Selective Equilibration of Spin-Polarized Quantum Hall Edge States in Graphene

Abstract

We report on transport measurements of dual-gated, single-layer graphene devices in the quantum Hall regime, allowing for independent control of the filling factors in adjoining regions. Progress in device quality allows us to study scattering between edge states when the fourfold degeneracy of the Landau level is lifted by electron correlations, causing edge states to be spin and/or valley polarized. In this new regime, we observe a dramatic departure from the equilibration seen in more disordered devices: edge states with opposite spins propagate without mixing. As a result, the degree of equilibration inferred from transport can reveal the spin polarization of the ground state at each filling factor. In particular, the first Landau level is shown to be spin polarized at half filling, providing an independent confirmation of a conclusion of Young et al. [Nat. Phys. 8, 550 (2012). The conductance in the bipolar regime is strongly suppressed, indicating that copropagating edge states, even with the same spin, do not equilibrate along PN interfaces. We attribute this behavior to the formation of an insulating ν = 0 stripe at the PN interface.

Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer

“…Because the state is made up of both p-doped and n-doped graphene, there will always be a pn junction formed when the contacts are of only one doping type. In fact, we observe that this effect can nearly shut off current injection into one of the layers, since the pn junction necessarily passes through zero density, which is insulating at high magnetic fields (31). A measurement of this effect is presented in Figure S14.…”

“…This is contrasted with the spin-degenerate (±2,∓2) states, where interlayer scattering leads to insulating behavior in the same devices ( Figure 2A). A simple explanation for the difference is that the counter-propagating modes of the (±1,∓1) states have opposite spin polarizations, which are the expected exchange-driven ground states for monolayer graphene at ν = ±1 (30,31). When the spin-wavefunctions on each layer are orthogonal, interlayer tunneling processes are forbidden and the edge states are protected from backscattering.…”

“…We label these states by the filling factors on each layer as (ν bottom , ν top ) = (0,-1) and (1,0). In monolayer graphene, the filling factor ν = ±1 states are thought to be spin polarized due to quantum Hall ferromagnetism (30,31). At ν = 1, the spin magnetic moment is aligned with the magnetic field; for the hole-like ν = -1 edge state the spin is flipped since it originates from the bulk excited state.…”

Equilibration of quantum hall edge states and its conductance fluctuations in graphene p-n junctions

“…This can be realized by making a p-n junction in graphene [6][7][8], where the four chiral states propagate along the junction preserving the valley degeneracy. In recent years graphene p-n junction with perpendicular magnetic field has gained a lot of attention in condensed matter physics [9][10][11][12][13][14][15][16][17][18][19]. Such a p-n junction exhibits unprecedented phenomena like snake states [9,12,13], where the interface state in a semi-classical picture alternatively propagate in the p and n side of the junction.…”

“…In an experiment, as there will be only one unique disorder configuration and thus, the CFs should emerge. For last one decade several experiments [7,8,10,11,17,[21][22][23][24][25][26][27][28][29][30][31] have been performed on graphene p-n junction devices. Most of the experiments were carried out on SiO 2 substrate as global back gate and Al 2 O 3 / HSQ/ PMMA/ air bridge as a local top gate.…”