Topological Quantum Chemistry
DIPC Seminars
 Speaker

Dr. Barry Bradlyn, University of Princeton
 When

2016/11/17
13:00  Place
 Donostia International Physics Center
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The interplay of topology and geometry has been  and continues to be  a
rich area of study for condensed matter physics. Recently, we have realized
that spatial symmetries allow for the stabilization of topological phases much
more exotic than those that can be found with timereversal symmetry alone;
however, a complete theory is still missing. In this talk, I will examine
topological metals and insulators stabilized by any of the 230 crystal
symmetry groups. I will develop a topological band theory that relates the
symmetry properties of real space Wannier functions to the global topology of
energy bands in momentum space. From this I will derive a predictive
classification of topological crystalline phases, well suited for both
predictions and abinitio materials searches. Focusing first on insulating
phases, I will show how our toplogical band theory sheds new light on old
topological insulators, before moving on to present a new slew of topological
insulators that we have predicted with our method. Additionally, I will show
how nonsymmorphic crystal symmetries can protect topological insulators with
novel surface states, through symmetry constraints on the band structure; this
includes a new toplogical phase whose surface spectrum consists of a single
fourfold degenerate Dirac fermion. Moving on to topological semimetals, I
will show how these same nonsymmorphic symmetries require the existence of
gapless freefermion excitations unlike any found in highenergy physics. This
includes the first natural generalization of the Weyl fermion, described by a
k⋅S Hamiltonian.