Charge ratchet from spin flip: Space-time symmetry paradox

Traditionally the charge ratchet effect is considered as a consequence of either the spatial symmetry breaking engineered by asymmetric periodic potentials, or time asymmetry of the driving fields. Here we demonstrate that electrically and magnetically driven quantum dissipative systems with spin-orbit interactions represent an exception from this standard idea. In contrast to the so far well established belief, a charge ratchet effect appears when both the periodic potential and driving are symmetric. We show that the source of this paradoxical charge ratchet mechanism is the coexistence of quantum dissipation with the spin-flip processes induced by spin-orbit interactions.

Figure 1

(Color online) A 2DEG with RSOI of strength $\alpha =9.94\times {10}^{-12}\text{eV}\cdot \text{m}$ is obtained by a gate voltage applied to an InGaAs/InP heterostructure using the ”back gate.” The electron effective mass is $m=0.037m_0$ with $m_0$ being the free electron mass and the effective gyroscopic factor is $g^{\ast }=-15$. A parabolic confinement of strength $\hslash {\omega }_0=0.225\text{meV}$ forms in the 2DEG a quasi-one-dimensional electron gas. The superlattice with period $L=0.25\mu \text{m}$ is shaped by the ”superlattice gates” which create a symmetric periodic potential. The system is driven by a longitudinal electric field $\mathbf{E}\left(t\right)$ and by a transverse magnetic field $\mathbf{H}\left(t\right)$ which are time symmetric.

Figure 2

(Color online) The charge and spin ratchet currents as functions of the amplitudes of the electric and magnetic fields. (a) Charge current. (b) Spin current. The amplitudes of the electric, $FL$, and magnetic, $g{\mu }_{\text{B}}H$, fields are in units of $\hslash {\omega }_0$. The currents are in units of $L{\omega }_0$. According to Eq. (6) the charge and spin currents are excited when both the electric and magnetic fields simultaneously drive the system.

Figure 3

(Color online) The charge (solid curve) and spin (dashed curve) ratchet currents as functions of the magnetic field amplitude. The magnetic amplitude, $g{\mu }_{\text{B}}H$, is in units of $\hslash {\omega }_0$. The electric amplitude is fixed, $FL=\hslash {\omega }_0$. The currents oscillate and have nonuniversal zero points which depend on concrete values of the physical parameters of the system-plus-bath complex.