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Effects of Coulomb Interaction on Photon-Assisted Current Noises

Kato Group

Photon-assisted transport through mesoscopic conductors has attracted much attention because the external fields open up additional transport channels via photon absorption and emission. It is known that nonperturbative effects of the time-dependent fields significantly modify the quantum nature of transport processes. In recent years, many studies have revealed that current noises provide significant information about the microscopic processes involved in photon-assisted transport. Photon-assisted current noise has been measured in various systems such as diffusive metals, diffusive normal metal-superconductor junctions, quantum point contacts, and tunnel junctions. Recently, the time-resolved current noise has been measured to evaluate the quantum purity of electrons emitted from on-demand electron sources. The coherent and spectroscopic nature of the photon-assisted current noise of noninteracting electrons has been studied theoretically based on the scattering approach or the Green's function approach [1,2]. These approaches are, however, of limited use to describe the effects of the Coulomb interaction.

Fig. 1 (a) The photon-assisted zero-bias noise (SLL) and the equilibrium thermal noise evaluated at the corresponding Teff are displayed as a function of ε1. Parameters are as follows: ΔL = ΔR = 1, εd = −U/2 = −1, kBT = 0.05, V = 0, and Ω = 5. The left inset: a schematic picture of the present model. The right inset: the effective temperature as a function of ε1. (b) The vertex corrections to the current noise for antiparallel spins (SLσL-σ) are displayed. Parameters are the same as (a).

We have studied photon-assisted transport in a single-level quantum dot coupled to two electrodes under a periodically oscillating field [3]. A schematic picture of our model is shown in the inset of Fig.1 (a). Hybridization between a dot and a lead is set to be unity (ΔL = ΔR = 1), and the energy level of the quantum dot is denoted with ε(t) = εd + ε1sin(Ωt). We focus on the particle symmetric case (εd = −U/2) for simplicity. Photon-assisted current noise in the presence of the Coulomb interaction has been described based on a gauge-invariant formulation of time-dependent transport. The current noises are expressed in this description by two terms, i.e., a bare part and a vertex correction. The latter contribution appears only in the presence of the Coulomb interaction, and reflects internal dynamics of the systems. We have derived the vertex corrections within the self-consistent Hartree-Fock approximation in terms the Floquet-Green's functions and have examined the effects of the Coulomb interaction on the photon-assisted current noise. Within the Hartree-Fock approximation, the vertex correction describes dynamical screening effect induced by the Coulomb interaction.

In Fig. 1(a), we show a current noise (SLL) for zero source-drain voltage bias. From Fig. 1(a), we find that as the amplitude of the oscillating field increases, the zero-bias current noise rapidly increases, and oscillates as a function of ε1 for large amplitude of the external field. This behavior is understood by considering an effective temperature defined by Teff = (SLL)V=0/4kBG (the inset of Fig.1 (a)), where is a linear conductance. We note that this definition equals the original temperature for ε1 = 0 by the dissipation-fluctuation relation, and provides a natural extension of the temperature toward nonequilibrium states. The thermal noise (Seq) estimated from the effective temperature (shown in Fig. 1(a)) qualitatively reproduces the behavior of the zero-bias current noise.

In Fig.1 (b), we show a current noise for antiparallel spins SLσL-σ as a function of the frequency. This noise always vanishes in noninteracting models, and equals the vertex correction in the presence of the Coulomb interaction. SLσL-σ is strongly frequency-dependent, and has structures at integral multiples of the driving frequency Ω in the presence of the external oscillating field. As the amplitude of the oscillating external field increases, the vertex corrections are suppressed on the whole. This suppression of the vertex corrections is understood using the effective temperature as follows. As the amplitude of the oscillating external field increases, the effective temperature rises for ε1 < 12 as shown in the inset of Fig. 1(a). The rise of the effective temperature leads to suppression of the dynamical screening effect, and weakens the current correlation with different spins. These effects are expected to be general in interacting electron systems. We note that the spin-dependent current noise SLσL-σ is appropriate for study of internal dynamics of interacting systems, and can in principle be measured using a spin filter.

Our result shows that the effect of Coulomb interaction is modified by external oscillating fields via nonequilibrium distribution functions. Our study will offer a useful viewpoint for understanding photon-assisted transport of other phenomena such as the Coulomb blockade and the Kondo effect.


References
  • [1] Ya. M. Blanter and M. Büttiker, Phys. Rep. 336, 1 (2000).
  • [2] G. H. Ding and B. Dong, Phys. Rev. B 87, 235303 (2013).
  • [3] T. J. Suzuki and T. Kato, Phys. Rev. B 91, 165302 (2015).
Authors
  • T. J. Suzuki and T. Kato