- Letter
- Open Access
Observation of Majorana-like bound states in metamaterial-based Kitaev chain analogs
Phys. Rev. Research 5, L012012 – Published 30 January, 2023
DOI: https://doi.org/10.1103/PhysRevResearch.5.L012012
Abstract
We experimentally demonstrate that Majorana-like bound states (MLBSs) can occur in quasi-one-dimensional metamaterials, analogous to Majorana zero modes (MZMs) in the Kitaev chain in terms of mode spectrum and mode wave functions. In a mechanical spinner ladder system, we observe a topological phase transition and spectral-gap-protected edge MLBSs. We characterize phase controllable hybridization and the decaying and oscillatory nature of these MLBS pairs. It is shown that the hybridization can be tuned to yield the analog of parity switching in MZMs. We find strong agreements with theory.
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References (51)
- E. Prodan and C. Prodan, Topological Phonon Modes and Their Role in Dynamic Instability of Microtubules, Phys. Rev. Lett. 103, 248101 (2009).
- S. D. Huber, Topological mechanics, Nat. Phys. 12, 621 (2016).
- C. L. Kane and T. C. Lubensky, Topological boundary modes in isostatic lattices, Nat. Phys. 10, 39 (2014).
- B. G.-G. Chen, B. Liu, A. A. Evans, J. Paulose, I. Cohen, V. Vitelli, and C. D. Santangelo, Topological Mechanics of Origami and Kirigami, Phys. Rev. Lett. 116, 135501 (2016).
- P. Gao, D. Torrent, F. Cervera, P. San-Jose, J. Sánchez-Dehesa, and J. Christensen, Majorana-like Zero Modes in Kekulé Distorted Sonic Lattices, Phys. Rev. Lett. 123, 196601 (2019).
- B. G.-G. Chen, N. Upadhyaya, and V. Vitelli, Nonlinear conduction via solitons in a topological mechanical insulator, Proc. Natl. Acad. Sci. USA 111, 13004 (2014).
- L. M. Nash, D. Kleckner, A. Read, V. Vitelli, A. M. Turner, and W. T. M. Irvine, Topological mechanics of gyroscopic metamaterials, Proc. Natl. Acad. Sci. USA 112, 14495 (2015).
- P. Wang, L. Lu, and K. Bertoldi, Topological Phononic Crystals with One-Way Elastic Edge Waves, Phys. Rev. Lett. 115, 104302 (2015).
- E. Majorana, Teoria simmetrica dell'elettrone e del positrone, Nuovo Cimento 14, 171 (1937).
- A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. 303, 2 (2003).
- C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. D. Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008)
- F. Wilczek, Majorana returns, Nat. Phys. 5, 614 (2009).
- R. M. Lutchyn, J. D. Sau, and S. D. Sarma, Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures, Phys. Rev. Lett. 105, 077001 (2010).
- Y. Oreg, G. Refael, and F. von Oppen, Helical Liquids and Majorana Bound States in Quantum Wires, Phys. Rev. Lett. 105, 177002 (2010).
- J. Alicea, New directions in the pursuit of Majorana fermions in solid state systems, Rep. Prog. Phys. 75, 076501 (2012).
- P. Hosur, P. Ghaemi, R. S. K. Mong, and A. Vishwanath, Majorana Modes at the Ends of Superconductor Vortices in Doped Topological Insulators, Phys. Rev. Lett. 107, 097001 (2011).
- M. Leijnse and K. Flensberg, Introduction to topological superconductivity and Majorana fermions, Semicond. Sci. Technol. 27, 124003 (2012).
- J. C. Teo and T. L. Hughes, Existence of Majorana-Fermion Bound States on Disclinations and the Classification of Topological Crystalline Superconductors in Two Dimensions, Phys. Rev. Lett. 111, 047006 (2013).
- S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDonald, B. A. Bernevig, and A. Yazdani, Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor, Science 346, 602 (2014).
- M. Sato and S. Fujimoto, Majorana fermions and topology in superconductors, J. Phys. Soc. Jpn. 85, 072001 (2016).
- A. Y. Kitaev, Unpaired Majorana fermions in quantum wires, Phys. Usp. 44, 131 (2001).
- Logic and Algebraic Structures in Quantum Computing, edited by J. Chubb, A. Eskandarian, and V. Harizanov (Cambridge University Press, Cambridge, 2016).
- B. Lian, X. Q. Sun, A. Vaezi, X. L. Qi, and S. C. Zhang, Topological quantum computation based on chiral Majorana fermions, Proc. Natl. Acad. Sci. USA 115, 10938 (2018).
- R. Aguado and L. Kouwenhoven, Majorana qubits for topological quantum computing, Phys. Today 73(6), 44 (2020).
- C. Tutschku, R. W. Reinthaler, C. Lei, A. H. MacDonald, and E. M. Hankiewicz, Majorana-based quantum computing in nanowire devices, Phys. Rev. B 102, 125407 (2020).
- T. L. Hughes, Majorana fermions inch closer to reality, Physics 4, 67 (2011).
