Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy.At low temperatures,theoretical predictions[Phys.Rev.A 72053604(2005)]and[arXiv:0706.1609]indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering.However,due to ergodic difficulties faced by Monte Carlo methods at low temperatures,this topological phase has not been numerically explored.We propose a linear cluster updating Monte Carlo method,which flips spins without rejection in the anisotropy limit but does not change the energy.Using this scheme and conventional Monte Carlo methods,we succeed in revealing the nature of topological phases with half-vortices and domain walls.In the constructed global phase diagram,Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier.We also propose and explore a wide range of quantities,including magnetism,superfluidity,specific heat,susceptibility,and even percolation susceptibility,and obtain consistent and reliable results.Furthermore,we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes,as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections.The critical exponents of different types of phase transitions are reasonably fitted.The results are useful to help cold atom experiments explore the half-vortex topological phase.

Topological edge and corner states of valley photonic crystals with zipper-like boundary conditions

We present a stable valley photonic crystal(VPC)unit cell with C_(3v)symmetric quasi-ring-shaped dielectric columns and realize its topological phase transition by breaking mirror symmetry.Based on this unit cell structure,topological edge states(TESs)and topological corner states(TCSs)are realized.We obtain a new type of wave transmission mode based on photonic crystal zipper-like boundaries and apply it to a beam splitter assembled from rectangular photonic crystals(PCs).The constructed beam splitter structure is compact and possesses frequency separation functions.In addition,we construct a box-shaped triangular PC structures with zipper-like boundaries and discover phenomena of TCSs in the corners,comparing its corner states with those formed by other boundaries.Based on this,we explore the regularities of the electric field patterns of TESs and TCSs,explain the connection between the characteristic frequencies and locality of TCSs,which helps better control photons and ensures low power consumption of the system.

Interacting topological magnons in a checkerboard ferromagnet

This work is devoted to studying the magnon-magnon interaction effect in a two-dimensional checkerboard ferromagnet with the Dzyaloshinskii-Moriya interaction.Using a first-order Green function method,we analyze the influence of magnon-magnon interaction on the magnon band topology.We find that Chern numbers of two renormalized magnon bands are different above and below the critical temperature,which means that the magnon band gap-closing phenomenon is an indicator for one topological phase transition of the checkerboard ferromagnet.Our results show that the checkerboard ferromagnet possesses two topological phases,and its topological phase can be controlled either via the temperature or the applied magnetic field due to magnon-magnon interactions.Interestingly,it is found that the topological phase transition can occur twice with the increase in the temperature,which is different from the results of the honeycomb ferromagnet.

RKKY interaction in helical higher-order topological insulators

We theoretically investigate the Ruderman–Kittel–Kasuya–Yosida(RKKY) interaction in helical higher-order topological insulators(HOTIs), revealing distinct behaviors mediated by hinge and Dirac-type bulk carriers. Our findings show that hinge-mediated interactions consist of Heisenberg, Ising, and Dzyaloshinskii–Moriya(DM) terms, exhibiting a decay with impurity spacing z and oscillations with Fermi energy εF. These interactions demonstrate ferromagnetic behaviors for the Heisenberg and Ising terms and alternating behavior for the DM term. In contrast, bulk-mediated interactions include Heisenberg, twisted Ising, and DM terms, with a conventional cubic oscillating decay. This study highlights the nuanced interplay between hinge and bulk RKKY interactions in HOTIs, offering insights into designs of next-generation quantum devices based on HOTIs.

Two-dimensional Sb net generated nontrivial topological states in SmAgSb_(2) probed by quantum oscillations

The REAgSb_(2)(RE = rare earth and Y) family has drawn considerable research interest because the two-dimensional Sb net in their crystal structures hosts topological fermions and hence rich topological properties. We report herein the magnetization and magnetotransport measurements of SmAgSb_(2) single crystal, which unveil very large magnetoresistance and high carrier mobility up to 6.2 × 10^(3)% and 5.58 × 10^(3)cm^(2)·V^(-1)·s^(-1), respectively. The analysis of both Shubnikov–de Haas and de Haas–van Alphen quantum oscillations indicates nontrivial Berry phases in the paramagnetic state while trivial Berry curvature in the antiferromagnetic state, indicating a topological phase transition induced by the antiferromagnetic order. It is also supported by the first-principles calculations. The results not only provide a new interesting topological material but also offer valuable insights into the correlation between magnetism and nontrivial topological states.

