Effect of strain and variable mass on the formation of antibonding hole ground states in InAs quantum dot molecules

Abstract

Using four-band k · p Hamiltonians, we study how biaxial strain and position-dependent effective masses influence hole tunneling in vertically coupled InAs/GaAs quantum dots. Strain reduces the tunneling and hence the critical interdot distance required for the ground state to change from bonding to antibonding. The reduced spin-orbit interaction in the GaAs matrix, which we account for using position-dependent Luttinger parameters, has the opposite effect. This compensation results in the critical distance being little affected. The possibility to induce the bonding-to-antibonding transition using longitudinal magnetic fields is also investigated. LuttingerKohn Hamiltonian predicts a magnetic enhancement of the heavy hole-light hole coupling which, in turn, leads to such transition. No such effect is, however, observed in magnetophotoluminescence experiments. An alternative implementation of the magnetic field in the envelope function Hamiltonian is given which retrieves the experimental behavior.

Magnetic field implementation in multibandk⋅pHamiltonians of holes in semiconductor heterostructures

“…28 The Hamiltonian is solved numerically for a structure formed by two vertically stacked cylindrical QDs. The QDs have radius R = 15 nm and height H = 2 nm, with an interdot barrier of thickness S = 2.8 nm.…”

“…The resulting Hamiltonian has no off-diagonal magnetic terms directly coupling HH and LH, and the results become then consistent with the experimental measurements. 25,28 In the present work, we extend Ref. 29 theory in order to account for the spin Zeeman term, and identify the coefficients that should accompany the magnetic terms in this approximation, which were pending clarification.…”

“…26 Similarly, in vertically coupled QDs, the Luttinger approximation predicts that an axial magnetic field can tune the hole tunneling rate, 27 but this effect is not observed in related experiments. 28 The underlying reason is that the Luttinger approximation includes off-diagonal magnetic terms in the Hamiltonian, which artificially enhance the heavy hole-light hole (HH-LH) band mixing. 25,28 In Ref.…”

“…28 The underlying reason is that the Luttinger approximation includes off-diagonal magnetic terms in the Hamiltonian, which artificially enhance the heavy hole-light hole (HH-LH) band mixing. 25,28 In Ref. 29, an alternative formulation of the magnetic interaction was suggested, in which the replacement of the canonical momentum by the kinetic one is carried out prior to the envelope function approximation (EFA).…”

“…29 theory in order to account for the spin Zeeman term, and identify the coefficients that should accompany the magnetic terms in this approximation, which were pending clarification. 28 The remote band influence is considered through the zero-field effective masses, which are known to provide a meaningful description even in strongly confined QDs [30][31][32][33] , and effective g-factors. We run calculations comparing this model with the Luttinger approximation and show that the magnitude of the Zeeman splitting we estimate is closer to experimental values for vertically coupled InGaAs QDs.…”