1
|
Tambovtsev IM, Leonov AO, Lobanov IS, Kiselev AD, Uzdin VM. Topological structures in chiral media: Effects of confined geometry. Phys Rev E 2022; 105:034701. [PMID: 35428094 DOI: 10.1103/physreve.105.034701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2022] [Accepted: 02/25/2022] [Indexed: 06/14/2023]
Abstract
We theoretically study orientational structures in chiral magnetics and cholesteric liquid crystal (CLC) nanosystems confined in the slab geometry. Our analysis is based on the model that, in addition to the exchange and the Dzyaloshinskii-Moriya interactions, takes into account the bulk and surface anisotropies. In CLC films, these anisotropies describe the energy of interaction with external magnetic/electric field and the anchoring energy assuming that magnetic/electric anisotropy is negative and the boundary conditions are homeotropic. We have computed the phase diagram and found that the ground state of the film is represented by various delocalized structures depending on the bulk and surface anisotropy parameters, κ^{b} and κ^{s}. These include the z helix and the z cone states, the oblique, and the x helicoids. The minimum energy paths connecting the ground state and metastable helicoids and the energy barriers separating these states are evaluated. We have shown that there is a variety of localized topological structures such as the skyrmion tube, the toron, and the bobber that can be embedded in different ground states including the z cone (conical phase) and tilted fingerprint states. We have also found the structure called the leech that can be viewed as an intermediate state between the toron and the skyrmion tube.
Collapse
Affiliation(s)
- I M Tambovtsev
- Department of Physics, St. Petersburg State University, St. Petersburg 198504, Russia and Faculty of Physics, ITMO University, 197101 St. Petersburg, Russia
| | - A O Leonov
- Department of Chemistry, Faculty of Science, Hiroshima University Kagamiyama, Higashi Hiroshima, Hiroshima 739-8526, Japan and IFW Dresden, Postfach 270016, D-01171 Dresden, Germany
| | - I S Lobanov
- Faculty of Physics, ITMO University, 197101 St. Petersburg, Russia
| | - Alexei D Kiselev
- Laboratory of Quantum Processes and Measurements, ITMO University, 199034 St. Petersburg, Russia
| | - V M Uzdin
- Faculty of Physics, ITMO University, 197101 St. Petersburg, Russia and Department of Physics, St. Petersburg State University, St. Petersburg 198504, Russia
| |
Collapse
|
2
|
De Matteis G, Martina L, Naya C, Turco V. Skyrmion tubes in achiral nematic liquid crystals. Phys Rev E 2022; 105:024701. [PMID: 35291124 DOI: 10.1103/physreve.105.024701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2021] [Accepted: 01/19/2022] [Indexed: 06/14/2023]
Abstract
We analyze the interaction with uniform external fields of nematic liquid crystals within a recent generalized free energy posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i.e., uniform heliconical structures, which correspond to the so-called twist-bend nematic phase and we also study the transition between this phase and the standard uniform nematic one. The twist-bend phase is further reproduced by three-dimensional simulations. Moreover, we find liquid crystal configurations, which closely resemble some novel, experimentally detected, structures called Skyrmion tubes. Skyrmion tubes are characterized by a localized cylindrically symmetric pattern surrounded by either twist-bend or uniform nematic phase. We study the equilibrium differential equations and find numerical solutions and analytical approximations.
Collapse
Affiliation(s)
- G De Matteis
- Dipartimento di Matematica e Fisica, Università del Salento, Via per Arnesano, C.P. 193 I-73100 Lecce, Italy
- INFN, Sezione di Lecce, Via per Arnesano, C. P. 193 I-73100 Lecce, Italy
- GNFM-INDAM, Città Universitaria - P.le Aldo Moro 5, C. P. 00185 Roma, Italy
| | - L Martina
- Dipartimento di Matematica e Fisica, Università del Salento, Via per Arnesano, C.P. 193 I-73100 Lecce, Italy
- INFN, Sezione di Lecce, Via per Arnesano, C. P. 193 I-73100 Lecce, Italy
| | - C Naya
- INFN, Sezione di Lecce, Via per Arnesano, C. P. 193 I-73100 Lecce, Italy
- Department of Physics, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden
| | - V Turco
- Dipartimento di Matematica e Fisica, Università del Salento, Via per Arnesano, C.P. 193 I-73100 Lecce, Italy
- INFN, Sezione di Lecce, Via per Arnesano, C. P. 193 I-73100 Lecce, Italy
- GNFM-INDAM, Città Universitaria - P.le Aldo Moro 5, C. P. 00185 Roma, Italy
| |
Collapse
|
3
|
De Matteis G, Martina L, Naya C, Turco V. Nonuniform localized distortions in generalized elasticity for liquid crystals. Phys Rev E 2020; 102:042705. [PMID: 33212623 DOI: 10.1103/physreve.102.042705] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2020] [Accepted: 10/07/2020] [Indexed: 11/07/2022]
Abstract
We analyze a recent generalized free-energy for liquid crystals posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i.e., uniform heliconical structures, and we find new liquid crystal configurations, which closely resemble some novel, experimentally detected, structures called Skyrmion tubes. These new configurations are characterized by a localized pattern given by the variation of the conical angle. We study the equilibrium differential equations and find numerical solutions and analytical approximations.
Collapse
Affiliation(s)
- G De Matteis
- Dipartimento di Matematica e Fisica, Università del Salento, Via per Arnesano, C.P. 73100 Lecce, Italy.,INFN, Sezione di Lecce, Via per Arnesano, C.P. 193, I-73100 Lecce, Italy.,GNFM-INDAM, Città Universitaria, Piazzale Aldo Moro 5, C.P. 00185 Roma, Italy
| | - L Martina
- Dipartimento di Matematica e Fisica, Università del Salento, Via per Arnesano, C.P. 73100 Lecce, Italy.,INFN, Sezione di Lecce, Via per Arnesano, C.P. 193, I-73100 Lecce, Italy
| | - C Naya
- INFN, Sezione di Lecce, Via per Arnesano, C.P. 193, I-73100 Lecce, Italy
| | - V Turco
- Dipartimento di Matematica e Fisica, Università del Salento, Via per Arnesano, C.P. 73100 Lecce, Italy.,INFN, Sezione di Lecce, Via per Arnesano, C.P. 193, I-73100 Lecce, Italy.,GNFM-INDAM, Città Universitaria, Piazzale Aldo Moro 5, C.P. 00185 Roma, Italy
| |
Collapse
|