Structural phase transition and transport properties in topological material candidate NaZn_(4)As_(3)

We report a comprehensive study on a layered-structure compound of NaZn_(4)As_(3),which has been predicted to be an ideal topological semimetal(TSM) candidate.It is found that NaZn_(4)As_(3) undergoes a structural transformation from high temperature rhombohedral to a low temperature monoclinic phase.The electric resistivity exhibits a metal-to-insulatorlike transition at around 100 K,and then develops a plateau at low temperature,which might be related to the protected topologically conducting surface states.Our first-principles calculation confirms further that NaZn_(4)As_(3) is a topological insulator(TI) for both different phases rather than a previously proposed TSM.The Hall resistivity reveals that the hole carriers dominate the transport properties for the whole temperature range investigated.Furthermore,an obvious kink possibly associated to the structure transition has been detected in thermopower around ~ 170 K.The large thermopower and moderate κ indicate that NaZn_(4)As_(3) and/or its derivatives can provide a good platform for optimizing and studying the thermoelectric performance.

Topological phases of a non-Hermitian coupled SSH ladder

We study topological phases of a non-Hermitian coupled Su-Schrieffer-Heeger(SSH) ladder. The model originates from the brick-wall lattices in the two-row limit. The Hamiltonian can be brought into block off-diagonal form and the winding number can be defined with the determine of the block off-diagonal matrix. We find the determine of the offdiagonal matrix has nothing to do with the interleg hopping of the ladder. So the topological phases of the model are the same as those of the chains. Further numerical simulations verify the analysis.

Topological properties of tetratomic Su-Schrieffer-Heeger chains with hierarchical long-range hopping

We propose a new generalized Su–Schrieffer–Heeger model with hierarchical long-range hopping based on a onedimensional tetratomic chain. The properties of the topological states and phase transition, which depend on the cointeraction of the intracell and intercell hoppings, are investigated using the phase diagram of the winding number. It is shown that topological states with large positive/negative winding numbers can readily be generated in this system. The properties of the topological states can be verified by the ring-type structures in the trajectory diagram of the complex plane. The topological phase transition is strongly related to the opening(closure) of an energy bandgap at the center(boundaries) of the Brillouin zone. Finally, the non-zero-energy edge states at the ends of the finite system are revealed and matched with the bulk–boundary correspondence.

Topological phase transitions driven by next-nearest-neighbor hopping in noncentrosymmetric cold Fermi gases

We investigate the topological phase marked by the Thouless–Kohmoto–Nightingale–Nijs（TKNN） number and the phase transitions driven by the next nearest neighbor（NNN） hopping in noncentrosymmetric cold Fermi gases, both spinsinglet pairing and spin-triplet pairing are considered. There exists a critical t＇c for the NNN hopping, at which the quantum phase transition occurs, and the system changes from an Abelian（non-Abelian） phase to a non-Abelian（Abelian） one. By numerically diagonalizing the Hamiltonian in the real space, the energy spectra with edge states for different topological phases and the Majorana zero modes are discussed. Although the spin-triplet pairing does not contribute to the gap closing and the phase diagram, it induces gapless states in the presence of a magnetic field, and the TKNN number in this region is still zero.

Creation of topological vortices using Pancharatnam-Berry phase liquid crystal holographic plates

Recently,physical fields with topological configurations are evoking increasing attention due to their fascinating structures both in fundamental researches and practical applications.Therein,topological light fields,because of their unique opportunity of combining experimental and analytical studies,are attracting more interest.Here,based on the Pancharatnam-Berry(PB)phase,we report the creation of Hopf linked and Trefoil knotted optical vortices by using phaseonly encoded liquid crystal(LC)holographic plates.Utilizing scanning measurement and the digital holographic interference method,we accurately locate the vortex singularities and map these topological nodal lines in three-dimensions.Compared with the common methods realized by the spatial light modulator(SLM),the phase-only LC plate is more efficient.Meanwhile,the smaller pixel size of the LC element reduces the imperfection induced by optical misalignment and pixellation.Moreover,we analyze the influence of the incident beam size on the topological configuration.

