Anomalous Conductance of a Spin-1 Quantum Dot

We interpret the recent observation of a zero-bias anomaly in spin-1 quantum dots in terms of an underscreened Kondo effect. Although spin-1 quantum dots are expected to undergo a two-stage quenching effect, in practice the log-normal distribution of Kondo temperatures leads to a broad temperature region dominated by underscreened Kondo physics. General arguments, based on the asymptotic decoupling between the partially screened moment and the leads, predict a singular temperature and voltage dependence of the conductance $G$ and differential conductance $g$, resulting in $dg/dT\sim 1/T$ and $dG/dV\sim 1/V$. Using a Schwinger boson approach, we show how these qualitative expectations are borne out in a detailed many body calculation.

Figure 1

The noncrossing approximation for the self-energies of conduction electrons and $\chi$ fermions. The solid line denotes the Larkin Ovchinnikov matrix propagator for the conduction electrons. The dashed line denotes the corresponding Green’s function of the auxiliary ($\chi$) fermions and the wavy line is the bosonic propagator. Thin lines denote the bare propagator and full lines the dressed propagator. Each vertex corresponds to the factor $\frac{\tilde{t}}{\sqrt{N}}$.

Figure 2

Imaginary part of dot $t$ matrix for a variety of voltages for the case $k=0.4$. As the voltage is increased, the singular central peak splits into two components.

Figure 3

Temperature dependence of the differential conductance, normalized with respect to $g_U=N\frac{e^2}{h}\mathrm{s}\mathrm{i}{\mathrm{n}}^2(\pi k)$ for the representative case $k=0.4$. Inset shows the $1/T$ divergence of the derivative $dg/dT$.

Figure 4

Voltage dependent conductance $G(V)=I(V)/V$ for the case $k=0.4$. Inset: derivative of $G(V)$ showing $1/V$ divergence.