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.

Phase Diagram of the Spin-1/2 Heisenberg Alternating Chain in a Magnetic Field

By using the infinite time-evolving block decimation, we study quantum fidelity and entanglement entropy in the spin-1/2 Heisenberg alternating chain under an external magnetic field.The effects of the magnetic field on the fidelity are investigated, and its relation with the quantum phase transition(QPT) is analyzed.The phase diagram of the model is given accordingly, which supports the Haldane phase, the singlet-dimer phase, the Luttinger liquid phase and the paramagnetic phase.The scaling of entanglement entropy in the gapless Luttinger liquid phase is studied, and the central charge c = 1 is obtained.We also study the relationship between the quantum coherence, string order parameter and QPTs.Results obtained from these quantum information observations are consistent with the previous reports.