[Paper Review] Universal chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact

Liam A. Cohen, Noah L. Samuelson+5 more|arXiv (Cornell University)|Dec 2, 2022

Quantum and electron transport phenomena4 citations

TL;DR

This study demonstrates universal chiral Luttinger liquid behavior in a graphene-based point contact connecting integer and fractional quantum Hall edge states. At weak coupling, conductance scales quadratically with temperature and voltage, confirming the predicted universal $T^2, V^2$ scaling for the $ u=1/3$ fractional quantum Hall state. At strong coupling, perfect Andreev reflection of fractionalized quasiparticles leads to a quantized conductance of $e^2/2h$, enabling a nearly dissipationless DC voltage step-up transformer with a 3/2 gain due to topological charge fractionalization.

ABSTRACT

One dimensional conductors are described by Luttinger liquid theory, which predicts a power-law suppression of the density of states near the Fermi level. The scaling exponent is non-universal in the general case, but is predicted to be quantized for the chiral edge states of the fractional quantum Hall effect. Here, we report conductance measurements across a point contact linking integer and fractional quantum Hall edge states. At weak coupling, we observe the predicted universal quadratic scaling with temperature and voltage. At strong coupling, the conductance saturates to e^2/2h, arising from perfect Andreev reflection of fractionalized quasi-particles at the point contact. We use the strong coupling physics to realize a nearly dissipationless DC voltage step-up transformer, whose gain of 3/2 arises directly from topological fractionalization of electrical charge.

Motivation & Objective

• To test the universal chiral Luttinger liquid theory in a controlled point contact geometry between integer and fractional quantum Hall edge states in graphene.
• To verify the predicted universal power-law scaling $G \propto T^2, V^2$ at weak coupling, independent of microscopic details.
• To probe strong coupling physics where fractionalized quasiparticles undergo perfect Andreev reflection, leading to quantized conductance.
• To demonstrate a topological voltage step-up transformer based on fractional charge and chiral edge states, achieving a 3/2 gain.

Proposed method

• Fabricated a graphene-based quantum point contact device with dual-gated top and bottom gates to tune the chemical potential across the $ u=1/3$ and $ u=1$ quantum Hall plateaus.
• Performed low-temperature conductance measurements ($T \leq 666$ mK) across the point contact under high magnetic fields ($B = 9$ T and $10$ T) to access chiral edge states.
• Used scaling collapse of conductance data as a function of $eV/(2\pi k_B T)$ to test the universal $T^2, V^2$ power-law behavior predicted by chiral Luttinger liquid theory.
• Applied the full quantum impurity model (Eq. 3) to describe the strong coupling regime, fitting the differential conductance to extract $T_0$ and validate the model.
• Measured the zero-bias conductance $G(V=0)$ as a function of temperature to confirm $T^2$ dependence and extract the universal scale $T_0$.
• Demonstrated a DC voltage step-up transformer by exploiting the $e^2/2h$ conductance plateau arising from Andreev reflection of anyonic quasiparticles.

Experimental results

Research questions

• RQ1 Does the conductance across a graphene point contact between $ u=1$ and $ u=1/3$ edge states exhibit universal $T^2, V^2$ scaling at weak coupling, as predicted by chiral Luttinger liquid theory?
• RQ2 What is the nature of the strong coupling regime in a fractional quantum Hall point contact, and does it lead to perfect Andreev reflection of fractionalized quasiparticles?
• RQ3 Can the $e^2/2h$ conductance plateau at strong coupling be harnessed to realize a nearly dissipationless voltage step-up transformer?
• RQ4 How robust is the universal scaling behavior across different magnetic fields and gate voltages, indicating insensitivity to microscopic details?

Key findings

• Conductance exhibits universal quadratic scaling with temperature and voltage, $G \propto T^2, V^2$, with a fitted exponent of $2.00 \pm 0.06$, consistent with the predicted $g=1/3$ chiral Luttinger liquid behavior.
• The extracted energy scale $T_0 = 9.02 \pm 0.007$ K from the $V$-dependence at $B=10$ T confirms the universal low-energy scale of the system.
• At strong coupling, the conductance saturates at $e^2/2h$, indicating perfect Andreev reflection of fractionalized quasiparticles at the point contact.
• The zero-bias conductance $G(V=0)$ scales as $T^2$ over a range of temperatures, with $T_0 = 4.09$ K at $B=9$ T, confirming the universal scaling collapse.
• Scaling collapse of conductance data across multiple temperatures and voltages confirms the validity of the chiral Luttinger liquid model with $g=1/3$.
• The system realizes a nearly dissipationless DC voltage step-up transformer with a gain of $3/2$, directly arising from topological fractionalization of charge.