral curves appear different, the critical Reynolds number remains same for all spanwise excitation wavenumbers. The significance of neutral curve in either spatial, or temporal or spatio-temporal frameworks is explained for both modal and non-modal component of the response field. It is shown that as spanwise wavenumber of input excitation increases, the critical Reynolds number increases, while the spatial amplification rate αi decreases. Thus, this establishes that increasing three-dimensionality of input excitation will shown enhanced stability of the flow, and helps one to understand the three-dimensional direct simulation of receptivity analysis for wall excitation reported very recently.

Domain-wall confinement and dynamics in a quantum simulator

Confinement is a ubiquitous mechanism in nature, whereby particles feel an attractive force that increases without bound as they separate. A prominent example is color confinement in particle physics, in which baryons and mesons are produced by quark confinement. Analogously, confinement can also occur in low-energy quantum many-body systems when elementary excitations are confined into bound quasiparticles. Here, we report the first observation of magnetic domain wall confinement in interacting spin chains with a trapped-ion quantum simulator. By measuring how correlations spread, we show that confinement can dramatically suppress information propagation and thermalization in such many-body systems. We are able to quantitatively determine the excitation energy of domain wall bound states from non-equilibrium quench dynamics. Furthermore, we study the number of domain wall excitations created for different quench parameters, in a regime that is difficult to model with classical computers. This work demonstrates the capability of quantum simulators for investigating exotic high-energy physics phenomena, such as quark collision and string breaking.

Valley-polarized domain wall magnons in 2D ferromagnetic bilayers

Valleytronics is a pioneering technological field relying on the valley degree of freedom to achieve novel electronic functionalities. Topological valley-polarized electrons confined to domain walls in bilayer graphene were extensively studied in view of their potentials in valleytronics. Here, we study the magnonic version of domain wall excitations in 2D honeycomb ferromagnetic bilayers (FBL) with collinear order. In particular, we explore the implications of Dzyaloshinskii-Moriya interaction (DMI) and electrostatic doping (ED) on the existence and characteristics of 1D magnons confined to layer stacking domain walls in FBL. The coexistence of DMI and ED is found to enrich the topology in FBL, yet the corresponding domain wall magnons do not carry a well-defined valley index. On the other hand, we show that layer stacking domain walls in DMI-free FBL constitute 1D channels for ballistic transport of topological valley-polarized magnons. Our theoretical results raise hope towards magnon valleytronic devices based on atomically thin topological magnetic materials.

Acoustic wave propagation at nonadiabatic conditions: The continuum limit of a thin acoustic layer

Existing studies on sound propagation in rarefied gases are extended to consider wave transmission at nonadiabatic ambient conditions, where arbitrarily large reference temperature and density gradients prevail. Asymptotic analysis of the acoustic field is carried out in the limit of small Knudsen numbers and high actuation frequencies, for both mechanical and thermal wall excitations.

Domain walls and their interactions in a two-component Bose–Einstein condensate**Project supported by the National Natural Science Foundation of China (Grant No. 11775176), the Major Basic Research Program of the Natural Science Foundation of Shaanxi Province, China (Grant No. 2018KJXX-094), and the Key Innovative Research Team of Quantum Many-Body Theory and Quantum Control in Shaanxi Province, China (Grant No. 2017KCT-12).

We investigate domain wall excitations in a two-component Bose–Einstein condensate with two-body interactions and pair-transition effects. It is shown that domain wall excitations can be described exactly by kink and anti-kink excitations in each component. The domain wall solutions are given analytically, which exist with different conditions compared with the domain wall reported before. Bubble-droplet structure can be also obtained from the fundamental domain wall, and their interactions are investigated analytically. Especially, domain wall interactions demonstrate some striking particle transition dynamics. These striking transition effects make the domain wall admit quite different collision behavior, in contrast to the collision between solitons or other nonlinear waves. The collisions between kinks induce some phase shift, which makes the domain wall change greatly. Their collisions can be elastic or inelastic with proper combination of fundamental domain walls. These characters can be used to manipulate one domain wall by interacting with other ones.

