The quantum Hall effect (QHE), one example of a quantum phenomenon that occurs on a truly macroscopic scale, has been attracting intense interest since its discovery in 1980 (1). The QHE is exclusive to two-dimensional (2D) metals and has elucidated many important aspects of quantum physics and deepened our understanding of interacting systems. It has also led to the establishment of a new metrological standard, the resistance quantum h/e 2 that contains only fundamental constants of the electron charge e and the Planck constant h (2). As many other quantum phenomena, the observation of the QHE usually requires low temperatures T, typically below the boiling point of liquid helium (1). Efforts to extend the QHE temperature range by, for example, using semiconductors with small effective masses of charge carriers have so far failed to reach T above 30K (3,4). These efforts are driven by both innate desire to observe apparently fragile quantum phenomena under ambient conditions and the pragmatic need to perform metrology at room or, at least, liquid-nitrogen temperatures. More robust quantum states, implied by their persistence to higher T, would also provide added freedom to investigate finer features of the QHE and, possibly, allow higher quantization accuracy (2). Here, we show that in graphene -a single layer of carbon atoms tightly packed in a honeycomb crystal lattice -the QHE can be observed even at room temperature. This is due to the highly unusual nature of charge carriers in graphene, which behave as massless relativistic particles (Dirac fermions) and move with little scattering under ambient conditions (5). Figure 1 shows the room-T QHE in graphene. The Hall conductivity σxy reveals clear plateaux at 2e 2 /h for both electrons and holes, while the longitudinal conductivity ρxx approaches zero (<10Ω) exhibiting an activation energy ∆E ≈600K (Fig. 1B). The quantization in σxy is exact within an experimental accuracy of ≈0.2% (see Fig. 1C Fig. 1B). This implies that, in our experiments at room temperature, ω h exceeded the thermal energy kBT by a factor of 10. Importantly, in addition to the large cyclotron gap, there are a number of other factors that help the QHE in graphene to survive to so high temperatures. First, graphene devices allow for very high carrier concentrations (up to 10 13 cm -2 ) with only a single 2D subband occupied, which is essential to fully populate the lowest LL even in ultra-high B. This is in contrast to traditional 2D systems (for example, GaAs heterostructures) which are either depopulated already in moderate B or exhibit multiple subband occupation leading to the reduction of the effective energy gap to values well below ω h . Second, the mobility µ of Dirac fermions in our samples does not change appreciably from liquid-helium to room temperature. It remains at ≈10,000 cm 2 /Vs, which yields a scattering time of 13 10 − τ sec so that the high field limit 1 >> ⋅ = B µ ωτ is reached in fields of several T. These characteristics of graphene foster hopes for the room-T QHE obs...

Pulsed magnetic fields of up to 55T are used to investigate the transport properties of the topological insulator Bi2Se3 in the extreme quantum limit. For samples with a bulk carrier density of n = 2.9 × 10 16 cm −3 , the lowest Landau level of the bulk 3D Fermi surface is reached by a field of 4T. For fields well beyond this limit, Shubnikov-de Haas oscillations arising from quantization of the 2D surface state are observed, with the ν =1 Landau level attained by a field of ∼ 35T. These measurements reveal the presence of additional oscillations which occur at fields corresponding to simple rational fractions of the integer Landau indices.The recent prediction and discovery that Bi 2 Se 3 and Bi 2 Te 3 are three-dimensional topological insulators (TI) [1][2][3][4][5] has sparked a flurry of investigations. In a magnetic field, their relativistic dispersion causes the energy spectrum to be quantized so that E ν ∝ √ Bν, where B is the magnetic field and ν = 1, 2, 3, .., is the energy level, known as the Landau level (LL). The progression of energy levels E ν has been recently observed in scanningtunneling microscopy (STM) on Bi 2 Se 3 [6,7]. Other experiments on bulk samples and nanoribbons have reported universal conductance fluctuations attributed to the surface state [8,9]. However, all of the unambiguous measurements for the existence of the surface state have been made by surface sensitive probes. In this letter, we study samples of (Bi 1−x Sb x ) 2 Se 3 in which the Fermi surface of the Dirac fermions is small enough that pulsed fields of up to 55 T can access their quantum limit -the limit in which only a few of the lowest LLs are occupied. This is achieved by depleting the carrier density of the bulk and thereby reducing the size of the Dirac Fermi surface [10,11]). We demonstrate for the first time, a system in which not only the transport properties of Dirac fermions can be studied, but studied in the 2D quantum limit where novel correlation effects are most likely to arise [12,13].Generally speaking, transport measurements in Bi 2 Se 3 and Bi 2 Te 3 are plagued by bulk conducting channels from either the conduction band or by impurity bands introduced by foreign dopants [14,15]. The materials challenge is therefore finding a way to cleanly eliminate the bulk conductivity so that the properties of the surface can be observed. However, the carrier densities reported to date in studies of TI remain only as low [2][3][4][5] and 33×10 16 cm −3 (red and orange curves on Figure 1 (a)) were obtained by slow cooling a binary melt with different Bi:Se ratio. The principal origin of these relatively high carrier densities is Se deficiency and antisite defects. Samples with n≤ 11 × 10 16 cm −3 were obtained by slow cooling a ternary melt containing progressively more Sb. Although Sb is isovalent with Bi, Sb substitution apparently acts to control the defect density in the bulk crystals, reducing the bulk carrier density. Before measurements were performed, samples were cleaved on both sides with a scalpel blade i...