Composite solitons in SU(3) spin–orbit-coupling Bose gases

We study solitons in a spin-1 Bose–Einstein condensates with SU(3) spin–orbit coupling. We obtain the ground state and the metastable solution for solitons with attractive interactions by the imaginary-time evolution method. Compared with the SU(2) spin–orbit coupling, it is found that the solitons in SU(3) spin–orbit coupling show a new feature due to breaking the symmetry. The solitons called the composite solitons have mixing manifolds of ferromagnetic and antiferromagnetic states. This has stimulated people to study the topological excitation properties of SU(3) spin–orbit coupling and it is expected to find new quantum phases.     

Floquet topological phase transition in two-dimensional quadratic band crossing system

We investigate the Hall effects of quadratic band crossing(QBC) fermions in a square optical lattice with spin–orbit coupling and orbital Zeeman term. We find that the orbital Zeeman term and shaking play critical roles in the systems,which can drive a topological transition from spin Hall phases to anomalous Hall phase with nonvanishing(spin) Chern numbers. Due to the interplay among the orbital Zeeman term, spin–orbit coupling, and the shaking, the phase diagram of the system exhibits rich phases, which are characterized by Chern number.     

Mott transition in ruby lattice Hubbard model

Mott transition in a ruby lattice with fermions described by the Hubbard model including on-site repulsive interaction is investigated by combining the cellular dynamical mean-field theory and the continuous-time quantum Monte Carlo algorithm. The effect of temperature and on-site repulsive interaction on the metallic–insulating phase transition in ruby lattice with fermions is discussed based on the density of states and double occupancy. In addition, the magnetic property of each phase is discussed by defining certain magnetic order parameters. Our results show that the antiferromagnetic metal is found at the low temperature and weak interaction region and the antiferromagnetic insulating phase is found at the low temperature and strong interaction region. The paramagnetic metal appears in whole on-site repulsive interaction region when the temperature is higher than a certain value and the paramagnetic insulator appears at the middle scale of temperature and on-site repulsive interaction.     

SU(3) spin–orbit-coupled Bose–Einstein condensate confined in a harmonic plus quartic trap

We consider a SU(3) spin–orbit coupled Bose–Einstein condensate confined in a harmonic plus quartic trap.The ground-state wave functions of such a system are obtained by minimizing the Gross–Pitaevskii energy functional, and the effects of the spin-dependent interaction and spin–orbit coupling are investigated in detail.For the case of ferromagnetic spin interaction, the SU(3) spin–orbit coupling induces a threefold-degenerate plane wave ground state with nontrivial spin texture.For the case of antiferromagnetic spin interaction, the system shows phase separation for weak SU(3) spin–orbit coupling, where three discrete minima with unequal weights in momentum space are selected, while hexagonal honeycomb lattice structure for strong SU(3) SOC, where three discrete minima with equal weights are selected.     

Spinor F=1 Bose–Einstein condensates loaded in two types of radially-periodic potentials with spin–orbit coupling

We consider two-dimensional spinor F = 1 Bose–Einstein condensates in two types of radially-periodic potentials with spin–orbit coupling, i.e., spin-independent and spin-dependent radially-periodic potentials. For the Bose–Einstein condensates in a spin-independent radially-periodic potential, the density of each component exhibits the periodic density modulation along the azimuthal direction, which realizes the necklacelike state in the ferromagnetic Bose–Einstein condensates. As the spin-exchange interaction increases, the necklacelike state gradually transition to the plane wave phase for the antiferromagnetic Bose–Einstein condensates with larger spin–orbit coupling. The competition of the spin-dependent radially-periodic potential, spin–orbit coupling, and spin-exchange interaction gives rise to the exotic ground-state phases when the Bose–Einstein condensates in a spin-dependent radially-periodic potential.     