Spin stiffness and domain walls in Dirac-electron mediated magnets

Spin interactions of magnetic impurities mediated by conduction electrons is one of the most interesting and potentially useful routes to ferromagnetism in condensed matter. In recent years such systems have received renewed attention due to the advent of materials in which Dirac electrons are the mediating particles, with prominent examples being graphene and topological insulator surfaces. In this paper, we demonstrate that such systems can host a remarkable variety of behaviors, in many cases controlled only by the density of electrons in the system. Uniquely characteristic of these systems is an emergent long-range form of the spin stiffnes when the Fermi energy resides at a Dirac point, becoming truly long-range as the magnetization density becomes very small. It is demonstrated that this leads to screened Coulomb-like interactions among domain walls, via a subtle mechanism in which the topology of the Dirac electrons plays a key role: the combination of attraction due to bound in-gap states that the topology necessitates, and repulsion due to scattering phase shifts, yields logarithmic interactions over a range of length scales. We present detailed results for domain walls in a particularly rich system, the (111) surface of a model topological crystalline insulator. This hosts two-fold and six- fold degenerate groundstates, with either short-range or emergent long-range interactions among the spins. In the latter case we demonstrate in detail the presence of in-gap states associated with domain walls, and argue that this stabilizes a pseudogap regime at finite temperature. Thus the topological nature of these systems, through its impact on domain wall excitations, leads to unique behaviors distinguishing them markedly from their non-topological analogs.

Localization of extended quantum objects

A quantum system of particles can exist in a localized phase, exhibiting ergodicity breaking and maintaining forever a local memory of its initial conditions. We generalize this concept to a system of extended objects, such as strings and membranes, arguing that such a system can also exhibit localization in the presence of sufficiently strong disorder (randomness) in the Hamiltonian. We show that localization of large extended objects can be mapped to a lower-dimensional many-body localization problem. For example, motion of a string involves propagation of point-like signals down its length to keep the different segments in causal contact. For sufficiently strong disorder, all such internal modes will exhibit many-body localization, resulting in the localization of the entire string. The eigenstates of the system can then be constructed perturbatively through a convergent 'string locator expansion.' We propose a type of out-of-time-order string correlator as a diagnostic of such a string localized phase. Localization of other higher-dimensional objects, such as membranes, can also be studied through a hierarchical construction by mapping onto localization of lower-dimensional objects. Our arguments are 'asymptotic' ($i.e.$ valid up to rare regions) but they extend the notion of localization (and localization protected order) to a host of settings where such ideas previously did not apply. These include high-dimensional ferromagnets with domain wall excitations, three-dimensional topological phases with loop-like excitations, and three-dimensional type-II superconductors with flux line excitations. In type-II superconductors, localization of flux lines could stabilize superconductivity at energy densities where a normal state would arise in thermal equilibrium.

Excitations of interface pinned domain walls in constrained geometries

We report a theoretical investigation of the equilibrium pattern and the spectra of head-to-head and Neel domain walls of flat Fe and Py stripes, exchange coupled with a vicinal antiferromagnetic substrate. We show that the domain wall excitation spectrum is tunable by the strength of the interface field. Furthermore, strong interface coupling favors localized wall excitations.

Hamiltonian truncation approach to quenches in the Ising field theory

In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.

Confinement in the q-state Potts model: an RG-TCSA study

In the ferromagnetic phase of the q-state Potts model, switching on an external magnetic field induces confinement of the domain wall excitations. For the Ising model (q = 2) the spectrum consists of kink-antikink states which are the analogues of mesonic states in QCD, while for q = 3, depending on the sign of the field, the spectrum may also contain three-kink bound states which are the analogues of the baryons. In recent years the resulting "hadron" spectrum was described using several different approaches, such as quantum mechanics in the confining linear potential, WKB methods and also the Bethe-Salpeter equation. Here we compare the available predictions to numerical results from renormalization group improved truncated conformal space approach (RG-TCSA). While mesonic states in the Ising model have already been considered in a different truncated Hamiltonian approach, this is the first time that a precision numerical study is performed for the 3-state Potts model. We find that the semiclassical approach provides a very accurate description for the mesonic spectrum in all the parameter regime for weak magnetic field, while the low-energy expansion from the Bethe-Salpeter equation is only valid for very weak fields where it gives a slight improvement over the semiclassical results. In addition, we confirm the validity of the recent predictions for the baryon spectrum obtained from solving the quantum mechanical three-body problem.

