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Register a new userHubbard model with Rashba or Dresselhaus spin-orbit coupling and Rotated Anti-ferromagnetic Heisenberg Model
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In this work, we investigate the possible dramatic effects of Rashba or Dresselhaus spin-orbit coupling (SOC) on fermionic Hubbard model in a 2d square lattice. In the strong coupling limit, it leads to the Rotated Anti-ferromagnetic Heisenberg model which is a new class of quantum spin model. For a special equivalent class, we identify a new spin-orbital entangled commensurate ground ( Y-y ) state subject to strong quantum fluctuations at $T=0$. We evaluate the quantum fluctuations by the spin wave expansion up to order $ 1/S^2 $. In some SOC parameter regime, the Y-y state supports a massive relativistic in-commensurate magnon ( C-IC ) with its two gap minima positions continuously tuned by the SOC parameters. The C-IC magnons dominate all the low temperature thermodynamic quantities and also lead to the separation of the peak positions between the longitudinal and the transverse spin structure factors. In the weak coupling limit, any weak repulsive interaction also leads to a weak Y-y state. There is only a crossover from the weak to the strong coupling. High temperature expansions of the specific heats in both weak and strong coupling are presented. The dramatic roles to be played by these C-IC magnons at generic SOC parameters or under various external probes are hinted. Experimental applications to both layered noncentrosymmetric materials and cold atom are discussed.
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Skyrmions are topological spin textures of interest for fundamental science and applications. Previous theoretical studies have focused on systems with broken bulk inversion symmetry, where skyrmions are stabilized by easy-axis anisotropy. We investigate here systems that break surface inversion symmetry, in addition to possible broken bulk inversion. This leads to two distinct Dzyaloshinskii-Moriya (DM) terms with strengths $D_perp$, arising from Rashba spin-orbit coupling (SOC), and $D_parallel$ from Dresselhaus SOC. We show that skyrmions become progressively more stable with increasing $D_perp/D_parallel$, extending into the regime of easy-plane anisotropy. We find that the spin texture and topological charge density of skyrmions develops nontrivial spatial structure, with quantized topological charge in a unit cell given by a Chern number. Our results give a design principle for tuning Rashba SOC and magnetic anisotropy to stabilize skyrmions in thin films, surfaces, interfaces and bulk magnetic materials that break mirror symmetry.
When the Rashba and Dresslhaus spin-orbit coupling are both presented for a two-dimensional electron in a perpendicular magnetic field, a striking resemblance to anisotropic quantum Rabi model in quantum optics is found. We perform a generalized Rashba coupling approximation to obtain a solvable Hamiltonian by keeping the nearest-mixing terms of Laudau states, which is reformulated in the similar form to that with only Rashba coupling. Each Landau state becomes a new displaced-Fock state with a displacement shift instead of the original Harmonic oscillator Fock state, yielding eigenstates in closed form. Analytical energies are consistent with numerical ones in a wide range of coupling strength even for a strong Zeeman splitting. In the presence of an electric field, the spin conductance and the charge conductance obtained analytically are in good agreements with the numerical results. As the component of the Dresselhaus coupling increases, we find that the spin Hall conductance exhibits a pronounced resonant peak at a larger value of the inverse of the magnetic field. Meanwhile, the charge conductance exhibits a series of plateaus as well as a jump at the resonant magnetic field. Our method provides an easy-to-implement analytical treatment to two-dimensional electron gas systems with both types of spin-orbit couplings.
Competing orders is a general concept to describe various quantum phases and transitions in various materials. One efficient way to investigate competing orders is to first classify different class of excitations in a given quantum phase, then study their competing responses under various external probes. This strategy may not only lead to deep understanding of the quantum phase itself, but also its deep connections to various other quantum phases nearby. We implement this approach by studying the Rotated Ferromagnetic Heisenberg model (RFHM) in two different transverse fields $h_x$ and $h_z$ which can be intuitively visualized as studying spin-orbit couplings (SOC) effects in 2d Ising or anisotropic XY model in a transverse field. At a special SOC class, it was known that the RFHM at a zero field owns an exact ground state called Y-x state. It supports non only the commensurate C-C$_0$ and C-C$_{pi} $ magnons, but also the in-commensurate C-IC magnons. These magnons are non-relativistic, not contained in the exact ground state, so need to be thermally excited. Their dramatic response under the longitudinal $ h_y $ field was recently worked out by the authors. Here we find they respond very differently under the two transverse fields. Any $h_x$ ($h_z$) changes the collinear Y-x state to a canted co-planar YX-x (YZ-x) state which suffers quantum fluctuations. The C-C$_0$, C-C$_{pi} $ and C-IC magnons sneak into the quantum ground state, become relativistic and play leading roles even at $ T=0 $. We map out the boundaries among the C-C$_0$, C-C$_{pi} $ and C-IC magnons, especially the detailed evolution of the C-IC magnons inside the canted phases. As $h_x$ ($h_z$) increases further, the C-C$_0$ magnons always win the competition and emerge as the seeds to drive a transition from the YX-x (YZ-x) to the X-FM ( Z-FM ) which is shown to be in the 3d Ising universality class.
The weak-coupling renormalization group method is an asymptotically exact method to find superconducting instabilities of a lattice model of correlated electrons. Here we extend it to spin-orbit coupled lattice systems and study the emerging superconducting phases of the Rashba-Hubbard model. Since Rashba type spin-orbit coupling breaks inversion symmetry, the arising superconducting phases may be a mixture of spin-singlet and spin-triplet states. We study the two-dimensional square lattice as a paradigm and discuss the symmetry properties of the arising spin-orbit coupled superconducting states including helical spin-triplet superconductivity. We also discuss how to best deal with split energy bands within a method which restricts paired electrons to momenta on the Fermi surface.
We consider the Higgs mode at nonzero momentum in superconductors and demonstrate that in the presence of Rashba spin-orbit coupling, it couples linearly with an external exchange field. The Higgs-spin coupling dramatically modifies the spin susceptibility near the superconducting critical temperature and consequently enhances the spin pumping effect in a ferromagnetic insulator/superconductor bilayer system. We show that this effect can be detected by measuring the magnon-induced voltage generated by the inverse spin Hall effect.
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