Maurice Kleman, a founder of the modern understanding of topological defects in ordered media, died on 29 January 2021, in Paris. Maurice contributed greatly to many branches of condensed matter physics, ranging from liquid crystals, magnetic systems, and quasicrystals to amorphous media and biological tissues.
Kleman’s Jewish parents emigrated to France from Poland. Maurice was born on 11 August 1934. The Second World War forced the family to seek refuge in the French province. On occasions, they went very close to being discovered. The feeling of gratitude to simple people who kept him safe engraved a strong message of humanity in Maurice. As he wrote in an autobiographic book, Chronologie d’un physicien (2016), “it was the gaze of these simple people that began to form in me my love for truth, for exact things.”
In 1969 Maurice joined Pierre-Gilles de Gennes, Georges Durand, and Madeleine Veyssié to study liquid crystals at the Laboratoire de Physique des Solides in Orsay. Maurice, working first with his scientific mentor and friend Jacques Friedel and then alone, gave a geometrical and analytical description of dislocations in chiral liquid crystals, explaining how their structure depends on the mutual orientation of the Burgers vector, helicoidal axis, and the director of molecular orientations.
In 1972 Kleman, with Patricia Cladis, published a groundbreaking demonstration that linear defects, disclinations, around which the director rotates by 360°, are unstable, as the director realigns parallel to the defect’s axis. Robert B. Meyer, who independently discovered the effect, called it an “escape into the third dimension.” If the rotation is 180°, which is permissible since the director is apolar, the disclination remains stable. Kleman also knew that 180° disclinations are impossible in media with polar ordering, described by true vectors such as magnetization. Contemplating on all these differences, Kleman arrived at probably the most important discovery of his scientific career—classification of defects in ordered media, proposed by him and Gérard Toulouse in 1976.
The classification is based on the homotopy theory, a part of algebraic topology. To establish which defect is permissible, the only thing one needs to know about a medium is the symmetries of order. The new language was introduced independently and simultaneously by Soviet physicists Grigori Volovik and Vladimir Mineev. The homotopy theory clarifies which defects should be expected (such as 180° disclinations in nematics), which are prohibited (180° disclinations in magnets), and which are trivial, i.e., smoothly transformable into a uniform state (360° lines in nematics). The homotopy classification demonstrated a deep connection between defects in ordered media and objects such as magnetic monopoles, instantons, and cosmic strings in elementary particles physics and cosmology.
Kleman’s longtime fascination was with the so-called focal conic domains in smectic liquid crystals that show a 1D translational order. These domains, appearing under a microscope as beautiful regular pairings of ellipses and hyperbolae, prompted Georges Friedel (the grandfather of Jacques Friedel) in 1922, prior to any x-ray studies, to recognize that the smectics must be stacks of equidistant fluid layers that could easily bend but could not change their thickness. Kleman deepened Friedel’s geometrical reasoning by constructing an analytical model of the domains, deriving their energetics, and establishing a relationship with grain boundaries and dislocations.
Deep knowledge of mathematical methods, abstract algebraic and geometrical thinking, and understanding of microscopy intricacies, both optical and electron, allowed Maurice to find the most precise theoretical descriptions of complex objects, from dislocations and disclinations to focal conic domains and chromosomes. His book on topological defects (Points, lines and walls: in liquid crystals, magnetic systems and various ordered media) remains an important reference in condensed matter physics.
Maurice was never a stranger to an adventure. One evening I received a telephone call from him: “Look, I am in the US, but not in the State of Washington where I was supposed to be, I am in Washington DC. I misunderstood where the conference would be. Since there are no flights to Seattle tonight, I decided not to go there. May I fly to Cleveland instead so that we could work on the book for a few days?” It was a pleasant surprise, and we had a wonderful time advancing what years later was published by Springer as Soft Matter Physics: An Introduction.
In 1980 Maurice was honored with the Prix de Physique Jean Ricard de la Société Française de Physique; in 2007, the Grand Prix de l’Académie des Sciences; and in 2018, he was elected an International Honorary Member of the American Academy of Arts & Sciences. I think Maurice knew that the biggest award was that his ideas of how topology and geometry reflect in physical systems continue to inspire researchers nowadays.
