Transport blocking and topological phases using ac magnetic fields

We analyze electron dynamics and topological properties of open double quantum dots driven by circularly polarized ac magnetic fields. In particular we focus on the system symmetries which can be tuned by the ac magnetic field. Remarkably, we show that in the electron spin resonance configuration, where the magnetic fields in each dot oscillate with a phase difference of $\pi$, charge localization occurs giving rise to transport blocking at arbitrary intensities of the ac field. The conditions for charge localization are obtained by means of Floquet theory and related with quasi-energies degeneracy. We also demonstrate that a topological phase transition can be induced in the adiabatic regime for a phase difference of $\pi$, either by tuning the coupling between dots or by modifying the intensity of the driving magnetic field.

Figure 1

Schematic figure of a DQD coupled to circularly polarized magnetic fields oscillating in phase opposition.

Figure 2

Quasi-energies vs $B_{ac}$ for $\phi =0$ (left) and $\phi =\pi$ (right), in resonance condition. The absence (presence) of ${\Pi }_T$ symmetry for $\phi =0$ ($\phi =\pi$) leads to nondegenerate (doubly degenerate) quasi-energies. The degeneracy, present for all $B_{ac}$ in the right figure, drives the system to charge localization. $t_{LR}=1/10$, and $B_{z,L}=B_{z,R}=\omega =1/2$.

Figure 3

Current vs $t$ for the case of $\Pi$ symmetry ($\phi =0$) at resonance condition. $B_{zL}=B_{zR}=\omega =0.5$, $B_{ac}=0.5$, $t_{LR}=0.1$, ${\rm Y}=0.01$, $T={10}^{-3}$, and ${\mu }_L-{\mu }_R\gg T,B_z,B_{ac}$. The inset shows the current vs time in the steady state $\langle I\rangle \simeq 2.5\times {10}^{-4}$ ($3.5\times {10}^{-2}\text{pA}$). All values are in energy units of $100\text{mT}$($5.788\mu \mathrm{eV}$). ($\omega \sim 4.4\text{GHz}$), the time unit scale is $\sim 0.23\text{ns}$.

Figure 4

Occupation probability in the left dot $P$ vs time for $B_{ac}=0.6$ in the presence of decoherence due to the leads. Note the spatial CL induced as a consequence of the quasi-energy degeneracy between Floquet states with opposite ${\Pi }_T$ symmetry. The inset shows the time evolution [Eq. (3)] for the closed system. $B_{z,L}=B_{z,R}=\omega =1/2$, ${\rm Y}=0.01$, $T={10}^{-3}$, $t_{LR}=1/10$, and $\phi =\pi$, all in units of $100\text{mT}$ (i.e., $5.788\mu \mathrm{eV}$) for ${\mu }_L-{\mu }_R\gg 0$.

Figure 5

$P_{\text{min}}$ vs $\Lambda$ in the presence of coupling with the leads for the steady state ($\phi =\pi$).

Figure 6

Current vs $\omega$ in the steady state for asymmetric Zeeman splittings. $\langle I\rangle$ drops to zero at $\omega ={\omega }_{\text{Av}}$ (${\omega }_{\text{Av}}=0.75$) for $\phi =\pi$, while for $\phi =0$ the current is finite. $B_{z,L}=0.5$, $B_{z,R}=1$,$B_{ac}=0.55$, $t_{LR}=0.1$, and ${\rm Y}=0.01$. Different temperatures have been considered, but they only affect the transitory regime.