Synthetic spin-1 chain in an array of InAsP quantum dots embedded in an InP nanowire*

Here we describe the potential realization of a synthetic spin-1 Haldane chain in an array of InAs­P quantum dots embedded in an InP nanowire for the possible construction of a topologically protected singlet-triplet qubit. Using an ab-initio derived tight-binding Hamiltonian for a single and a double InAsP quantum dot containing millions of atoms, the single particle states were obtained. Though the distribution of As atoms in each quantum dot is random, the conduction band states of a quantum dot array can still be understood in terms of s, p, and d quantum dot orbitals with interdot tunneling. We then constructed the many-body Hamiltonian in the basis of N-electron configurations with the single particle states from the tight-binding model. Using exact diagonalization, we determined that the ground state of a single quantum dot with a half filled p­-shell has a total electronic spin of S = 1 and that the ground state for a double dot is a singlet with total spin S = 0, which is consistent with Heisenberg model¹. The low-energy spectrum of the double quantum dot array was then successfully fitted to both the Hubbard-Kanamori and Heisenberg model Hamiltonians to confirm that the quantum dot array with 4 electrons in each dot hosts the Haldane quasipartcles of a spin-1 chain.