Single-Electron-Phonon Interaction in a Suspended Quantum Dot Phonon Cavity

An electron-phonon cavity consisting of a quantum dot embedded in a freestanding $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ membrane is characterized using Coulomb blockade measurements at low temperatures. We find a complete suppression of single electron tunneling around zero bias leading to the formation of an energy gap in the transport spectrum. The observed effect is induced by the excitation of a localized phonon mode confined in the cavity. This phonon blockade of transport is lifted at discrete magnetic fields where higher electronic states with nonzero angular momentum are brought into resonance with the phonon energy.

Figure 1

(a) Suspended quantum dot cavity and in-plane gate formed in the 130 nm thin $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ membrane. The inset shows the blocked differential conductance in the linear transport regime. (b) Level diagrams for single electron tunneling including phonon blockade: (i) In the orthodox model electrons sequentially tunnel through the dot, if the chemical potential $\mu (N+1)$ is aligned between the reservoirs. (ii) Tunneling into the phonon cavity results in the excitation of a cavity phonon with energy $\hslash {\Omega }_{\mathrm{p}\mathrm{h}}$, leading to a level mismatch ${ϵ}_0$ and thus to phonon blockade. (iii) Single electron tunneling is reestablished by a resonant higher electronic state ${\mu }^{*}(N+1)$ which is enabled to coherently reabsorb the phonon and to hereby replace the ground state.

Figure 2

Transport spectrum of the suspended quantum dot and conductance near zero bias: (a) Single electron resonances taken at an electron temperature of 100 mK and a perpendicular magnetic field of 500 mT. (b) At zero magnetic field conductance is suppressed for bias voltages below $100\mu \mathrm{V}$ due to phonon excitation. (c) The conductance pattern at 350 mK shows that phonon blockade starts to be surpassed because of thermal broadening of the Fermi function supplying empty states in the reservoirs.

Figure 3

Transport spectrum for (a) $B=0$, (b) 170, (c) 260, and (d) 450 mT. The line plots give the conductance near zero bias. At certain magnetic fields (b),(d) excited quantum dot states with higher magnetic momentum are brought into resonance with the cavity phonon reenabling single electron tunneling. Otherwise (a),(c) transport is suppressed due to phonon blockade with an excitation barrier of around $100\mu \mathrm{e}\mathrm{V}$.

Figure 4

(a) Line plot of conductance resonances $\alpha$ and $\beta$ at different source drain bias voltages between 0 and $-800\mu \mathrm{V}$. Ground and excited states are marked by lines. The conductance at $V_{\mathrm{s}\mathrm{d}}\approx 0\mu \mathrm{V}$ is suppressed. (b) Conductance near zero bias for resonance $\alpha$ plotted against gate voltage $V_{\mathrm{g}}$ and magnetic field $B$. Finite conductance appears for 57, 170, and 400 mT. (c) Similar plot for resonance $\beta$. Nonzero conductance is found for 230 and 510 mT.