Imaging quasiparticle wave functions in quantum dots via tunneling spectroscopy

We show that in quantum dots the physical quantities probed by local tunneling spectroscopies—namely, the quasiparticle wave functions of interacting electrons—can considerably deviate from their single-particle counterparts as an effect of Coulomb correlation. From the exact solution of the few-particle Hamiltonian for prototype dots, we find that such deviations are crucial to predict wave function images at low electron densities or high magnetic fields.

Figure 1

Quasiparticle wave function (solid line) vs $\mathbf{\varrho }$ for different $(N-1)\to N$ transitions, with $\lambda =2$. The dashed line represents the noninteracting orbital $(\lambda =0)$. The ground states are $(M,S)=(0,1∕2)$,(0,0),$(1,1∕2)$,(0,1),$(1,1∕2)$,(0,0), for $N$ going from 1 to 6, respectively. $S_z=0$ $(S_z=1∕2)$ if $N$ is even (odd). The norm of the $\lambda =2$ wave function is 1,0.84,0.84,0.40,0.37,0.73, respectively. Insets: total ground-state charge densities $n\left(\mathbf{\varrho }\right)$ (arb. units) for $N$ going from 1 (top left) to 6 (right bottom). The length unit is ${\ell }_{\mathrm{QD}}$.

Figure 2

Top: quasiparticle wave function vs $\mathbf{\varrho }$ for different values of $\lambda$, as the sixth electron tunnels into the QD. The wave function norm, for $\lambda$ going from 0.5 to 10, is 0.97,0.73,0.48,0.32,0.22,0.15, respectively. Bottom: six-electron total density $n\left(\mathbf{\varrho }\right)$ vs $\mathbf{\varrho }$. The ground states for $N=5,6$ are $(M,S)=(1,1∕2)$, (0,0), respectively, for all $\lambda$.