The 2016 Nobel Prize in Physics was awarded to David Thouless (University of Washington), Michael Kosterlitz (Brown University), and Duncan Haldane (Princeton University) for their pioneering work on topology associated with exotic states of matter. Not to be outdone, the next day the Nobel Prize in Chemistry (awarded to Jean-Pierre Sauvage, University of Strasbourg; Sir J. Fraser Stoddart, Northwestern University; and Bernard L. Feringa, University of Groningen) also involved topology in terms of supramolecular chemistry linking ring-shaped molecules to form molecular motors. The chemistry Nobel triumvirate utilized topologically challenging structures (e.g., catenanes, rotaxanes), topological entanglement, and topological chemistry.

Topology refers to “elastic geometry” in that, under continuous deformation, certain properties of a material remain unchanged. For example, transport properties such as electrical current in a wire remain invariant regardless of how the wire is bent without touching itself. This apparently esoteric mathematical notion has now ushered in a growing new class of molecules, materials, and phases ranging, for example, from topological insulators and topological superconductors to Dirac materials and Weyl semi-metals. Some essential properties of these topological materials are characterized by topological numbers such as genus (number of holes), winding number (number of times a closed curve goes around a given point), and Chern number (an integer characterizing two distinct topological phases). These materials are now beginning to find many applications including those in information storage and manipulation as well as in (quantum) computing.

In this context, the Materials Research Society (MRS) was indeed prescient when during the 2012 MRS Fall Meeting in Boston (Symposium V) and again in 2015 (Symposium TT), a symposium was devoted to Topology in Materials Science covering various topological concepts in a variety of topological materials encompassing carbon allotropes; soft, polymeric and biomaterials; optoelectronic materials; and Dirac materials, for example. Advanced notions of topological synthesis, characterization, and topological metrology were introduced and the paradigm of geometry/topology → property → functionality was clearly enunciated.

This confluence of topological ideas resulted in a review article on this subject in MRS Bulletin entitled, “A Topological Twist on Materials Science,” [S. Gupta and A. Saxena, MRS Bulletin 39, 265 (March 2014)]. This article delineated topological phase transitions and the role of topological defects such as vortices and skyrmions on materials properties along with multiphoton-generated topological phases in soft matter.

With this year’s Nobel Prize awarded on this topic both in physics and chemistry, it is hoped that in the coming years, topology and metrology will find a firm footing in materials science in the synthesis, characterization, and molecular modeling of an increasing number of important materials relevant for numerous industries and applications. Indeed, the prospects for discovering and exploring topological materials are very exciting and the possibilities appear to be endless.