Electronic and magnetic properties of many-electron complexes in charged InAsxP1−x quantum dots in InP nanowires

We present here a microscopic theory of electronic complexes in charged $\mathrm{In}{\mathrm{As}}_x{\mathrm{P}}_{1\ensuremath{-}x}$ 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 $s{p}³{d}⁵{s}^*$ 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 ${N}_e=4$ 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.