Kadanoff Seminar - Topology of three-dimensional Dirac semimetals: a tale of SO(5) monopoles and Hopf defects, Pallab Goswami, Northwestern University

1:30 pm MCP 201

Topology of three-dimensional Dirac semimetals: a tale of SO(5) monopoles and Hopf defects
Pallab Goswami, Northwestern University

Three-dimensional massless Dirac fermions can describe the dynamics of ultra-relativistic particles, as well as the low-energy physics of emergent, gapless excitations for many solid-state systems that preserve spatial-inversion and time-reversal symmetries. Such solid-state materials are collectively known as Dirac semimetals, which support linear touching of two Kramers-degenerate bands at isolated points in momentum space. For example, the massless Dirac fermions can arise as stable excitations in Cd3As2 and Na3Bi, and also as unstable excitations at topological quantum phase transitions in bismuth-antimony alloys and indium doped bismuth selenide.  

What are the bulk topological invariants of Dirac semimetals? Are the surface states of stable Dirac semimetals topologically protected? In this talk, I will provide affirmative answers to these open questions, by considering minimal models of band-structures for Dirac semimetals. These models generally involve a five-component vector field defined in momentum space, whose amplitude vanishes at Dirac points. By addressing the nature of non-Abelian SO(5) Berry’s vector potential, I will show that the topological properties of unstable and stable Dirac semimetals can be respectively understood in terms of Hopf defects and  a pair of monopole and anti-monopole. I will discuss the absence of helical Fermi arcs, the precise nature of surface states, and the bulk-boundary correspondence for stable Dirac semimetals, and additional experimental consequences for many materials.   

Event Type


Feb 3