Quantized Landau level spectrum and its density dependence in graphene

Abstract

Scanning tunneling microscopy and spectroscopy in magnetic field was used to study Landau quantization in graphene and its dependence on charge carrier density. Measurements were carried out on exfoliated graphene samples deposited on a chlorinated SiO 2 thermal oxide which allowed observing the Landau level sequences characteristic of single layer graphene while tuning the density through the Si backgate. Upon changing the carrier density we find abrupt jumps in the Fermi level after each Landau level is filled. Moreover, the Landau level spacing shows a marked increase at low doping levels, consistent with an interaction-induced renormalization of the Dirac cone. One of the hallmarks of the relativistic charge carriers 1,2 in graphene is the appearance in a magnetic field of an unusual Landau level (LL) at zero energy which reflects the chiral symmetry of the low lying excitations. The presence of this LL has been inferred in magnetotransport measurements employing the standard configuration of graphene supported on SiO 2 3,4 from the conspicuous absence of a quantum Hall plateau at zero filling-factor. Remarkably because in graphene the carriers reside right at the surface, the LLs (including the LL at zero-energy) can be accessed directly through scanning tunneling spectroscopy (STS) as was demonstrated in studies of graphene samples supported on the surface of graphite 5,6 .However, the LLs were not observed in STS measurements on graphene samples supported on insulating substrates which allow control of the carrier density through gating. This is because due to the purely two dimensional nature of graphene, substrate induced potential fluctuations obscure the intrinsic physics of the charge carriers close to the Dirac point.One way to overcome this limitation is to use suspended samples 7,8 where transport measurements have shown that in the absence of the substrate the intrinsic Dirac point physics including interaction effects is revealed 9,10 . The use of suspended samples is however limited due to their fragility, small size and reduced range of gating. Finding a minimally invasive insulating substrate on which graphene can be gated and also visualized is therefore of great interest.By using scanning tunneling microscopy (STM) and spectroscopy (STS) we show that for graphene supported on SiO 2 substrates which were treated by chlorination to minimize trapped charges and in sufficiently large magnetic fields, the LL sequence specific to single layer graphene and its dependence on carrier density can be accessed. Upon varying the carrier-density sudden jumps of the Fermi-energy are observed after filling each LL. Moreover the measured density-dependence of the LL spacing shows a rapid increase upon approaching the Dirac-point, consistent with an interaction-induced renormalization of the Dirac cone.A simple method for preparing high quality graphene samples is mechanical exfoliation from graphite followed by deposition on the surface of SiO 2 capping a Si crystal 3 . This relative ease of samp...

Nanoelectrical analysis of single molecules and atomic-scale materials at the solid/liquid interface

“…Figure 4b shows a well-resolved dI /dV spectrum (acquired over the sites indicated in the in situ STM image, Fig. 4a) with a distinctive line shape resembling the energy spectrum of graphene, similar to previous STS observations of graphene on non-metallic substrates [51][52][53] . The minimum in each of the directly measured spectral curves corresponds to the charge-neutral Dirac point (E D ) located at positive bias energy slightly above the Fermi level.…”

Probing Electronic Properties of Graphene on the Atomic Scale by Scanning Tunneling Microscopy and Spectroscopy

“…Xue et al also observed the signi cantly reduced charge inhomogeneities in graphene/BN by STM/STS [165]. Due to the improved electronic quality of graphene on BN, the fractional quantum Hall e ect [170], unconventional quantum Hall effect in tri-layer graphene [171] and ballistic transport at room temperature [172] The Landau level quantization was observed for graphene on SiO in STM and STS measurements in a magnetic eld [72,163]. Compared to graphene on conductive substrates, graphene on insulating SiO is convenient for controlling the charge carrier density in graphene with a back gate, and thus the dependence of Landau quantization on the charge carrier density can be measured.…”

“…High resolution STM images have been achieved for graphene on SiO [56,[161][162][163][164][165] as well as on BN [57,165]. The measured root-mean-square (RMS) surface roughness of graphene/SiO is 1.5 -5.0 Å (∼ 1.5 Å, 60 nm ×60 nm [56]; ∼ 1.5 Å, 30 nm ×30 nm [58]; ∼ 1.9 Å, 250 nm ×200 nm [161]; ∼ 5.0 Å, 10 nm ×10 nm [162]; ∼ 3.5 Å, 195 nm ×178 nm [164]; ∼ 2.2 Å, 100 nm ×100 nm [165]).…”

“…Stolyarova et al observed the hexagonal honeycomb lattice for single-layer graphene on SiO and the triangular lattice, arising from the three-fold symmetry due to Bernal (AB) stacking, for multi-layer graphene on SiO [162]; and no prominent signs of substrate-induced perturbations to graphene were observed in their STM measurements [162]. Zhang et al and Luican et al also observed the hexagonal honeycomb lattice for single-layer graphene on SiO [56,58,163]. The hexagonal honeycomb lattice was observed for graphene on BN in STM measurements [57,165].…”

“…STM and STS measurements of graphene/SiO and graphene/BN have revealed interesting electronic properties of graphene including phonon-mediated inelastic electron tunneling [56,57], charge puddles [57,58], charge carrier dependence of Landau levels [163], and localization resonances in high magnetic elds [72].…”