Tunneling density of states in quantum dots with anisotropic exchange

TL;DR

This paper analyzes the tunneling density of states in quantum dots with uniaxial anisotropic exchange, deriving exact results and clarifying the behavior near the Stoner instability.

Contribution

It extends the universal Hamiltonian to include uniaxial anisotropic exchange and provides exact analytical results for the tunneling density of states.

Findings

Maximum in density of states near Stoner instability

No additional extrema beyond the maximum predicted by non-perturbative analysis

Results applicable to arbitrary single-particle spectra

Abstract

We reexamine the tunneling density of states in quantum dots and nanoparticles within the model which is extension of the universal Hamiltonian to the case of uniaxial anisotropic exchange. We derive the exact analytical result for the tunneling density of states in the case of arbitrary single-particle energy spectrum. We find that, similar to the case of the isotropic exchange, the tunneling density of states as a function of energy has the maximum due to a finite value of the total spin of the ground state near the Stoner instability. We demonstrate that there are no additional extrema which have been predicted on the basis of perturbative analysis [M.N. Kiselev and Y. Gefen, Phys. Rev. Lett. {\bf 96}, 066805 (2006)].