Topological nonsymmorphic crystalline superconductors

Wang, Qingze; Liu, Chaoxing

doi:10.1103/physrevb.93.020505

Cited by 44 publications

(42 citation statements)

References 74 publications

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“…TCSC hosts gapless boundary states on a surface preserving the crystalline symmetry, and such topological crystalline phases may be stable against disorders preserving the relevant symmetries on average [3], as evidenced for weak topological insulators and topological crystalline insulators [52][53][54][55][56]. Among various TCSC phases, TCSC in nonsymmorphic crystals forms a special class, dubbed topological nonsymmorphic crystalline superconductivity (TNCS) [51,[57][58][59][60]. In particular, TNCS enriched by glide symmetry possesses surfaces preserving the symmetry, and therefore, has symmetry-protected surface states.…”

Section: Realization Of Topological Superconductivity (Tsc)mentioning

confidence: 99%

Z4 Topological Superconductivity in UCoGe

2019

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Topological nonsymmorphic crystalline superconductivity (TNCS) is an intriguing phase of matter, offering a platform to study the interplay between topology, superconductivity, and nonsymmorphic crystalline symmetries. Interestingly, some of TNCS are classified into Z4 topological phases, which have unique surface states referred to as a Möbius strip or an hourglass, and have not been achieved in symmorphic superconductors. However, material realization of Z4 TNCS has never been known, to the best of our knowledge. Here we propose that the paramagnetic superconducting phase of UCoGe under pressure is a promising candidate of Z4-nontrivial TNCS enriched by glide symmetry. We evaluate Z4 invariants of UCoGe by deriving the formulas relating Z4 invariants to the topology of Fermi surfaces. Applying the formulas and previous ab-initio calculations, we clarify that three odd-parity representations, out of four, are Z4-nontrivial TNCS, while the other is also Z2-nontrivial TNCS. We also discuss possible Z4 TNCS in CrAs and related materials. PACS numbers: 74.20.-z, 74.70.-b arXiv:1803.07786v2 [cond-mat.supr-con]

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Section: Realization Of Topological Superconductivity (Tsc)mentioning

confidence: 99%

Z4 Topological Superconductivity in UCoGe

2019

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“…Cracks propagate preferentially through regions where the glass network is under-constrained, since there are fewer bonds to break. As a result, the toughness and damage resistance of glass can potentially be enhanced through tailoring the localized bond fluctuations [20].…”

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confidence: 99%

Statistical mechanics of topological fluctuations in glass-forming liquids

Kirchner

Kim

Mauro

2018

Physica A: Statistical Mechanics and its Applications

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All liquids are topologically disordered materials; however, the degree of disorder can vary as a result of internal fluctuations in structure and topology. These fluctuations depend on both the composition and temperature of the system. Most prior work has considered the mean values of liquid or glass properties, such as the average number of topological degrees of freedom per atom; however, the localized fluctuations in properties also play a key role in governing the macroscopic characteristics of any glass-forming system. This paper proposes a generalized approach for modeling topological fluctuations in glass-forming liquids by linking the statistical mechanics of the disordered structure to topological constraint theory. In doing so we introduce the contributions of localized fluctuations into the calculation of the topological degrees of freedoms in the network. With this approach the full distribution of properties in the disordered network can be calculated as an arbitrary function of composition, temperature, and thermal history (for the nonequilibrium glassy state). The scope of this current investigation focuses on describing topological fluctuations in liquids, concentrating on composition and temperature effects.

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“…Moreover, there are additional symmetries along x and y directions, which are represented by M x : x → −x, σ x ↔ σ y and M y : y → −y, σ x ↔ −σ y , respectively. Following the argument in reference [29], one concludes that such band crossing must occur at the zone boundary, as…”

Section: The Model and Its Realisationmentioning

confidence: 89%

“…This is not surprising, since G x+y = G x−y Tŷ(d), and H is commutable with both Tŷ(d) and G x−y (d). Nonsymmorphic crystalline symmetry has been considered in a variety of systems [27][28][29][30]. Here, we have the nonsymmorphic crystalline symmetry along both directions in this two-dimensional lattice.…”

Section: The Model and Its Realisationmentioning

confidence: 99%

Nodal Brillouin-zone boundary from folding a Chern insulator

2017

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Chern insulator is a building block of many topological quantum matters, ranging from quantum spin Hall insulators to fractional Chern insulators. Here, we discuss a new type of insulator, which consists of two half filled ordinary Chern insulators. On the one hand, the bulk energy spectrum is obtained from folding that of either Chern insulator. Such folding gives rise to a nodal boundary of the Brillouin zone, at which the band crossing is protected by the symmetries of the two-dimensional lattice that is invariant under combined transformations in the spatial and the spin space. It also provides one a natural platform to explore the non-abelian Berry curvature and the resultant quantum phenomena. On the other hand, these two underlying Chern insulators are distinguished from each other by nonsymmorphic operators, which lead to intriguing properties absent in conventional Chern insulators. A new degree of freedom, the parity of the nonsymmorphic symmetry, needs to be introduced for describing the topological pumping, if the edge respects the nonsymmorphic symmetry .In the band structure of a crystal, if different bands are separated from each other by finite band gaps, a Chern number [1], which is the integral of the abelian Berry curvature in the Brillouin zone (BZ), can be assigned to each individual band. A Chern insulator[2] arises if filling electrons to these bands leads to a finite total Chern number. Such Chern insulators are fundamental elements of a wide range of topological quantum matters [3][4][5]. For instance, one may obtain quantum spin Hall insulators [6][7][8] by assembling two insulators with both opposite spins and Chern numbers. Introducing interactions, fractional Chern insulators may emerge, in analogy to fractional quantum Hall states [9][10][11][12][13].The study of topological matters using ultracold atoms has been growing fast in the past a few years [14,15]. Using highly controllable atomic samples, a number of fundamentally important theoretical models have been realised, such as the Harper-Hofstadter model with a large magnetic flux per unit cell [16,17] and the topological Haldane model [18]. Meanwhile, many topological quantum quantities or phenomena, which are difficult to trace in solids, have been directly observed. For instance, both Zak phase and Chern numbers have been directly measured in optical lattices [19,20]. Topological charge pumping has also been realised recently [21,22]. Whereas most of the current studies have been focusing on abelian topological matters, it is promising that ultracold atoms may provides physicists a platform to explore non-abelian topological matters, as well as new quantum states and phenomena that have not been studied in the literature.In this Article, we study a new type of topological matter, whose bulk energy spectrum consists of two half filled ordinary Chern insulators. The band structure can be obtained from folding of that of either Chern insulator, which has BZ doubling the one of the realistic system. As a result of the folding, en...

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Topological nonsymmorphic crystalline superconductors

Cited by 44 publications

References 74 publications

Z4 Topological Superconductivity in UCoGe

Z4 Topological Superconductivity in UCoGe

Statistical mechanics of topological fluctuations in glass-forming liquids

Nodal Brillouin-zone boundary from folding a Chern insulator

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