Topological superconductivity in multifold fermion metals

Abstract

Abstract Recently, multifold fermions characterized by band crossings with multifold degeneracy and Fermi surfaces with higher Chern numbers have been discovered experimentally in AlPt (Schroter et al. in Nat Phys 15:759–765, 2019) and XSi(X = Rh,Co) (Sanchez et al. in Nature 567:500–505, 2019; Rao et al. in Nature 567:496–499, 2019; Takane et al. in Phys Rev Lett 122:076402, 2019). In this work, we largely expand the family of multifold fermion materials by pointing out that several well-studied noncentrosymmetric superconductors are indeed multifold fermion metals. Importantly, their normal state topological properties, which have been ignored in previous studies, play an important role in the superconducting properties. Taking $\mathrm{Li} _{2}\mathrm{Pd} _{3}\mathrm{B}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Li</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>Pd</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mi>B</mml:mi> </mml:math> and $\mathrm{Li} _{2}\mathrm{Pt} _{3}\mathrm{B}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Li</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>Pt</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mi>B</mml:mi> </mml:math> as examples, we found a large number of unconventional degenerate points, such as double spin-1, spin-3/2, Weyl and double Weyl topological band crossing points near the Fermi energy, which result in finite Chern numbers on Fermi surfaces. Long Fermi arc states in $\mathrm{Li} _{2}\mathrm{Pd} _{3}\mathrm{B}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Li</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>Pd</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mi>B</mml:mi> </mml:math> , originating from the nontrivial band topology were found. Importantly, it has been shown experimentally that $\mathrm{Li} _{2}\mathrm{Pd} _{3}\mathrm{B}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Li</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>Pd</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mi>B</mml:mi> </mml:math> and $\mathrm{Li} _{2}\mathrm{Pt} _{3}\mathrm{B}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Li</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>Pt</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mi>B</mml:mi> </mml:math> are fully gapped and gapless superconductors, respectively. By analyzing the possible pairing symmetries, we suggest that $\mathrm{Li} _{2}\mathrm{Pd} _{3}\mathrm{B}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Li</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>Pd</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mi>B</mml:mi> </mml:math> is a conventional s-wave superconductor or DIII class topological superconductor with Majorana surface states. $\mathrm{Li} _{2}\mathrm{Pt} _{3}\mathrm{B}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Li</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>Pt</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mi>B</mml:mi> </mml:math> , being gapless, is likely to be a nodal topological superconductor with dispersionless surface Majorana modes. We further identified that several noncentrosymmetric superconductors, such as $\mathrm{Mo} _{3}\mathrm{Al} _{2}\mathrm{C}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Mo</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:msub> <mml:mi>Al</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mi>C</mml:mi> </mml:math> , PdBiSe, $\mathrm{Y}_{2}\mathrm{C}_{3}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Y</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> and $\mathrm{La} _{2}\mathrm{C}_{3}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>La</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> , are multifold fermion superconductors. This work calls for a revisit for the study of noncentrosymmtric superconductors which provide platforms for investigating the interplay between superconductivity and topologically nontrivial Fermi surfaces.