Weak Localization in Mesoscopic Hole Transport: Berry Phases and Classical Correlations

We consider phase-coherent transport through ballistic and diffusive two-dimensional hole systems based on the Kohn-Luttinger Hamiltonian. We show that intrinsic heavy-hole–light-hole coupling gives rise to clear-cut signatures of an associated Berry phase in the weak localization which renders the magnetoconductance profile distinctly different from electron transport. Nonuniversal classical correlations determine the strength of these Berry phase effects and the effective symmetry class, leading even to antilocalization-type features for circular quantum dots and Aharonov-Bohm rings in the absence of additional spin-orbit interaction. Our semiclassical predictions are confirmed by numerical calculations.

Figure 1

Probability distributions to find an orbit with enclosed area $A$ and accumulated angle $\alpha$ for (a) a chaotic cavity [inset of Fig. 3a] and (b) a disk [inset of Fig. 3b]. [Central (red) regions correspond to high probability.]

Figure 2

Dependence of (a) the depth $\delta T_{U(L)}(B_{\min })$ and (b) the position $B_{\min }$ of the magnetotransmission weak localization dip on $ka$ [governing the effective HH-LH coupling, see Eq. (7)] for HH transport through a chaotic quantum dot [inset of Fig. 3a]. Numerical quantum results (symbols) are compared to the semiclassical predictions (13, 14), [(green) lines] for ${\gamma }_1=6.85$, $\overline{\gamma }=2.5$ (for GaAs).

Figure 3

HH-LH coupling-induced Berry phase effects on weak localization in various mesoscopic hole gases. The WL correction $\delta T$ is shown for a ballistic chaotic cavity (a), disk (b), AB ring (c), and a diffusive strip (d). Red (▵) and blue (▽) triangles denote quantum mechanical transmissions $\delta T_U(B)$, $\delta T_L(B)$ adding up to the full $\delta T(B)$ [green bullets, see text below Eq. (3)]. The red and blue dotted curves in (a) and (b) show our semiclassical results (12) with the horizontal displacements given by the Berry field (14) reflecting geometrical correlations [based on the calculated classical quantities $A_0\simeq 12200$ $[56129]{\mathrm{nm}}^2$, ${\alpha }_0\simeq 1.92$ [5.89], $\rho \simeq 0.5$ [0.8] in (a) [(b)]]. In (c), (d) the lines are guides to the eye of the quantum results. See 22 for the parameters used.