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The Topological Origin of the Peierls-Nabarro Barrier



Proc. Roy. Soc. A 478 (2022) 20210725, by Brook J. Hocking, Helen S. Ansell, Randall D. Kamien, and Thomas Machon

Crystals and other condensed matter systems described by density waves often exhibit dislocations. Here we show, by considering the topology of the ground state manifolds (GSMs) of such systems, that dislocations in the density phase field always split into disclinations, and that the disclinations themselves are constrained to sit at particular phase values in the GSM. This constraint on the location of the disclinations results in an energy barrier to dislocation glide. Consequently, the topology of the GSM alone gives rise to a Peierls–Nabarro barrier.

General News (News Archive)

  • David King arrives from Cambridge! Welcome! (October 2021)

  • Helen Ansell successfully defends her thesis! Congratulations Dr. Ansell! (April 2021)

  • Helen Ansell accepts postdoctoral position at Northwestern University! (March 2021)

  • Nandita Chaturvedi accepts postdoctoral position at the National Centre for Biological Sciences in Bangalore! (November 2020)

  • Daria Atkinson arrives from UMass Amherst! Welcome! (September 2020)

  • Nandita Chaturvedi successfully defends her thesis! Congratulations Dr. Chaturvedi! (August 2020)

  • Lisa Tran wins 2020 Glenn Brown Dissertation Prize of the International Liquid Crystal Society For her outstanding work on the geometric confinement introducing complex defect structures and revealing new insight into liquid crystal self-organization. Her work exploits an elegant interplay of topological constraints and geometric frustration to guide the formation of unexpected self-assembled complex structures. (May 2020)

  • Lisa Tran accepts faculty position at Utrecht University. (May 2019)

  • Eric Horsley successfully defends thesis! (January 2019)

  • Hillel Aharoni accepts faculty position at the Weizmann Institute! (November 2018)

  • Helen Ansell awarded Department of Physics and Astronomy's 2018 Werner B. Teutsch Prize, Awarded annually to the graduate student who, by his or her performance in the first year courses, shows the most promise for outstanding achievement in research. (June 2018)

  • Hillel Aharoni wins 2018 Michi Nakata Prize for Early Career Achievements of the International Liquid Crystal Society For his impressive evolution of research on topological and geometric applications in soft matter physics from the pattern formation in smectic liquid crystals, demonstrating how nature uses simple geometric principles for achieving complex functionality. His unusual broad view on the soft matter physics including liquid crystal physics, based on strong mathematical and geometrical skills, will make him grow as a prominent scientist. (June 2018)

  • Ex-postdoc Tom Machon wins 2018 Glenn Brown Dissertation Prize of the International Liquid Crystal Society For his theoretical work on the topology and field states in soft matters, especially in complex liquid crystalline environments, with the goal to predict and determine topological properties of the objects such as field knots and topological defects. Another aspect of his contribution to soft matter, the stability of minimal surfaces, opens up a fascinating new field at the intersection of physics and mathematics. (June 2018)

  • Ex-student Dan Beller accepts faculty position at UC Merced! (June 2018)

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Last Modified 12 May 2022