With high quality topological insulator Bi(2)Se(3) thin films, we report thickness-independent transport properties over wide thickness ranges. Conductance remained nominally constant as the sample thickness changed from 256 to ∼8  QL (where QL refers to quintuple layer, 1  QL≈1  nm). Two surface channels of very different behaviors were identified. The sheet carrier density of one channel remained constant at ∼3.0×10(13)  cm(-2) down to 2 QL, while the other, which exhibited quantum oscillations, remained constant at ∼8×10(12)  cm(-2) only down to ∼8  QL. The weak antilocalization parameters also exhibited similar thickness independence. These two channels are most consistent with the topological surface states and the surface accumulation layers, respectively.

We show that a number of transport properties in topological insulator (TI) Bi 2 Se 3 exhibit striking thickness-dependences over a range of up to five orders of thickness (3 nm -170 µm). Volume carrier density decreased with thickness, presumably due to diffusion-limited formation of selenium vacancies. Mobility increased linearly with thickness in the thin film regime and saturated in the thick limit. The weak anti-

2Graphene and related two-dimensional materials are promising candidates for atomically thin, flexible, and transparent optoelectronics 1,2 . In particular, the strong light-matter interaction in graphene 3 has allowed for the development of state-of-the-art photodetectors 4,5 , optical modulators 6 , and plasmonic devices 7 .In addition, electrically biased graphene on SiO 2 substrates can be used as a low-efficiency emitter in the mid-infrared range 8,9 . However, emission in the visible range has remained elusive. Here we report the observation of bright visible-light emission from electrically biased suspended graphenes. In these devices, heat transport is greatly minimised 10 ; thus hot electrons (~ 2800 K) become spatially localised at the centre of graphene layer, resulting in a 1000-fold enhancement in the thermal radiation efficiency 8,9 . Moreover, strong optical interference between the suspended graphene and substrate can be utilized to tune the emission spectrum. We also demonstrate the scalability of this For the realisation of graphene-based bright and broadband light-emitters, a radiative electron-hole recombination process in gapless graphene is not efficient because of the rapid energy relaxation that occurs through electron-electron and electron-phonon interactions [11][12][13] .Alternatively, graphene's superior strength 14 and high-temperature stability may enable efficient thermal light emission. However, the thermal radiation from electrically biased graphene supported on a substrate 8,9,[15][16][17] has been found to be limited to the infrared range and 3 to be inefficient as an extremely small fraction of the applied energy (~ 10 -6 ) 8,9 is converted into light radiation. Such limitations are the direct result of heat dissipation through the underlying substrate 18 and significant hot electron relaxation from dominant extrinsic scattering effects such as charged impurities 19 and surface polar optical phonon interaction 20 , limiting the maximum operating temperatures.On the other hand, a freely suspended graphene is mostly immune to such undesirable vertical heat dissipation 10 and extrinsic scattering effects 21,22 , promising much more efficient and brighter radiation in the infrared-to-visible range. Fortuitously, due to the strong Umklapp phonon-phonon scattering 23 , we find that the thermal conductivity of graphene at high lattice temperatures (1800 ± 300 K) is greatly reduced (~ 65 Wm -1 K -1 ), which additionally suppresses lateral heat dissipation; therefore, hot electrons (~ 2800 K) become spatially localised at the centre of the suspended graphene under modest electric fields (~ 0.4 V/µm), greatly increasing the efficiency and brightness of the light emission. The bright visible thermally emitted light interacts with the reflected light from the separated substrate surface, allowing interference effects that can be utilized to tune the wavelength of the emitted light.We fabricate the freely suspended graphene devices with mechanically exfoliated graphene flakes, and for d...