Light-hole exciton in a nanowire quantum dot

Quantum dots inserted inside semiconductor nanowires are extremely promising candidates as building blocks for solid-state-based quantum computation and communication. They provide very high crystalline and optical properties and offer a convenient geometry for electrical contacting. Having a complete determination and full control of their emission properties is one of the key goals of nanoscience researchers. Here we use strain as a tool to create in a single magnetic nanowire quantum dot a light-hole exciton, an optically active quasiparticle formed from a single electron bound to a single light hole. In this frame, we provide a general description of the mixing within the hole quadruplet induced by strain or confinement. A multi-instrumental combination of cathodoluminescence, polarization-resolved Fourier imaging, and magneto-optical spectroscopy, allows us to fully characterize the hole ground state, including its valence band mixing with heavy-hole states.

Figure 1

(a) Energy levels inside the QD participating to the luminescence, along with the corresponding transitions with their oscillator strength and polarization. (b) Schematic of the experiment. The light emission is mapped onto the Fourier plane to allow polarization analysis of the photons with respect to the direction $(\theta ,\phi )$. The inset present a zoom of the nanowire in the vicinity of the quantum dot. (c), (d) Theoretical far field intensity maps for the $\sigma$ or $\pi$ transition, respectively. The QD is assumed to be in an infinite space made of ZnTe. The green lines in (c) and (d) represent the time evolution the electric field in the $(x,y)$ plane for a set of directions. For each direction the electric field origin is centered on the $(\theta ,\phi )$ coordinate.

Figure 2

(a) µPL spectrum of ZnTe core and CdTe quantum dot luminescence, along with the integrated spectral range for cathodoluminescence imaging. (b) SEM image of the nanowire along with (c) spectrally resolved CL image and SEM image superimposed, and (d) cut profile of the spectrally resolved CL signal along the nanowire axis. The contribution of each part of the spectrum is colored according to the spectrum in (a).

Figure 3

Coordinate system is the same as in Fig 1. In each panel we present the normalized unpolarized far-field radiation diagram with two cross sections along the direction of the red and green arrows, the linearly polarized radiation diagrams at $\{0^o,{90}^o\}$ and $\{{45}^o,{135}^o\}$ sharing the same normalization factor (direction of polarizer is indicated by gray arrow), and the S1 and S2 stokes parameter maps. (a) experimental results for the ZnTe emission line. (b) Corresponding simulation results ($\rho /{\mathrm{\Delta }}_{LH}=0.14$, $\sigma /{\mathrm{\Delta }}_{LH}=0.24$, $\psi ={112}^{\circ }$, $\chi ={186}^{\circ }$, or conversely ${\rho }_0/{\mathrm{\Delta }}_{LH0}=0.14$, $\widehat{\alpha }={100}^{\circ }$, $\widehat{\beta }=5^{\circ }$ and $\widehat{\gamma }={12}^{\circ }$). (c) Experimental results for the QD emission line. (d) Corresponding simulations ($\rho /{\mathrm{\Delta }}_{LH}=-0.23$, $\sigma /{\mathrm{\Delta }}_{LH}=-0.06$, $\psi ={170}^{\circ }$, $\chi ={137}^{\circ }$, or conversely ${\rho }_0/{\mathrm{\Delta }}_{LH0}=-0.23$, $\widehat{\alpha }={20}^{\circ }$, $\widehat{\beta }={16}^{\circ }$ and $\widehat{\gamma }={150}^{\circ }$).

Figure 4

(a) Zeeman diagram of the electron and hole confined levels split by the exchange interactions with Mn atoms. The dashed arrows labeled $X_{LH}$ ($X_{HH}$) corresponds to the LH (HH) exciton transitions. The low-energy transition involving a LH creates a $|-1/2\rangle$ electron in the conduction band and a $|+1/2\rangle$ hole in the valence band, hence it is linearly polarized along the $z$ axis. The low-energy transition involving a HH creates a $|-1/2\rangle$ electron in the conduction band and a $|+3/2\rangle$ hole in the valence band, hence it is ${\sigma }^{+}$ polarized. (b) Photoluminescence spectra of the QD emission line recorded at 10K in zero field and at $B=11T$ (corresponding to a QD magnetic moment $M/M_{\mathrm{sat}}=0.84$). The magnetic field is applied along the nanowire axis oriented parallel to the optical axis. Both circular polarizations (${\sigma }^{+}$ in green and ${\sigma }^{-}$ in dashed blue) are shown. The intensity of the zero-field spectrum has been multiplied by 2.5. (c) Zeeman shift of the LH and HH exciton lines proportional to the QD magnetic moment $M/M_{\mathrm{sat}}$. The continuous lines correspond to the theoretical shift expected for a (Cd, Mn)Te quantum dot with a Mn concentration of 10% (see text). (d) Circular polarization rates of the LH and HH exciton lines under magnetic field. The continuous lines corresponds to the expected values taking into account the valence band mixing induced by a constant perturbation term $\left|\sigma \right|=3.9\mathrm{meV}$.

Figure 5

Magneto-optical spectroscopy. (a) Photoluminescence spectra at $T=10\mathrm{K}$ with a magnetic field applied along the nanowire axis, from $B=0–11$ T by steps of 1 T. The spectra at 0 and 11 T are displayed in Fig. 4 of main text. (b) Plot of the position of the low-energy line as a function of $5{\mu }_{B}B/k_B(T+T_{AF}$).

Figure 6

Light-hole exciton dipole radiation. (a) Principal axes $(x_0,y_0,z_0)$ of the ellipsoid defined by Eq. (B6) and calculated for $\psi ={40}^{\circ }$, $\chi ={110}^{\circ }$, $\rho /{\mathrm{\Delta }}_{LH}=0.1$, $\sigma /{\mathrm{\Delta }}_{LH}=0.3$ and $E_0/{\mathrm{\Delta }}_{LH}=2$. They are obtained by three rotations with the Euler angles $\widehat{\alpha }={40}^{\circ }$, $\widehat{\beta }={19}^{\circ }$ and $\widehat{\gamma }=0^{\circ }$. (b) Orientation of the three elementary orthogonal linear dipoles associated to the light-hole exciton. They are oriented along the axes $(x_0,y_0,z_0)$. The $\pi$ ($\sigma$) polarized exciton transitions are associated to the dipole along $z_0$ ($x_0$ and $y_0$). The figure is calculated for the same Euler angles as above and for the hole anisotropy parameters $\epsilon =0.214$ (${\rho }_0/{\mathrm{\Delta }}_{LH0}=0.0406$). The lengths of the colored lines are proportional to the dipole magnitudes $d_{x_0}$, $d_{y_0}$, and $d_{z_0}$ (see text).