Melting of Interference in the Fractional Quantum Hall Effect: Appearance of Neutral Modes

We attempted to measure interference of the outer edge mode in the fractional quantum hall regime with an electronic Mach-zehnder interferometer. The visibility of the interferometer wore off as we approached ${\nu }_B=1$ and the transmission of the quantum point contacts (QPCs) of the interferometer simultaneously developed a $v=1/3$ conductance plateau accompanied by shot noise. The appearance of shot noise on this plateau indicates the appearance of nontopological neutral modes resulting from edge reconstruction. We have confirmed the presence of upstream neutral modes measuring upstream noise emanating from the QPC. The lack of interference throughout the lowest Landau level was correlated with a proliferation of neutral modes.

Figure 1

Device schematic. Schematic of the structure. The outer periphery is defined by an etched mesa. The MZI is defined by two QPCs, labeled as ${\mathrm{QPC}}_L$ and ${\mathrm{QPC}}_R$, with the upper path separated by an etched mesa (a white arc). The modulation gate, affecting the area of the MZI, is labeled as MG. The path of the interfering edge channel along the mesa is shown in black broken lines with arrows defining the chirality. Shot-noise measurements were performed using ${\mathrm{QPC}}_0$, whereas for conductance measurements all the QPCs were used. ${\mathrm{QPC}}_0$ can also be used to switch between $I_{S1}$ and $I_{S2}$ as the impinging edge channels on the MZI.

Figure 2

Correlation between the appearance of a $\mathit{\nu }=1/3$ noisy plateau and the diminishing interference in the MZI. (a) A “two-probe” quantum Hall resistance as a function of magnetic field in bulk filling ${\nu }_B=2$ to ${\nu }_B=1$. Filling factors corresponding to observed plateaus are noted with arrows showing the plateaus. The colored squares show the places where the experiments for (b) and (c) were performed. (b) Plots show the conductance vs gate voltage applied to ${\mathrm{QPC}}_L$ at different bulk states. The dotted magenta lines are a guide to the eye of the $\nu =1/3$ conductance plateau in the QPC. (c) Plots show the corresponding interference signal of the outermost edge mode as a function of MG voltage in the MZI. Note the diminishing visibility of interference once $1/3$ plateau in the QPC appears. The interference quenches once the plateau is fully grown at ${\nu }_B=1$.

Figure 3

Differential conductance and shot noise at ${\nu }_{\mathrm{QPC}}=1/3$ at bulk filling ${\nu }_B=1$. The peripheral axes are defined for transmission through ${\mathrm{QPC}}_0$ as a function of gate voltage. A plateau at $t=1/3$ (dotted magenta line) shows the formation of $e^2/3h$ conductance plateau in the QPC. (a) The nonlinear differential conductance of ${\mathrm{QPC}}_0$ as a function of dc bias applied to the source at $t=1/3$. (b) Shot noise at the $t=1/3$ plateau. Black solid line shows the fitting curve to the shot-noise data. Partitioned quasiparticles charge (here, the Fano factor) and temperature as obtained by the fitting curve is provided as inset text.

Figure 4

Differential conductance and shot-noise in the hole-conjugate states ${\nu }_B=\frac{2}{3},\frac{3}{5},\frac{4}{7}$. The transmissions through ${\mathrm{QPC}}_0$ as a function of applied voltage on the split gates, showing conductance plateaus for three different filling factors (${\nu }_B=2/3–v=1/3$ plateau; ${\nu }_B=3/5–v=1/3$ and $2/5$ plateaus; ${\nu }_B=4/7–v=1/3$, $2/5$, and $3/7$ plateaus). (Insets) Excess noise measured on the $v=1/3$ plateau in each filling factor. Fitted lines through the noise data gives the Fano factors corresponding to each bulk filling.