Smearing of charge fluctuations in a grain by spin-flip assisted tunneling

Abstract

We investigate the charge fluctuations of a grain coupled to a lead via a small quantum dot in the Kondo regime. We show that the strong entanglement of charge and spin flips in this setup can result in a stable SU(4) Kondo fixed point, which considerably smears out the Coulomb staircase behavior already in the weak tunneling limit. This behavior is robust enough to be experimentally observable.PACS numbers: 75.20.Hr,71.27.+a,73.23.Hk Recently, quantum dots have attracted a considerable interest due to their potential applicability as single electron transistors or as basic building blocks (qubits) in the fabrication of quantum computers [1]. One of their most important features is the Coulomb blockade phenomenon, i.e., as a result of the strong repulsion between electrons, the charge of a quantum dot is quantized in units of the elementary charge e. Even when the quantum dot is weakly-coupled to a bulk lead, so that electrons can hop from the lead to the dot and back, the dot charge remains to a large extent quantized. This quantization has been thoroughly investigated both theoretically [2] and experimentally [3]. The quantity of interest here is the average dot charge as a function of the voltage applied to a back-gate. For a weakly-coupled dot, at low temperatures, this function generally exhibits sharp steps, resulting in the "Coulomb staircase". We emphasize the fact that a direct measurement of the average dot charge can be performed with sensitivity well below a single charge [4].In this Letter, we investigate the shape of the steps of the Coulomb staircase in the presence of spin-flip assisted tunneling. The setup we examine consists of a (large) dot or grain coupled to a reservoir through a smaller dot (Fig.1). We assume that the smaller dot contains an odd number of electrons and acts as an S=1/2 Kondo impurity [5]. A different limit where the small dot rather acts as a resonant level has been partially studied in Ref. 6 where it was shown that the resonant level can smear the Coulomb blockade (nevertheless, for a narrow resonance at the Fermi energy, the effect is weak). Furthermore, the charge of the grain in such a device can be used to measure the occupation of the dot [6].In the following analysis, we focus on the regime where the back-gate voltage is such that the charging states of the grain with 0 or 1 electron are degenerate. We show below that in this case, the charge degrees of freedom of the grain become strongly entangled with the spin degrees of freedom of the small dot resulting in a stable fixed point with an SU(4) symmetry. The major consequence of this enlarged symmetry in our setup is that the dot's capacitance exhibits instead of a logarithmic singularity [2]-a strongly reduced peak as a function of the back-gate voltage, smearing charging effects in the grain considerably. The Coulomb staircase behavior becomes smeared out already in the weak tunneling limit due to the prominence of spin-flip assisted tunneling. The possibility of a strongly correlated ground state possessing...

Kondo effect in a topological insulator quantum dot

“…The corresponding Kondo temperature is given by T K ≈ D exp (−1/4ρ 0 J). Similar results have been examined in carbon nanotube systems 13 , vertical quantum dots systems 26,67 , grain-dot systems 27 and parallel double quantum dots systems 31,68,69 . This discussion based on the RG analysis demonstrates the existence of SU (4) Kondo states in the TIQD.…”

“…It is the quantum fluctuations among QD's four internal degrees of freedom that result in the spin-orbital Kondo effect. The spin-orbital Kondo effect has been investigated in great amount in CNQDs, [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] vertical quantum dots, 26 grain-dot systems, 27,28 and parallel quantum dots. [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] Compared with the conventional Kondo effect, in which only spin degrees of freedom are involved, the spin-orbital Kondo effect is characterized by the intra-dot and interdot interactions in DQD systems.…”

Admittance of the SU(2) and SU(4) Anderson quantumRCcircuits

“…We finally give a further application of the Fermi liquid approach [42,43] by considering an additional orbital degeneracy in the dot responsible for SU(4) Kondo behavior at low energy [39,40]. The existence of a Fermi liquid ground state [49,50] in the case of a SU(4) symmetry allows us to derive an analog of Eq.…”

“…It includes in particular the Kondo regime where the spin on the dot is strongly correlated with the Fermi sea in the reservoir lead. Our analysis shall also include the more exotic SU(4) Kondo regimes relevant for dots with an additional orbital degree of freedom [39,40].…”

Orbital caloritronic transport in strongly interacting quantum dots

“…Hence, the crossover between SU (2) and SU(4) Kondo effects involves two strongly correlated states with rather different temperature scales (the Kondo temperatures T SU (2) K and T SU (4) K that typically fulfill T SU (4) K T SU (2) K ). Such crossover has been investigated both experimentally [6][7][8] and theoretically [9][10][11][12][13][14][15][16]. In particular, an applied magnetic field in nanotubes couples differently to the spin and orbital quantum numbers [4], lifting the degeneracy and allowing for a tunable conversion from SU(4) Kondo physics to a purely spin or orbital Kondo effect [6].…”