Holographic dual of a conical defect

We consider a moving conical defect in the pure AdS3 space-time and calculate two-point correlation functions of a corresponding two-dimensional boundary quantum field theory in the geodesic approximation. We show that the presence of the defect leads to a gravitational lensing of geodesics, and this results in a finite number of similar terms in the Green’s function that correspond to winding geodesics in the bulk around the conical singularity. We show that for the quantized deficit angle γ = π/2n, the lensing produces domain wall excitations in the spectrum of the boundary theory.

Anyon condensation and tensor categories

Instead of studying anyon condensation in various concrete models, we take a bootstrap approach by considering an abstract situation, in which an anyon condensation happens in a 2-d topological phase with anyonic excitations given by a modular tensor category C; and the anyons in the condensed phase are given by another modular tensor category D. By a bootstrap analysis, we derive a relation between anyons in D-phase and anyons in C-phase from natural physical requirements. It turns out that the vacuum (or the tensor unit) A in D-phase is necessary to be a connected commutative separable algebra in C, and the category D is equivalent to the category of local A-modules as modular tensor categories. This condensation also produces a gapped domain wall with wall excitations given by the category of A-modules in C. A more general situation is also studied in this paper. We will also show how to determine such algebra A from the initial and final data. Multi-condensations and 1-d condensations will also be briefly discussed. Examples will be given in the toric code model, Kitaev quantum double models, Levin–Wen types of lattice models and some chiral topological phases.

Domain wall fluctuations in ferroelectrics coupled to strain

Using a Ginzburg--Landau--Devonshire model that includes the coupling of polarization to strain, we calculate the fluctuation spectra of ferroelectric domain walls. The influence of the strain coupling differs between 180 degree and 90 degree walls due to the different strain profiles of the two configurations. The finite speed of acoustic phonons, $v_s$, retards the response of the strain to polarization fluctuations, and the results depend on $v_s$. For $v_s \to \infty$, the strain mediates an instantaneous electrostrictive interaction, which is long-range in the 90 degree wall case. For finite $v_s$, acoustic phonons damp the wall excitations, producing a continuum in the spectral function. As $v_s\ to 0$, a gapped mode emerges, which corresponds to the polarization oscillating in a fixed strain potential.

Domain Walls and Their Experimental Signatures ins+isSuperconductors

Arguments were recently advanced that hole-doped Ba(1-x)K(x)Fe2As2 exhibits the s+is state at certain doping. Spontaneous breaking of time-reversal symmetry in the s+is state dictates that it possess domain wall excitations. Here, we discuss what are the experimentally detectable signatures of domain walls in the s+is state. We find that in this state the domain walls can have a dipolelike magnetic signature (in contrast to the uniform magnetic signature of domain walls p+ip superconductors). We propose experiments where quench-induced domain walls can be stabilized by geometric barriers and observed via their magnetic signature or their influence on the magnetization process, thereby providing an experimental tool to confirm the s+is state.

Existence of staggered fields in the Ising-like antiferromagnetic compounds CsCoCl3 and CsCoBr3

The line shapes of dynamical spin correlation functions of the Ising-like antiferromagnetic compounds, CsCoCl3 and CsCoBr3, show asymmetry about its peak positions in which the spectral weights mainly concentrate in the low energy side. We consider a one-dimensional Ising-like S=12 Heisenberg antiferromagnetic Hamiltonian and study the dynamics of domain wall excitations in the presence of a staggered magnetic field hx along the transverse direction in order to explain those asymmetric line shapes. We obtain dynamical spin correlation functions along the magnetic field Sxx(q,ω) and perpendicular to it Syy(q,ω). It is shown that the line shapes of Sxx(q,ω) and Syy(q,ω) are highly asymmetric at all values of q and hx. An excellent agreement with the experimental data throughout the whole Brillouin zone is observed upon considering a finite value of the staggered fields for both the compounds CsCoCl3 and CsCoBr3. The existence of staggered fields is justified by considering the zigzag orientations of the nonmagnetic atoms about the magnetic Co atoms.

