When a superconductor is cooled below Tc, an energy gap opens in the single particle density of states, forming a gap much like that found in an insulator. Consequently, the recent advances demonstrating the crucial importance of topology, and the incompleteness of prior classification schemes, in true insulators and semimetals should apply to superconductors as well. Indeed, recent work by co-PI Li has shown that the traditional superconductor classification scheme, based on spherical harmonics, is incomplete, missing those that require “monopole” harmonics. We will design, synthesize, and characterize materials to explore and exploit the role of topology in superconductivity. Potential significant milestones in this decade-long effort include:

• Discovery of superconductivity in a Dirac Semimetal
• Demonstration of transformation of a Dirac Semimetal to a Weyl semimetal by time-reversal symmetry breaking (shared with the “Topological Magnetic Semimetals” thrust)
• Demonstration of proximity-induced superconductivity in a Dirac and/or Weyl semimetal
• Demonstration of monopole or related forms of superconducting pairing in a real superconductor