Universal chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact

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.