Electron Phase Shift at the Zero-Bias Anomaly of Quantum Point Contacts

The Kondo effect is the many-body screening of a local spin by a cloud of electrons at very low temperature. It has been proposed as an explanation of the zero-bias anomaly in quantum point contacts where interactions drive a spontaneous charge localization. However, the Kondo origin of this anomaly remains under debate, and additional experimental evidence is necessary. Here we report on the first phase-sensitive measurement of the zero-bias anomaly in quantum point contacts using a scanning gate microscope to create an electronic interferometer. We observe an abrupt shift of the interference fringes by half a period in the bias range of the zero-bias anomaly, a behavior which cannot be reproduced by single-particle models. We instead relate it to the phase shift experienced by electrons scattering off a Kondo system. Our experiment therefore provides new evidence of this many-body effect in quantum point contacts.

Figure 1

(a) QPC conductance versus gate voltage at 30 mK (different cool down than other figures). Inset: image of the metallic split gate. (b) Differential conductance versus source-drain bias at 25 mK and different gate voltages. (c) Temperature dependence of the 0.7 anomaly from 50 to 900 mK. (d) Temperature dependence of the ZBA from 25 to 870 mK.

Figure 2

(a) Principle of scanning gate interferometry. (b) Potential landscape created by the split gate and the tip. (c) SGM image of the conductance at 25 mK when the QPC is tuned to the first conductance plateau. The QPC center is located at the coordinates ($-500\mathrm{nm}$, 650 nm).

Figure 3

(a) Interference fringes along line 1 [Fig. 2] versus source-drain bias at $-0.67\mathrm{V}$ gate voltage in (b). The conductance is differentiated with respect to tip position. Top panel: conductance curve for the tip position indicated by the arrow. Right panel: 3D plot showing the position of the phase shift at the bottom of the zero-bias peak. (b) Interference fringes along the same line versus gate voltage (at zero bias). The pinch-off voltage is shifted by 40 mV in the presence of the polarized tip with respect to Fig. 1. Top panel: conductance curve for the tip position indicated by the arrow. Right panel: 3D plot showing the position of the phase shift at the border of the plateau.

Figure 4

(a) Interference fringes along line 1 on the plateau (first panel) and below the plateau (second panel) at respectively $-0.65\mathrm{V}$ and $-0.67\mathrm{V}$ gate voltages in Fig. 3. Third panel: conductance curve at the tip position of the arrow, below the plateau (red curve) and on the plateau (blue curve). Bottom panel: the phase of the fringes exhibits a shift in the bias range of the ZBA (red curve) and evolves linearly on the plateau (blue curve). (b) Interference fringes along line 2 at a gate voltage below the plateau at 760 mK (first panel) and 25 mK (second panel). Third panel: conductance curve at the tip position of the arrow, at 25, 240, 440, and 760 mK from top to bottom. Bottom panel: phase of the fringes at the same temperatures.

Figure 5

(a) Interference fringes when the tip is scanned along line 3. Bottom panel: average conductance curve (blue) and phase of the fringes (red) showing a shift by $\pi$ within the ZBA. (b) Model of the SGM-based interferometry experiment where the QPC is represented by an asymmetric QD. Bottom panel: conductance in the symmetric case (blue) and phase of the interference fringes versus energy, for different asymmetries of the tunneling rates ${\mathrm{\Gamma }}_L$ and ${\mathrm{\Gamma }}_R$ (red to yellow). Central panel: tip-induced interference fringes for the asymmetry of the red curve.