Inelastic Kondo-Andreev tunneling in a vibrating quantum dot

Abstract

Phonon-assisted electronic tunnelings through a vibrating quantum dot embedded between normal and superconducting leads are studied in the Kondo regime. In such a hybrid device, with the bias applied to the normal lead, we find a series of Kondo sidebands separated by half a phonon energy in the differential conductance, which are distinct from the phonon-assisted sidebands previously observed in the conventional Andreev tunnelings and in systems with only normal leads. These Kondo sidebands originate from the Kondo-Andreev cooperative cotunneling mediated by phonons, which exhibit a novel Kondo transport behavior due to the interplay of the Kondo effect, the Andreev tunnelings, and the mechanical vibrations. Our result could be observed in a recent experiment setup [J. Gramich et al., PRL 115, 216801 (2015)], provided that their carbon nanotube device reaches the Kondo regime at low temperatures.

Quantum transport through a quantum dot side-coupled to a Majorana bound state pair in the presence of electron-phonon interaction

“…In the absence of MBSs (|λ| = 0, shown by solid black line), the resonant peak is red-shifted at the renormalized QD energy level ε = εd = ε d -gω 0 with g = (β/ω 0 ) 2 . Beside the main peak, a series of phonon-assisted additional channels develop in the spectrum of A d (ε) [51,111,116,128]. The phonon-assisted channels manifest as satellite peaks emerging in the spectrum at energies ε = εd ± pω 0 with p an integer.…”

“…The vast majority of theoretical work in the past years focuses on the properties of phonon-assisted Andreev tunneling in N-QD-SC [111][112][113][114][115][116] or ferromagnet-QD-SC junctions [117][118][119][120][121]. The phonon-assisted Andreev tunneling was likely observed in experiments for a carbon nanotube QD coupled to NM and Nb SC leads [122].…”

Nonequilibrium Kondo effect by the equilibrium numerical renormalization group method: The hybrid Anderson model subject to a finite spin bias

“…On the other hand, the S lead influences the spin Kondo effect in a strikingly different way. It is known [63][64][65][66][67][68][69][70][71][72][73][74] that at equilibrium the increasing Γ S can drive a crossover from the spin Kondo singlet to the BCS singlet, featuring characteristic spectral evolution as follows. Two Andreev resonances, which are split from the Hubbard bands at Γ S = 0, move toward the Fermi energy and merge with the Kondo peak to produce a single resonance at ε = 0.…”

“…Remarkably, before it merges with the Andreev peaks, as Γ S increases, the nonequilibrium Kondo resonance is enhanced and its splitting shrinks [see the curves with ΓS Γ = 0 ∼ 5 in Fig. 2(c)], due to the occurrence of excess Andreev-normal cotunneling [73][74][75] in this regime. Co- herent superposition of this Andreev-normal cotunneling process and the conventional two-electron Kondo cotunneling at the N-QD interface results in the enhancement of the spin Kondo effect.…”

Phonon-assisted Andreev reflection at a Majorana zero mode

“…Some reports have shown the spectroscopy of phonon-assisted Andreev reflection, where a series of peaks appear with the equal peak interval ωp 2 with ω p being the frequency of the phonon. [36][37][38][39][40] However, the Majorana induced Andreev reflection is a kind of special Andreev reflection which is more like resonance tunneling. The normal lead plays a role of both electron lead and hole lead, and the MZM acts as a quantum dot with a single zero energy level.…”