Anomalous in-plane magneto-optical anisotropy of self-assembled quantum dots

We report on a complex nontrivial behavior of the optical anisotropy of quantum dots that is induced by a magnetic field in the plane of the sample. We find that the optical axis either rotates in the opposite direction to that of the magnetic field or remains fixed to a given crystalline direction. A theoretical analysis based on the exciton pseudospin Hamiltonian unambiguously demonstrates that these effects are induced by isotropic and anisotropic contributions to the heavy-hole Zeeman term, respectively. The latter is shown to be compensated by a built-in uniaxial anisotropy in a magnetic field $B_C=0.4\mathrm{T}$, resulting in an optical response typical for symmetric quantum dots.

Figure 1

(Color online) (a) Schematic layout of the angle-resolved experiments where $\alpha$ is the rotation angle of the sample. The detection frame ${\rho }_{\gamma }$ is rotated by an angle $\gamma$ (equal to $0°$ or $45°$) with respect to the magnetic field $\mathbf{B}$. (b)–(d) Different scenarios for magneto-optical anisotropy (shown in the sample frame). (b) The polarization axis follows the magnetic field and $\theta =\phi$, leading to a zeroth harmonic in the angle scan. (c) The polarization axis is fixed $(\theta =\mathrm{const})$, resulting in a second harmonic in the angle scan. (d) The polarization axis rotates away from the magnetic field with $\theta =-\phi$, leading to a fourth harmonic in the angle scan.

Figure 2

(Color online) (a) PL emission spectrum of the $\mathrm{CdSe}∕\mathrm{ZnSe}$ QD sample. (b) Three-dimensional 3D plot of the linear polarization ${\rho }_{45}(\alpha ,B)$ as function of the rotation angle $\alpha$ and magnetic inductance $B$. Light (red) and dark (blue) areas correspond to positive and negative values of ${\rho }_{45}(\alpha ,B)$, respectively. (c) Amplitudes of the zeroth $\left(a_0\right)$, second $\left(a_2\right)$, and fourth $\left(a_4\right)$ spherical harmonics vs $B$. The symbols are experimental data and the solid lines result from calculations. The arrows in (b) and (c) indicate the compensating field $B_C$ where the linear polarization is $(\pi ∕2)$-periodic $(a_2=0)$.

Figure 3

(Color online) Angle scans of the linear polarization of the luminescence. The symbols are experimental data; solid lines represent calculations based on the Hamiltonian of Eq. (7). (a) Built-in linear polarization $(B=0\mathrm{T})$. (b) A highly symmetrical optical response [i.e., $(\pi ∕2)$-periodic] appears at a compensating field $B_c\approx 0.4\mathrm{T}$. (c) Angle scan in a magnetic field $B=1\mathrm{T}$ exceeding $B_C$. (d) Angle scan in the saturation regime, $B=4\mathrm{T}$. The detection frame ${\rho }_{\gamma }$ in (a)–(c) is rotated by an angle $\gamma =45°$; in (d) $\gamma =0°$. The arrows indicate the points where the orientation of the magnetic field aligns with high-symmetry directions in the sample frame.