Berezinskii– Kosterlitz–Thouless phase transitions in PbTiO3/SrTiO3 superlattices
ABSTRACT: In the present work we shall study the basic theory behind the cellebrated Berezinskii– Kosterlitz–Thouless (BKT) topological phase transitions. In order to do so, we first introduce the simple XY-model, where these phase transitions where initially discovered. Within this context, we compu...
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| Format: | master thesis |
| Publication Date: | 2020 |
| Country: | España |
| Institution: | Universidad de Cantabria (UC) |
| Repository: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Language: | English |
| OAI Identifier: | oai:repositorio.unican.es:10902/19002 |
| Online Access: | http://hdl.handle.net/10902/19002 |
| Access Level: | Open access |
| Keyword: | BKT Topological phase transitions Mermin-Wagner theorem Correlation functions Vortices Ferroelectricity Second-principles simulations PbTiO3/SrTiO3 superlattices. Transición de fase topológicas Teorema de Mermin-Wagner Función de correlación Vórtices Ferroelectricidad Simulaciones desde segundos-principios Superredes PbTiO3/SrTiO3 |
| Summary: | ABSTRACT: In the present work we shall study the basic theory behind the cellebrated Berezinskii– Kosterlitz–Thouless (BKT) topological phase transitions. In order to do so, we first introduce the simple XY-model, where these phase transitions where initially discovered. Within this context, we compute the energy of an isolated topological defect (a vortex) and the interaction energy between a collection of localized defects. Then, with the help of the correlation functions, we characterize the different orderings of the phases that appear as a function of temperature: from the quasi-long-range order at low temperatures to a fully disordered phase at high-temperature. This study sets the grounds for introducing the Berezinskii– Kosterlitz–Thouless (BKT) topological phase transitions. A bibliographic search is made to study how the different assumptions present in the XY-model (dimensionality of space, dimensionality of the order parameter, presence of long-range interactions and/or continuous symmetry in the Hamiltonian), affect the eventual existence of such phase transitions. Special attention is paid to the recent discovery of BKT transitions in ferroelectricsystems. Finally, we carry out second-principles simulations in PbTiO3/SrTiO3 superlattices and reveal the presence of topological phase transitions both when the polarization in the PbTiO3 layers is fully contained in the xy-plane, and where the polarization texture displays alternating clockwise/counter-clock-wise vortices in the xz-plane. |
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