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Hyper-honeycombs Produce Electronic Surprise

Posted: December 20, 2015

Unit cell for the H-0 hyper honeycomb lattice, with 4 different atoms. All atoms are connected with three plannar and equally spaced bonds, as in the honeycomb lattice.

The simplest 3D generalization of the honeycomb lattice, the H-0 lattice.

Unit cell of the H-1 lattice, with 8 atoms in the unit cell. An infinite number of combinations are allowed.

In all lattice realizations of those structures, the two lowest branches in the electronic spectra cross at zero energy along a closed loop.

OU scientists have proposed a new family of structures called "hyper-honeycomb lattices". The atoms in those structures all posess the same planar trigonal connectivity in graphene, but are three dimensional.  In a recent publication in Physical Review Letters, Profs. Bruno Uchoa, Kieran Mullen and Dan Glatzhofer showed that those structures describe a new class of Dirac materials, which have been called "Dirac-line semimetals", and could lead to the realization of the 3D quantum Hall effect.

Honeycomb lattices,  the subject of the 2010 Nobel prize in Physics, are unusual in that the electrons move as relativistic massless neutrinos, and have many unusual properties such as a high mobility and exotic electron transport in a magnetic field.  The OU scientists have shown that this pattern can be generalized to a family of lattices in three dimensions.   These hyper-honeycomb structures can be thought of as a lattice of honeycomb ribbons, with each layer oriented at right angles to the one above it.  

This simple lattice produces a remarkable result. Normally the energy of electrons varies with the square of their momentum.  in graphene and Dirac materials, the energy of electons vanishes at special values of momentum and varies linearly away from those points. In hyper-honeycomb lattices the energy of electrons can vanish on a continuous loop of possible momenta, called a Dirac loop.  Again, this unusual behavior produces  transport properties that have very rarely been seen before, such as the possibility of quantized Landau levels in a three dimensional system, a property where electrons form cyclotronic orbits with quantized energy spectrum in the presence of a magnetic field. This property is usually observed in 2D systems, but is theoretically possible in crystals with a very anisotropic and multiply connected Fermi surface.  If the proposed structures can be experimentally realized in carbon form, the new ways to arrange carbon atoms would add to the ever-growing number of new carbon allotropes. The scientists also predict that, among its interesting properties, the hyper-honeycomb of carbon atoms could potentially be even more stable than diamond.

Read more at: http://phys.org/news/2015-07-scientists-3d-graphene-like-hyper-honeycomb.html#jCp