Degenerate topological line surface phonons in quasi-1D double helix crystal SnIP

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jats:titleAbstract</jats:title>jats:pDegenerate points/lines in the band structures of crystals have become a staple of the growing number of topological materials. The bulk-boundary correspondence provides a relation between bulk topology and surface states. While line degeneracies of bulk excitations have been extensively characterised, line degeneracies of surface states are not well understood. We show that SnIP, a quasi-one-dimensional van der Waals material with a double helix crystal structure, exhibits topological nodal rings/lines in both the bulk phonon modes and their corresponding surface states. Using a combination of first-principles calculations, symmetry-based indicator theories and Zak phase analysis, we find that two neighbouring bulk nodal rings form doubly degenerate lines in their drumhead-like surface states, which are protected by the combination of time-reversal symmetry jats:inline-formulajats:alternativesjats:tex-math$${{{\mathcal{T}}}}$$</jats:tex-math><mml:math xmlns:mml=""> mml:miT</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> and glide mirror symmetry jats:inline-formulajats:alternativesjats:tex-math$${\bar{M}}{y}$$</jats:tex-math><mml:math xmlns:mml=""> mml:msub mml:mrow mml:mover mml:mrow mml:miM</mml:mi> </mml:mrow> mml:mo¯</mml:mo> </mml:mover> </mml:mrow> mml:mrow mml:miy</mml:mi> </mml:mrow> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>. Our results indicate that surface degeneracies can be generically protected by symmetries such as jats:inline-formulajats:alternativesjats:tex-math$${{{\mathcal{T}}}}{\bar{M}}{y}$$</jats:tex-math><mml:math xmlns:mml=""> mml:mrow mml:miT</mml:mi> mml:msub mml:mrow mml:mover mml:mrow mml:miM</mml:mi> </mml:mrow> mml:mo¯</mml:mo> </mml:mover> </mml:mrow> mml:mrow mml:miy</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>, and phonons provide an ideal platform to explore such degeneracies.</jats:p>

51 Physical Sciences, 5104 Condensed Matter Physics
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npj Computational Materials
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Springer Science and Business Media LLC
Engineering and Physical Sciences Research Council (EP/P020259/1)