| 1. |
- Autieri, Carmine, et al.
(författare)
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Gap opening and large spin–orbit splitting in MX2 (M = Mo,W; X = S,Se,Te) from the interplay between crystal field and hybridisations : insights from ab-initio theory
- 2017
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Ingår i: Philosophical Magazine. - : Informa UK Limited. - 1478-6435 .- 1478-6443. ; 97:35, s. 3381-3395
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Tidskriftsartikel (refereegranskat)abstract
- By means of first-principles density functional calculations, we study the maximally localised Wannier functions for the 2D transition metal dichalcogenides MX2 (M = Mo, W; X = S, Se, Te). We have found that part of the energy gap is opened by the crystal field splitting induced by the X-2-like atoms. The inversion of the band character between the Gamma and the K points of the Brillouin zone is due to the M-M hybridisation. The consequence of this inversion is the closure of the gap in absence of the M-X hybridisation. The M-X hybridisation is the only one that tends to open the gap at every k-point. It is found that the change in the M-X and M-M hybridisation is the main responsible for the difference in the gap between the different dichalcogenide materials. The inversion of the bands gives rise to different spinorbit splitting at Gamma and K point in the valence band. The different character of the gap at Gamma and K point offers the chance to manipulate the semiconducting properties of these compounds. For a bilayer system, the hybridisation between the out-of-plane orbitals and the hybridisation between the in-plane orbitals split the valence band respectively at the Gamma and K point. The splitting in the valence band is opened also without spin-orbit coupling and occurs due to the M-M and X-X hybridisation between the two monolayers. The transition from direct to indirect band gap is governed by the hybridisation between out-of-plane orbitals of different layers and in-plane orbitals of different layers.
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| 2. |
- Awoga, Oladunjoye A., et al.
(författare)
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Domain walls in a chiral d-wave superconductor on the honeycomb lattice
- 2017
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 96:1
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Tidskriftsartikel (refereegranskat)abstract
- We perform a fully self-consistent study of domain walls between different chiral domains in chiral d(x2-y2) +/- id(xy) -wave superconductors with an underlying honeycomb lattice structure. We investigate domain walls along all possible armchair and zigzag directions and with a finite global phase shift across the domain wall, in addition to the change of chirality. For armchair domain walls we find the lowest domain wall energy at zero global phase shift, while the most favorable zigzag domain wall has a finite global phase shift dependent on the doping level. Belowthe van Hove singularity the armchair domain wall is most favorable, while at even higher doping the zigzag domain wall has the lowest energy. The domain wall causes a local suppression of the superconducting order parameter, with the superconducting recovery length following a universal curve for all domain walls. Moreover, we always find four subgap states crossing zero energy and well localized to the domain wall. However, the details of their energy spectrum vary notably, especially with the global phase shift across the domain wall.
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| 3. |
- Bouhon, Adrien, et al.
(författare)
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Geometric approach to fragile topology beyond symmetry indicators
- 2020
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Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 102:11
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Tidskriftsartikel (refereegranskat)abstract
- We present a framework to systematically address topological phases when finer partitionings of bands are taken into account, rather than only considering the two subspaces spanned by valence and conduction bands. Focusing on C2T-symmetric systems that have gained recent attention, for example, in the context of layered van-der-Waals graphene heterostructures, we relate these insights to homotopy groups of Grassmannians and flag varieties, which in turn correspond to cohomology classes and Wilson-flow approaches. We furthermore make use of a geometric construction, the so-called Plucker embedding, to induce windings in the band structure necessary to facilitate nontrivial topology. Specifically, this directly relates to the parametrization of the Grassmannian, which describes partitioning of an arbitrary band structure and is embedded in a better manageable exterior product space. From a physical perspective, our construction encapsulates and elucidates the concepts of fragile topological phases beyond symmetry indicators as well as non-Abelian reciprocal braiding of band nodes that arises when the multiple gaps are taken into account. The adopted geometric viewpoint most importantly culminates in a direct and easily implementable method to construct model Hamiltonians to study such phases, constituting a versatile theoretical tool.
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| 4. |
- Bouhon, Adrien, et al.
