Helical quantum Hall edge modes in bilayer graphene: a realization of quantum spin-ladders

The rich phase diagram of quantum spin-ladder systems has attracted much attention in the theoretical literature. The progress in experimental realizations of this fascinating physics however has been much slower. While materials with a ladder-like structure exist, one always has coupling between the ladders to muddy the waters. In addition, such materials exhibit limited (if any) tunability in terms of the magnetic exchange parameters, and experimental probing of the different phases is a great challenge. In this work, we show that a realization of spin-ladder physics can occur in an engineered nanostructure made out of bilayer graphene in the $\nu =0$ quantum Hall state. Specifically, we describe a split-double-gated setup in which a domain wall (DW) is explicitly induced in the middle of the sample, and show that an effective spin-ladder forms along this DW. The interaction strengths of the ladder are tunable by adjusting magnetic and electric fields as well as the spacing between the gates. Furthermore, we demonstrate that the effective spin ladder has a helical nature, meaning that the spin-correlations may be probed rather simply with charge transport experiments. We describe the phase diagram of this system, and show that certain transport measurements are very sensitive to the phase.