Nonlinear Quasiparticle Tunneling between Fractional Quantum Hall Edges

Remarkable nonlinearities in the differential tunneling conductance between fractional quantum Hall edge states at a constriction are observed in the weak-backscattering regime. In the $\nu =1/3$ state a peak develops as temperature is increased and its width is determined by the fractional charge. In the range $2/3\le \nu \le 1/3$ this width displays a symmetric behavior around $\nu =1/2$. We discuss the consistency of these results with available theoretical predictions for interedge quasiparticle tunneling in the weak-backscattering regime.

Figure 1

Main panel: differential tunneling conductance ($d{I}_T/d{V}_T$) as a function of driving current ($I_{\mathrm{d}\mathrm{c}}$) at the constriction for filling factors $\nu =2$ at $T=30\mathrm{m}\mathrm{K}$ and $\nu =1/3$ at $T=400\mathrm{m}\mathrm{K}$. Inset (a): sketch of the device and experimental setup. Inset (b): longitudinal ($R_{AB}$) and transverse ($R_{AC}$) resistances as a function of magnetic field at $I_{\mathrm{d}\mathrm{c}}=0$ and $T=30\mathrm{m}\mathrm{K}$.

Figure 2

(a) Differential tunneling conductance ($d{I}_T/d{V}_T$) for filling factor $\nu =1/3$ at different temperatures (30, 100, 200, 300, 400, 500, 700, 900 mK from bottom to top). (b) Calculated $d{I}_T/d{V}_T$ [derivative of Eq. (1)] in the weak-backscattering regime at $T=500$, 700, and 900 mK. (c) Selected differential tunneling conductance curves at the same temperatures as in (b).

Figure 3

Color plots of the differential tunneling conductance ($d{I}_T/d{V}_T$) as a function of the driving current $I_{\mathrm{d}\mathrm{c}}$ and magnetic field [$V_T={\rho }_{xy}(B)I_{\mathrm{d}\mathrm{c}}$] at different temperatures. $\nu =1/3$ occurs at $B\approx 6\mathrm{T}$. Bright yellow regions correspond to a high value of the tunneling conductance.

Figure 4

Representative differential tunneling conductance ($d{I}_T/d{V}_T$) at three values of magnetic field and $T=500\mathrm{m}\mathrm{K}$. The inset reports the evolution of the peak width (as derived from a Lorentzian best-fit procedure) as a function of magnetic field for $T=400\mathrm{m}\mathrm{K}$ (filled circles) and $T=500\mathrm{m}\mathrm{K}$ (open circles). [See Fig. 1 inset (b) to relate magnetic field to the filling factor.]