Tunable Topological Acoustic Tamm States in Comblike Structures Based on Band Inversion around Flat Bands
We investigate the existence of acoustic Tamm states at the interface between two one-dimensional (1D) comblike phononic crystals (PnCs) based on slender tubes and discuss their topological or trivial character. The PnCs consist of stubs grafted periodically along a waveguide and the two crystals di...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Crystals |
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| Online Access: | https://www.mdpi.com/2073-4352/12/12/1685 |
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| author | Soufyane Khattou Yamina Rezzouk Madiha Amrani Mohamed El Ghafiani El Houssaine El Boudouti Abdelkrim Talbi Bahram Djafari-Rouhani |
| author_facet | Soufyane Khattou Yamina Rezzouk Madiha Amrani Mohamed El Ghafiani El Houssaine El Boudouti Abdelkrim Talbi Bahram Djafari-Rouhani |
| author_sort | Soufyane Khattou |
| collection | DOAJ |
| description | We investigate the existence of acoustic Tamm states at the interface between two one-dimensional (1D) comblike phononic crystals (PnCs) based on slender tubes and discuss their topological or trivial character. The PnCs consist of stubs grafted periodically along a waveguide and the two crystals differ by their geometrical parameters (period and length of the stubs). We use several approaches to discuss the existence of Tamm states and their topology when connecting two half-crystals. First, we derive a necessary and sufficient condition on the existence of interface states based on the analysis of the bulk band structure and the symmetry of the band edge states. This approach is equivalent to an analysis of the Zak phases of the bulk bands in the two crystals. Indeed, a topological interface state should necessarily exist in any common bandgap of the two PnCs for which the lower (upper) band edges have opposite symmetries. A novelty of our structure consists in the fact that the symmetry inversion results from a band closure (flat band) rather than from a gap closure, in contrast to previous works. Then, such interface states are revealed through different physical quantities, namely: (i) the local density of states (LDOS), which exhibits a high localization around the interface; (ii) sharp peaks in the transmission spectra in the common bandgap when two finite crystals are connected together; (iii) the phases of the reflection coefficients at the boundary of each PnC with a waveguide, which have a direct relationship with the Zak phases. In addition, we show that the interface states can transform to bound states in the continuum (BICs). These BICs are induced by the cavity separating both PnCs and they remain robust to any geometrical disorder induced by the stubs and segments around this cavity. Finally, we show the impossibility of interface states between two connected PnCs with different stub lengths and similar periods. The sensitivity of these states to interface perturbations can find many practical applications in PnC sensors. |
| first_indexed | 2024-03-09T17:10:26Z |
| format | Article |
| id | doaj.art-8cc5a13dc0d74d15aa56fc3c55e19b49 |
| institution | Directory Open Access Journal |
| issn | 2073-4352 |
| language | English |
| last_indexed | 2024-03-09T17:10:26Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Crystals |
| spelling | doaj.art-8cc5a13dc0d74d15aa56fc3c55e19b492023-11-24T14:09:12ZengMDPI AGCrystals2073-43522022-11-011212168510.3390/cryst12121685Tunable Topological Acoustic Tamm States in Comblike Structures Based on Band Inversion around Flat BandsSoufyane Khattou0Yamina Rezzouk1Madiha Amrani2Mohamed El Ghafiani3El Houssaine El Boudouti4Abdelkrim Talbi5Bahram Djafari-Rouhani6LPMR, Département de Physique, Faculté des Sciences, Université Mohammed I, Oujda 60000, MoroccoLPMR, Département de Physique, Faculté des Sciences, Université Mohammed I, Oujda 60000, MoroccoLPMR, Département de Physique, Faculté des Sciences, Université Mohammed I, Oujda 60000, MoroccoLPMR, Département de Physique, Faculté des Sciences, Université Mohammed I, Oujda 60000, MoroccoLPMR, Département de Physique, Faculté des Sciences, Université Mohammed I, Oujda 60000, MoroccoUniv. Lille, CNRS, Centrale Lille, Université Polytechnique Hauts-de-France, UMR 8520-IEMN, LIA LICS, 59000 Lille, FranceInstitut d’Electronique, de Microélectronique et de Nanotechnologie (IEMN), UMR CNRS 8520, Département de Physique, Université de Lille, 59655 Villeneuve d’Ascq, FranceWe investigate the existence of acoustic Tamm states at the interface between two one-dimensional (1D) comblike phononic crystals (PnCs) based on slender tubes and discuss their topological or trivial character. The PnCs consist of stubs grafted periodically along a waveguide and the two crystals differ by their geometrical parameters (period and length of the stubs). We use several approaches to discuss the existence of Tamm states and their topology when connecting two half-crystals. First, we derive a necessary and sufficient condition on the existence of interface states based on the analysis of the bulk band structure and the symmetry of the band edge states. This approach is equivalent to an analysis of the Zak phases of the bulk bands in the two crystals. Indeed, a topological interface state should necessarily exist in any common bandgap of the two PnCs for which the lower (upper) band edges have opposite symmetries. A novelty of our structure consists in the fact that the symmetry inversion results from a band closure (flat band) rather than from a gap closure, in contrast to previous works. Then, such interface states are revealed through different physical quantities, namely: (i) the local density of states (LDOS), which exhibits a high localization around the interface; (ii) sharp peaks in the transmission spectra in the common bandgap when two finite crystals are connected together; (iii) the phases of the reflection coefficients at the boundary of each PnC with a waveguide, which have a direct relationship with the Zak phases. In addition, we show that the interface states can transform to bound states in the continuum (BICs). These BICs are induced by the cavity separating both PnCs and they remain robust to any geometrical disorder induced by the stubs and segments around this cavity. Finally, we show the impossibility of interface states between two connected PnCs with different stub lengths and similar periods. The sensitivity of these states to interface perturbations can find many practical applications in PnC sensors.https://www.mdpi.com/2073-4352/12/12/1685topological interface statesphononic crystalscomblike structureZak phase |
| spellingShingle | Soufyane Khattou Yamina Rezzouk Madiha Amrani Mohamed El Ghafiani El Houssaine El Boudouti Abdelkrim Talbi Bahram Djafari-Rouhani Tunable Topological Acoustic Tamm States in Comblike Structures Based on Band Inversion around Flat Bands Crystals topological interface states phononic crystals comblike structure Zak phase |
| title | Tunable Topological Acoustic Tamm States in Comblike Structures Based on Band Inversion around Flat Bands |
| title_full | Tunable Topological Acoustic Tamm States in Comblike Structures Based on Band Inversion around Flat Bands |
| title_fullStr | Tunable Topological Acoustic Tamm States in Comblike Structures Based on Band Inversion around Flat Bands |
| title_full_unstemmed | Tunable Topological Acoustic Tamm States in Comblike Structures Based on Band Inversion around Flat Bands |
| title_short | Tunable Topological Acoustic Tamm States in Comblike Structures Based on Band Inversion around Flat Bands |
| title_sort | tunable topological acoustic tamm states in comblike structures based on band inversion around flat bands |
| topic | topological interface states phononic crystals comblike structure Zak phase |
| url | https://www.mdpi.com/2073-4352/12/12/1685 |
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