First experimental confirmation of Dirac cones in borophene
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First experimental confirmation of Dirac cones in borophene
G
raphene has, in just a few short years, captured the fancy of materials scientists and physicists because of its unique properties and the potential for tailoring them to obtain desired behaviors. Graphene has linear (as opposed to the usual parabolic ones) electron bands near the Fermi energy known as Dirac cones. Branching out from graphene, researchers have looked for analogous behavior in monolayers of other elements. A joint Japanese-Chinese-United States collaboration headed by Iwao Matsuda of The University of Tokyo has now provided the first experimental confirmation of the existence of Dirac cones in monolayer boron (or borophene). Moreover, they discovered a way to split the cones and possibly enlarge the spectrum of possible properties. “Our work not only suggests borophene could be a platform for developing new quantum devices but also opens a door to atomic-scale engineering in lattices with large unit cells to produce materials with novel properties,” says Baojie Feng, the first author of the report in Physical Review Letters (doi:10.1103/ PhysRevLett.118.096401). The Dirac cones in graphene are a consequence of the atomic structure of carbon and the resulting two-dimensional (2D) hexagonal or honeycomb lattice with two atoms per unit cell. The cones are primarily π and π* bands derived from pz orbitals. Researchers have sought Dirac cones in other monolayer materials with the same kind of honeycomb lattice, such as silicene, germanene, and stanene. Borophene, says Feng, was predicted to exist about 10 years ago but was only recently synthesized. One form of borophene on a silver substrate was observed to have a modified honeycomb lattice known as a β12 sheet, whose rows of honeycombs are alternately filled with an extra boron atom. Boron has one fewer electron than carbon, and the extra boron atoms are needed to stabilize the lattice. Matsuda’s group set out to explore the electronic properties of borophene, combining tight-binding and first-principles
calculations (density functional theory) of electronic structure with angleresolved photoemission spectroscopy (ARPES) studies at the Photon Factory synchrotron radiation facility at the KEK Laboratory in Tsukuba, Japan. With a simple tight-binding model involving only pz orbitals, the group was able to show the existence of Dirac cones, despite the apparent absence of a honeycomb lattice. When it comes to electronic structure, details of the quantum wave functions play an important role. Analyzing the pz wave function amplitudes at the boron atoms, the researchers showed that the β12 sheet could be decomposed into two sublattices. The extra boron atom sites were the only ones with zero amplitude in both sublattices. Superimposing the two resulted in an effective honeycomb lattice with nonzero amplitudes at its lattice sites. “From the tight-binding calculations, we know that the Dirac bands originate from an equivalent honeycomb lattice,” says Feng, “so the tight-binding calculations are
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