Generic model with unconventional Rashba bands and giant spin galvanic effect

In a two-dimensional system, Rashba spin-orbit coupling can lift spin degeneracy and give the opposite spin chirality to two split Fermi circles from two Rashba bands. Here, we propose a generic model that can produce unconventional Rashba bands. In such cases, the two Fermi circles from the two bands exhibit the same spin chirality. When various interactions are taken into account, many unique physics can emerge in systems with unconventional Rashba bands compared to those with conventional Rashba bands. For instance, we study the spin galvanic effect by considering two cases: one with potential impurity scattering and the other with magnetic impurity scattering. In both cases, we find that the efficiency of the spin galvanic effect is strongly enhanced in unconventional Rashba bands compared to conventional Rashba bands. More intriguingly, we find that the efficiency of conventional Rashba bands is insensitive to either potential or magnetic impurity scattering. However, the efficiency of unconventional Rashba bands can be further enhanced by magnetic impurity scattering compared to the potential impurity scattering. Thus, unconventional Rashba bands can produce giant spin galvanic effect. These results demonstrate that this model is useful for exploring abnormal physics in systems with unconventional Rashba bands.

Figure 1

(a) A schematic diagram of the two-dimensional hexagonal lattice, with a direct lattice on the left, where ${\mathbf{a}}_1$ and ${\mathbf{a}}_2$ are direct lattice vectors, and a reciprocal lattice on the right, where ${\mathbf{b}}_1$ and ${\mathbf{b}}_2$ are reciprocal lattice vectors. (b) The band structure along a high symmetry path, where the plot on the right shows the spin texture at $-12\text{eV}$. (c) The global spin texture corresponding to each band corresponds one-to-one with the band color in (b). For (b) and (c), the parameters are set to $t=-2\text{eV},\lambda =3\text{eV},{\lambda }_R=0.7\text{eV}\text{Å}$, respectively.

Figure 2

(a) A schematic diagram of the two-dimensional square lattice, with a direct lattice on the left, where ${\mathbf{a}}_1$ and ${\mathbf{a}}_2$ are direct lattice vectors, and a reciprocal lattice on the right, where ${\mathbf{b}}_1$ and ${\mathbf{b}}_2$ are reciprocal lattice vectors. (b) The band structure along a high symmetry path, where the plot on the right shows the spin texture at the $-8\text{eV}$. (c) The global spin texture corresponding to each band corresponds one-to-one with the band color in (b). For (b) and (c), the parameters are set to $t=-2\text{eV},\lambda =3\text{eV},{\lambda }_R=0.7\text{eV}\text{Å}$, respectively.

Figure 3

After injecting spin along the $\mathbf{z}$ direction or applying an electric field in the $\mathbf{y}$ direction, (a) and (b) correspond to the movement of the inner and outer circles of conventional and unconventional Rashba bands, respectively.

Figure 4

(a) Group velocity and (b) density of states of the inner and outer circles. (c) The interband scattering factor $|\langle {\psi }_{-\eta }(k,\theta )|{\psi }_{\eta }(k,{\theta }^{\prime }){|}^2$ as a function of Fermi energy. (d) The total spin polarization of conventional and unconventional Rashba bands, where we adopt the same parameter of Rashba coupling ${\lambda }_R$.

Figure 5

(a) The relative spin current $j_s\left(E_F\right)/j_s\left(0\right)$ and the relative charge current $j_c\left(E_F\right)/j_c\left(0\right)$ as the function as the Fermi energy for the unconventional Rashba bands. (b) The spin-to-charge conversion efficiency ${\lambda }_{\mathrm{IEE}}$ of conventional and unconventional Rashba bands as the function as the Fermi energy.

Figure 6

(a) Group velocity and (b) density of states of inner and outer circles. (c) The interband scattering factor $|\langle {\psi }_{-\eta }(k,\theta )|{\psi }_{\eta }(k,{\theta }^{\prime }){|}^2$ as a function of Fermi energy. (d) The total spin polarization of the unconventional Rashba bands. (e) The relative spin current $j_s\left(E_F\right)/j_s\left(0\right)$ and the relative charge current $j_c\left(E_F\right)/j_c\left(0\right)$ as the function as the Fermi energy for the unconventional Rashba bands. (f) The spin-to-charge conversion efficiency ${\lambda }_{\mathrm{IEE}}$ of the unconventional Rashba bands as the function as the Fermi energy.

Figure 7

Self-energy: (a) lowest-order approximation; (b) first-order Born approximation.

Figure 8

(a) The total spin polarization of conventional and unconventional Rashba bands. (b) The spin-to-charge conversion efficiency ${\lambda }_{\mathrm{IEE}}$ of conventional and unconventional Rashba bands as the function as the Fermi energy.