Anisotropy of interband transitions in InAs quantum wires: An atomistic theory

The electronic and optical properties of [001]-oriented free-standing InAs cylindrical quantum wires (QWRs) with diameters 10–100 Å are calculated using an atomistic, empirical pseudopotential plane-wave method. We analyze the effect of different degrees of mixing between valence bands on the optical properties of these nanostructures, by switching on and off the spin-orbit interaction. The fundamental transition in these QWRs exhibit a large anisotropy, with emission polarized prevalently along the wire axis $z$. The magnitude of such an anisotropy is found to depend on both degree of valence band mixing and wire size. In higher energy interband transitions, we find anisotropies close to 100% with emission polarized perpendicular to the wire axis. Furthermore, in large wires, transitions involving highly excited valence states show in-plane polarization anisotropies between the [110] and $\left[1\overline{1}0\right]$ directions. InAs wires can therefore switch between $z$-polarized to $xy$-polarized emission/absorption for different excitation energies. This makes them ideally suited for application in orientation-sensitive devices.

Figure 1

Schematics of the calculated single-particle energy levels (labeled with their main angular momentum component) for 3 InAs $D_{2d}$ cylindrical wires with sizes $d=1.2$, 3.6, 9.6 nm, respectively. The dashed lines connect, respectively, CBM and VBM in the different wires. Only a few states are shown that were used in the calculations of the optical properties.

Figure 2

(a) Matrix elements squared and (b) degree of linear polarization for the interband transitions $h_i\to e_j$ ($i=1,\dots ,5$, $j=1,2,3$), as a function of the transition energy for the $d=3.6\mathrm{nm}$ InAs wire.

Figure 3

(a) Matrix elements squared and (b) degree of linear polarization for the interband transitions $h_i\to e_j$ ($i=1,\dots ,5$, $j=1,2,3$), as a function of the transition energy for the $d=9.6\mathrm{nm}$ InAs wire.

Figure 4

(a) Degree of linear polarization of the fundamental transition $h_1\to e_1$ as a function of wire diameter, calculated at $T=2\mathrm{K}$ and $T=300\mathrm{K}$ both considering (W/SO) and not considering (N/SO) SO splitting. (b) Dipole matrix elements, for the same transition, polarized parallel $\left(z\right)$ and perpendicular $\left(x\right)$ to the wire axis, in the finite and zero SO splitting approximations.

Figure 5

Degree of linear polarization of the fundamental transition $h_1\to e_1$ as a function of temperature $T$ for the different wire diameters considered.

Figure 6

PL polarization spectra around the energy of the fundamental $h_1\to e_1$ transition, calculated at $T=2\mathrm{K}$ and $T=300\mathrm{K}$ for a (a) $d=1.2\mathrm{nm}$ and a (b) $d=9.6\mathrm{nm}$ wire (with 50 meV broadening). The arrows mark the position in energy of the transitions $h_i\to e_1$ with $i=1,\dots ,5$.

Figure 7

PL polarization spectra at $T=300\mathrm{K}$ calculated for a $d=1.2\mathrm{nm}$ (a), and a $d=9.6\mathrm{nm}$ (b) wire for different values of the line broadening.

Figure 8

(a) In-plane matrix elements squared and (b) degree of linear polarization for the interband transitions $h_4\to e_1$, as a function of the transition energy measured from the band gap (lower $x$ axis) and wire diameter (upper $x$ axis), in $D_{2d}$ InAs wires.

Figure 9

(a) In-plane matrix elements squared and (b) degree of linear polarization for the interband transitions $h_5\to e_1$, as a function of the transition energy measured from the band gap (lower $x$ axis) and wire diameter (upper $x$ axis), in $D_{2d}$ InAs wires.