Microscopic Theory for the 0.7 Anomaly in Quantum Point Contacts - the Role of Geometry- and Interaction-Enhanced Spin-Fluctuations

We present a detailed microscopic analysis of some local observables of a quantum point contact (QPC) to gain better understanding of the origin of the 0.7 conductance anomaly. We model the system by a one-dimensional tight binding model with local interactions, a smooth potential barrier and a homogeneous magnetic field. We calculate conductance $G$, local density $n$ and local magnetization $m$ as a function of magnetic field at zero temperature, using the functional Renormalization Group (fRG). Our potential can be tuned to describe the smooth crossover from a single barrier, representing a QPC, to a double barrier, modelling a quantum dot (QD) exhibiting the Kondo effect. We find that both geometries show interaction-enhanced spin-fluctuations, manifested via an enhanced local spin susceptibility, for gate voltages that lead to an anomalously large negative magnetoconductance, characterized by an anomalously small low-energy scale $B_*$. This finding explains why both the Kondo effect and the 0.7-anomaly exhibit a very similar conductance behavior at sufficiently low magnetic fields and temperatures ($T,B \ll T_*$), amenable to a similar Fermi-liquid description. We also show that at high fields ($B \gg B_*$) the analogy between Kondo effect and 0.7-anomaly breaks down.