Spin Seebeck effect in an (In,Ga)As quantum well with equal Rashba and Dresselhaus spin-orbit couplings

We demonstrate that a spin-dependent Seebeck effect can be detected in quantum wells with zinc-blend structure with equal Rashba-Dresselhaus spin-orbit couplings. This theory is based on the establishment of an itinerant antiferromagnetic state, a low total-energy configuration realized in the presence of the Coulomb interaction enabled by the $\mathbf{k}=0$ degeneracy of the opposite-spin single-particle energy spectra. Transport in this state is modeled by using the solutions of a Boltzmann equation obtained within the relaxation time approximation. Numerical estimates performed for realistic GaAs samples indicate that at low temperatures, the amplitude of the spin Seebeck coefficient can be increased by scattering on magnetic impurities.

Figure 1

The single particle spectrum of a 2D electron system with equal Rashba-Dresselhaus linear couplings. The opposite-spin energies ${\varepsilon }_{\uparrow }$ and ${\varepsilon }_{\downarrow }$ are degenerate at $\mathbf{k}=0$, the source of a spin instability that leads to the formation of two new quasiparticles of energies $E_{-}$ and $E_{+}$. The states that overlap at $\mathbf{k}=0$ are plane waves of the same momentum.

Figure 2

The variation of the gap function at the center of the Fermi surface and of the spin polarization for a screening constants ${\mu }_1={10}^{-3}$ in a GaAs quantum well with $n=4\times {10}^{15}{\mathrm{m}}^{-2},Q=7.2\times {10}^{-3}{k}_F$ as a function of temperature.

Figure 3

The variation of the spin Seebeck coefficient, expressed in $k_B/e=86.3\mu \text{V}/\text{K}$ units, for the normal in (a) and parallel in (b) mode with temperature for different values of the ratio $J/V$. The gap value is $0.2E_F$, while the polarization is $10\%$. The temperature unit is set by the spin-flip energy and corresponds to 35 K.