Spin texturing in a parabolically confined quantum wire with Rashba and Dresselhaus spin–orbit interactions

In this study, we investigate theoretically the effect of spin–orbit coupling on the energy level spectrum and spin texturing of a quantum wire with a parabolic confining potential subjected to the perpendicular magnetic field. Highly accurate numerical calculations have been carried out using a finite element method. Our results reveal that the interplay between the spin–orbit interaction and the effective magnetic field significantly modifies the band structure, producing additional subband extrema and energy gaps. Competing effects between external field and spin–orbit interactions introduce complex features in spin texturing owing to the couplings in energy subbands. We obtain that spatial modulation of the spin density along the wire width can be considerably modified by the spin–orbit coupling strength, magnetic field and charge carrier concentration.     

Phase diagram,correlations,and quantum critical point in the periodic Anderson model

Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matrix embedding theory, we study the ground state properties of the periodic Anderson model on a two-dimensional square lattice. We systematically investigate the phase diagram away from half filling. We find three different phases in this region, which are distinguished by the local moment and the spin–spin correlation functions. The phase transition between the two antiferromagnetic phases is of first order. It is the so-called Lifshitz transition accompanied by a reconstruction of the Fermi surface. As the filling is close to half filling, there is no difference between the two antiferromagnetic phases. From the results of the spin–spin correlation, we find that the Kondo singlet is formed even in the antiferromagnetic phase.     

Spin excitation spectra of spin–orbit coupled bosons in an optical lattice

Spin-wave excitation plays important roles in the investigation of the magnetic phases. In this paper, we study the spin-wave excitation spectra of two-component Bose gases with spin–orbit coupling in a deep square optical lattice using the spin-wave theory. We find that, while the excitation spectrum of the vortex crystal phase is gapless with a linear dispersion in the vicinity of the minimum point, the spectra of the commensurate spiral spin phase and the skyrmion crystal phase are gapped. Significantly, the spin fluctuations strongly destabilize the classical ground state of the skyrmion phase with the appearance of an imaginary part in the eigenfrequencies of spin excitations. Such features of the spin excitation spectra provide further insights into the exotic spin phases.     

Spin transport properties of a Dresselhaus-polygonal quantum ring

We propose a theoretical method to investigate the effect of the Dresselhaus spin–orbit coupling(DSOC) on the spin transport properties of a regular polygonal quantum ring with an arbitrary number of segments. We find that the DSOC can break the time reversal symmetry of the spin conductance in a polygonal ring and that this property can be used to reverse the spin direction of electrons in the polygon with the result that a pure spin up or pure spin down conductance can be obtained by exchanging the source and the drain. When the DSOC is considered in a polygonal ring with Rashba spin–orbit coupling(RSOC) with symmetric attachment of the leads, the total conductance is independent of the number of segments when both of the two types of spin–orbit coupling(SOC) have the same value. However, the interaction of the two types of SOC results in an anisotropic and shape-dependent conductance in a polygonal ring with asymmetric attachment of the leads. The method we proposed to solve for the spin conductance of a polygon can be generalized to the circular model.     

Antiferromagnetism and Kondo screening on a honeycomb lattice

Magnetic adatoms in the honeycomb lattice have received tremendous attention due to the interplay between Ruderman–Kittel–Kasuya–Yosida interaction and Kondo coupling leading to very rich physics. Here we study the competition between the antiferromagnetism and Kondo screening of local moments by the conduction electrons on the honeycomb lattice using the determinant quantum Monte Carlo method. While changing the interband hybridization V, we systematically investigate the antiferromagnetic-order state and the Kondo singlet state transition, which is characterized by the behavior of the local moment, antiferromagnetic structure factor, and the short range spin-spin correlation. The evolution of the single particle spectrum are also calculated as a function of hybridization V, we find that the system presents a small gap in the antiferromagnetic-order region and a large gap in the Kondo singlet region in the Fermi level. We also find that the localized and itinerant electrons coupling leads to the midgap states in the conduction band in the Fermi level at very small V. Moreover, the formation of antiferromagnetic order and Kondo singlet are studied as on-site interaction U or temperature T increasing, we have derived the phase diagrams at on-site interaction U(or temperature T) and hybridization V plane.     

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number C_s for energy-bands of trilayer graphene having the essence of intrinsic spin–orbit coupling is analytically calculated. We find that for each valley and spin, C_s is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states,consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin–orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin–orbit(RSO) interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin–orbit coupling, while the other two layers have zero intrinsic spin–orbit coupling.Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.     

