Microwave response of fractional quantum Hall droplets with quasiparticle tunneling

Abstract

We theoretically study microwave absorption spectroscopy of fractional quantum Hall droplets in the presence of quasiparticle tunneling across a quantum point contact. This contact-free probe provides access to collective edge dynamics beyond conventional transport measurements. We develop a nonperturbative path-integral Monte Carlo approach that enables computation of the frequency-dependent response at finite temperature and for arbitrary droplet geometries, and benchmark the method against analytical results in the weak-tunneling regime. We find that tunneling produces measurable shifts and broadening of resonance peaks, with systematic dependence on tunneling strength and device geometry. Such shifts and broadenings are not obtained in perturbative treatments acting directly on the response function, but emerge when interaction-kernel effects are properly incorporated. Our results indicate experimentally accessible signatures of edge-mode interference and tunneling-induced renormalization of collective excitations, and support the use of microwave spectroscopy as a quantitative probe of quasiparticle dynamics in mesoscopic quantum Hall structures.

Figures (11)

• Figure 1: Schematic view of the setup: a fractional quantum Hall (FQH) droplet with a chiral edge state (blue line) containing a quantum point contact (yellow), allowing tunneling of fractional quasiparticles. The droplet is driven by a time-varying microwave electric field (large red arrow), assumed spatially uniform over the droplet scale.
• Figure 2: Schematic of a quantum Hall droplet with circular geometry at filling $\nu$. The coordinate $y$ is defined parallel to the oscillating microwave electric field, while the coordinate $s$ parametrizes the circumference of the droplet. The points $s_{1}$ and $s_{2}$ denote the positions of the QPCs. Although a realistic droplet would exhibit constrictions at these locations, we consider an idealized setup in which the droplet remains circular and particle (or quasiparticle) tunneling occurs at $s_{1}$ and $s_{2}$.
• Figure 3: Schematic and notation used in the exact IQHE calculation. The droplet is circular, with perimeter $L$. The quantum point contact connects the points at $s=0$ and $s=L/2$, and is characterized by reflection and transmission amplitudes $r$ and $t$.
• Figure 4: Imaginary part of the dielectric function ${\rm Im}\,\epsilon^{R}(\omega)$ for the $\nu=1$ IQH droplet, shown in units of $L^2/\omega_T$. The temperature is set to $T/\omega_T = 0.1$. Solid and dashed lines show the results of scattering theory [Eq. \ref{['eq:ele epsilon exact']}] and second-order perturbation theory [Eqs. \ref{['eq:Gamma(2)']}-\ref{['eq:epsilon up to 2nd perturb']}], respectively, while symbols with error bars represent numerical data obtained using the PIMC method. Dimensionless coupling strengths are $V/\omega_T = 0.25$, $8.192$, and $16$. For visual clarity, delta functions are broadened into Lorentzians with linewidth $\delta = \omega_T/100$.
• Figure 5: Imaginary part of the dielectric function ${\rm Im}\,\epsilon^{R}(\omega)$ for FQH droplets with (a) $\nu=1/3$ and (b) $\nu=1/5$ at temperature $T/\omega_T = 0.1$. Solid lines show results from second-order perturbation theory, whereas symbols with error bars represent data obtained using PIMC. Coupling strengths are $V/\omega_T = 0.25, 0.75, 1.024, 1.5,$ and $2.048$. A finite broadening $\delta = \omega_T/100$ is used.