Coulomb Blockade and Kondo Effect in a Quantum Hall Antidot

We propose a general capacitive model for an antidot, which has two localized edge states with different spins in the quantum Hall regime. The capacitive coupling of localized excess charges, which are generated around the antidot due to magnetic flux quantization, and their effective spin fluctuation can result in Coulomb blockade, $h/(2e)$ Aharonov-Bohm oscillations, and the Kondo effect. The resultant conductance is in qualitative agreement with recent experimental data.

Figure 1

(a) A quantum Hall antidot with antidot states and extended edge channels ($M,M^{\prime },N,N^{\prime }$) with their spins (solid arrows), which come from the first (the antidot states, $M,M^{\prime }$) and the second Landau levels ($N,N^{\prime }$). The intra- and the inter-Landau level couplings are drawn as dashed and dotted lines, respectively. $B$ is applied perpendicularly to the plane. (b) Schematic diagram of electron density shift (solid arrows) around an antidot as $B$ increases; this generates local charge imbalance with respect to the background charge. (c) An experimental result under 25 mK and zero bias (see Ref. 10). Inset: $G(B)$ for one AB period around $B=1.25\mathrm{T}$.

Figure 2

($\delta q_{\uparrow }$, $\delta q_{\downarrow }$) evolves along a solid-arrow trajectory as $B$ increases. When one of the resonance conditions is met, ($\delta q_{\uparrow }$, $\delta q_{\downarrow }$) jumps following horizontal (normal spin-up electron tunneling), vertical (spin down), or diagonal dashed-dot arrows (Kondo resonance). Solid, dashed, and dotted lines indicate resonance conditions of Eqs. (2, 3, 4), respectively. Two different parameters are used: (a) $\alpha \equiv |C_{\uparrow \downarrow }|/C_{\uparrow \uparrow }=0.95$ and (b) $0.5$. For both the cases, we choose $C_{\downarrow \downarrow }/C_{\uparrow \uparrow }=1.2$.

Figure 3

Calculated $G(B)$ and $G_{\sigma }(B)$ around a magnetic field $B_0$ ($\sim 1\mathrm{T}$). $G(B)$ matches well the experimental data.