Finite-frequency noise properties of the nonequilibrium Anderson impurity model

We analyze the spectrum of the electric-current autocorrelation function (noise power) in the Anderson impurity model biased by a finite transport voltage. Special emphasis is placed on the interplay of nonequilibrium effects and electron-electron interactions. Analytic results are presented for a perturbation expansion in the interaction strength $U$. Compared to the noninteracting setup we find a suppression of noise for finite frequencies in equilibrium and an amplification in nonequilibrium. Furthermore, we use a diagrammatic resummation scheme to obtain nonperturbative results in the regime of intermediate $U$. At finite voltage, the noise spectrum shows sharp peaks at positions related to the Kondo temperature instead of the voltage.

Figure 1

Unsymmetrized noise spectrum for the noninteracting case. The negative/positive $\omega$ part can be interpreted as emission/absorption of energy by the system to/from the environment. Steps emerge whenever the energy $\omega$ of a fluctuation is about $\pm V/2\pm \Delta$. The inset shows the symmetrized spectrum for the same parameters.

Figure 2

Diagrammatic representation of the parallel-spin current correlations in the second-order perturbation theory for the electron-hole symmetric case. All arrows represent nonequilibrium Keldysh GF exact in the $U=0$ model. The wiggly line represents instantaneous Coulomb interaction. Dashed green arrows describe particles with the opposite spin of the solid black ones. $t$ and 0 label the two external points of the currents in Eq. (2). Information about Keldysh indices and lead affiliation (especially if of the homogeneous or inhomogeneous kind) of the GF are omitted.

Figure 3

Diagrammatic representation of the antiparallel-spin current correlations in the second-order perturbation theory for the electron-hole symmetric case.

Figure 4

Correction to the noise spectrum in the second-order perturbation theory in the resonant configuration $\Delta =-U/2$ in units of $U^2$.

Figure 5

Reduction of the noise to the two-particle GF $\Gamma$. A distinction between correlations of antiparallel-spin particles and of parallel-spin particles has to be made but was omitted in this figure. To express the noise in this way one needs two free lead GF $g_{L/R}$ expressed by the dotted arrows.

Figure 6

The complete summation over all diagrams that contribute to $\Gamma$ in our approximation. All arrows in this case represent the dot GF $D_0$ of the $U=0$ model which is exact in tunneling. Every second diagram is for antiparallel-spin current correlations.

Figure 7

Interaction correction to the noise. The interaction strength is set to $U=0.99$ where ${\Gamma }^{klmn}$ is regular. The $V=0$ curve is enlarged by a factor of 10.

Figure 8

Interaction correction to the noise with $U=1.5$ in the nonregular regime of ${\Gamma }^{klmn}$. The $V=0$ curve is enlarged by a factor of 10.

Figure 9

The full noise power for $V=4$ and different interaction strengths calculated with the diagrammatic resummation scheme. For $U=0$ one recovers the step structure.

Figure 10

Position of the peaks in the noise spectrum for $V=20$ and various values of $U$. The black line shows a $\sqrt{U}$ behavior.