Dual Symmetry in Bent-Core Liquid Crystals and Unconventional Superconductors

doi:10.3390/sym2010015

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Symmetry 2010, 2(1), 15-39; doi:10.3390/sym2010015

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Dual Symmetry in Bent-Core Liquid Crystals and Unconventional Superconductors

Bruno Mettout^1,* and Vladimir Lorman²

¹ PSC, Faculté des Sciences d'Amiens, Université de Picardie, 33 rue St Leu, 80039 Amiens, France ² Laboratoire de Physique Théorique et Astroparticules, Université Montpellier II, Place Eugène Bataillon, 34095 Montpellier, France

* Author to whom correspondence should be addressed.

Received: 24 September 2009; in revised form: 17 December 2009 / Accepted: 1 January 2010 / Published: 11 January 2010

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Abstract: We extend the Landau theory of bent-core mesophases and d-wave high-Tc superconductors by considering additional secondary pseudo-proper order parameters. These systems exhibit a remarkable analogy relating their symmetry groups, lists of phases, and an infinite set of physical tensors. This analogy lies upon an internal dual structure shared by the two theories. We study the dual operator transforming rotations into translations in liquid crystals, and gauge symmetries into rotations in superconductors. It is used to classify the bent-core line defects, and to analyze the electronic gap structure of lamellar d-wave superfluids.

Keywords: bent core liquid crystals; unconventional superconductors; dual symmetry

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Cite This Article

MDPI and ACS Style

Mettout, B.; Lorman, V. Dual Symmetry in Bent-Core Liquid Crystals and Unconventional Superconductors. Symmetry 2010, 2, 15-39.

AMA Style

Mettout B, Lorman V. Dual Symmetry in Bent-Core Liquid Crystals and Unconventional Superconductors. Symmetry. 2010; 2(1):15-39.

Chicago/Turabian Style

Mettout, Bruno; Lorman, Vladimir. 2010. "Dual Symmetry in Bent-Core Liquid Crystals and Unconventional Superconductors." Symmetry 2, no. 1: 15-39.

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