Gate-Voltage-Driven Quantum Phase Transition at $0.7 (2e^2/h)$ in Quantum Point Contacts

Abstract: The complex gate-voltage-dependent differential conductance in quantum point contacts, shaped by entangled-state tunneling, was demonstrated through the movement of a localized spin. This spin responds to variations in side gate voltage, triggering a quantum phase transition (QPT) between symmetric and asymmetric Kondo coupling states, with the states separated by conductance regions $G \geq 0.7 G_0$ and $G \leq 0.7 G_0$, where $G_0 = 2e^2/h$, respectively. The asymmetric state has two Kondo temperatures, while the symmetric state has only one. The presence of two Kondo temperatures in the asymmetric state clarifies previously unresolved issues, such as the indeterminate Kondo temperature and anomalous behavior in the width of the zero-bias anomaly (ZBA) in the $G \leq 0.7 G_0$ region. The QPT was investigated by analyzing the gate-voltage-dependent ZBA energy, calculated using the corresponding local density of states at the site of the localized spin, obtained during the replication of the differential conductance.