Onset of an Insulating Zero-Plateau Quantum Hall State in Graphene

We analyze the dissipative conductance of the zero-plateau quantum Hall state appearing in undoped graphene in strong magnetic fields. Charge transport in this state is assumed to be carried by a magnetic domain wall, which forms by hybridization of two counterpropagating edge states of opposing spin due to interactions. The resulting nonchiral edge mode is a Luttinger liquid of parameter $K$, which enters a gapped, perfectly conducting state below a critical value $K_c\approx 1/2$. Backscattering in this system involves spin flip, so that interaction with localized magnetic moments generates a finite resistivity $R_{xx}$ via a “chiral Kondo effect.” At finite temperatures $T$, $R_{xx}(T)$ exhibits a crossover from metallic to insulating behavior as $K$ is tuned across a threshold $K_{MI}$. For $T\to 0$, $R_{xx}$ in the intermediate regime $K_{MI}<K<K_c$ is finite, but diverges as $K$ approaches $K_c$. This model provides a natural interpretation of recent experiments.

Figure 1

Phase diagram of the DW coupled to a magnetic impurity via a fixed Kondo interaction. The solid blue curve depicts the gap ${\Delta }_s(K)$. The dashed lines mark the boundaries between distinct transport regimes (see text).

Figure 2

Noninteracting energy levels near the edge. Solid black lines are spin up states, dashed red (or gray) lines are spin down states. The dotted line denotes the chemical potential at zero energy.