Magnetoanisotropy of electron-correlation-enhanced tunneling through a quantum dot

We investigate the effect of an applied magnetic field on resonant tunneling of electrons through the bound states of self-assembled InAs quantum dots (QDs) embedded within an (AlGa)As tunnel barrier. At low temperatures $(⩽2\mathrm{K})$, a magnetic field $\mathbf{B}$ applied either parallel or perpendicular to the direction of current flow causes a significant enhancement of the tunnel current. For the latter field configuration, we observe a strong angular anisotropy of the enhanced current when $\mathbf{B}$ is rotated in the plane of the quantum dot layer. We attribute this behavior to the effect of the lowered symmetry of the QD eigenfunctions on the electron-electron interaction.

Figure 1

$I\left(V\right)$ curve at $T=0.5\mathrm{K}$ and $\mathbf{B}=0\mathrm{T}$ for a mesa diode of diameter $50\mu \mathrm{m}$. The inset shows schematically our coordinate scheme relative to the crystallographic axes and electron tunneling through a QD in forward bias.

Figure 2

(a) $I\left(V\right)$ curve of the current peak $A$ at different temperatures and $\mathrm{B}=0\mathrm{T}$. (b) $I\left(V\right)$ curve for $\mathbf{B}\Vert \mathbf{J}$ at $7.5\mathrm{T}$ at $T=0.4\mathrm{K}$. The dots represent the curve $I\sim {(V-V_0)}^{-\gamma }$ with $\gamma \sim 0.84$. The dashed line is the $I\left(V\right)$ curve at $T=0.4\mathrm{K}$ and $\mathrm{B}=0\mathrm{T}$. (c) $I\left(V\right)$ characteristic for $\mathbf{B}\perp \mathbf{J}$ at $6.5\mathrm{T}$ and $T=0.4\mathrm{K}$. The dots represent the curve $I\sim {(V-V_0)}^{-\gamma }$ with $\gamma =0.77$. (d) Temperature dependence of peak $A$ in $I\left(V\right)$ with $\mathbf{B}\perp \mathbf{J}$ at $6.5\mathrm{T}$. The inset shows the $T$-dependence of the maximum of the peak current (stars) and the curve $I\sim T^{-\gamma }$ with $\gamma =0.65$.

Figure 3

Magnetic field dependence from $0\text{to}8\mathrm{T}$ of peak $A$ in $I\left(V\right)$ with $\mathbf{B}\perp \mathbf{J}$ at (a) $T=0.4\mathrm{K}$ and (b) $T=4.2\mathrm{K}$. $\mathbf{B}$ is oriented along one of the ⟨110⟩ crystalline axes in the (001) plane. (c) Dependence of peak current on magnetic field $\mathbf{B}$ applied along ⟨110⟩ at $T=0.4$ and $4.2\mathrm{K}$.

Figure 4

(Color) Color plots of the anisotropy for different orientations of $\mathbf{B}$ in the (001) crystalline plane of the peak current for (a) resonance $A$ at $T=4.2$ and $0.4\mathrm{K}$, (b) resonance $B$, and (c) resonance $C$. The ${\mathrm{B}}_{\mathrm{x}}$ and ${\mathrm{B}}_{\mathrm{y}}$ axes are parallel to the two orthogonal ⟨110⟩ axes of the plane. $\mathrm{B}=10\mathrm{T}$ corresponds to an in-plane k-vector equal to $0.5{\mathrm{nm}}^{-1}$.