THREE-DIMENSIONAL TOPOLOGICAL ANALYSIS OF Nd-Fe-B AND Pr-Fe-B PHASE DIAGRAMS

With the aid of 3-dimensional topological analysis methodology,relationships among phage regions on the isothermal section of the Nd-Fe-B phase diagram at 1000℃ and those on vertical sections of the Pr-Fe-B phase diagram passing through Pr_2 Fe_(14)B point have been re-discussed and modified.

Topological phase transition in a ladder of the dimerized Kitaev superconductor chains

We investigate the topological properties of a ladder model of the dimerized Kitaev superconductor chains.The topological class of the system is determined by the relative phase θ between the inter-and intra-chain superconducting pairing.One topological class is the class BDI characterized by the Z index,and the other is the class D characterized by the Z;index.For the two different topological classes,the topological phase diagrams of the system are presented by calculating two different topological numbers,i.e.,the Z index winding number W and the Z;index Majorana number M,respectively.In the case of θ=0,the topological class belongs to the class BDI,multiple topological phase transitions accompanying the variation of the number of Majorana zero modes are observed.In the case of θ = π/2 it belongs to the class D.Our results show that for the given value of dimerization,the topologically nontrivial and trivial phases alternate with the variation of chemical potential.

Electronic properties and topological phases of ThXY(X= Pb, Au, Pt and Y= Sb, Bi, Sn) compounds

The electronic properties and topological phases of ThXY （X = Pb, Au, Pt, Pd and Y = Sb, Bi, Sn） compounds in the presence of spin-orbit coupling, using density functional theory are investigated. The ThPtSn compound is stable in the ferromagnetic phase and the other ThXY compounds are stable in nonmagnetic phases. Band structures of these compounds in topological phases （insulator or metal） and normal phases within generalized gradient approximation （GGA） and Engel- Vosko generalized gradient approximation （GGA_EV） are compared. The ThPtSn, ThPtBi, ThPtSb, ThPdBi, and ThAuBi compounds have topological phases and the other ThXY compounds have normal phases. Band inversion strengths and topological phases of these compounds at different pressure are studied. It is seen that the band inversion strengths of these compounds are sensitive to pressure and for each compound a second-order polynomial fitted on the band inversion strengths-pressure curves.

TOPOLOGICAL STRUCTURE OF THE SINGULAR POINTS OF THE THIRD ORDER PHASE LOCKED LOOP EQUATIONS WITH THE CHARACTER OF DETECTED PHASE BEING g(φ)=(1+k)sinφ/(1+kcosφ)

In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(?) =(1+k)sin?/1+kcos?.

Topological phase diagrams and Majorana zero modes of the Kitaev ladder and tube

In this paper,we study two quasi-one-dimensional（1 D） Kitaev models with ladder-like and tube-like spatial structures,respectively.Our results provide the phase diagrams and explicit expressions of the Majorana zero modes.The topological phase diagrams are obtained by decomposing the topological invariants and the topological conditions for topologically nontrivial phases are given precisely.For systems which belongs to topological class BDI,we obtain the regions in the phase diagrams where the topological numbers show even-odd effect.For the Kitaev tube model a phase factor induced by the magnetic flux in the axial direction of the tube is introduced to alter the classification of the tube Hamiltonian from class BDI to D.The Kitaev tube of class D is characterized by the Z2 index when the number of chains is odd while 0,1,2 when the number of chains is even.The phase diagrams show periodic behaviors with respect to the magnetic flux.The bulk-boundary correspondence is demonstrated by the observations that the topological conditions for the bulk topological invariant to take nontrivial values are precisely those for the existence of the Majorana zero modes.

