Nonequilibrium frequency-dependent noise through a quantum dot: A real-time functional renormalization group approach

We construct a real time current-conserving functional renormalization group (RG) scheme on the Keldysh contour to study frequency-dependent transport and noise through a quantum dot in the local moment regime. We find that the current vertex develops a nontrivial nonlocal structure in time that is governed by a new set of RG equations. Solving these RG equations, we compute the complete frequency and temperature dependence of the noise spectrum. For voltages that are large compared to the Kondo temperature (i.e., $\mathit{eV}\gg k_B{T}_K$), two sharp antiresonances are found in the noise spectrum at frequencies $\hslash \omega =\pm eV$ and, correspondingly, two Kondo-assisted peaks appear in the ac conductance through the dot.

Figure 1

Voltage dependence of the symmetric noise as computed by FRG for $\hslash \omega =30k_B{T}_K$.

Figure 2

Voltage and temperature dependence of the emission noise as computed through FRG for $\hslash \omega =5k_B{T}_K$.

Figure 3

Temperature dependence of the symmetric noise, as computed by FRG for $T_K=6.3\times {10}^{-5}\hslash /a_0$. Inset: Comparison with third-order bare perturbation theory (PT) and renormalized perturbation theory (RPT) using a reduced cutoff, $\mathrm{ã}=\hslash /(10\mathit{eV})$ and the corresponding couplings $j_{\mathit{LR}}(\mathrm{ã})$ and effective second-order perturbation theory (EPT) with renormalized couplings $j_{\mathit{LR}}(\mathrm{ã}=\hslash /(\mathit{eV}))$, but still using the original bandwidth. None of these methods are able to get close to the FRG results.

Figure 4

Ac conductance for $\omega >0$ and $T=0$.