Coulomb Blockade with Neutral Modes

We study transport through a quantum dot in the fractional quantum Hall regime with filling factors $\nu =2/3$ and $\nu =5/2$, weakly coupled to the leads. We account for both injection of electrons to or from the leads, and quasiparticle rearrangement processes between the edge and the bulk of the quantum dot. The presence of neutral modes introduces topological constraints that modify qualitatively the features of the Coulomb blockade (CB). The periodicity of CB peak spacings doubles and the ratio of spacing between adjacent peaks approaches (in the low temperature and large dot limit) a universal value: $2:1$ for $\nu =2/3$ and $3:1$ for $\nu =5/2$. The corresponding CB diamonds alternate their width in the direction of the bias voltage and allow for the determination of the neutral mode velocity, and of the topological numbers associated with it.

Figure 1

A quantum dot in the $\nu =2/3$ regime. The two renormalized edge channels represent the charge mode (dashed line, black) and the neutral mode (solid line, red). The bulk of the quantum dot is represented by a puddle (green).

Figure 2

Energy spectra and quantum numbers in the CB $\nu =2/3$ quantum dot. Parabolas, plotted vs the (normalized) gate voltage, are characterized by three quantum numbers, ($N,q,l$): the total number of electrons, the charge moved from the edge from to the bulk, and the number of neutral zero mode excitations. Each value of $N$ is represented by a parabola centered at that $N$ and same-color satellite parabolas, which are shifted horizontally and vertically. Coulomb blockade peaks are obtained at the crossing of different color (different $N$) parabolas. The CB peaks occur at (blue) circles. The shaded area between the ground state curve and the first excited state corresponding to a different value of $N$ (different color parabola), describes Coulomb diamonds (cf. Fig. 3).

Figure 3

Schematic CB diamonds for $\nu =2/3$. The green regions denote regions with zero conductivity [29], while the purple areas represent regions of parameters where the conductance is finite, but small since charge transfer involves both lead-edge and edge-bulk processes. Note the energy (voltage) scales that depend on $v_{\mathrm{n}}/L$.

Figure 4

Energy spectra, quantum numbers ($N,q,l$), and Klein factors ($\sigma ,I,\epsilon$) for $\nu =5/2$. Degeneracy of various states are indicated. The CB peaks occur at (red) circles.