Tunneling density of states in quantum dots with anisotropic exchange

We reexamine the tunneling density of states in quantum dots and nanoparticles within the model which is an 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 an 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. 96, 066805 (2006).].

Figure 1

Tunneling of an electron with spin-up (left) and spin-down (right) into a quantum dot with a finite value of spin in the ground state.

Figure 2

The sketch of dependence of the tunneling density of states on energy at zero temperature. The shaded areas are equal (see text).

Figure 3

The tunneling density of states in the Coulomb valley. The solid (dotted) curve corresponds to $J_z/\delta =0.92,J_{\perp }/\delta =0.85$, and $T/\delta =1.02 \left(T/\delta =3\right)$. The dashed curve corresponds to $J_z/\delta =J_{\perp }/\delta =0.92$ and $T/\delta =1.02$.