Conductance fluctuations and partially broken spin symmetries in quantum dots

Conductance fluctuations in GaAs quantum dots with spin-orbit and Zeeman coupling are investigated experimentally and compared to a random matrix theory formulation that defines a number of regimes of spin symmetry depending on experimental parameters. Accounting for orbital coupling of the in-plane magnetic field, which can break time-reversal symmetry, yields excellent overall agreement between experiment and theory.

Figure 1

Conductance average $⟨g\left(B_{\perp }\right)⟩$ (solid dots) and variance $\mathrm{var}g\left(B_{\perp }\right)$ (open circles and squares) as a function of perpendicular magnetic field $B_{\perp }$ with $B_{\Vert }=0$, for large and small dots on the high-density material, at $T=300\mathrm{mK}$. (a) Antilocalization in $⟨g\left(B_{\perp }\right)⟩$ for the $8\text{−}\mu {\mathrm{m}}^2$ dot. (b) Weak localization in $⟨g\left(B_{\perp }\right)⟩$ for the $1.2\text{−}\mu {\mathrm{m}}^2$ dot, demonstrating confinement suppression of SO effects. Both dots show an enhancement of $\mathrm{var}g$ at $B_{\perp }=0$. Fits of RMT (Ref. 1) to $⟨g\left(B_{\perp }\right)⟩$ (dashed curves) and $\mathrm{var}g\left(B_{\perp }\right)$ (solid curves) using fit parameters determined from fits to $⟨g⟩$ plus an overall scale factor for $\mathrm{var}g$ (see text). The insets show device micrographs.

Figure 2

Conductance average $⟨g\left(B_{\perp }\right)⟩$ (solid dots) and variance $\mathrm{var}g\left(B_{\perp }\right)$ (open triangles and diamonds) as a function of perpendicular field $B_{\perp }$ with $B_{\Vert }=0$, for (a) large and (b) small dots, both fabricated on low-density material. Both devices display weak localization in $⟨g\left(B_{\perp }\right)⟩$. Fits to RMT are shown as dashed and solid curves, as described in the caption of Fig. 1. Insets show device micrographs; geometry of large device is identical to large dot in high density material.

Figure 3

Variance of conductance fluctuations, $\mathrm{var}g$, in high-density dots, as a function of in-plane field $B_{\Vert }$ with $B_{\perp }\ne 0$ sufficient to break TRS (open symbols) and $B_{\perp }=0$ (solid symbols). The big dot shows less reduction in $\mathrm{var}g(B_{\perp }\ne 0)$ with $B_{\Vert }$ than the small dot, consistent with RMT (see text). The insets show quantum correction to average conductance, $\delta g\left(B_{\Vert }\right)=⟨g(B_{\perp }=0,B_{\Vert })⟩-⟨g(B_{\perp }\ne 0,B_{\Vert })⟩$. In both main figure and insets, dashed curves are fits to RMT, solid curves (labeled $\mathrm{RMT}+\mathrm{FJ}$) are fits to RMT including orbital coupling of $B_{\Vert }$ (see text).

Figure 4

As in Fig. 3, but for low-density dots. In this case, both dots have a reduction factor $R\sim 4$ in parallel field, consistent with RMT (curves). Orbital coupling of $B_{\Vert }$ breaks TRS, making $\mathrm{var}g$ independent of $B_{\perp }$ and quenching the quantum correction to average conductance, $\delta g\to 0$ (insets) on the same (dot-size-dependent) scale of $B_{\Vert }$.