Probing the Extended-state Width of Disorder-broadened Landau Levels in Epitaxial Graphene

Keiko Takase¹, Hiroki Hibino², and Koji Muraki¹
¹Physical Science Laboratory, ²Materials Science Laboratory

　 Graphene is theoretically predicted to have a zero-energy Landau level, the energy width of which depends on the types of disorder; the energy width is ideally nearly zero in the presence of typical hopping disorder such as ripples, owing to protected chiral symmetry associated with graphene sublattice-symmetry. Previously, we developed transport energy-spectroscopy techniques relaying on densities of interface states involved in epitaxial graphene device [1]. Using the technique, here we report temperature dependences of the energy widths of the extended states of the zero-energy and first excited Landau levels, from which we can also deduce exponents corresponding to the critical exponents used in the quantum Hall plateau-plateau transition. The energy widths obtained from the spectroscopy technique are also compared with the energy widths deduced from the activation gap measurements [2].
　Figure 1(a) shows longitudinal resistance as a function of gate voltage (V_g) and magnetic field (B). Due to the presence of the interface states in gate insulator or in SiC underneath the graphene (Fig. 1(b)), trajectories of the longitudinal-resistance peaks become parabolic, reflecting the unequally-spaced graphene Landau levels. Such a V_g-B relation enables us to deduce the energy width ∆E_N of the extended states of the Nth Landau level. Figure 1(c) and (d) show temperature (T) dependences of ∆E₀ and ∆E₁. These show that ∆E₀ and ∆E₁ have similar magnitudes and are proportional to T^η with η = 0.30 - 0.31 for ∆E₀ and η = 0.32 - 0.35 for ∆E₁. These values are comparable to the critical components previously deduced from the plateau-plateau transition in quantum Hall regimes. Moreover, we deduced the energy widths independently using activation gap measurements. The energy width for N = 1 Landau level show a good agreement between two different types of measurement methods, while the energy width for the N = 0 Landau level obtained from activation gap measurement is larger by 30 meV than that deduced from the transport energy-spectroscopy.
　Using these two different measurement techniques systematically, we demonstrate that our device include random disorder rather than typical hopping disorder such as ripples.
　This work was partly supported by KAKENHI.