Minimal Excitations in the Fractional Quantum Hall Regime

We study the minimal excitations of fractional quantum Hall edges, extending the notion of levitons to interacting systems. Using both perturbative and exact calculations, we show that they arise in response to a Lorentzian potential with quantized flux. They carry an integer charge, thus involving several Laughlin quasiparticles, and leave a Poissonian signature in a Hanbury Brown–Twiss partition noise measurement at low transparency. This makes them readily accessible experimentally, ultimately offering the opportunity to study real-time transport of Abelian and non-Abelian excitations.

Figure 1

Main setup. A quantum Hall bar equipped with a QPC connecting the chiral edge states of the fractional quantum Hall effect (FQHE). The left-moving incoming edge is grounded at contact 2 while the right-moving one is biased at contact 1 with a time-dependent potential $V(t)$.

Figure 2

Excess noise in units of $S^0=(2/T)(e^{*}{\mathrm{\Gamma }}_0/v_F{)}^2(\mathrm{\Omega }/\mathrm{\Lambda }{)}^{2\nu -2}$ as a function of the number of electrons per pulse $q$, for different reduced temperatures $\theta$ and filling factor $\nu =1/3$, in the case of a square (bottom), a cosine (middle), and a periodic Lorentzian drive with half width at half maximum $\eta =W/T=0.1$ (top).

Figure 3

Rescaled excess noise $\mathrm{\Delta }\mathcal{S}/\gamma$ in units of $(e^2/T)$ as a function of the number of electrons per pulse $q$, for different values of the dimensionless tunneling parameter $\gamma =(|{\mathrm{\Gamma }}_0{|}^2/\pi a{v}_F\mathrm{\Omega })$. Results are obtained at zero temperature, with filling factor $\nu =1/2$, in the case of a square (bottom), a cosine (middle), and a periodic Lorentzian drive with $\eta =0.1$ (top).

Figure 4

Normalized HOM noise $\mathrm{\Delta }Q$ at $q=1$, as a function of the time delay $\tau$ between pulses. Results are presented in the WB case at $\nu =1/3$ and $\theta =0.1$, for a square, a cosine, and a periodic Lorentzian drive with $\eta =0.1$. Inset: HOM setup with applied drives on both incoming arms.

Figure 5

Averaged backscattered current $\overline{⟨I_B(t)⟩}$ as a function of the number of electrons per pulse $q$, in the case of a square, cosine, and periodic Lorentzian drive with $\eta =0.1$ and $\theta =0.1$. Results are presented for $\nu =1/3$ in the perturbative regime in units of $I^0=\frac{e^{*}}{T}({\mathrm{\Gamma }}_0/v_F{)}^2(\mathrm{\Omega }/\mathrm{\Lambda }{)}^{2\nu -2}$ (top) and for the exact treatment at $\nu =1/2$ in units of $(e/T)$ (bottom).