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Register a new userMagnetic field effects on the finite-frequency noise and ac conductance of a Kondo quantum dot out of equilibrium
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We present analytic results for the finite-frequency current noise and the nonequilibrium ac conductance for a Kondo quantum dot in presence of a magnetic field. Using the real-time renormalization group method, we determine the line shape close to resonances and show that while all resonances in the ac conductance are broadened by the transverse spin relaxation rate, the noise at finite field additionally involves the longitudinal rate as well as sharp kinks resulting in singular derivatives. Our results provide a consistent theoretical description of recent experimental data for the emission noise at zero magnetic field, and we propose the extension to finite field for which we present a detailed prediction.
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We present a detailed study for the finite-frequency current noise of a Kondo quantum dot in presence of a magnetic field by using a recently developed real time functional renormalization group approach [Phys. Rev. B $mathbf{83}$, 201303(R) (2011)]. The scaling equations are modified in an external magnetic field; the couplings and non-local current vertices become strongly anisotropic, and develop new singularities. Consequently, in addition to the natural emission threshold frequency, $hbaromega = |eV|$, a corresponding singular behavior is found to emerge in the noise spectrum at frequencies $hbar omega approx |eVpm B|$. The predicted singularities are measurable with present-day experimental techniques.
We present here the details of a method [A. B. Culver and N. Andrei, Phys. Rev. B 103, L201103 (2021)] for calculating the time-dependent many-body wavefunction that follows a local quench. We apply the method to the voltage-driven nonequilibrium Kondo model to find the exact time-evolving wavefunction following a quench where the dot is suddenly attached to the leads at $t=0$. The method, which does not use Bethe ansatz, also works in other quantum impurity models and may be of wider applicability. We show that the long-time limit (with the system size taken to infinity first) of the time-evolving wavefunction of the Kondo model is a current-carrying nonequilibrium steady state that satisfies the Lippmann-Schwinger equation. We show that the electric current in the time-evolving wavefunction is given by a series expression that can be expanded either in weak coupling or in strong coupling, converging to all orders in the steady-state limit in either case. The series agrees to leading order with known results in the well-studied regime of weak antiferromagnetic coupling and also reveals a universal regime of strong ferromagnetic coupling with Kondo temperature $T_K^{(F)} = D e^{-frac{3pi^2}{8} rho |J|}$ ($J<0$, $rho|J|toinfty$). In this regime, the differential conductance $dI/dV$ reaches the unitarity limit $2e^2/h$ asymptotically at large voltage or temperature.
We calculate the current and differential conductance for the junction between a superconducting (SC) STM tip and a Luttinger liquid (LL). For an infinite single-channel LL, the SC coherence peaks are preserved in the tunneling conductance for interactions weaker than a critical value, while for strong interactions (g <0.38), they disappear and are replaced by cusp-like features. For a finite-size wire in contact with non-interacting leads, we find however that the peaks are restored even for extremely strong interactions. In the presence of a source-drain voltage the peaks/cusps split, and the split is equal to the voltage. At zero temperature, even very strong interactions do not smear the two peaks into a broader one; this implies that the recent experiments of Y.-F. Chen et. al. (Phys. Rev. Lett. 102, 036804 (2009)) do not rule out the existence of strong interactions in carbon nanotubes.
A study of the conductance noise in a two-dimensional electron system (2DES) in Si at low temperatures (T) reveals the onset of large, non-Gaussian noise after cooling from an equilibrium state at a high T with a fixed carrier density n_s. This behavior, which signifies the falling out of equilibrium of the 2DES as T->0, is observed for n_s<n_g (n_g - glass transition density). A protocol where density is changed by a small value Delta n_s at low T produces the same results for the noise power spectra. However, a detailed analysis of the non-Gaussian probability density functions (PDFs) of the fluctuations reveals that Delta n_s has a qualitatively different and more dramatic effect than Delta T, suggesting that Delta n_s induces strong changes in the free energy landscape of the system as a result of Coulomb interactions. The results from a third, waiting-time (t_w) protocol, where n_s is changed temporarily during t_w by a large amount, demonstrate that non-Gaussian PDFs exhibit history dependence and an evolution towards a Gaussian distribution as the system ages and slowly approaches equilibrium. By calculating the power spectra and higher-order statistics for the noise measured over a wide range of the applied voltage bias, it is established that the non-Gaussian noise is observed in the regime of Ohmic or linear response, i.e. that it is not caused by the applied bias.
Recent experiments have measured the signatures of the Kondo effect in the zero-field thermopower of strongly correlated quantum dots [Svilans {em et al.,} Phys. Rev. Lett. {bf 121}, 206801 (2018); Dutta {em et al.,} Nano Lett. {bf 19}, 506 (2019)]. They confirm the predicted Kondo-induced sign change in the thermopower, upon increasing the temperature through a gate-voltage dependent value $T_{1}gtrsim T_{rm K}$, where $T_{rm K}$ is the Kondo temperature. Here, we use the numerical renormalization group (NRG) method to investigate the effect of a finite magnetic field $B$ on the thermopower of such quantum dots. We show that, for fields $B$ exceeding a gate-voltage dependent value $B_{0}$, an additional sign change takes place in the Kondo regime at a temperature $T_{0}(Bgeq B_{0})>0$ with $T_0<T_1$. The field $B_{0}$ is comparable to, but larger than, the field $B_{c}$ at which the zero-temperature spectral function splits in a magnetic field. The validity of the NRG results for $B_{0}$ are checked by comparison with asymptotically exact higher-order Fermi-liquid calculations [Oguri {em et al.,} Phys. Rev. B {bf 97}, 035435 (2018)]. Our calculations clarify the field-dependent signatures of the Kondo effect in the thermopower of Kondo-correlated quantum dots and explain the recently measured trends in the $B$-field dependence of the thermoelectric response of such systems [Svilans {em et al.,} Phys. Rev. Lett. {bf 121}, 206801 (2018)].
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