Twisted Boundary Research Articles

Hollow carbon spheres with rich nitrogen–oxygen dopants and highly disordered adsorption boundaries for advanced lithium and sodium storage

The hollow carbon spheres with abundant doping elements and adsorption boundaries are achieved by utilizing cobaltous oxide as template and polypyrrole as carbon/nitrogen sources through low-temperature pyrolysis under inert gas atmosphere. The redox reaction and mutual interaction between metal oxide and polymer might account for rich nitroge-noxygen (N/O) dopants, while low-temperature pyrolysis results in hydrogen-terminated (H) edges. Furthermore, the functionalized carbon layer and highly disordered microstructure are promoted to form in the amorphous carbon. For N/O-rich carbon hollow sphere (NOCHS), the unique twisted boundaries, numerous adsorption sites and porous shell are strongly linked with its electrochemical performances in lithium and sodium storage, which demonstrate dominant storage capacity, ultra-stable storage ability and superior rate capability over other amorphous carbon materials beyond typical graphite.

Variant selection during BCC to HCP phase transformation in selective laser melted Ti-6Al-4V

The transformed α grains of selective laser melted Ti-6Al-4V display a strong (0001) fiber texture along the building direction, whereas during SLM printing, the parent high temperature β grains have preferentially grown in the <001> parallel to the building direction. In the current work, we have studied the phenomenon of variant selection occuring during the cubic to hexagonal phase transformation by investigating in detail the distribution of misorientation pairs and intervariant boundaries observed in orientation contrast maps acquired by EBSD. It was found that local variant selection within a single parent grain governed the martensitic transformation as it was observed that the experimentally assessed distribution of intervariant axis/angle pairs significantly differed from the one that can be expected if the Burgers orientation relationship applies with equal probability of the 12 possible variants. The variant selection could be explained by considering the degree of self-accommodation, which is corroborated by the characteristic morphologies formed by three- variant clusters as observed in the orientation contrast maps. Irrespective of the misorientation, the grain boundary characterization distribution revealed a strong anisotropic distribution of the internal interfaces with a tendency of alignment of these interfaces with the {hki0} prismatic planes. The dominant [10¯553¯]/ 63.26° intervariant boundaries displayed primarily twist and 180-tilt (3¯210) boundary planes.

Aspects of Jackiw-Teitelboim gravity in Anti-de Sitter and de Sitter spacetime

We discuss JT gravity in AdS and dS space in the second order formalism. For the pure dS JT theory without matter, we show that the path integral gives rise in general to the Hartle-Hawking wave function which describes an arbitrary number of disconnected universes produced by tunnelling “from nothing”, or to transition amplitudes which describe the tunnelling of an initial state consisting of several contracting universes to a final state of several expanding universes. These processes can be described by a hologram consisting of Random Matrix Theory (RMT) or, we suggest, after some modification on the gravity side, by a hologram with the RMT being replaced by SYK theory. In the presence of matter, we discuss the double trumpet path integral and argue that with suitable twisted boundary conditions, a divergence in the moduli space integral can be avoided and the system can tunnel from a contracting phase to an expanding one avoiding a potential big bang/big crunch singularity. The resulting spectrum of quantum perturbations which are produced can exhibit interesting departures from scale invariance. We also show that the divergence in moduli space can be avoided for suitable correlators which involve different boundaries in the AdS/dS cases, and suggest that a hologram consisting of the SYK theory with additional matter could get rid of these divergences in general. Finally, we analyse the AdS double trumpet geometry and show that going to the micro-canonical ensemble instead of the canonical one, for the spectral form factor, does not get rid of the divergence in moduli space.

Homogeneous Yang-Baxter deformations as undeformed yet twisted models

The homogeneous Yang-Baxter deformation is part of a larger web of integrable deformations and dualities that recently have been studied with motivations in integrable σ-models, solution-generating techniques in supergravity and Double Field Theory, and possible generalisations of the AdS/CFT correspondence. The σ-models obtained by the homogeneous Yang-Baxter deformation with periodic boundary conditions on the worldsheet are on-shell equivalent to undeformed models, yet with twisted boundary conditions. While this has been known for some time, the expression provided so far for the twist features non-localities (in terms of the degrees of freedom of the deformed model) that prevent practical calculations, and in particular the construction of the classical spectral curve. We solve this problem by rewriting the equation defining the twist in terms of the degrees of freedom of the undeformed yet twisted model, and we show that we are able to solve it in full generality. Remarkably, this solution is a local expression. We discuss the consequences of the twist at the level of the monodromy matrix and of the classical spectral curve, analysing in particular the concrete examples of abelian, almost abelian and Jordanian deformations of the Yang-Baxter class.

