Pairing of Spin Excitations in Lateral Quantum Dots

We demonstrate the existence of correlated electronic states as paired spin excitations of lateral quantum dots in the integer quantum Hall regime. Starting from the spin-singlet filling-factor $\nu =2$ droplet, by increasing the magnetic field we force the electrons to flip spins and increase the spin polarization. We identify the second spin-flip process as one accompanied by correlated, spin depolarized phases, interpreted as pairs of spin excitons. The correlated states are identified experimentally in few-electron lateral quantum dots using high source-drain voltage spectroscopy.

Figure 1

(a)–(c) Three possible lowest-Landau-level configurations with angular momentum $L=+2$ and $S=0$. The dashed line denotes the Fermi level. (d) Energies of singlets and triplets with $L=2$: Hamiltonian diagonal terms (left) and correlated eigenstates (right) (see text).

Figure 2

(a)–(c) Three out of five possible lowest-Landau-level configurations with angular momentum $L=+3$ and $S_z=-1$. The dashed line denotes the Fermi energy. (d) Energies of the $L=+3$ states for three and five states: Hartree-Fock (left), correlated eigenstates with the three-configuration (middle) and the full five-configuration basis (right).

Figure 3

(a) Charge densities for the states $\nu =2$, first spin flip, correlated biexciton, internal spin flip, and the second spin flip (from left to right, respectively), calculated within the one-Landau-level approximation. The dashed line denotes the Fermi level. (b) Boundaries between phases of an even-electron droplet as a function of the number of electrons and the magnetic field for ${\omega }_0=6\mathrm{m}\mathrm{e}\mathrm{V}$, $E_Z=0$.

Figure 4

Main plot: Positions of maxima of the differential conductance tracing the addition spectrum of the eighth electron to a seven-electron dot measured with a lateral gated quantum-dot device in the high source-drain voltage regime. The differential conductance trace for the magnetic field $B=1.2\mathrm{T}$ is shown in the inset. Arrows in the bottom part of the figure indicate the first and the second spin flip. In the vicinity of the second spin flip we interpret the excited states as (from left to right): the correlated triplet (marked by $\mathrm{x}$ symbols), the correlated internal spin flip (marked by crosses) and the second spin flip (filled circles); the diagrams show schematically their corresponding charge densities. The empty squares mark the region of the negative differential conductance (see text for details).