The enigma of the quantum Hall effect in graphene

Abstract

We apply Laughlin's gauge argument to analyze the ν = 0 quantum Hall effect observed in graphene when the Fermi energy lies near the Dirac point, and conclude that this necessarily leads to divergent bulk longitudinal resistivity in the zero temperature thermodynamic limit. We further predict that in a Corbino geometry measurement, where edge transport and other mesoscopic effects are unimportant, one should find the longitudinal conductivity vanishing in all graphene samples which have an underlying ν = 0 quantized Hall effect. We argue that this ν = 0 graphene quantum Hall state is qualitatively similar to the high field insulating phase (also known as the Hall insulator) in the lowest Landau level of ordinary semiconductor two-dimensional electron systems. We establish the necessity of having a high magnetic field and high mobility samples for the observation of the divergent resistivity as arising from the existence of disorder-induced density inhomogeneity at the graphene Dirac point.A single two-dimensional (2D) layer of carbon atoms forming a honeycomb lattice, i.e., a graphene layer, has unusual physical properties attracting a great deal of current interest. 1 Among its intriguing properties, the effective low-energy dispersion is linear in 2D momentum: E = v|k|, where v, the graphene Fermi velocity, is a constant (v ∼ c/300 where c is speed of light), and electron wave functions formally obey a Dirac-like continuum equation with zero Dirac mass, rather than the Schrodinger's equation. Associated with this Dirac nature is the fact that the single-particle spectrum has a two-fold pseudo-spin (or valley) degeneracy, in addition to the usual (double) spin degeneracy. Thus the lowenergy spectrum of graphene is made of particle or hole excitations near a double-cone Fermi surface; the apex of the cones are the Dirac points where electron and hole dispersions cross each other, or where the valence and conduction bands become degenerate. The combined 4-fold spin/pseudospin degeneracy gives rise to an emergent SU(4) symmetry, which is useful in analyzing the low-energy properties of graphene and plays a central role in our discussion below. Obviously this is a very unusual band structure, which has attracted much attention both theoretically and experimentally.The observation of quantum Hall effect (QHE) 2,3 when an external, perpendicular magnetic field (B) is applied, provides the most compelling evidence for the 2D massless Dirac nature of electrons in graphene. In particular, such a system is predicted 4,5,6 to support integer QHE with quantized values of Hall conductance given by:with n = 0, 1, 2, · · · is an integer, and g s = g v = 2 are respectively the spin and pseudospin/valley degeneracies; the latter is inherent in the chiral, massless Dirac equation describing 2D graphene. The half integer form in Eq.(1) arises from the Berry phase associated with the pseudospin index, and the experimental observation of the sequence predicted in the form of Eq. (1) is a direct reflection of the massless chiral Dir...

Quantum Hall effect on top and bottom surface states of topological insulator (Bi1−xSbx)2Te3 films

“…This n ¼ 0 state can hence be viewed as a pseudo-spin Hall insulator, if we consider the top and bottom degree of freedom as the pseudospin variable. Such an observation of a zero conductance plateau has been reported also in disordered graphene under very high magnetic field [23][24][25][26] and analysed theoretically 27 , as well as in the 2D TIs, the quantum wells of HgTe 28 and InAs/GaSb 29 . From the analyses shown in the following, we propose here that the major origin for the presence of s xy ¼ 0 is more like the energy difference of the top/bottom Dirac points rather than other effects such as electron-hole puddles due to composition inhomogeneity.…”

Intra-Landau-level magnetoexcitons and the transition between quantum Hall states in undoped bilayer graphene

“…Similar behavior has been observed in monolayers 7 and in particle-hole symmetric semiconductor systems. 8 While this is unusual, it does not rule out quantum Hall physics, because Laughlin's gauge argument 9 connects a vanishing longitudinal conductivity σ xx to the quantized Hall conductivity σ xy , which is consistent 10 with a divergent ρ xx = ρ yy for ρ xy = 0. While Zhao et al 2 found that the gap at ν = 0 depends on the field as √ B ⊥ , as expected of Coulomb interaction effects, Feldman et al, 1 using high-mobility suspended samples, measured a gap that opens linearly with B ⊥ and hardly depends on B .…”

Metal to Insulator Transition on theN=0Landau Level in Graphene

“…The nature of the electronic states at the N ¼ 0 LL at present remains unclear. While some theories predict unusual metallic transport via gapless edge states [6][7][8] other suggest that a gap may open at high magnetic fields, resulting in an insulating state near the charge-neutrality, n s ¼ 0, point (CNP) [9][10][11]. However, theories mainly focus on quantum Hall transport in the absence of strong electrostatic disorder, which, along with the Coulomb interaction, plays key role in defining the electron localization in 2DEGs [12][13][14][15][16][17][18][19].…”