The nature of localization in graphene under quantum Hall conditions

Abstract

Particle localization is an essential ingredient in quantum Hall physics [1,2]. In conventional high mobility two-dimensional electron systems Coulomb interactions were shown to compete with disorder and to play a central role in particle localization [3]. Here we address the nature of localization in graphene where the carrier mobility, quantifying the disorder, is two to four orders of magnitude smaller [4,5,6,7,8,9,10]. We image the electronic density of states and the localized state spectrum of a graphene flake in the quantum Hall regime with a scanning single electron transistor [11]. Our microscopic approach provides direct insight into the nature of localization. Surprisingly, despite strong disorder, our findings indicate that localization in graphene is not dominated by single particle physics, but rather by a competition between the underlying disorder potential and the repulsive Coulomb interaction responsible for screening.Comment: 18 pages, including 5 figure

Nonequilibrium mesoscopic conductance fluctuations as the origin of 1/f noise in epitaxial graphene

“…They are the origin of line structures parallel to integer filling factors observed in the n-B plane of (trans)conductance [57,59,60], as well as of scanning single-electron-transistor measurements of GaAs/AlGaAs heterostructure [61] and graphene [62] quantum Hall effect (QHE) devices. The typical size of the compressible dots is found to be about 60-400 nm [57,[61][62][63]. Fingerprints of Coulomb blockade physics in these states and the existence of a network of dots in graphene have been confirmed by Lee et al [57], who observed the typical Coulomb diamonds near the ν = 0 state.…”

“…Such quantum-dot-like localized quantum Hall states have been associated with conductance fluctuations in the regime of quantum Hall transitions before [57,59,60]. They are the origin of line structures parallel to integer filling factors observed in the n-B plane of (trans)conductance [57,59,60], as well as of scanning single-electron-transistor measurements of GaAs/AlGaAs heterostructure [61] and graphene [62] quantum Hall effect (QHE) devices. The typical size of the compressible dots is found to be about 60-400 nm [57,[61][62][63].…”

Local Compressibility Measurements of Correlated States in Suspended Bilayer Graphene

“…Therefore, it is desirable to directly probe electronic properties in a thermodynamic measurement. Here, we report the use of a scanning single-electron transistor (SET) [22][23][24][25] to measure the local compressibility of a suspended bilayer graphene flake. Investigations into the compressibility of bilayer graphene were recently reported on unsuspended samples [26,27] with particular attention paid to the gap induced by an electric field, but disorder in these systems was too large to observe the broken-symmetry states discussed above.…”

Scale-invariant puddles in graphene: Geometric properties of electron-hole distribution at the Dirac point

“…Besides the subtleties concerning experimental characterization of mono-layer graphene (MLG) 4,5,[7][8][9]24 and bi-layer graphene (BLG) 10 , the coexistence of interaction and (in-plane and out-plane) disorder makes this system less tractable theoretically 29 . Many theoretical attempts have been made to capture the electronic structure of graphene in the presence of disrder, especially the physics of EHPs 2,19,28 , each of which has its own strengths and weaknesses, for review see 29 .…”

“…EHPs. EHPs has been observed and analyzed further using other (direct and indirect) techniques 7,9,[12][13][14] . The first STM experiments on exfoliated graphene showed that in current exfoliated graphene samples the rippling of graphene are independent of the charge density inhomogeneities, i.e.…”