Quantum-Hall activation gaps in graphene
The quantum Hall effect (QHE) observed in two-dimensional electron systems (2DESs) is one of the fundamental quantum phenomena in solid state physics. Since its discovery in 1980 by K. von Klitzing it has been important for fundamental physics and application to quantum metrology. Recently a new member joined the family of 2DESs: graphene, a single layer of carbon atoms. Graphene displays a unique charge carrier spectrum of chiral Dirac fermions and enriches the QHE with a half integer QHE of massless relativistic particles observed in single-layer graphene and a novel type of integer QHE of massive chiral fermions in bilayers. Moreover, the band structure of graphene even allows the observation of the QHE up to room temperature. Since localization in conventional quantum Hall systems is already fully destroyed at moderate temperatures, no QHE has been observed at temperatures above 30 K until very recently. Therefore, understanding a room temperature QHE in graphene goes far beyond our comprehension of the traditional QHE.
In order to access this intriguing phenomenon in more detail we preformed systematic measurements of the inter Landau level activation gap in graphene for magnetic fields up to 32 T and temperatures from 4 K to 300 K. We observed that the gap between the zeroth and the first Landau level approaches the bare, unbroadened Landau-level separation for high magnetic fields and we explain these findings by a much narrower lowest Landau level compared to the other ones. In contrast, for higher Landau levels, the measured activation gap behaves as expected for equally broadened states.
Figure: (a) Scanning electron micrograph of the graphene multiterminal device. (b) Hall conductivity σxy and (c) conductivity σxx at 4.2 K (purple, solid) and at RT (red, dashed) as a function of the gate voltage at B = 30 T. (d) Energy gaps between two Landau levels as a function of magnetic field for ν = +2 (full red triangles) ν = -2 (open black circles) and ν = 6 (full blue squares). The dashed (red) and dotted (blue) lines are the theoretically expected energy gaps for sharp Landau levels. The insert shows schematically the density of states for a sharp zeroth Landau level and broadened higher Landau levels for electrons and holes at 30 T. The form and width of the higher Landau levels were extracted from experimental data. Extended states are represented by the white areas, localized states by the dashed areas.
This work was published in:
A.J.M. Giesbers, U. Zeitler, M.I. Katsnelson, L.A. Ponomarenko, T.M. Mohiuddin, J.C. Maan, Quantum-Hall activation gaps in graphene, Physical Review Letters 99, 206803 (2007).
Also available in Virtual Journal of Nanoscale Science & Technology, Nov. 26, Vol. 16, Issue 22 (2007).
Graphene: Quantum physics gets hot