Unified Theory of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>P</mml:mi><mml:mi>T</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>Invariant Topological Metals and Nodal Superconductors

Zhao, Y. X.; Schnyder, Andreas P.; Wang, Z. D.

doi:10.1103/physrevlett.116.156402

Cited by 184 publications

(197 citation statements)

References 59 publications

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“…The fully gapped topological phases have been classified in terms of the existence of various antiunitary symmetriese.g., time-reversal and particle-hole symmetries [4,5]-and also the importance of the unitary symmetries is understood [6][7][8][9][10][11][12]. Recently there have been attempts to classify also the gapless topological phases [13][14][15][16][17][18][19][20]. In an ordinary d-dimensional metal a d − 1-dimensional Fermi surface separates the filled and empty states.…”

Section: Introductionmentioning

confidence: 99%

Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines

Hyart

Heikkilä

2016

Phys. Rev. B

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Three-dimensional topological semimetals come in different variants, either containing Weyl points or Dirac lines. Here we describe a more complicated momentum-space topological defect where several separate Dirac lines connect with each other, forming a momentum-space equivalent of the real-space nexus considered before for Helium-3. Close to the nexus the Dirac lines exhibit a transition from type I to type II lines. We consider a general model of stacked honeycomb lattices with the symmetry of Bernal (AB) stacked graphite and show that the structural mirror symmetries in such systems protect the presence of the Dirac lines, and also naturally lead to the formation of the nexus. By the bulk-boundary correspondence of topological media, the presence of Dirac lines lead to the formation of drumhead surface states at the side surfaces of the system. We calculate the surface state spectrum, and especially illustrate the effect of the nexus on these states.

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Section: Introductionmentioning

confidence: 99%

Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines

Hyart

Heikkilä

2016

Phys. Rev. B

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“…It has recently been shown that Fermi surfaces of Hamiltonians with CP symmetry squaring to +1 can possess a non-trivial Z 2 charge, making them topologically stable against CP -preserving perturbations [32,33]. We now express the invariant in terms of the Pfaffian P (k).…”

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confidence: 99%

Bogoliubov Fermi Surfaces in Superconductors with Broken Time-Reversal Symmetry

2017

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It is commonly believed that in the absence of disorder or an external magnetic field, there are three possible types of superconducting excitation gaps: the gap is nodeless, it has point nodes, or it has line nodes. Here, we show that for an even-parity nodal superconducting state which spontaneously breaks time-reversal symmetry, the low-energy excitation spectrum generally does not belong to any of these categories; instead it has extended Bogoliubov Fermi surfaces. These Fermi surfaces can be visualized as two-dimensional surfaces generated by "inflating" point or line nodes into spheroids or tori, respectively. These inflated nodes are topologically protected from being gapped by a Z2 invariant, which we give in terms of a Pfaffian. We also show that superconducting states possessing these Fermi surfaces can be energetically stable. A crucial ingredient in our theory is that more than one band is involved in the pairing; since all candidate materials for even-parity superconductivity with broken time-reversal symmetry are multiband systems, we expect these Z2-protected Fermi surfaces to be ubiquitous.

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“…This interpretation naturally follows from the picture presented here. That Fermi surfaces may be topologically stable features of a gap structure follows from a topological Z 2 invariant associated with nodes of codimension-1 in even-parity time-reversal symmetry-broken superconductors [61,64]. Additional Bogoliubov Fermi surfaces generically occur on the Fermi surface equator, i.e., in the vicinity k z ¼ 0, of even-parity chiral pairings with odd M. For odd M, jJ; Mi is odd under twofold rotation about the z axis.…”

Section: Pseudospin-singlet Hamiltonian From Symmetrymentioning

confidence: 99%

“…Pseudospin-triplet pairing must be of odd-parity type, and therefore, nodes of codimension-1 (i.e., surfaces) are not topologically stable [61,64]. Since chiral pairing states are generically spin selective, the effective pseudopsin splitting δ is nonzero, implying that point nodes on the rotation axis (if they exist) are nondegenerate.…”

Section: Pseudospin-triplet Hamiltonian From Symmetrymentioning

confidence: 99%

Pairing States of Spin- 32 Fermions: Symmetry-Enforced Topological Gap Functions

Venderbos¹,

Savary²,

Ruhman³

et al. 2018

Phys. Rev. X

100

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We study the topological properties of superconductors with paired j ¼ 3 2 quasiparticles. Higher spin Fermi surfaces can arise, for instance, in strongly spin-orbit coupled band-inverted semimetals. Examples include the Bi-based half-Heusler materials, which have recently been established as low-temperature and low-carrier density superconductors. Motivated by this experimental observation, we obtain a comprehensive symmetry-based classification of topological pairing states in systems with higher angular momentum Cooper pairing. Our study consists of two main parts. First, we develop the phenomenological theory of multicomponent (i.e., higher angular momentum) pairing by classifying the stationary points of the free energy within a Ginzburg-Landau framework. Based on the symmetry classification of stationary pairing states, we then derive the symmetry-imposed constraints on their gap structures. We find that, depending on the symmetry quantum numbers of the Cooper pairs, different types of topological pairing states can occur: fully gapped topological superconductors in class DIII, Dirac superconductors, and superconductors hosting Majorana fermions. Notably, we find a series of nematic fully gapped topological superconductors, as well as double-and triple-Dirac superconductors, with quadratic and cubic dispersion, respectively. Our approach, applied here to the case of j ¼ 3 2 Cooper pairing, is rooted in the symmetry properties of pairing states, and can therefore also be applied to other systems with higher angular momentum and high-spin pairing. We conclude by relating our results to experimentally accessible signatures in thermodynamic and dynamic probes.

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Unified Theory ofPTandCPInvariant Topological Metals and Nodal Superconductors

Cited by 184 publications

References 59 publications

Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines

Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines

Bogoliubov Fermi Surfaces in Superconductors with Broken Time-Reversal Symmetry

Pairing States of Spin- 32 Fermions: Symmetry-Enforced Topological Gap Functions

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