Non-Fermi-liquid behavior in nonequilibrium transport through Co-doped Au chains connected to fourfold symmetric leads

We calculate the differential conductance as a function of temperature and bias voltage, $G(T,V)$, through Au monatomic chains with a substitutional Co atom as a magnetic impurity, connected to a fourfold symmetric lead. The system was recently proposed as a possible scenario for observation of the overscreened Kondo physics. Stretching the chain, the system could be tuned through a quantum critical point (QCP) with three different regimes: overscreened, underscreened, and non-Kondo phases. We present calculations of the impurity spectral function by using the numerical renormalization group for the three different regimes characterizing the QCP. Nontrivial behavior of the spectral function is reported near the QCP. Comparison with results using the noncrossing approximation (NCA) shows that the latter is reliable in the overscreened regime, when the anisotropy is larger than the Kondo temperature. For these parameters, which correspond to realistic previous estimates, $G(T,V)$ calculated within NCA exhibits clear signatures of the non-Fermi-liquid behavior within the overscreened regime.

Figure 1

Sketch of the pure chain with (a) a substitutional Co and (b) a trimer connected to a fourfold symmetric axis leads.

Figure 2

Spectral density of the Co atom as a function of frequency in a logarithmic scale for different values of $D$ (NRG). The upper and lower panels show the data for positive and negative $\omega$, respectively. The arrows stand for the charge transfer energy $E_{32}$ and the anisotropy $D$.

Figure 3

Analysis of the low-energy scale $T^{*}$ extracted from the NRG data (using even iterations $n$, with similar data and conclusions for odd iterations [not shown]). For the determination of $T^{*}$, the exponential convergence of the rescaled and iteratively subtracted ground-state energy $E_0^{\left(n\right)}$ at iteration $n$ deep into the low-energy fixed point was extrapolated towards larger energies (smaller $n)$, such that $\Delta {\tilde{E}}_0^{\left(n^{*}\right)}:=1$ (in rescaled energies) with $\Delta {\tilde{E}}_0^{\left(n\right)}$ the plain exponential fit to $|E_0^{\left(n\right)}-E_0^{\left(\infty \right)}|<0.01$. With this, the low energy scale $T^{*}:={\Lambda }^{-n^{*}/2}$ was determined individually for each value of the anisotropy $D$. Finally, the fit to the analytical expression for $T^{*}$ was carried out for $x>3$ (indicated by the vertical dotted line), i.e., $D<0.11T_K$.

Figure 4

Spectral density per channel and spin for different values of the ratio $D/T_K$ (NRG).

Figure 5

Spectral density per channel and spin for different negative values of the ratio $D/T_K$ (NRG).

Figure 6

NCA impurity contribution to the entropy (at equilibrium) as a function of temperature for $D=0$ and $D=\pm 0.0017$ eV. Energies are given in units of the half bandwidth $W$.

Figure 7

NCA spectral density per channel and spin for different values of the ratio $D/T_K$ at equilibrium.

Figure 8

Total differential conductance as a function of the bias voltage for several values of temperature. The model parameters correspond to the real configuration of the trimer sketched in Fig. 1 with the parameters given in the text. Temperatures are given in units of meV.

Figure 9

Scaling plot of the differential conductance $G(T,V)$ for different values of the ratio $r=D/T_K^{D=0}$ at a very low temperature, $T=0.001T_K$. Parameters are $W=1,E_{32}=-0.67,\Delta =0.225$. Here we define $T_K$, for each set, from the half width at the half maximum of the Kondo resonance of the spectral function at equilibrium. The red dashed line indicates the limiting behavior of Eq. (20) for large $x$.

Figure 10

Differential conductance $G(T,V)$ for different temperatures in units of the Kondo temperature $T_K\sim 0.8$ meV given by the NCA for parameters corresponding to the trimer configuration, for which the anisotropy was found to be $D\sim 1.7$ meV.