Abstract
We study transport through strongly interacting quantum dots with $N$ energy levels that are weakly coupled to generic multi-channel metallic leads. In the regime of coherent sequential tunneling, where level spacing and broadening are of the same order but small compared to temperature, we present a unified, $SU(N)$-invariant form of the kinetic equation for the reduced density matrix of the dot and the tunneling current. This is achieved by introducing the concept of flavor polarization for the dot and the reservoirs, and splitting the kinetic equation in terms of flavor accumulation, anisotropic flavor relaxation, as well as exchange-field- and detuning-induced flavor rotation. In particular, we identify the exchange field as the cause of negative differential conductance at off-resonance bias voltages appearing in generic quantum-dot models. To illustrate the notion of flavor polarization, we analyze the non-linear current through a triple quantum-dot device.
Highlights
The spatial confinement of electrons in quantum dots gives rise to both a charging energy and a discrete spectrum of single-particle energy levels
We show that the kinetic equations governing the dot dynamics can be cast in a universal SU(N )-invariant form containing terms that describe dot-flavor accumulation, relaxation, and rotation, suggesting the term flavortronics to describe transport through N-level quantum dots
While the perfect blockade in the absence of flavor rotation is not a generic feature, this reasoning applies to negative differential conductance (NDC) in any multilevel-dot model: The exchange field rotates the flavor polarization into an orientation that increases nd · g, i.e., couples more strongly to the drain, and an NDC appears because |Bex| decays with increasing voltage
Summary
The spatial confinement of electrons in quantum dots gives rise to both a charging energy and a discrete spectrum of single-particle energy levels. The SU(2) framework for the spin degree of freedom is transferred to other two-level systems by introducing an isospin This includes the valley degree of freedom in the band structure of graphene and carbon nanotubes, studied in the field of valleytronics [12,13]. We will present a unified theoretical framework for the regime where the level spacing and the broadening are of the same order and small compared to temperature T , which we refer to as the coherent-sequential-tunneling regime It is of particular interest since it exhibits quantum coherence in weak coupling and is most accessible to experiments.
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