  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.