(författare)
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Global band topology of simple and double Dirac-point semimetals
- 2017
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Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 95:24
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Tidskriftsartikel (refereegranskat)abstract
- We combine space group representation theory together with the scanning of closed subdomains of the Brillouin zone with Wilson loops to algebraically determine the global band-structure topology. Considering space group No. 19 as a case study, we show that the energy ordering of the irreducible representations at the high-symmetry points {Gamma, S, T, U} fully determines the global band topology, with all topological classes characterized through their simple and double Dirac points.
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| 5. |
- Bouhon, Adrien, et al.
(författare)
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Non-Abelian reciprocal braiding of Weyl points and its manifestation in ZrTe
- 2020
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Ingår i: Nature Physics. - : Springer Science and Business Media LLC. - 1745-2473 .- 1745-2481. ; 16, s. 1137-1143
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Tidskriftsartikel (refereegranskat)abstract
- Weyl points in three-dimensional systems with certain symmetry carry non-Abelian topological charges, which can be transformed via non-trivial phase factors that arise upon braiding these points inside the reciprocal space. Weyl semimetals in three-dimensional crystals provide the paradigm example of topologically protected band nodes. It is usually taken for granted that a pair of colliding Weyl points annihilate whenever they carry opposite chiral charge. In stark contrast, here we report that Weyl points in systems that are symmetric under the composition of time reversal with a pi rotation are characterized by a non-Abelian topological invariant. The topological charges of the Weyl points are transformed via braid phase factors, which arise upon exchange inside symmetric planes of the reciprocal momentum space. We elucidate this process with an elementary two-dimensional tight-binding model that is implementable in cold-atom set-ups and in photonic systems. In three dimensions, interplay of the non-Abelian topology with point-group symmetry is shown to enable topological phase transitions in which pairs of Weyl points may scatter or convert into nodal-line rings. By combining our theoretical arguments with first-principles calculations, we predict that Weyl points occurring near the Fermi level of zirconium telluride carry non-trivial values of the non-Abelian charge, and that uniaxial compression strain drives a non-trivial conversion of the Weyl points into nodal lines.
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| 6. |
- Bouhon, Adrien, et al.
(författare)
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Topological correspondence between magnetic space group representations and subdimensions
- 2021
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Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 103:24
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Tidskriftsartikel (refereegranskat)abstract
- The past years have seen rapid progress in the classification of topological materials. These diagnostical methods are increasingly getting explored in the pertinent context of magnetic structures. We report on a general class of electronic configurations within a set of antiferromagnetic-compatible space groups that are necessarily topological. Interestingly, we find a systematic correspondence between these antiferromagnetic phases to necessarily nontrivial topological ferro/ferrimagnetic counterparts that are readily obtained through physically motivated perturbations. Addressing the exhaustive list of magnetic space groups in which this mechanism occurs, we also verify its presence on planes in 3D systems that were deemed trivial in existing classification schemes. This leads to the formulation of the concept of subdimensional topologies, featuring nontriviality within part of the system that coexists with stable Weyl points away from these planes, thereby uncovering novel topological materials in the full 3D sense that have readily observable features in their bulk and surface spectrum.
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| 7. |
- Bouhon, Adrien, et al.
(författare)
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Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice
- 2018
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Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 97:10
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Tidskriftsartikel (refereegranskat)abstract
- We establish the topology of the spin-singlet superconducting states in the bare hyperhoneycomb lattice, and we derive analytically the full phase diagram using only symmetry and topology in combination with simple energy arguments. The phase diagram is dominated by two states preserving time-reversal symmetry. We find a line-nodal state dominating at low doping levels that is topologically nontrivial and exhibits surface Majorana flatbands, which we show perfectly match the bulk-boundary correspondence using the Berry phase approach. At higher doping levels, we find a fully gapped state with trivial topology. By analytically calculating the topological invariant of the nodal lines, we derive the critical point between the line-nodal and fully gapped states as a function of both pairing parameters and doping. We find that the line-nodal state is favored not only at lower doping levels but also if symmetry-allowed deformations of the lattice are present. Adding simple energy arguments, we establish that a fully gapped state with broken time-reversal symmetry likely appears covering the actual phase transition. We find this fully gapped state to be topologically trivial, while we find an additional point-nodal state at very low doing levels that also break time-reversal symmetry and has nontrivial topology with associated Fermi surface arcs. We eventually address the robustness of the phase diagram to generalized models also including adiabatic spin-orbit coupling, and we show how all but the point-nodal state are reasonably stable.
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| 8. |
- Bouhon, Adrien, et al.
