Dynamical Coulomb Blockade as a Local Probe for Quantum Transport

Quantum fluctuations are imprinted with valuable information about transport processes. Experimental access to this information is possible, but challenging. We introduce the dynamical Coulomb blockade (DCB) as a local probe for fluctuations in a scanning tunneling microscope (STM) and show that it provides information about the conduction channels. In agreement with theoretical predictions, we find that the DCB disappears in a single-channel junction with increasing transmission following the Fano factor, analogous to what happens with shot noise. Furthermore we demonstrate local differences in the DCB expected from changes in the conduction channel configuration. Our experimental results are complemented by ab initio transport calculations that elucidate the microscopic nature of the conduction channels in our atomic-scale contacts. We conclude that probing the DCB by STM provides a technique complementary to shot noise measurements for locally resolving quantum transport characteristics.

Figure 1

(a) Schematic representation of an atomic tunnel junction in the DCB regime and corresponding energy diagram highlighting the environmental interaction. (b) Topography of a single Al adatom adsorbed on the Al(100) surface. The Al adatom is located in the lower half, in the upper part an intrinsic defect is visible. (c) Approach curve on the Al adatom with an Al tip (both in the normal conducting state) at a bias voltage well above the DCB dip. In (d) the dip in the normal conducting $dI/dV$ curve, prototypical for the DCB, is shown with a $P(E)$ fit in the low-conductance limit.

Figure 2

DCB dip as a function of junction conductance. In (a) we present $dI/dV$ data with junction conductances ranging from $0.03G_0$ up to $0.99G_0$. The data is normalized to the conductance values outside of the DCB dip. (b) The theoretical dependence based on Ref. [40]. Parameters were determined by the $P(E)$ fit in Fig. 1, the color code corresponds to (a). (c) The $dI/dV$ reduction at zero bias $\delta G(0)/G_N$ dependent on junction conductance, is plotted as blue circles for the single atom and as a yellow diamond for the dimer. We added a linear fit to the data assuming a single-channel junction ${\tau }_t={\tau }_1$, where the dip reduces in magnitude with increasing conductance as $(1-{\tau }_1)$ from its value in the tunneling limit. For comparison, a dashed line $(1-{\tau }_t/2)$ is shown, representing the behavior of a corresponding junction with two equal channels ${\tau }_1={\tau }_2={\tau }_t/2$.

Figure 3

Simulation of a single-atom Al junction based on the DFT-NEGF approach. In (a) the assumed geometry is displayed. Tip and surface are oriented in the (100) direction. (b) The obtained approach curve. The total transmission ${\tau }_t$ is determined to excellent approximation by the transmission of the first channel ${\tau }_1$. Transmissions of channels two ${\tau }_2$ and three ${\tau }_3$ are about 2 orders of magnitude reduced in comparison to those of channel one. In (c) the calculated wave functions of channels 1, 2, and 3 are shown, impinging on the junction from the sample at $0.58G_0$. Colors encode the phase of the complex-valued channel wave functions, while identical absolute values are visualized through the isosurface.

Figure 4

Transport through a dimer on the substrate surface. (a) Topography of the dimer. (b) Comparison of experimentally determined transport through a monomer on the substrate surface to transport through a dimer. The DCB dip on the dimer is significantly stronger than those on the monomer at a similar total conductance of $0.58G_0$. (c) Calculated wave functions and channel transmissions for the surface dimer for electrons entering from the substrate, at a total transmission corresponding to the experimental conductance in (b). Tip and surface are oriented along the (100) direction. The representation of the transmission channel wave functions is identical to Fig. 3.

Figure 5

Temperature range, where the DCB effect is detectable in the STM. (a) Measurement of the DCB dip at about 1.32 K, where it is still accessible with our junction capacitance of 21.7 fF. The orange line models the data based on the $P(E)$ function, using the same values as for the low-temperature data, only adjusting $T$. (b) Calculated values of $\delta G(0)/G_N$ for a range of $C_J$ and $T$ (10 mK to 1.5 K) predict that clear changes of the DCB should be observable even above 1 K.