Antibonding Ground States in InAs Quantum-Dot Molecules

Coherent tunneling between two InAs quantum dots forms delocalized molecular states. Using magnetophotoluminescence spectroscopy we show that when holes tunnel through a thin barrier, the lowest energy molecular state has bonding orbital character. However, as the thickness of the barrier increases, the molecular ground state changes character from a bonding orbital to an antibonding orbital, confirming recent theoretical predictions. We explain how the spin-orbit interaction causes this counterintuitive reversal by using a four-band $k·p$ model and atomistic calculations that account for strain.

Figure 1

Photoluminescence (PL) measurement of the electric field-induced anticrossing of $X^0$ at zero magnetic field for a sample with 2 nm barrier. $\Delta$ indicates the anticrossing energy gap. Insets: If the hole energy levels are out of resonance (left) the hole is localized in one of the individual dots. When the hole levels are tuned into resonance by the applied electric field, coherent tunneling leads to the formation of bonding (bottom right) and antibonding (upper right) molecular wave functions.

Figure 2

Zeeman energy splitting as a function of applied electric field for $B=6\mathrm{T}$. (a),(b) Energies of the $X^0$ PL lines for QDMs with 2 and 4 nm barriers. Solid lines and dashed lines calculated using Eq. (2) indicate the two separate spin configurations. (c)–(f) QDMs have a barrier thickness of (c) 2, (d) 3, (e) 4, and (f) 6 nm. Solid curves are calculated with Eq. (3) using $(h_0,h^{\prime })=(-0.368,0.229),(-0.446,0.082),(-0.404,0.076)\mathrm{meV}$ for 2, 3, and 4 nm, respectively.

Figure 3

(a),(b) Energy of the ground and first excited molecular states as a function of $d$ calculated using (a) the single-band effective mass and (b) $k·p$ theory. Scale bars are 5 meV. Insets show the orbital character of the dominant hole spinor component. (c) Tunneling rates of a single hole versus $d$ calculated as described in the text. Inset: Schematic depiction of a QDM. (d) Schematic depiction of the SO induced mixing between bonding ($E^b$) and antibonding ($E^a$) molecular states of the heavy ($E_H$) and light ($E_L$) holes.

Figure 4

(a) Molecular ground states for each charge configuration are determined by sequentially filling molecular orbitals with holes. (b) Calculated energy levels for the $X^{2+}$ transition (from three holes plus one electron to two holes) and the $X^0$ transition (from one hole plus one electron to zero holes). (c) Electric field dependence of the Zeeman splitting for the $X^0$ and $X^{2+}$ molecular ground states in a QDM with 2 nm barrier at $B=6\mathrm{T}$. The resonances peak at two different values of the electric field ($f_{X^0}$ and $f_{X^{2+}}$) because of different Coulomb interactions.