(författare)
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Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time-reversal symmetry
- 2019
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Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 100:19
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Tidskriftsartikel (refereegranskat)abstract
- We present a general methodology toward the systematic characterization of crystalline topological insulating phases with time-reversal symmetry. In particular, taking the two-dimensional spinful hexagonal lattice as a proof of principle, we study windings of Wilson loop spectra over cuts in the Brillouin zone that are dictated by the underlying lattice symmetries. Our approach finds a prominent use in elucidating and quantifying the recently proposed "topological quantum chemistry" concept. Namely, we prove that the split of an elementary band representation (EBR) by a band gap must lead to a topological phase. For this we first show that in addition to the Fu-Kane-Mele Z(2) classification, there is C2T-symmetry-protected Z classification of two-band subspaces that is obstructed by the other crystalline symmetries, i.e., forbidding the trivial phase. This accounts for all nontrivial Wilson loop windings of split EBRs that are independent of the parametrization of the flow of Wilson loops. Then, by systematically embedding all combinatorial four-band phases into six-band phases, we find a refined topological feature of split EBRs. Namely, we show that while Wilson loop winding of split EBRs can unwind when embedded in higher-dimensional band space, two-band subspaces that remain separated by a band gap from the other bands conserve their Wilson loop winding, hence revealing that split EBRs are at least "stably trivial," i.e., necessarily nontrivial in the nonstable (few-band) limit but possibly trivial in the stable (many-band) limit. This clarifies the nature of fragile topology that has appeared very recently. We then argue that in the many-band limit, the stable Wilson loop winding is only determined by the Fu-Kane-Mele Z(2) invariant implying that further stable topological phases must belong to the class of higher-order topological insulators.
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| 9. |
- Chen, Siyu, et al.
(författare)
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Non-Abelian braiding of Weyl nodes via symmetry-constrained phase transitions
- 2022
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Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 105:8
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Tidskriftsartikel (refereegranskat)abstract
- Weyl semimetals are arguably the most paradigmatic form of a gapless topological phase. While the stability of Weyl nodes, as quantified by their topological charge, has been extensively investigated, recent interest has shifted to the manipulation of the location of these Weyl nodes for non-Abelian braiding. To accomplish this braiding it is necessary to drive significant Weyl node motion using realistic experimental parameter changes. We show that a family of phase transitions characterized by certain symmetry constraints impose that the Weyl nodes have to reorganize by a large amount, shifting from one high-symmetry plane to another. Additionally, for a subset of pairs of nodes with nontrivial Euler class topology, this reorganization can only occur through a braiding process with adjacent nodes. As a result, the Weyl nodes are forced to move a large distance across the Brillouin zone and to braid, all driven by small temperature changes, a process we illustrate with Cd2Re2O7.
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| 10. |
- Chen, Xin, et al.
(författare)
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PAI-graphene : A new topological semimetallic two-dimensional carbon allotrope with highly tunable anisotropic Dirac cones
- 2020
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Ingår i: Carbon. - : Elsevier BV. - 0008-6223 .- 1873-3891. ; 170, s. 477-486
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Tidskriftsartikel (refereegranskat)abstract
- Using evolutionary algorithm for crystal structure prediction, we present a new stable two-dimensional (2D) carbon allotrope composed of polymerized as-indacenes (PAI) in a zigzag pattern, namely PAI-graphene whose energy is lower than most of the reported 2D allotropes of graphene. Crucially, the crystal structure realizes a nonsymmorphic layer group that enforces a nontrivial global topology of the band structure with two Dirac cones lying perfectly at the Fermi level. The absence of electron/hole pockets makes PAI-graphene a pristine crystalline topological semimetal having anisotropic Fermi velocities with a high value of 7.0×105" role="presentation"> m/s. We show that while the semimetallic property of the allotrope is robust against the application of strain, the positions of the Dirac cone and the Fermi velocities can be modified significantly with strain. Moreover, by combining strain along both the x- and y-directions, two band inversions take place at Γ" role="presentation"> leading to the annihilation of the Dirac nodes demonstrating the possibility of strain-controlled conversion of a topological semimetal into a semiconductor. Finally we formulate the bulk-boundary correspondence of the topological nodal phase in the form of a generalized Zak-phase argument finding a perfect agreement with the topological edge states computed for different edge-terminations.
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