Topologically protected moiré exciton at a twist-boundary in a van der Waals heterostructure

A twin boundary in one of the layers of a twisted van der Waals heterostructure separates regions with near opposite inter-layer twist angles. In a MoS2/WSe2 bilayer, the regions with and stacking registry that defined the sub-lattices of the moiré honeycomb pattern would be mirror-reflected across such a twist boundary. In that case, we demonstrate that topologically protected chiral moiré exciton states are confined at the twist boundary. These are one-dimensional and uni-directional excitons with opposite velocities for excitons composed by electronic states with opposite valley/spin character, enabling intrinsic, guided, and far reaching valley-polarized exciton currents.

Classical string solutions in non-relativistic AdS5 × S5: closed and twisted sectors

We find classical closed string solutions to the non-relativistic AdS5 × S5 string theory which are the analogue of the BMN and GKP solutions for the relativistic theory. We show that non-relativistic AdS5 × S5 string theory admits a orbifold symmetry which allows us to impose twisted boundary conditions. Among the solutions in the twisted sector, we find the one around which the semiclassical expansion in arXiv:2102.00008 takes place.

The impact of misorientation on the grain boundary energy in bi-crystal copper: an atomistic simulation study.

Atomistic simulations were performed to investigate the relationships among the misorientation, dislocation density, and grain boundary energy of twist and tilt bi-crystal grain boundaries. In this work, the grain boundary energies were calculated based on the embedded-atom method interatomic potential for Cu. The results show that the dislocation density of the grain boundary changes with the rotation angle, thereby affecting the grain boundary energy. Furthermore, the grain boundary energy of a grain boundary with no dislocations is greater than that of a grain boundary with dislocations, which results from the distribution of the atomic potential energy on the grain boundaries. Additionally, the grain boundary energy increases with the dislocation density of the grain boundary in the case of dislocations on the grain boundary. On this basis, a new relationship is proposed for the misorientation angle and grain boundary energy. We assume that when the driving force of dislocation nucleation breaks through the grain boundary energy barrier, the grain boundary energy declines.

Grain boundary energies in yttria‐stabilized zirconia

AbstractThe three‐dimensional microstructure of 8% yttria‐stabilized zirconia (YSZ) was measured by electron backscatter diffraction and focused ion beam serial sectioning. The relative grain boundary energies as a function of all five crystallographic grain boundary parameters were determined based on the assumption of thermodynamic equilibrium at the internal triple junctions. Grain boundaries with (100) orientations have low energies compared to boundaries of other orientations, and all [100] twist boundaries have relatively low energies. Other classes of boundaries with lower than average energies include [100] symmetric tilt boundaries with disorientations less than 40° and [111] twist boundaries with disorientations greater than 20°. At fixed misorientations, the relative areas of boundaries are inversely correlated to the relative grain boundary energy. The results suggest that texturing microstructures to increase the relative areas of [100] twist boundaries might increase the oxygen ion conductivity of YSZ ceramics.

Bloch and Bethe Ansätze for the Harper model: A butterfly with a boundary

Based on a recent generalization of Bloch's theorem, we present a Bloch Ansatz for the Harper model with an arbitrary rational magnetic flux in various geometries, and solve the associated Ansatz equations analytically. In the case of a cylinder and a particular boundary condition, the energy spectrum of edge states has no dependence on the length of the cylinder, which allows us to construct a quasi-one-dimensional edge theory that is exact and describes two edges simultaneously. We prove that energies of bulk states, generating the so-called Hofstadter's butterfly, depend on a single geometry-dependent spectral parameter and have exactly the same functional form for the cylinder and the torus with general twisted boundary conditions, and argue that the (edge) bulk spectrum of a semi-infinite cylinder in an irrational magnetic field is (the complement of) a Cantor set. Finally, realizing that the bulk projection of the Harper Hamiltonian is a linear form over a deformed Weyl algebra, we introduce a Bethe Ansatz valid for both cylinder and torus geometries.

