Resonances, mobility edges and gap-protected Anderson localization in generalized disordered mosaic lattices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912288350404608 |
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| author | Longhi, Stefano |
| author_facet | Longhi, Stefano |
| contents | Mosaic lattice models have been recently introduced as a special class of disordered systems displaying resonance energies, multiple mobility edges and anomalous transport properties. In such systems on-site potential disorder, either uncorrelated or incommensurate, is introduced solely at every equally-spaced sites within the lattice, with a spacing $M \geq 2$. A remarkable property of disordered mosaic lattices is the persistence of extended states at some resonance frequencies that prevent complete Anderson localization, even in the strong disorder regime. Here we introduce a broader class of mosaic lattices and derive general expressions of mobility edges and localization length for incommensurate sinusoidal disorder, which generalize previous results [Y. Wang {\it et al.}, Phys. Rev. Lett. {\bf 125}, 196604 (2020)]. For both incommensurate and uncorrelated disorder, we prove that Anderson localization is protected by the open gaps of the disorder-free lattice, and derive some general criteria for complete Anderson localization. The results are illustrated by considering a few models, such as the mosaic Su-Schrieffer-Heeger (SSH) model and the trimer mosaic lattice. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_19521 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Resonances, mobility edges and gap-protected Anderson localization in generalized disordered mosaic lattices Longhi, Stefano Disordered Systems and Neural Networks Quantum Physics Mosaic lattice models have been recently introduced as a special class of disordered systems displaying resonance energies, multiple mobility edges and anomalous transport properties. In such systems on-site potential disorder, either uncorrelated or incommensurate, is introduced solely at every equally-spaced sites within the lattice, with a spacing $M \geq 2$. A remarkable property of disordered mosaic lattices is the persistence of extended states at some resonance frequencies that prevent complete Anderson localization, even in the strong disorder regime. Here we introduce a broader class of mosaic lattices and derive general expressions of mobility edges and localization length for incommensurate sinusoidal disorder, which generalize previous results [Y. Wang {\it et al.}, Phys. Rev. Lett. {\bf 125}, 196604 (2020)]. For both incommensurate and uncorrelated disorder, we prove that Anderson localization is protected by the open gaps of the disorder-free lattice, and derive some general criteria for complete Anderson localization. The results are illustrated by considering a few models, such as the mosaic Su-Schrieffer-Heeger (SSH) model and the trimer mosaic lattice. |
| title | Resonances, mobility edges and gap-protected Anderson localization in generalized disordered mosaic lattices |
| topic | Disordered Systems and Neural Networks Quantum Physics |
| url | https://arxiv.org/abs/2410.19521 |