Abstract
We propose that doped Weyl semimetals with {time-reversal and certain crystalline symmetries} are natural candidates to realize higher-order topological superconductors, which exhibit a fully gapped bulk while the surface hosts robust gapless chiral hinge states. We show that in such a doped Weyl semimetal, a featureless finite-range attractive interaction favors a p+ip pairing symmetry. By analyzing its topological properties, we identify such a chiral pairing state as a higher-order topological superconductor, which depending on the existence of a four-fold rotoinversion symmetry, is either intrinsic, {meaning that the corresponding hinge states can only be removed by closing the bulk gap, rather than modifying the surface states}, or extrinsic. We achieve this understanding via various methods recently developed for higher-order topology, including Wannier representability, Wannier spectrum, and defect classification approaches. For the four-fold rotoinversion symmetric case, we provide a complete classification of the higher-order topological superconductors. We show that such second-order topological superconductors exhibit chiral hinge modes that are robust in the absence of interaction effects but can be eliminated at the cost of introducing surface topological order.
Highlights
The notion of band topology has recently been extended to higher-order topology [7–29], with protected gapless states localized at the corners and hinges of the sample
Using the defect classification approach that we developed for higher-order topology in an earlier work [47], we find that the defect Hamiltonian H(k, θ ) for a tube enclosing the hinge has a second Chern number protected by the four-fold rotoinversion symmetry
We have shown that in a time-reversal symmetric doped Weyl semimetal, the combination of symmetry constraints (R4z and T) and momentum space structure of a finiterange attractive interaction naturally leads to a chiral superconducting state
Summary
Topological superconductivity [1–3, 3] combines two fascinating topics in condensed matter physics, topological phases of matter and unconventional superconductivity, and is the key component of fault-tolerant topological quantum computation [4, 5]. The notion of band topology has recently been extended to higher-order topology [7–29], with protected gapless states localized at the corners and hinges of the sample This opens up a new avenue for novel topological superconductivity [10,30–36], where many interesting open questions abound, including classification of such phases and its potential application in topological quantum computation. There have been several recent proposals along these lines, including potential higher-order topological superconducting phases (HOTSC) in FeSeTe, in two-dimensional Dirac semimetals [10,32,33,37–41], and in superconductors with unconventional p + id pairing symmetry [10, 42] It has been pointed out in several recent works [43, 44] that superconducting proximity effects between a quantum spin Hall insulator and a d-wave superconductor realizes a HOTSC phase. While the resulting superconductor is fully gapped in the bulk, it hosts gapless chiral Majorana modes at its hinges that are perpendicular to the plane of Weyl points These gapless hinge states are characteristic of second-order topology.
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