Graphene 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 p z 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 angle-resolved 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 p z 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 p z 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 very important.” The more complete first-principles calculations not only verified these conclusions, but also revealed additional information, such as the placement of the Dirac point (where the upper and lower cones intersect) at about 2 eV above the Fermi energy level, as compared to graphene where they intersect at the Fermi energy. One thing the calculations did not show was whether there was an energy gap at the Dirac point, because spin–orbit interactions were not included in the calculations. This is an important requirement for semiconductor-type applications.
Experimentally, borophene samples were prepared by molecular beam epitaxy on an Ag(111) substrate. Though weak, there is interaction between the borophene and the substrate that affects the electronic structure, including the Dirac cones. Matsuda’s group ascribed this interaction to a lattice mismatch that gives rise to a long-range modulated charge distribution on the surface that is observable as a Moiré pattern with scanning tunneling microscopy. One consequence of the periodic perturbation is the splitting of the Dirac cones. ARPES measurements provided a detailed catalog of these and other band-structure properties, including the observation that the Dirac point was now 0.25 eV below the Fermi energy because of hybridization between silver orbitals and the boron p z orbitals. The energy resolution of the measurements was not sufficient to detect a gap at the Dirac point. Applying first-principles calculations to the borophene-silver system yielded good agreement between experiment and theory.
Dirac cones for three lattices. (a) Honeycomb structure characteristic of graphene with a single cone; (b) β12 sheet characteristic of unperturbed borophene, also with a single cone; and (c) the β12 sheet with a periodic perturbation due to a weak interaction with the silver substrate that modifies the electronic structure and splits the cone—the blue and green balls represent the boron atoms with different on-site energies due to the perturbation in a tight-binding analysis. Note that the Dirac cones are in momentum space (energy versus momentum in x and y directions), whereas the lattices are in real space. Credit: Baojie Feng, The University of Tokyo.
“There are not that many two-dimensional materials that show a Dirac cone, so there is a lot of excitement when a new one is found, and it is important to investigate them thoroughly,” says graphene researcher Eli Rotenberg of the Lawrence Berkeley National Laboratory. The next step in investigating borophene, or indeed any of the 2D materials that may be produced, is tight integration of sample synthesis and characterization. “A difficulty with working with borophene films on silver is that the borophene exhibits multiple grain orientations, so ARPES sees an average of the different grain types,” Rotenberg says. “Up-and-coming nanoARPES instruments with state-of-the-art sample synthesis and preparation tools chambers may become useful to probe individual borophene grains in the future.”
