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| Dirac cone | |
|---|---|
| Name | Dirac cone |
| Field | Condensed matter physics |
| Introduced | 1928 |
| Discovered by | Paul Dirac |
Dirac cone A Dirac cone is a linear energy–momentum relation manifesting as a conical dispersion surface in the band structure of materials, where quasiparticles behave like relativistic Dirac fermions. It appears in systems with specific lattice symmetries and topology, leading to massless excitations that influence transport, optics, and magnetotransport. Dirac cones connect theoretical work by Paul Dirac, experimental breakthroughs associated with Andre Geim, Konstantin Novoselov, and materials studies involving Geim's collaborators, and have inspired research across institutions such as CERN, Max Planck Society, MIT, and Harvard University.
Dirac cones arise where conduction and valence bands meet at discrete points in the Brillouin zone, producing linear dispersion analogous to the relativistic equation introduced by Paul Dirac. Recognition of Dirac-like quasiparticles gained prominence after isolation of monolayer carbon in experiments by Andre Geim and Konstantin Novoselov at University of Manchester, which led to the Nobel Prize in Physics awarded to them. Related research paths involve theoretical contributions from Gordon Semenoff, Fritz Hassler, Eugene Wigner and experimental efforts at laboratories such as Bell Labs, IBM Research, and National High Magnetic Field Laboratory. Materials harboring Dirac cones connect to work on graphene, topological insulators, Weyl semimetals, and organic conductors investigated at Princeton University, Stanford University, and University of Cambridge.
Mathematically, a Dirac cone is described by a linearized Hamiltonian near a band-crossing point, often written in a 2×2 form analogous to the Dirac equation developed by Paul Dirac and earlier relativistic contexts considered by P.A.M. Dirac. The low-energy Hamiltonian typically involves Pauli matrices akin to formalisms used by Wolfgang Pauli and symmetry analysis methods from Emmy Noether and Hermann Weyl. Band topology classification invokes concepts from work by Michael Berry and Thouless such as Berry phase and Chern numbers, with mathematical tools used by researchers at ETH Zurich and Courant Institute. Brillouin zone geometry links to crystallographic groups cataloged by Eugene Wigner and analyses performed by groups at National Institute of Standards and Technology and Brookhaven National Laboratory.
Physical realizations include two-dimensional lattices like graphene studied at University of Manchester and three-dimensional analogues such as Na3Bi and Cd3As2 characterized by teams at Princeton University and Argonne National Laboratory. Surface Dirac cones occur on Bi2Se3 and Bi2Te3 investigated by researchers at Stanford University and Lawrence Berkeley National Laboratory. Organic conductors explored by groups at ETH Zurich and Tohoku University also show Dirac-like spectra. Engineered systems such as cold atoms in optical lattices developed at MIT and Max Planck Institute for Quantum Optics and photonic crystals fabricated by teams at Harvard University and IBM Research realize Dirac cones in synthetic settings. Discovery narratives involve collaborations among institutions including Columbia University, University of Tokyo, Tel Aviv University, and University of California, Berkeley.
Angle-resolved photoemission spectroscopy (ARPES) pioneered at Stanford University and Max Planck Society laboratories maps Dirac cones in materials like Bi2Se3 and graphene. Scanning tunneling microscopy (STM) developed at IBM Research and University of Zurich probes local density of states near Dirac points. Magnetotransport experiments at National High Magnetic Field Laboratory and Los Alamos National Laboratory reveal quantum Hall effects tied to Dirac dispersions, while cyclotron resonance measured at Bell Labs and University of Cambridge extracts velocity parameters. Optical spectroscopy groups at Columbia University and University College London use infrared and Raman techniques to study interband transitions, and cold-atom groups at MIT and ENS Paris employ time-of-flight imaging to reconstruct band structures.
Dirac cones impart high carrier mobility in graphene as shown by work at University of Manchester and Columbia University, and lead to unconventional quantum Hall sequences observed at Bell Labs and National High Magnetic Field Laboratory. Topological protection linked to time-reversal symmetry appears in Bi2Se3 studies by Stanford University and Lawrence Berkeley National Laboratory. Linear dispersion leads to relativistic-like phenomena analyzed by theorists at Harvard University, Princeton University, and Cornell University, including Klein tunneling studied by groups at University of Texas and University of Maryland. Anomalous magnetotransport in Weyl semimetals and related Dirac materials has been measured by teams at Argonne National Laboratory, Los Alamos National Laboratory, and Rice University.
Symmetry breaking by magnetic order investigated at Oak Ridge National Laboratory and Max Planck Institute for Solid State Research can gap Dirac cones, as seen in magnetic topological insulator work at University of California, Berkeley and University of Basel. Spin–orbit coupling effects central to Bi2Se3 investigations at Stanford University and Lawrence Berkeley National Laboratory open gaps and induce topological phases studied by theorists at MIT and Caltech. Strain engineering implemented by groups at University of Manchester and Columbia University shifts Dirac points or creates pseudo-magnetic fields; substrate interactions explored by IBM Research and National Institute for Materials Science also modify dispersions. Interaction-driven instabilities leading to mass generation have been modeled by teams at CERN, Perimeter Institute, and Institute for Advanced Study.
Applications exploit high mobility and tunable optical responses in electronics and optoelectronics pursued by researchers at IBM Research, Intel Corporation, Samsung Electronics, and HP Labs. Quantum technologies leveraging surface Dirac states are explored for spintronics at Hitachi and Sony research centers and for quantum computing applications by groups at Microsoft Research and Google Quantum AI. Sensor technologies utilizing graphene and topological materials have development efforts at Honeywell and Bosch while energy-related applications are being studied at Oak Ridge National Laboratory and National Renewable Energy Laboratory. Fundamental-platform experiments connecting to particle physics analogies engage collaborations across CERN, SLAC National Accelerator Laboratory, and Fermi National Accelerator Laboratory.