Abstract
Gyroscopic metamaterials, mechanical structures composed of interacting spinning tops, have recently been found to support one-way topological edge waves. In these structures, the time-reversal symmetry breaking that enables their topological behavior emerges directly from the lattice geometry. Here we show that variations in the lattice geometry can give rise to more complex band topology than has been previously described. A “spindle” lattice (or truncated hexagonal tiling) of gyroscopes possesses both clockwise and counterclockwise edge modes distributed across several band gaps. Tuning the interaction strength or twisting the lattice structure along a Guest mode opens and closes these gaps and yields bands with Chern numbers of |C| > 1 without introducing next-nearest-neighbor interactions or staggered potentials. A deformable honeycomb structure provides a simple model for understanding the role of lattice geometry in constraining the effects of time-reversal symmetry and inversion symmetry breaking. Last, we find that topological band structure generically arises in gyroscopic networks, and a simple protocol generates lattices with topological excitations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
R. Süsstrunk, S.D. Huber, Observation of phononic helical edge states in a mechanical topological insulator. Science 349(6243), 47–50 (2015)
L.M. Nash, D. Kleckner, A. Read, V. Vitelli, A.M. Turner, W.T.M. Irvine, Topological mechanics of gyroscopic metamaterials. Proc. Nat. Acad. Sci. 112(47), 14495–14500 (2015)
C.L. Kane, T.C. Lubensky, Topological boundary modes in isostatic lattices. Nat. Phys. 10(1), 39–45 (2013)
R. Fleury, D.L. Sounas, C.F. Sieck, M.R. Haberman, A. Alù, Sound Isolation and giant linear nonreciprocity in a compact acoustic circulator. Science 343(6170), 516–519 (2014)
D.J. Thouless, M. Kohmoto, M.P. Nightingale, M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49(6), 405–408 (1982)
N.P. Mitchell, L.M. Nash, W.T.M. Irvine, Realization of a topological phase transition in a gyroscopic lattice. Phys. Rev. B 97(10), 100302 (2018)
N.P. Mitchell, L.M. Nash, W.T.M. Irvine, Tunable band topology in gyroscopic lattices. Phys. Rev. B 98(17), 174301 (2018)
N.P. Mitchell, L.M. Nash, D. Hexner, A.M. Turner, W.T.M. Irvine, Amorphous topological insulators constructed from random point sets. Nat. Phys. 14(4), 380–385 (2018)
M.C. Rechtsman, J.M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, Photonic floquet topological insulators. Nature 496(7444), 196–200 (2013)
P. Wang, L. Lu, K. Bertoldi, Topological phononic crystals with one-way elastic edge waves. Phys. Rev. Lett. 115(10), 104302 (2015)
F.D.M. Haldane, Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “Parity Anomaly”. Phys. Rev. Lett. 61(18), 2015–2018 (1988)
F.D.M. Haldane, S. Raghu, Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100(1), 013904 (2008)
R. Fleury, A.B. Khanikaev, A. Alù, Floquet topological insulators for sound. Nat. Commun. 7, 11744 (2016)
A.B. Khanikaev, R. Fleury, S.H. Mousavi, A. Alù, Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice. Nat. Commun. 6, 8260 (2015)
A. Souslov, B.C. van Zuiden, D. Bartolo, V. Vitelli, Topological sound in active-liquid metamaterials. Nat. Phys. 13(11), 1091–1094 (2017)
S. Maayani, R. Dahan, Y. Kligerman, E. Moses, A.U. Hassan, H. Jing, F. Nori, D.N. Christodoulides, T. Carmon, Flying couplers above spinning resonators generate irreversible refraction. Nature 558(7711), 569–572 (2018)
J.E. Avron, R. Seiler, B. Simon, Homotopy and quantization in condensed matter physics. Phys. Rev. Lett. 51(1), 51–53 (1983)
R.B. Laughlin, Quantized Hall conductivity in two dimensions. Phys. Rev. B 23(10), 5632–5633 (1981)
J.L. Mañes, F. Guinea, M.A.H. Vozmediano, Existence and topological stability of Fermi points in multilayered graphene. Phys. Rev. B 75(15), 155424 (2007)
N.W. Ashcroft, N.D. Mermin, Solid State Physics, 1st edn. (Cengage Learning, New York, 1976)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Mitchell, N. (2020). Tunable Band Topology in Gyroscopic Lattices. In: Geometric Control of Fracture and Topological Metamaterials. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-36361-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-36361-1_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-36360-4
Online ISBN: 978-3-030-36361-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)