Observation of the Underscreened Kondo Effect in a Molecular Transistor

We present the first quantitative experimental evidence for the underscreened Kondo effect, an incomplete compensation of a quantized magnetic moment by conduction electrons, as originally proposed by Nozières and Blandin. The device consists of an even charge spin $S=1$ molecular quantum dot, obtained by electromigration of ${\mathrm{C}}_{60}$ molecules into gold nanogaps and operated in a dilution fridge. The persistence of logarithmic singularities in the low temperature conductance is demonstrated by a comparison to the fully screened configuration obtained in odd charge spin $S=1/2$ Coulomb diamonds. We also discover an extreme sensitivity of the underscreened Kondo resonance to the magnetic field that we confirm on the basis of numerical renormalization group calculations.

Figure 1

(a) Summary of the different types of Kondo effects according to impurity spin $S$ and number of screening channels $n_{\mathrm{sc}}$. (b) Tunneling model of our single molecule transistor: two orbital levels couple to two leads. (c) Conductance map of sample $A$ recorded at $T=35\mathrm{mK}$. Dashed lines are positioned at the gate voltages where more detailed studies where performed. (d) Conductance map for sample $B$. (e) Zoom inside the dotted rectangle defined in the even diamond of sample $A$. The white arrows represent the singlet-triplet splitting in both samples.

Figure 2

(a) Derivative of the conductance versus temperature recorded at gate $V_g=2.17\mathrm{V}$ and bias $V_b=0\mathrm{V}$ in the even Coulomb diamond of sample $A$ (same data on a log scale in the inset, showing two distinct $1/T$ behaviors). The best fit is obtained for an underscreened Kondo model (solid line) and gives $G_0=0.14$ (in units of $2e^2/h$) and $T_K=1.1\mathrm{K}$. (b) Derivative of the conductance versus temperature recorded at $V_g=1.2\mathrm{V}$ and $V_b=0\mathrm{V}$ in the odd Coulomb diamond. The best fit is obtained for a fully screened Kondo model (dashed line) and gives $G_0=0.34$ and $T_K=4.4\mathrm{K}$. (c) Conductance data of (a) and (b) compared to the relevant NRG curves. The background was adjusted to follow the convention $G(T_K)=G_0/2$, giving $G_{\mathrm{bg}}=0.055$ in the fully screened case and $G_{\mathrm{bg}}=0.022$ in the underscreened case. (d) Differential conductance at the base temperature rescaled in universal form, with $G_0^{\prime }=G(T_{\mathrm{base}})$ and $G_{\mathrm{bg}}^{\prime }$ such that the conductance is $G_0^{\prime }/2$ at $e{V}_b=k_B{T}_K$.

Figure 3

(a), (b) Differential conductance versus bias voltage and magnetic field for sample $B$ in the odd and even diamonds (lines are linear fits to the $B$ dependence of the Zeeman peaks of sample $B$). (c) Positions of the Zeeman peaks of both samples and odd (even) diamonds as extracted from above. Linear fits provide the critical field $B_c$ by extrapolation to zero bias. Both bias voltage and magnetic field were renormalized by $T_K$ deduced from the HWHM at $B=0\mathrm{T}$ for each case. (d), (e) NRG calculations of the energy $E$ dependent equilibrium local density of states $A(E,B,T=0)$ at zero temperature, normalized to its $E=B=0$ value, for the spin $S=1/2$ and $S=1$ single-channel Kondo models and magnetic field values $g{\mu }_{B}B/k_B{T}_K=0$, $1/8$, $1/4$, $1/2$, and 1 (top to bottom).