Tunable Luttinger liquid physics in biased bilayer graphene

Electronically gated bilayer graphene behaves as a tunable gap semiconductor under a uniform interlayer bias $V_{g}$. Imposing a spatially varying bias, which changes polarity from $-V_g$ to $+V_g$, leads to one dimensional (1D) chiral modes localized along the domain wall of the bias. Due to the broad transverse spread of their low-energy wavefunctions, we find that the dominant interaction between these 1D electrons is the forward scattering part of the Coulomb repulsion. Incorporating these interactions and the gate voltage dependence of the dispersion and wavefunctions, we find that these 1D modes behave as a strongly interacting Tomonaga-Luttinger liquid with three distinct mode velocities and a bias dependent Luttinger parameter, and discuss its experimental signatures.