Thermodynamic behaviour of Rashba quantum dot in the presence of magnetic field

The thermodynamic properties of an In Sb quantum dot have been investigated in the presence of Rashba spin–orbit interaction and a static magnetic field. The energy spectrum and wave-functions for the system are obtained by solving the Schrodinger wave-equation analytically. These energy levels are employed to calculate the specific heat, entropy,magnetization and susceptibility of the quantum dot system using canonical formalism. It is observed that the system is susceptible to maximum heat absorption at a particular value of magnetic field which depends on the Rashba coupling parameter as well as the temperature. The variation of specific heat shows a Schottky-like anomaly in the low temperature limit and rapidly converges to the value of 2kB with the further increase in temperature. The entropy of the quantum dot is found to be inversely proportional to the magnetic field but has a direct variation with temperature. The substantial effect of Rashba spin–orbit interaction on the magnetic properties of quantum dot is observed at low values of magnetic field and temperature.     

Antiferromagnetic and topological states in silicene:A mean field study

It has been widely accepted that silicene is a topological insulator, and its gap closes first and then opens again with increasing electric field, which indicates a topological phase transition from the quantum spin Hall state to the band insulator state. However, due to the relatively large atomic spacing of silicene, which reduces the bandwidth, the electron–electron interaction in this system is considerably strong and cannot be ignored. The Hubbard interaction, intrinsic spin orbital coupling(SOC), and electric field are taken into consideration in our tight-binding model, with which the phase diagram of silicene is carefully investigated on the mean field level. We have found that when the magnitudes of the two mass terms produced by the Hubbard interaction and electric potential are close to each other, the intrinsic SOC flips the sign of the mass term at either K or K for one spin and leads to the emergence of the spin-polarized quantum anomalous Hall state.     

Interaction and spin–orbit effects on a kagome lattice at 1/3 filling

We investigate the competing effects of spin-orbit coupling and electron--electron interaction on a kagome lattice at 1/3 filling. We apply the cellular dynamical mean-field theory and its real-space extension combined with the continuous time quantum Monte Carlo method, and obtain a phase diagram including the effects of the interaction and the spin-orbit coupling at T = 0. 1t, where T is the temperature and t is the hopping energy. We find that without the spin-orbit coupling, the system is in a semi-metal phase stable against the electron--electron interaction. The presence of the spin-orbit coupling can induce a topological non-trivial gap and drive the system to a topological insulator, and as the interaction increases, a larger spin--orbit coupling is required to reach the topological insulating phase.     

Enhancing von Neumann entropy by chaos in spin–orbit entanglement

For a quantum system with multiple degrees of freedom or subspaces, loss of coherence in a certain subspace is intimately related to the enhancement of entanglement between this subspace and another one. We investigate intra-particle entanglement in two-dimensional mesoscopic systems, where an electron has both spin and orbital degrees of freedom and the interaction between them is enabled by Rashba type of spin–orbit coupling. The geometric shape of the scattering region can be adjusted to produce a continuous spectrum of classical dynamics with different degree of chaos. Focusing on the spin degree of freedom in the weak spin–orbit coupling regime, we find that classical chaos can significantly enhance spin–orbit entanglement at the expense of spin coherence. Our finding that classical chaos can be beneficial to intra-particle entanglement may have potential applications such as enhancing the bandwidth of quantum communications.     

Spin texturing in quantum wires with Rashba and Dresselhaus spin–orbit interactions and in-plane magnetic field

In this work, we investigate the effects of interplay of spin–orbit interaction and in-plane magnetic fields on the electronic structure and spin texturing of parabolically confined quantum wire. Numerical results reveal that the competing effects between Rashba and Dresselhaus spin–orbit interactions and the external magnetic field lead to a complicated energy spectrum. We find that the spin texturing owing to the coupling between subbands can be modified by the strength of spin–orbit couplings as well as the magnitude and the orientation angle of the external magnetic field.     

