Dissipationless Spin-Charge Conversion in Excitonic Pseudospin Superfluid

Spin-charge conversion by the inverse spin Hall effect or inverse Rashba-Edelstein effect is prevalent in spintronics but dissipative. We propose a dissipationless spin-charge conversion mechanism by an excitonic pseudospin superfluid in an electron-hole double-layer system. Magnetic exchange fields lift singlet-triplet degeneracy of interlayer exciton levels in the double-layer system. Condensation of the singlet-triplet hybridized excitons breaks both a U(1) gauge symmetry and a pseudospin rotational symmetry around the fields, leading to spin-charge coupled superflow in the system. We demonstrate the mechanism by deriving spin-charge coupled Josephson equations for the excitonic superflow from a coupled quantum-dot model.

Figure 1

The fourfold spin degeneracy is lifted by the exchange fields. When $|h|>|h^{\prime }|$ ($|h|<|h^{\prime }|$), the lowest band is the transverse (longitudinal) hybrid mode, where the pseudospin polarization is in the $yz$ ($0x$) plane. $(yz/0x,\pm )$ are exciton levels whose pseudospin polarization field $\overrightarrow{\varphi }$ are in the $yz/0x$ plane, and $\pm$ specifies a relative position between the real and imaginary part of the four-component exciton field $\overrightarrow{\varphi }$ within the $yz/0x$ plane. The figure is for $h>-h^{\prime }>0$.

Figure 2

The charge current ($I_C$) induced by the spin voltage ($V_S$). (a) The spin voltage is added at the Josephson junction in the hole layer. The charge currents can be measured by the two external circuits attached to the electron and hole layers, respectively. (b) The a.c. behavior of $\tilde{\psi }(t)$ and $I_C(t)$ according to Eq. (18) for small $|{\overline{h}}_{\pm }|$. $\tilde{\psi }(t)$ shows an oscillating behavior for $|{\overline{h}}_{\pm }k|<1$ and a stepping behavior for $|{\overline{h}}_{\pm }k|>1$.