Graphene at High Magnetic Fields I kyky E kxkx Recently, a new form of carbon has become a laboratory for new physics: a single sheet of graphite, known as graphene, consists of a sub-nanometer, hexagonal array of carbon atoms. Graphene is simply a single sheet of graphite, the material found in pencils everywhere, and consists of a hexagonal array of carbon atoms (above). PI: Philip Kim, Department of Physics, Columbia University Supported by NSF (No. DMR and No. CHE ), NYSTAR DOE (No. DE-AIO2-04ER46133 and No. DE-FG02-05ER46215), and Keck Foundation PI: Gregory S. Boebinger, National High Magnetic Field Laboratory Florida State University, University of Florida, Los Alamos National Laboratory Supported by NSF (No. DMR ), and State of Florida The traditionally hidden quantum scale is becoming increasingly evident in new, state-of-the-art materials, including semiconductors for electronics, optical devices for communications, superconductors for (MRI) magnets, and ultra-strong composites for aircraft. The broadest challenge for 21st century materials research is the understanding, prediction, design, and control of the complex quantum phenomena found in Quantum Matter. The Quantum Matter studied in the MagLab user program is extremely varied, increasingly complex in its behavior, and often nano-structured… …graphene is one of the weirder examples… The hexagonal symmetry of the lattice and the nano-scale size of the hexagons combine to give the electrons in graphene an unusual “relativistic” property: a linear dependence of energy on momentum (left) This gives rise to new quantum behaviors…different from those seen in familiar semiconductors.

Using the Magnet Lab’s unique 45 tesla hybrid magnet, researchers have discovered Quantum Hall states in graphene at seven different filling factors: -6, -4, -2, and -1, as well as at filling factors +1, +2, and +4 (labeled at right). These quantum Hall states, seen only at high magnetic fields, are evidenced by the zero resistance in the longitudinal resistance (R xx black lines at right) and precisely quantized plateaus in the Hall resistance (R xy, red lines). kyky E kxkx Y. Zhang, Z. Jiang, J.P. Small, M.S. Purewal, Y.-W. Tan, M. Fazlollahi, J.D. Chudow, J.A. Jaszczak, H.L. Stormer, and P. Kim, Physical Review Letters, 96 (13), (2006) PI: Philip Kim, Department of Physics, Columbia University Supported by NSF (No. DMR and No. CHE ), NYSTAR DOE (No. DE-AIO2-04ER46133 and No. DE-FG02-05ER46215), and Keck Foundation In collaboration with the National High Magnetic Field Laboratory : PI: Greg Boebinger, Supported by NSF (No. DMR Florida State University, University of Florida, Los Alamos National Laboratory Recently, a new form of carbon has become a laboratory for new physics: a single sheet of graphite, known as graphene. B = 45T T = 1.4K h/e 2 The existence of Quantum Hall states at -4, -1, +1, and +4 is surprising, as it implies that an unknown broken symmetry – and hence a violated conservation law – is playing a role in graphene’s quantum behavior. The Quantum Hall effect (QHE) is one example of a quantum phenomenon that occurs on a truly macroscopic scale. The QHE, exclusive to two- dimensional metals, has led to the establishment of a new metrological standard, the resistance quantum,, that contains only fundamental constants. h/e 2 Graphene at High Magnetic Fields II

[2] Z. Jiang, E.A. Henriksen, L.C. Tung, Y.-J. Wang, M.E. Schwartz, M.Y. Han, P. Kim, and H.L. Stormer, Physical Review Letters, 98 (19), (2007). Most quantum phenomena require low temperatures (T <10K) to observe. In graphene, however, the Quantum Hall states at filling factors -2 and +2 are so robust that they persist all the way up to room temperature [1] -- ten times hotter than any other observation of a Quantum Hall state. This striking example of a new quantum phenomenon at room temperature might enable new applications once the underlying physics is well-understood. [1] K.S. Novoselov, Z. Jiang, Y. Zhang, S.V. Morozov, H.L. Stormer, U. Zeitler, J.C. Maan, G.S. Boebinger, P. Kim, and A.K. Geim, Science, 315 (5817), 1379 (2007). Recently, a new form of carbon has become a laboratory for new physics: a single sheet of graphite, known as graphene. ~ Recent infrared transmission measurements have directly observed the excitation of electrons between quantized energy levels, the Landau Levels, that result from the magnetic field [2]. The observed inter-Landau Level transition energies change as the square root of the magnetic field (right), unlike the linear dependence in semiconductors. This behavior allows researchers to distinguish several inter-Landau Level transitions in graphene, in striking contrast to traditional semiconductors, in which only one transition – the classical cyclotron resonance – is ever seen. This is another quantum mechanical phenomenon seen in graphene, and not seen in other materials. Figure: B-field dependence of the resonance energies in graphene. [2] Left inset, an infrared transmission spectrum at B=18T. Right inset, schematic of inter-Landau Level transitions. Graphene at High Magnetic Fields III