Theory of frequency-dependent spin current noise through correlated quantum dots

We analyze the equilibrium and nonequilibrium frequency-dependent spin current noise and spin conductance through a quantum dot in the local moment regime. Spin current correlations are shown to behave markedly differently from charge correlations: Equilibrium spin crosscorrelations are suppressed at frequencies below the Kondo scale and are characterized by a universal function that we determine numerically for $T=0$ temperature. For asymmetrical quantum dots dynamical spin accumulation resonance is found at the Kondo energy, $\omega \sim T_K$. At higher temperatures surprising low-frequency anomalies related to overall spin conservation appear.

Figure 1

(Color online) Zero-temperature universal functions $s$ and $\tilde{s}$ computed by NRG. Inset: universal spin-conductance functions $g$ and $\tilde{g}$.

Figure 2

Diagrams contributing to the noise. The reduced density matrix of the spin evolves along the upper and lower Keldysh contours. Triangles denote the bare current vertices and dots indicate the exchange interaction. Arrows correspond to conduction electron propagators. To leading order, the current-current correlation function is given by the connected diagrams (top), $S_{\text{conn}}\left(\omega \right)$, and the “disconnected” diagrams (second line), $S_{\text{disc}}\left(\omega \right)$, with $\Pi$ the propagator describing the evolution of the reduced density matrix of the spin (third line). The dressed current vertex $W_{r\sigma }$ is given by diagrams similar to those of the self-energy, $\Sigma$ (last line), with one of the dots replaced by a triangle.

Figure 3

(Color online) Top: sketch of consecutive spin-flip processes. Bottom: equilibrium and nonequilibrium noise spectra $S_{LR}^{\sigma {\sigma }^{\prime }}\left(\omega \right)$ in the perturbative regime, $\text{max}\left\{T,\omega ,E_K\right\}>T_K$, as computed from a diagrammatic approach. In the nonequilibrium case a simple current bias was assumed, $V_L^{\sigma }\equiv V$ and $V_R^{\sigma }\equiv 0$, while $j=0.07$ and $\varphi =\pi /2$ in both cases.