- V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven, Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices, Science 336, 1003 (2012).
- L. P. Rokhinson, X. Liu, and J. K. Furdyna, The fractional a.c. Josephson effect in a semiconductor-superconductor nanowire as a signature of Majorana particles, Nat. Phys. 8, 795 (2012).
- A. Das, Y. Ronen, Y. Most, Y. Oreg, M. Heiblum, and H. Shtrikman, Zero-bias peaks and splitting in an Al-InAs nanowire topological superconductor as a signature of Majorana fermions, Nat. Phys. 8, 887 (2012).
- S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, and C. M. Marcus, Exponential protection of zero modes in Majorana islands, Nature (London) 531, 206 (2016).
- M. T. Deng, S. Vaitiekenas, E. B. Hansen, J. Danon, M. Leijnse, K. Flensberg, J. Nygård, P. Krogstrup, and C. M. Marcus, Majorana bound state in a coupled quantum-dot hybrid-nanowire system, Science 354, 1557 (2016).
- R. M. Lutchyn, E. P. A. M. Bakkers, L. P. Kouwenhoven, P. Krogstrup, C. M. Marcus, and Y. Oreg, Majorana zero modes in superconductor-semiconductor heterostructures, Nat. Rev. Mater. 3, 52 (2018).
- Z. Wang, J. O. Rodriguez, L. Jiao, S. Howard, M. Graham, G. D. Gu, T. L. Hughes, D. K. Morr, and V. Madhavan, Evidence for dispersing 1D Majorana channels in an iron-based superconductor, Science 367, 104 (2020).
- S. Vishveshwara and D. M. Weld, phases and Majorana spectroscopy in paired Bose-Hubbard chains, Phys. Rev. A 103, L051301 (2021).
- A. McDonald, T. Pereg-Barnea, and A. A. Clerk, Phase-Dependent Chiral Transport and Effective Non-Hermitian Dynamics in a Bosonic Kitaev-Majorana Chain, Phys. Rev. X 8, 041031 (2018).
- Y. Barlas and E. Prodan, Topological Braiding of Non-Abelian Midgap Defects in Classical Metamaterials, Phys. Rev. Lett. 124, 146801 (2020).
- K. Padavić, S. S. Hegde, W. DeGottardi, and S. Vishveshwara, Topological phases, edge modes, and the Hofstadter butterfly in coupled Su-Schrieffer-Heeger systems, Phys. Rev. B 98, 024205 (2018).
- W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in Polyacetylene, Phys. Rev. Lett. 42, 1698 (1979).
- Z. Guo, J. Jiang, H. Jiang, J. Ren, and H. Chen, Observation of topological bound states in a double Su-Schrieffer-Heeger chain composed of split ring resonators, Phys. Rev. Res. 3, 013122 (2021).
- H.-C. Kao, Chiral zero modes in superconducting nanowires with Dresselhaus spin-orbit coupling, Phys. Rev. B 90, 245435 (2014).
- S. Hegde, V. Shivamoggi, S. Vishveshwara, and D. Sen, Quench dynamics and parity blocking in Majorana wires, New J. Phys. 17, 053036 (2015).
- S. S. Hegde and S. Vishveshwara, Majorana wave-function oscillations, fermion parity switches, and disorder in Kitaev chains, Phys. Rev. B 94, 115166 (2016).
- D. J. Apigo, K. Qian, C. Prodan, and E. Prodan, Topological edge modes by smart patterning, Phys. Rev. Mater. 2, 124203 (2018).
- K. Qian, D. J. Apigo, C. Prodan, Y. Barlas, and E. Prodan, Topology of the valley-Chern effect, Phys. Rev. B 98, 155138 (2018).
- K. Qian, L. Zhu, K. H. Ahn, and C. Prodan, Observation of Flat Frequency Bands at Open Edges and Antiphase Boundary Seams in Topological Mechanical Metamaterials, Phys. Rev. Lett. 125, 225501 (2020).
- L. Zhu, E. Prodan, and K. H. Ahn, Flat energy bands within antiphase and twin boundaries and at open edges in topological materials, Phys. Rev. B 99, 041117(R) (2019).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L012012 for the slow motion videos of bulk modes and MLBSs for Figs. 1, 1, 2, 2, and 2.
- M. A. Hasan, K. Runge, and P. A. Deymier, Experimental classical entanglement in a 16 acoustic qubit-analogue, Sci. Rep. 11, 24248 (2021).
- J. Ávila, E. Prada, P. San-Jose, and R. Aguado, Majorana oscillations and parity crossings in semiconductor nanowire-based transmon qubits, Phys. Rev. Res. 2, 033493 (2020).
- The difference between theory and experiments for the system is likely originated from disorders present in the experimental setup. For example, the two theoretically predicted MLBS peaks are close enough that they could be switched in the experiments due to disorders. A possible source of the disorders includes the moments of inertia of the attached accelerometers.
- J. Sau, S. Simon, S. Vishveshwara, and J. R. Williams, From anyons to Majoranas, Nat. Rev. Phys. 2, 667 (2020).