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Tight-binding design having constructing 3d HO topological phases

Tight-binding design having constructing 3d HO topological phases

Contour 1

(a) three dimensional rigid-binding design. New half dozen orbitals in for each and every unit telephone means several other sublattices (coloured spheres). t 0 ‘s the intracell coupling, and you will t step 1 and t 2 will be inside-airplane and you may aside-of-airplane intercell couplings. (b) Faster topological phase drawing to your 2D monolayer system. New superficial and you may HO TI phase has actually some other topological indices ? ( 6 ) = ( [ M ] , [ K ] ) and you can Wannier facilities (black groups) to your down around three rings. The new bluish groups outline three you’ll evolution scenarios of your own k z cuts when h k z varies from ? ? so you’re able to ? . (c) Several three-dimensional HO topological stages understood from the all of our model, and TI and you will Dirac, Weyl, and you may nodal-ring (NR) semimetals. Brand new coloured affairs (rings) term the new HO Dirac otherwise Weyl items (NRs) that can come in the pairs. (d) Majority ring build having a set of couplings with which has HO DPs. The latest rings is actually branded of the C six v irreducible representations at higher-proportion momenta and also the C 2 parities along side ? An excellent line. (e) Topological indices ? ( six ) = ( [ Meters ] , [ K ] ) plotted as the a function of k z . (f) Hinge-projected range computed for an infinitely a lot of time hexagonal prism. They provides Murfreesboro escort service zero-energy hinge modes (purple outlines) connecting this new estimated DPs. Inset: Normal inside-airplane eigenfields of your hinge modes.

Contour 2

Acoustic summation of the (type-II) HO DPs. (a) In-flat lattice and design of our own three dimensional DSC. (b) Most ring design along highest-proportion tips. In the high-proportion affairs, a reduced three bands is characterized by an identical irreducible representations with the reasonable around three groups in Fig. step 1, with a nontrivial [ Yards ] list getting | k z | > k D (inset). (c) Hinge-estimated spectrum.