# Building Weyl fermions from topological insulators

Topological insulators are all the rage these days. Our group got in on the ground floor (you can read our old web posting on this here ), in this paper , where we actually coined the term topological insulators. The most interesting property of a topological insulator is that it has "protected" gapless states bound to its surface, regardless of the nature of the surface (provided time reversal symmetry is maintained). By now there are several good reviews on the subject, such as this one .

A more recent development is that theorists have noticed that protected surface states can arise even in gapless systems. An interesting case is what has recently been called a "Weyl semimetal". What this is in fact is a case when two bands accidentally touch at isolated points in the Brillouin zone. Such accidental touchings can occur without fine tuning in three dimensions, provided the bands are non-degenerate. The latter condition means that at least one of time reversal or inversion symmetry is broken, and spin-orbit coupling is not negligible. Such accidental touchings have been known since the beginnings of the quantum theory of solids, but the implications for the surface are new.

The surface states, which give rise to "Fermi arcs", were pointed out in this paper. Another nice recent paper is here . You might also like to read a short "Viewpoint" article on the APS web site I wrote - here . ^ TOP

# Our work:

The above papers focused on a rather complicated material,
relying on * ab initio * LDA+U calculations to obtain the band
structure and magnetic state. With Anton Burkov , we showed that a Weyl semimetal
can be engineered by building a superlattice of topological
insulators separated by tunnel barriers. In this way we obtain a
much simpler example of a Weyl semimetal, and obtain its properties.
One new finding is that the Weyl semimetal is really a metal in the
sense of low-temperature DC transport, with a large conductivity when
disorder is weak. Previously, it had erroneously been claimed to be
an insulator.

Read the paper.