Phonon-assisted tunneling through quantum dot stacks

The impact of electron-phonon interaction on the coherent transport through a quantum dot stack is investigated using the nonequilibrium Green’s function technique. While the main resonance is due to the alignment of the single dot levels, satellite peaks occur due to resonances with phonon replica of the bare levels. This effect is analyzed in detail and we show that the inclusion of nondiagonal self-energies leads to a significant reduction of the induced current, which is interpreted as an interference effect.

Figure 1

(Color online) Scheme of the conduction band edge of the quantum dot stack connected to an emitter and collector contact with Fermi levels ${\mu }_E$ and ${\mu }_C$, respectively.

Figure 2

Current-voltage characteristic for a quantum dot stack including phonon scattering. Parameters as in Table .

Figure 3

Phonon-induced current peak for different correlation matrix elements $M_{1212}$ calculated in SCBA (full line), with Eq. (22) (dash-dotted line), and with Eq. (26) (dotted line). Other parameters as in Table .

Figure 4

Phonon-induced current peak for different contact couplings. Parameters are as in Table , unless stated otherwise. (a) Full line: ${\gamma }_E=10.5\mathrm{\mu }\mathrm{eV}$, dotted line: ${\gamma }_E=21\mathrm{\mu }\mathrm{eV}$, dashed line: ${\gamma }_E=42\mathrm{\mu }\mathrm{eV}$, dash-dotted line: ${\gamma }_E=84\mathrm{\mu }\mathrm{eV}$. (b) Full line: ${\gamma }_C=10.5\mathrm{\mu }\mathrm{eV}$, dotted line: ${\gamma }_C=21\mathrm{\mu }\mathrm{eV}$, dashed line: ${\gamma }_C=42\mathrm{\mu }\mathrm{eV}$, dash-dotted line: ${\gamma }_C=84\mathrm{\mu }\mathrm{eV}$.

Figure 5

(a) Logarithmic plot of spectral function $A_{22}\left(E\right)=-2\mathrm{Im}\left\{G_{22}^{\mathrm{ret}}\right(E\left)\right\}$ in 1BA (only local scattering) for parameters from Table in the energy range around $E_1\approx E_2+E_{\mathrm{ph}}$ for a range of bias $V$. (b) Real parts of the two poles of $G^{\mathrm{ret}}$ corresponding to the level $E_1$ and the induced level $E_2+E_{\mathrm{ph}}$.

Figure 6

(a) Logarithmic plot of spectral function $A_{22}\left(E\right)$ in 1BA with parameters from Table in the energy range around $E_1\approx E_2+E_{\mathrm{ph}}$ for a range of bias $V$. Local and correlation matrix elements $M_{1111∕2222}$ and $M_{1212∕2121}$ are included. (b) Real parts of the three poles of $G^{\mathrm{ret}}$ around $E_1$.