Electronic and magnetic properties of many-electron complexes in charged In As_x P_1-x quantum dots in InP nanowires

We present here a microscopic theory of electronic complexes in charged InAs_xP_1-x quantum dots in InP nanowires with a hexagonal cross section and determine the potential use of an array of such quantum dots as a synthetic spin chain for the possible construction of a topological qubit. The single-particle energies and wave functions are obtained by diagonalizing a microscopic atomistic tight-binding Hamiltonian of multiple quantum dots in the basis of sp³d⁵s∗ local atomic orbitals for a given random distribution of arsenic (As) vs phosphorus (P) atoms. The conduction band electronic states are found grouped into s, p, and d quantum dot shells. For a double dot, the electronic shells can be understood in terms of interdot tunneling despite the random distribution of As atoms in each quantum dot. The single- and double-dot structures were charged with a finite number of electrons. The many-body Hamiltonian including Coulomb electron-electron interactions was constructed using single atomistic particle states and then diagonalized in the space of many-electron configurations. For a single dot filled with N_e=1-7 electrons, the ground state of a half-filled p-shell configuration with Ne=4 was found with total electronic spin S=1. The low-energy spectrum obtained using exact diagonalization of a Hamiltonian of a charged double dot filled with N_e=8 electrons, i.e., half-filled p shells in each dot, was successfully fitted to the Hubbard-Kanamori and antiferromagnetic Heisenberg spin-1 Hamiltonians. The atomistic simulation confirmed the potential of InAsP/InP quantum dots in a nanowire for the design of synthetic spin chains.