Scanning tunneling shot-noise spectroscopy in Kondo systems

Using a large-$N$ theory in combination with the Keldysh nonequilibrium Green's function formalism, we investigate the current, differential conductance, zero-frequency shot noise, and Fano factor as measured by scanning tunneling shot-noise spectroscopy (STSNS) using a scanning tunneling microscope (STM) near single Kondo impurities and in Kondo lattices. We show that the Fano factor $F$ exhibits a characteristic bias dependence arising from Kondo screening that is similar to the Kondo resonance observed in the differential conductance. Moreover, the line shape of $F$ is strongly dependent on the ratio of the tunneling amplitudes for electron tunneling from the STM tip into the conduction band and electronic levels of the magnetic adatoms. We demonstrate that the Fano factor can be enhanced or suppressed due to interference effects and as such, is not only a sensitive probe for the correlation effects arising from Kondo screening, but also for quantum interference between tunneling electrons. We identify a correlation between the form of the differential conductance and the Fano factor that could be tested in future STSNS experiments.

Figure 1

Paths of electrons tunneling from the STM tip either into the conduction-band sites (grey spheres) or into the magnetic level of the Kondo impurity (green sphere), with tunneling amplitudes $t_c$ and $t_f$, respectively.

Figure 2

(a) $dI/dV$, (b) current $I$, (c) noise $S_0$, and (d) Fano factor $F$ for two different values of $t_f/t_c=-0.066$ and $t_f/t_c=0.01$, as well as away from the Kondo impurity at $r=\infty$. Results are shown for zero temperature.

Figure 3

The three contributions to the total current from the weak-tunneling limit of Eq. (7) which are proportional to $t_c^2,t_f^2$, and $2t_c{t}_f$ for (a) $t_f/t_c=-0.066$, and (b) $t_f/t_c=+0.01$.

Figure 4

Evolution of the Fano factor $F$ with increasing $t_c$ for (a) $t_f/t_c=-0.066$, and (b) $t_f/t_c=0.01$.

Figure 5

(a) Line cut of $F$ through the site the magnetic adatom for $t_c=0.1\mathrm{eV},V=5\mathrm{mV}$, and $t_f/t_c=-0.066$. (b) Spatial plot of $F$.

Figure 6

Comparison of the zero-frequency noise, $S(\omega =0)$, at $T=0$ and $T=4\text{K}$ for $t_c=0.1\mathrm{eV}$ and (a) $t_f/tc=-0.066$, and (b) $t_f/tc=0.01$ (note the different $x$- and $y$-axis scales). Temperature evolution of the Fano factor for $t_c=0.1\mathrm{eV}$ and (c) $t_f/tc=-0.066$, and (d) $t_f/tc=0.01$.

Figure 7

The dispersions $E_{\mathbf{k}}^{\pm }$ from Eq. (14) along $(0,0)\to (\pi ,\pi )$ with $t=500\text{meV},\mu =-3.618t,N=2,J=500\mathrm{meV},N_t=1{\text{eV}}^{-1}$, for (a) Kondo lattice 1 with $I/J=0.001$ yielding $s=48.5\mathrm{meV},{\varepsilon }_f=1.2\mathrm{meV}$, and ${\chi }_0=0.17\mathrm{meV}$, and (b) Kondo lattice 2 with $I/J=0.015$ yielding $s=48.0\mathrm{meV},{\varepsilon }_f=0.94\mathrm{meV}$, and ${\chi }_0=2.59\mathrm{meV}$.

Figure 8

For Kondo lattice 1, (a) $dI/dV$, (b) current, (c) noise, and (d) Fano factor with $t_c=0.1\mathrm{eV}$ and two different values of $t_f/t_c$.

Figure 9

Evolution of the Fano factor $F$ with increasing $t_c$ in Kondo lattice 1 for (a) $t_f/t_c=-0.015$, and (b) $t_f/t_c=0.015$.

Figure 10

For Kondo lattice 2, (a) $dI/dV$, (b) current, (c) noise, and (d) Fano factor with $t_c=0.1\mathrm{eV}$ and two different values of $t_f/t_c$.