Topological phase transition in cavity optomechanical system with periodical modulation

We investigate the topological phase transition and the enhanced topological effect in a cavity optomechanical system with periodical modulation.By calculating the steady-state equations of the system,the steady-state conditions of cavity fields and the restricted conditions of effective optomechanical couplings are demonstrated.It is found that the cavity optomechanical system can be modulated to different topological Su–Schrieffer–Heeger(SSH)phases via designing the optomechanical couplings legitimately.Meanwhile,combining the effective optomechanical couplings and the probability distributions of gap states,we reveal the topological phase transition between trivial SSH phase and nontrivial SSH phase via adjusting the decay rates of cavity fields.Moreover,we find that the enhanced topological effect of gap states can be achieved by enlarging the size of system and adjusting the decay rates of cavity fields.

Acoustic topological phase transition induced by band inversion of high-order compound modes and robust pseudospin-dependent transport

A simple two-dimensional phononic crystal hosting topologically protected edge states is proposed to emulate the quantum spin Hall effect in electronic systems, whose phononic topological phase can be reconfigured through the rotation of scatters. In particular, the band inversion occurs between two pairs of high-order compound states, resulting in topological phase transition from trivial to nontrivial over a relatively broad high-frequency range. This is further evidenced by an effective Hamiltonian derived by the k·p perturbation theory. The phononic topology is related to a pseudo-timereversal symmetry constructed by the point group symmetry of two doubly degenerate eigenstates. Numerical simulations unambiguously demonstrate robust helical edge states whose pseudospin indices are locked to the propagation direction along the interface between topologically trivial and nontrivial phononic crystals. Our designed phononic systems provide potential applications in robust acoustic signal transport along any desired path over a high-frequency range.

Photoinduced Weyl semimetal phase and anomalous Hall effect in a three-dimensional topological insulator

Motivated by the fact that Weyl fermions can emerge in a three-dimensional topological insulator on breaking either time-reversal or inversion symmetries,we propose that a topological quantum phase transition to a Weyl semimetal phase occurs under the off-resonant circularly polarized light,in a three-dimensional topological insulator,when the intensity of the incident light exceeds a critical value.The circularly polarized light effectively generates a Zeeman exchange field and a renormalized Dirac mass,which are highly controllable.The phase transition can be exactly characterized by the first Chern number.A tunable anomalous Hall conductivity emerges,which is fully determined by the location of the Weyl nodes in momentum space,even in the doping regime.Our predictions are experimentally realizable through pump-probe angle-resolved photoemission spectroscopy and raise a new way for realizing Weyl semimetals and quantum anomalous Hall effects.

Atomic-Ordering-Induced Quantum Phase Transition between Topological Crystalline Insulator and Z_2 Topological Insulator

Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topological Dirac phases.It is a fundamental challenge to realize quantum transition between Z_2 nontrivial topological insulator（TI） and topological crystalline insulator（TCI） in one material because Z_2 TI and TCI have different requirements on the number of band inversions. The Z_2 TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Taking PbSnTe_2 alloy as an example, here we demonstrate that the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and Z_2 TI phase in a single material. Our results suggest that the atomic-ordering provides a new platform towards the realization of reversibly switching between different topological phases to explore novel applications.

Characterization of topological phase of superlattices in superconducting circuits

The recent experimental observation of topological magnon insulator states in a superconducting circuit chain marks a breakthrough for topological physics with qubits, in which a dimerized qubit chain has been realized. Here, we extend such a dimer lattice to superlattice with arbitrary number of qubits in each unit cell in superconducting circuits, which exhibits rich topological properties. Specifically, by considering a quadrimeric superlattice, we show that the topological invariant(winding number) can be effectively characterized by the dynamics of the single-excitation quantum state through time-dependent quantities. Moreover, we explore the appearance and detection of the topological protected edge states in such a multiband qubit system. Finally, we also demonstrate the stable Bloch-like-oscillation of multiple interface states induced by the interference of them. Our proposal can be readily realized in experiment and may pave the way towards the investigation of topological quantum phases and topologically protected quantum information processing.