Detect topological quantum phases in a one-dimensional interactional fermion system

Based on the Su-Schriefferheeger (SSH) and Kitaev hybrid fermion model, we study the Berry phase in detecting different types of topological phases. We find that, under the twist boundary condition, the low energy spectra play remarkable roles in determining the Berry phase value. The non-zero Berry phase combined with the low energy spectra can be used to distinguish different types of topological quantum states. Furthermore, we consider the influence of interactions on the system. Through analysis of the Berry phase, the entanglement entropy, and the electron occupation, a new quantum phase is found and the influence law of the interactions on different types of topological phases are revealed. The quantum phase diagram of the system under these interactions is finally given.

Memory efficient finite volume schemes with twisted boundary conditions

In this paper we explore a finite volume renormalization scheme that combines three main ingredients: a coupling based on the gradient flow, the use of twisted boundary conditions and a particular asymmetric geometry, that for SU(N) gauge theories consists on a hypercubic box of size l^2 times (Nl)^2, a choice motivated by the study of volume independence in large N gauge theories. We argue that this scheme has several advantages that make it particularly suited for precision determinations of the strong coupling, among them translational invariance, an analytic expansion in the coupling and a reduced memory footprint with respect to standard simulations on symmetric lattices, allowing for a more efficient use of current GPU clusters. We test this scheme numerically with a determination of the Lambda parameter in the SU(3) pure gauge theory. We show that the use of an asymmetric geometry has no significant impact in the size of scaling violations, obtaining a value Lambda _{overline{mathrm{MS}}}sqrt{8 t_0} =0.603(17) in good agreement with the existing literature. The role of topology freezing, that is relevant for the determination of the coupling in this particular scheme and for large N applications, is discussed in detail.

Strain localization and fatigue crack formation at [formula omitted] twist boundaries in titanium alloys

The process of crack initiation has been investigated in three widely used titanium alloys with different microstructures and loading conditions. Using low-cycle fatigue tests, a unique crack nucleation mechanism involving strain localization at (0001) twist boundaries has been identified. In order to constitute a potential crack initiation site, the twist boundary must experience a high resolved shear stress and a high normal stress. Crack initiation at these boundaries is most frequently associated with twist angles spanning the 10° - 20° range. Deformation prior to crack initiation at these rare microstructural configurations has been characterized using transmission electron microscopy and high-resolution digital image correlation across large fields of view. The (0001) twist boundaries are preferential locations for early and intense strain localization. Prior to crack nucleation, deformation proceeds via shear along such boundaries where no β layer at the interface was evidenced. The presently discussed crack formation mechanism is believed to be of broad relevance as it is not significantly influenced by microstructural parameters such as the α grain size, the degree of microtexture, the β phase fraction or the surrounding microstructure as well as α and β compositions.

Twist boundary defects in penta-twinned silver nanowires

Twist boundary defects in penta-twinned silver nanowires

The Yangian relations of Heisenberg spin chain model

In this paper, we investigate the Yangian relations of Heisenberg spin chain systems. Firstly, we consider the closed XXZ spin chain model, through the Heisenberg spin XXZ model, we found the Hamiltonians for one kind system of three adjacent partial particles interaction systems. The model’s constitution rules of energy levels and energy states which expand from the few-particle system to multi-particle system have good regularity. In this system, we found Yangian’s law and illustrate it through graphs. Secondly, we further consider the closed XXZ spin chain’s generalization of other three neighboring particles interaction systems from few-particle system to multi-particle system. Finally, we also discussed the laws of the three adjacent particles system of some models, they are the XXZ model with twist boundary condition, the open XXZ spin chain model and the XXZ model containing the next neighbor. In addition, not only XXZ model, XXX model, XY model and Ising model, but the relevant laws of spin-1 systems of these models were also discussed, they have similar rules to the XXZ model. Through calculation and research, the eigensystems of these models all have good Yangian and constitution laws.

Real-space representation of the winding number for a one-dimensional chiral-symmetric topological insulator

The winding number has been widely used as an invariant for diagnosing topological phases in one-dimensional chiral-symmetric systems. We put forward a real-space representation for the winding number. Remarkably, our method reproduces an exactly quantized winding number even in the presence of disorders that break translation symmetry but preserve chiral symmetry. We prove that our real-space representation of the winding number, the winding number defined through the twisted boundary condition, and the real-space winding number derived previously in [Phys. Rev. Lett. 113, 046802 (2014)], are equivalent in the thermodynamic limit at half filling. Our method also works for the case of filling less than one half, where the winding number is not necessarily quantized. Around the disorder-induced topological phase transition, the real-space winding number has large fluctuations for different disordered samples, however, its average over an ensemble of disorder samples may well identify the topological phase transition. Besides, we show that our real-space winding number can be expressed as a Bott index, which has been used to represent the Chern number for two-dimensional systems.

