Magnetic-field-influenced nonequilibrium transport through a quantum ring with correlated electrons in a photon cavity

We investigate magnetic-field-influenced time-dependent transport of Coulomb interacting electrons through a two-dimensional quantum ring in an electromagnetic cavity under nonequilibrium conditions described by a time-convolutionless non-Markovian master equation formalism. We take into account the full electromagnetic interaction of electrons and cavity photons. A bias voltage is applied to semi-infinite leads along the $x$ axis, which are connected to the quantum ring. The magnetic field is tunable to manipulate the time-dependent electron transport coupled to a photon field with either $x$ or $y$ polarization. We find that the lead-system-lead current is strongly suppressed by the $y$-polarized photon field at magnetic field with two flux quanta due to a degeneracy of the many-body energy spectrum of the mostly occupied states. On the other hand, the lead-system-lead current can be significantly enhanced by the $y$-polarized field at magnetic field with half-integer flux quanta. Furthermore, the $y$-polarized photon field perturbs the periodicity of the persistent current with the magnetic field and suppresses the magnitude of the persistent current. The spatial and temporal density distributions reflect the characteristics of the many-body spectrum. The vortex formation in the contact areas to the leads influences the charge circulation in the ring.

Figure 1

Equipotential lines in the central ring system connected to the left and right leads. Note that the isolines are refined close to the bottom of the ring structure.

Figure 2

MB energy spectrum of system Hamiltonian ${\widehat{H}}_S$ vs magnetic field $B$ in units of tesla (T). The states are differentiated according to their electron content $N_e$: zero-electron states ($N_e=0$, 0ES, green dots), single-electron states ($N_e=1$, 1ES, red dots) and two-electron states ($N_e=2$, 2ES, blue crosses). The photon field is $x$ polarized.

Figure 3

Switching function ${\chi }^l\left(t\right)$ (solid red), charge of all 1ES for $B={10}^{-5}$ T (long-dashed green) and $B=1.0$ T (short-dashed blue), and charge of all 2ES for $B={10}^{-5}$ T (dotted purple) and $B=1.0$ T (dash-dotted cyan) as a function of time. The photon field is $x$-polarized.

Figure 4

The left charge current $I_L$ (solid red) and the right charge current $I_R$ (long-dashed green) vs the magnetic field with (w) $x$-polarized photon field at $t=200\mathrm{ps}$. For comparison: left charge current $I_L$ (short-dashed blue) and right charge current $I_R$ (dotted purple) in a purely electronic central system, i.e., without (w/o) photon cavity.

Figure 5

Normalized charge current density vector field in the central system for (a) $B=0.1$ T, (b) $B=0.225$ T, and (c) $B=0.425$ T at $t=200$ ps in the case of $x$-polarized photon field.

Figure 6

Charge in the left [$Q_S^L\left(t\right)$] or right [$Q_S^R\left(t\right)$] half of the central quantum ring system as a function of time for (a) $B=0.1$ and (b) $0.225$ T. The photon field is $x$-polarized.

Figure 7

Charge density distribution $\rho (\mathbf{r},t)(e/a_w^2)$ in the central system for (a) $B=0.1$, (b) $0.225$, and (c) $0.425$ T in the $x$-polarized photon field case at $t=200$ ps.

Figure 8

Local current through the top arm of the ring $I_{\mathrm{top}}$ (solid red), local current through the bottom arm of the ring $I_{\mathrm{bottom}}$ (long-dashed green), total local current $I_{\mathrm{tl}}$ (short-dashed blue), and the circular local current $I_{\mathrm{cl}}$ (dotted purple) versus the magnetic field averaged over the time interval $[180,220]\mathrm{ps}$ in the case of $x$-polarized photon field.

Figure 9

MB energy spectrum of the system Hamiltonian ${\widehat{H}}_S$ vs magnetic field $B$ within the bias window energy range for (a) $x$-polarized and (b) $y$-polarized photon field. The states are differentiated according to their electron content $N_e$: zero-electron ($N_e=0$, 0ES, green dots) and single-electron ($N_e=1$, 1ES, red dots) states.

Figure 10

Left charge current $I_L$ (solid red) and right charge current $I_R$ (long-dashed green) vs the magnetic field with (w) $y$-polarized photon field at $t=200\mathrm{ps}$. For comparison: left charge current $I_L$ (short-dashed blue) and right charge current $I_R$ (dotted purple) in a purely electronic central system, i.e., without (w/o) photon cavity.

Figure 11

Normalized charge current density vector field in the central system for (a) $B=0.1$, (b) $0.225$, and (c) $0.425$ T at $t=200$ ps in the case of $y$-polarized photon field.

Figure 12

Charge in the left [$Q_S^L\left(t\right)$] or right [$Q_S^R\left(t\right)$] half of the central system as a function of time for (a) $B=0.1$ T and (b) $B=0.225$ T. The photon field is $y$ polarized.

Figure 13

Charge density distribution $\rho (\mathbf{r},t)(e/a_w^2)$ in the central system for (a) $B=0.1$, (b) $0.225$, and (c) $0.425$ T in the $y$-polarized photon field case at $t=200$ ps.

Figure 14

Local current through the top $I_{\mathrm{top}}$ (solid red) and bottom $I_{\mathrm{bottom}}$ (long-dashed green) ring arms and total $I_{\mathrm{tl}}$ (short-dashed blue) and circular $I_{\mathrm{cl}}$ (dotted purple) local currents vs the magnetic field and averaged over the time interval $[180,220]\mathrm{ps}$ in the case of $y$-polarized photon field.