Evolution of microscopic localization in graphene in a magnetic field from scattering resonances to quantum dots

Abstract

Graphene is a unique two-dimensional material with rich new physics and great promise for applications in electronic devices. Physical phenomena such as the half-integer quantum Hall effect and high carrier mobility are critically dependent on interactions with impurities/substrates and localization of Dirac fermions in realistic devices. We microscopically study these interactions using scanning tunneling spectroscopy (STS) of exfoliated graphene on a SiO2 substrate in an applied magnetic field. The magnetic field strongly affects the electronic behavior of the graphene; the states condense into welldefined Landau levels with a dramatic change in the character of localization. In zero magnetic field, we detect weakly localized states created by the substrate induced disorder potential. In strong magnetic field, the two-dimensional electron gas breaks into a network of interacting quantum dots formed at the potential hills and valleys of the disorder potential. Our results demonstrate how graphene properties are perturbed by the disorder potential; a finding that is essential for both the physics and applications of graphene.The exposed and tunable two-dimensional graphene electronic system offers a convenient test bed for an understanding of microscopic transport processes and the physics of localization. * These authors contributed equally to this work † To whom correspondence should be addressed: nikolai.zhitenev@nist.gov, joseph.stroscio@nist.gov 2 Graphene's high transport carrier mobility and broad tunability of electronic properties promise multiple applications [1][2][3] . As in semiconductor devices, these features are ultimately determined by electron interactions and scattering from disorder including the surrounding environment of the device. Direct access to the graphene with scanned probes allows for the measurement of these interactions in greater detail 4-13 than possible in conventional semiconductor devices where the transport layers are buried below the surface. For example, STS with atomic resolution has been used 4,5 to study the local density of states of graphene and the role of disorder at zero magnetic field. Scanning single-electron transistor experiments, sensitive to local electric fields, produced local charge density maps with a spatial resolution of 150 nm 6 and detected singleelectron charging phenomena at high magnetic fields 7 .In this article, we present STS measurements of a gated single-layer exfoliated graphene device in magnetic fields ranging from zero to the quantum Hall regime. With the ability to control the charge density of Dirac fermions with an electrostatic back gate with fine resolution, which was missing in previous STS studies 5,[8][9][10][11][12][13][14] , we can investigate local density of states and localization in graphene at the atomic scale while varying the Fermi energy (E F ) with respect to the Dirac (charge neutrality, E D ) point. At zero magnetic field, we observe density fluctuations arising from the disorder potential variations due to charged imp...

Structure of graphene and its disorders: a review

“…More specifically, intrinsic ripples are expected to influence the electrical properties of graphene by changing band gap [239], creating polarized carrier puddles [240] and inducing pseudo-magnetic fields [241]. Whereas wrinkles and crumples result in several electronic phenomena, such as electron-hole puddles [189,242], carrier scattering [195,243], band gap opening [244], suppression of weak localization [245] and quantum corrections [246]. …”

Configuration-enriched magneto-electronic spectra of AAB-stacked trilayer graphene

“…However, this splitting is hardly observable at higher energies. The AA-stacked trilayer graphene exhibits three groups of monolayer-like sequence of peaks [86,88,89] located at energies described by the simple relationship E c,v ∝ √ n c,v B, as indicated in Fig. 9(a).…”

“…The exceptionally high peak at the Fermi level is a superposition of three peaks corresponding to the Dirac points; its intensity is proportional to the number of graphene layers. The essential differences of the DOS can be verifed by STS [86][87][88][89]; those profiles can then be used as a tool to identify the stacking configuration of graphene sheets.…”

Microscopic polarization in bilayer graphene

“…The topographic height fluctuations on the bilayer (Fig. 2b) are dominated by the underlying SiO 2 surface roughness, as they are in the single layer 29 . We have obtained the spatial profile of the bilayer disorder potential as shown in Fig.…”

“…Accordingly, the interplay between the interactions, external and disorder-induced local electric fields, and localized states in the gap is becoming the central issue in the physics of the bilayer graphene system. Direct atomic-scale probing with scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) has been proven as a powerful technique [26][27][28] for studying this physics, particularly in revealing the effects of disorder on the graphene electronic states [29][30][31] .In this article, we present the first STM/STS measurements of a gated bilayer graphene device in magnetic fields ranging from zero to the quantum Hall regime. We investigate the local density of states and the formation of an energy band gap affected by disorder while tuning the total charge density, as the Fermi energy (E F ) is varied with an electrostatic back gate with respect to E D .…”