Counterpropagating Edge States Research Articles

Quantum Hall resistances of a multiterminal top-gated graphene device

Four-terminal resistances, both longitudinal and diagonal, of a locally gated graphene device are measured in the quantum-Hall (QH) regime. In sharp distinction from previous two-terminal studies [J. R. Williams et al., Science 317, 638 (2007); B. \"Ozyilmaz et al., Phys. Rev. Lett. 99, 166804 (2007)], asymmetric QH resistances are observed, which provide information on reflection as well as transmission of the QH edge states. Most quantized values of resistances are well analyzed by the assumption that all edge states are equally populated. Contrary to the expectation, however, a 5/2 transmission of the edge states is also found, which may be caused by incomplete mode mixing and/or by the presence of counterpropagating edge states. This four-terminal scheme can be conveniently used to study the edge-state equilibration in locally gated graphene devices as well as monolayer and multilayer graphene hybrid structures.

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} approximately 1/2. Backscattering in this system involves spin flip, so that interaction with localized magnetic moments generates a finite resistivity Rxx via a "chiral Kondo effect." At finite temperatures T, Rxx(T) exhibits a crossover from metallic to insulating behavior as K is tuned across a threshold K_{MI}. For T --> 0, Rxx 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.

Resonant Dephasing in the Electronic Mach-Zehnder Interferometer

We address the recently observed unexpected behavior of Aharonov-Bohm oscillations in the electronic Mach-Zehnder interferometer that was realized experimentally in a quantum Hall system [I. Neder, Phys. Rev. Lett. 96, 016804 (2006)10.1103/PhysRevLett.96.016804]. We argue that the measured lobe structure in the visibility of oscillations and the phase rigidity result from a strong long-range interaction between two adjacent counterpropagating edge states, which leads to a resonant scattering of plasmons. The visibility and phase shift, which we express in terms of the transmission coefficient for plasmons, can be used for the tomography of edge states.

Dissipative Quantum Hall Effect in Graphene near the Dirac Point

We report on the unusual nature of the nu=0 state in the integer quantum Hall effect (QHE) in graphene and show that electron transport in this regime is dominated by counterpropagating edge states. Such states, intrinsic to massless Dirac quasiparticles, manifest themselves in a large longitudinal resistivity rho(xx) > or approximately h/e(2), in striking contrast to rho(xx) behavior in the standard QHE. The nu=0 state in graphene is also predicted to exhibit pronounced fluctuations in rho(xy) and rho(xx) and a smeared zero Hall plateau in sigma(xy), in agreement with experiment. The existence of gapless edge states puts stringent constraints on possible theoretical models of the nu=0 state.