TY - JOUR

T1 - Topological nodal cooper pairing in doped weyl metals

AU - Li, Yi

AU - Haldane, F. D.M.

N1 - Funding Information:
Y. L. thanks N. P. Ong and C. Wu for consistent encouragement on this project. Y. L. was supported by the Princeton Center for Theoretical Science at Princeton University and in part by the U.S. Department of Energy, Office of Basic Science, Division of Materials Sciences and Engineering, Grant No. DE-FG02-08ER46544. F. D. M. H. was supported in part by the MRSEC program at Princeton Center for Complex Materials, Grant No. NSF-DMR-1420541, and by the W. M. Keck Foundation.
Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/2/9

Y1 - 2018/2/9

N2 - We generalize the concept of Berry connection of the single-electron band structure to that of a two-particle Cooper pairing state between two Fermi surfaces with opposite Chern numbers. Because of underlying Fermi surface topology, the pairing Berry phase acquires nontrivial monopole structure. Consequently, pairing gap functions have topologically protected nodal structure as vortices in the momentum space with the total vorticity solely determined by the pair monopole charge qp. The nodes of gap function behave as the Weyl-Majorana points of the Bogoliubov-de Gennes pairing Hamiltonian. Their relation with the connection patterns of the surface modes from the Weyl band structure and the Majorana surface modes inside the pairing gap is also discussed. Under the approximation of spherical Fermi surfaces, the pairing symmetry are represented by monopole harmonic functions. The lowest possible pairing channel carries angular momentum number j=|qp|, and the corresponding gap functions are holomorphic or antiholomorphic functions on Fermi surfaces. After projected on the Fermi surfaces with nontrivial topology, all the partial-wave channels of pairing interactions acquire the monopole charge qp independent of concrete pairing mechanism.

AB - We generalize the concept of Berry connection of the single-electron band structure to that of a two-particle Cooper pairing state between two Fermi surfaces with opposite Chern numbers. Because of underlying Fermi surface topology, the pairing Berry phase acquires nontrivial monopole structure. Consequently, pairing gap functions have topologically protected nodal structure as vortices in the momentum space with the total vorticity solely determined by the pair monopole charge qp. The nodes of gap function behave as the Weyl-Majorana points of the Bogoliubov-de Gennes pairing Hamiltonian. Their relation with the connection patterns of the surface modes from the Weyl band structure and the Majorana surface modes inside the pairing gap is also discussed. Under the approximation of spherical Fermi surfaces, the pairing symmetry are represented by monopole harmonic functions. The lowest possible pairing channel carries angular momentum number j=|qp|, and the corresponding gap functions are holomorphic or antiholomorphic functions on Fermi surfaces. After projected on the Fermi surfaces with nontrivial topology, all the partial-wave channels of pairing interactions acquire the monopole charge qp independent of concrete pairing mechanism.

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U2 - 10.1103/PhysRevLett.120.067003

DO - 10.1103/PhysRevLett.120.067003

M3 - Article

C2 - 29481220

AN - SCOPUS:85041925028

SN - 0031-9007

VL - 120

JO - Physical Review Letters

JF - Physical Review Letters

IS - 6

M1 - 067003

ER -