Spin–orbit-coupled spin-1 Bose–Einstein condensates confined in radially periodic potential

We investigate the ground states of spin-1 Bose–Einstein condensates (BECs) with spin–orbit coupling in a radiallyperiodic potential by numerically solving the coupled Gross–Pitaevskii equations. In the radially periodic potential, wefirst demonstrate that spin–orbit-coupled antiferromagnetic BECs support a multiring petal phase. Polar–core vortex canbe observed from phase profiles, which is manifested as circularly symmetric distribution. We further show that spin–orbitcoupling can induce multiring soliton structure in ferromagnetic BECs. It is confirmed especially that the wave-functionphase of the ring corresponding to uniform distribution satisfies the rotational symmetry, and the wave-function phase ofthe ring corresponding to partial splitting breaks the rotational symmetry. Adjusting the spin–orbit coupling strength cancontrol the number of petal in antiferromagnetic BECs and the winding numbers of wave-function in ferromagnetic BECs.Finally, we discuss effects of spin-independent and spin-dependent interactions on the ground states.     

Generalized Rashba Coupling Approximation to a Resonant Spin Hall Effect of the Spin–Orbit Coupling System in a Magnetic Field

We introduce a generalized Rashba coupling approximation to analytically solve confined two-dimensional electron systems with both the Rashba and Dresselhaus spin–orbit couplings in an external magnetic field. A solvable Hamiltonian is obtained by performing a simple change of basis, which has the same form as that with only Rashba coupling. Each Landau state becomes a new displaced-Fock state instead of the original Harmonic oscillator Fock state. Analytical energies are consistent with the numerical ones in a wide range of coupling strength even for a strong Zeeman splitting, exhibiting the validity of the analytical approximation. By using the eigenstates, spin polarization correctly displays a jump at the energy-level crossing point, where the corresponding spin conductance exhibits a pronounced resonant peak. As the component of the Dresselhaus coupling increases,the resonant point shifts to a smaller value of the magnetic field. In contrast to pure Rashba couplings, we find that the Dresselhaus coupling and Zeeman splittings tend to suppress the resonant spin Hall effect. Our method provides an easy-to-implement analytical treatment to two-dimensional electron gas systems with both types of spin–orbit couplings by applying a magnetic field.     

Phonon dichroism in proximitized graphene

We systematically investigate the phonon dichroism in proximitized graphene with broken time-reversal symmetry.We find that in the absence of any type of spin–orbit coupling, phonon dichroism vanishes. Linear and circular phonon dichroism occur in the presence of uniform(staggered) intrinsic spin–orbit coupling and ferromagnetic(antiferromagnetic)exchange coupling. All these situations can be distinguished by their specific behaviors of phonon absorption at the transition point. Our finding prov...     

Entangled multi-knot lattice model of anyon current

We proposed an entangled multi-knot lattice model to explore the exotic statistics of anyons. Long-range coupling interaction is a fundamental character of this knot lattice model. The short-range coupling models, such as the Ising model,Hamiltonian model of quantum Hall effect, fermion pairing model, Kitaev honeycomb lattice model, and so on, are the short-range coupling cases of this knot lattice model. The long-range coupling knot lattice model bears Abelian and nonAbelian anyons, and shows integral and fractional filling states like the quantum Hall system. The fusion rules of anyons are explicitly demonstrated by braiding crossing states. The eigenstates of quantum models can be represented by a multilayer link lattice pattern whose topology is characterized by the linking number. This topological linking number offers a new quantity to explain and predict physical phenomena in conventional quantum models. For example, a convection flow loop is introduced into the well-known Bardeen–Cooper–Schrieffer fermion pairing model to form a vortex dimer state that offers an explanation of the pseudogap state of unconventional superconductors, and predicts a fractionally filled vortex dimer state. The integrally and fractionally quantized Hall conductance in the conventional quantum Hall system has an exact correspondence with the linking number in this multi-knot lattice model. The real-space knot pattern in the topological insulator model has an equivalent correspondence with the Lissajous knot in momentum space. The quantum phase transition between different quantum states of the quantum spin model is also directly quantified by the change of topological linking number, which revealed the topological character of phase transition. Circularized photons in an optical fiber network are a promising physical implementation of this multi-knot lattice, and provide a different path to topological quantum computation.