Charge fractionalization in artificial Tomonaga-Luttinger liquids with controlled interaction strength

We investigate charge fractionalizations in artificial Tomonaga-Luttinger liquids (TLLs) composed of two capacitively coupled quantum Hall edge channels (ECs) in graphene. The interaction strength of the artificial TLLs can be controlled through distance $W$ between the ECs. We show that the fractionalization ratio $r$ and the TLL mode velocity $v$ vary with $W$. The experimentally obtained relation between $v$ and $r$ follows a unique function predicted by the TLL theory. We also show that charged wave packets are reflected back and forth multiple times at both ends of the TLL region.