The Shear-Driven Fluid Motion Using Oscillating Boundaries

A classical Stokes’ second problem has been known for a long time and represents one of the few exact solutions of nonlinear Navier-Stokes equations. However, oscillatory flow in a semi-infinite domain of Newtonian fluid under harmonic boundary excitation only leads to fluid wind-milling back and forth in close wall vicinity. In this study, we are presenting the mathematical model and the numerical simulations of the Newtonian fluid and the shear-thinning non-Newtonian blood-mimicking fluid flow. Positive flow rates were obtained by periodic yet nonharmonic oscillatory motion of one or two infinite boundary flat walls. The oscillatory flows in semi-infinite or finite 2D geometry with sawtooth or periodic rectified-sine boundary conditions are presented. Rheological human blood models used were: Power-Law, Sisko, Carreau, and Herschel-Bulkley. A one-dimensional time-dependent nonlinear coupled conservative diffusion-type boundary layer equations for mass, linear momentum, and energy were solved using the finite-differences method with finite-volume discretization. It was possible to test the accuracy of the in-house developed computational programs with the few isothermal flow analytical solutions and with the celebrated classical Stokes’ first and second problems. Positive flow rates were achieved in various configurations and in absence of the adverse pressure gradients. Body forces, such as gravity, were neglected. The calculations utilizing in-phase sawtooth and rectified-sine wall excitations resulted in respectable net flow which stabilizes and becomes quasi-steady, starting from rest, after three to ten periods depending on the fluid rheology. It was assumed that rapid return stroke of the wall actuator resulted in total wall slip while forward wall motion existed with no-slip boundary condition. Shear “driving” and “driven” fluid regions were identified. The shear-thinning fluid rheology delivered many interesting results, such as pluglike flow. Constructive interference of diffusive penetration layers from multiple flat surfaces could be used as practical pumping mechanism in micro-scales.

Direct numerical simulation of two-dimensional wall-bounded turbulent flows from receptivity stage

Deterministic route to turbulence creation in 2D wall boundary layer is shown here by solving full Navier-Stokes equation by dispersion relation preserving (DRP) numerical methods for flow over a flat plate excited by wall and free stream excitations. Present results show the transition caused by wall excitation is predominantly due to nonlinear growth of the spatiotemporal wave front, even in the presence of Tollmien-Schlichting (TS) waves. The existence and linear mechanism of creating the spatiotemporal wave front was established in Sengupta, Rao and Venkatasubbaiah [Phys. Rev. Lett. 96, 224504 (2006)] via the solution of Orr-Sommerfeld equation. Effects of spatiotemporal front(s) in the nonlinear phase of disturbance evolution have been documented by Sengupta and Bhaumik [Phys. Rev. Lett. 107, 154501 (2011)], where a flow is taken from the receptivity stage to the fully developed 2D turbulent state exhibiting a k(-3) energy spectrum by solving the Navier-Stokes equation without any artifice. The details of this mechanism are presented here for the first time, along with another problem of forced excitation of the boundary layer by convecting free stream vortices. Thus, the excitations considered here are for a zero pressure gradient (ZPG) boundary layer by (i) monochromatic time-harmonic wall excitation and (ii) free stream excitation by convecting train of vortices at a constant height. The latter case demonstrates neither monochromatic TS wave, nor the spatiotemporal wave front, yet both the cases eventually show the presence of k(-3) energy spectrum, which has been shown experimentally for atmospheric dynamics in Nastrom, Gage and Jasperson [Nature 310, 36 (1984)]. Transition by a nonlinear mechanism of the Navier-Stokes equation leading to k(-3) energy spectrum in the inertial subrange is the typical characteristic feature of all 2D turbulent flows. Reproduction of the spectrum noted in atmospheric data (showing dominance of the k(-3) spectrum over the k(-5/3) spectrum in Nastrom et al.) in laboratory scale indicates universality of this spectrum for all 2D turbulent flows. Creation of universal features of 2D turbulence by a deterministic route has been established here for the first time by solving the Navier-Stokes equation without any modeling, as has been reported earlier in the literature by other researchers.

Chiral Topological Phases and Fractional Domain Wall Excitations in One-Dimensional Chains and Wires

According to the general classification of topological insulators, there exist one-dimensional chirally (sublattice) symmetric systems that can support any number of topological phases. We introduce a zigzag fermion chain with spin-orbit coupling in magnetic field and identify three distinct topological phases. Zero-mode excitations, localized at the phase boundaries, are fractionalized: two of the phase boundaries support ±e/2 charge states while one of the boundaries support ±e and neutral excitations. In addition, a finite chain exhibits ±e/2 edge states for two of the three phases. We explain how the studied system generalizes the Peierls-distorted polyacetylene model and discuss possible realizations in atomic chains and quantum spin Hall wires.