Experimental Test of the Dynamical Coulomb Blockade Theory for Short Coherent Conductors

We observed the recently predicted quantum suppression of dynamical Coulomb blockade on short coherent conductors by measuring the conductance of a quantum point contact embedded in a tunable on-chip circuit. Taking advantage of the circuit modularity we measured most parameters used by the theory. This allowed us to perform a reliable and quantitative experimental test of the theory. Dynamical Coulomb blockade corrections, probed up to the second conductance plateau of the quantum point contact, are found to be accurately normalized by the same Fano factor as quantum shot noise, in excellent agreement with the theoretical predictions.

Figure 1

(a) $E$-beam micrograph of the sample tailored in a $\mathrm{GaAs}/\mathrm{Ga}(\mathrm{Al})\mathrm{As}$ heterojunction. The 2DEG is patterned by chemical etching, etched areas are darker. Active top metal gates are colorized in the lighter gray. Electrode labels $S$, $D$ and SC stand, respectively, for source, drain and short circuit. (b) Magnified view of the metallic split gate used to tune the QPC. (c) Schematic representation of the sample.

Figure 2

Resistance variation $\delta R$ of the QPC in series with the on-chip resistance $R_S=1.2\mathrm{k}\Omega$ (▪) or $R_S=7\mathrm{k}\Omega$ (□) plotted versus the voltage $V_{\mathrm{SC}}$ that controls the high frequency short circuit (SC) switch [see Fig. 1c]. For $V_{\mathrm{SC}}<-0.3\mathrm{V}$ the SC switch is open and $\delta R$ exhibits a linear dependence with $V_{\mathrm{SC}}$ due to the direct capacitive cross talk with the QPC. The DCB signal $\delta R_{\mathrm{DCB}}$ is the difference between the resistance measured at $V_{\mathrm{SC}}\simeq 0$ (SC switch closed) and the resistance measured for an open SC switch taking into account the linear capacitive contribution (dashed line).

Figure 3

Measured temperature dependence of relative DCB corrections $G_{\mathrm{QPC}}\delta R_{\mathrm{DCB}}$ at $G_{\mathrm{QPC}}=0.33G_Q$ and $B=0.2\mathrm{T}$, for $R_S=1.2\mathrm{k}\Omega$ (▪) and $R_S=7\mathrm{k}\Omega$ (□). Predictions of the DCB theory are shown as continuous lines. The only fit parameter in the calculation is the high frequency residual resistance of the short circuit path $R_{\mathrm{SC}}=1\mathrm{k}\Omega$ (see text).

Figure 4

Measured relative DCB corrections (▪) plotted versus the QPC conductance. The continuous line is the predicted reduction by the Fano factor $F=\sum _n{\tau }_n(1-{\tau }_n)/\sum _n{\tau }_n$. Inset: Measured QPC conductance (□) plotted versus the split gate bias voltage $V_{\mathrm{QPC}}$. The best fit using a quadratic confinement potential [14] is shown as a continuous line.