Antiferromagnetic State in κ-type Molecular Conductors: Spin Splitting and Mott Gap

We numerically investigate the dynamical properties of $\kappa$-type molecular conductors in their antiferromagnetic Mott insulating state. By treating the extended Hubbard model on the two-dimensional $\kappa$-type lattice within the Lanzcos exact diagonalization method, we calculate the one-particle spectral function $A(\boldsymbol{k}, \omega)$ and the optical absorption spectra taking advantage of twisted boundary conditions. We find spin splitting in $A(\boldsymbol{k}, \omega)$ predicted by a previous Hartree-Fock study [M. Naka et al., Nat. Commun. 10, 4305 (2019)]; namely, their up- and down-spin components become different in the general $\boldsymbol{k}$-points of the Brillouin zone, even without the spin-orbit coupling. Furthermore, we demonstrate the variation in the optical properties near the Mott gap by the presence or absence of the antiferromagnetic order, tuned by a small staggered magnetic field.

Twisted Boundary Condition and Lieb-Schultz-Mattis Ingappability for Discrete Symmetries

We discuss quantum many-body systems with lattice translation and discrete on-site symmetries. We point out that, under a boundary condition twisted by a symmetry operation, there is an exact degeneracy of ground states if the unit cell forms a projective representation of the on-site discrete symmetry. Based on the quantum transfer matrix formalism, we show that, if the system is gapped, the ground-state degeneracy under the twisted boundary condition also implies a ground-state (quasi)degeneracy under the periodic boundary conditions. This gives a compelling evidence for the recently proposed Lieb-Schultz-Mattis-type ingappability due to the on-site discrete symmetry in two and higher dimensions.

Secondary epitaxial orientations in high lattice mismatch systems: A case study for YBa2Cu3O7-δ and SrO thin films deposited on (0 0 1)MgO

High lattice mismatch epitaxy is receiving wide attention with demands increasing for bonding together materials of differing types to manage defect content. One interesting aspect of heteroepitaxial growth is in the formation of secondary epitaxial orientations in, often, high lattice mismatch systems. Two examples explored here are the cases of epitaxial thin films of YBa2Cu3O7-δ (YBCO) grown onto (0 0 1)MgO (8.55% lattice mismatch) and SrO on (0 0 1)MgO (12.2% lattice mismatch). Under certain conditions, these materials have been found, using electron microscopy, to contain large twist boundary rotated grains which adopt well defined orientations. In the case of YBCO (SrO) on MgO the most frequent in-plane orientations observed occur at 23.5° (27.4°) on MgO, respectively. These values show that there is an increase in the twist angle of the most frequently observed grain orientations with lattice mismatch as observed experimentally. These have been explained, in the present work, in terms of a novel means of describing the coincident site lattice theory. Indeed, an equation has been derived using this novel theory which closely matched these experimental observations.

Spin-orbit coupling in the kagome lattice with flux and time-reversal symmetry

We study the topological properties of a spin-orbit coupled Hofstadter model on the Kagome lattice. The model is time-reversal invariant and realizes a $\mathbb{Z}_2$ topological insulator as a result of artificial gauge fields. We develop topological arguments to describe this system showing three inequivalent sites in a unit cell and a flat band in its energy spectrum in addition to the topological dispersive energy bands. We show the stability of the topological phase towards spin-flip processes and different types of on-site potentials. In particular, we also address the situation where on-site energies may differ inside a unit cell. Moreover, a staggered potential on the lattice may realize topological phases for the half-filled situation. Another interesting result is the occurrence of a topological phase for large on-site energies. To describe topological properties of the system we use a numerical approach based on the twisted boundary conditions and we develop a mathematical approach, related to smooth fields.

Fracture Energy Measurement of Prismatic Plane and \u03a32 Boundary in Cemented Carbide

The grain boundary network of WC in WC-Co is important, as cracks often travel intergranularly. This motivates the present work, where we experimentally measure the fracture energy of Σ2 twist grain boundaries between WC crystals using a double cantilever beam opened with a wedge under displacement control in a WC-10wt%Co sample. The fracture energy of this boundary type was compared with cleaving {10overline{1}0} prismatic planes in a WC single crystal. Fracture energies of 7.04 ± 0.36 Jm−2 and 3.57 ± 0.28 Jm−2 were measured for {10overline{1}0} plane and Σ2 twist boundaries, respectively.