Project

Discipline

magnetism, frustration, strong correlations; Strongly correlated physics, fractional quantum Ha

Lead
En physique, le r\'esultat de la comp\'etition entre divers interactionsqui ne peuvent pas \^etre simultan\'ement optimis\'ee est nomm\'e``frustration''. Des exemples de frustration se trouventdans toutes les disciplines de la physique.
Lay summary
Ce projet de recherche a pour but d'\'etudier la physique des frustrations fortes comme elles se manifestent parfois dans certains syst\`emes magn\'etiques localis\'es et dans certains syst\`emes d'\'electrons itin\'erant. La physique des frustrations fortes est caus\'ee par une d\'eg\'en\'erescence massive des fondamenteaux lorsque seul l'interaction dominante est consid\'er\'ee. Cette situation se retrouve: Sur un r\'eseau triangulaire occup\'e par des spin d'Ising lorsque l'interaction entre plus proche voisin et antiferromagn\'etique. Un r\'eseau de t\'etra\`edres dont les sommets sont occup\'es par des spin d'Ising dont l'interaction est entre plus proche voisin et antiferromagn\'etique. L'effet fractionel quantique dans du graph\`ene suspendu. Notre but sera d'explorer th\'eoriquement les manifestations de la frustration forte dans des syst\`emes magn\'etiques, d'\'electrons itin\'erants, et plus g\'en\'eralement dans des syst\`emes mariant le magn\'etisme avec des \'electrons itin\'erants. Il y a plusieurs groupes exp\'erimentaux \`a l'institut Paul Scherrer qui \'etudient des mat\'eriaux caract\'eris\'es par de la frustration forte, Ca${}_{3}$Co${}_{2}$O${}_{6}$, Tb${}_{2}$Ti${}_{2}$O${}_{7}$, pour lesquels il n'existe pas de mod\`ele th\'eorique pleinement satisfaisant. Un des buts de ce projet est de pallier \`a ce d\'eficit.

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Last update: 24.02.2015

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In physics, the result of the competition between interactions that cannot be simultaneously optimized is called frustration.Examples of frustration can be found across all disciplines inphysics. This theoretical proposal aims at understanding the physics of strong frustration, either for localized magneticmoments or for itinerant electrons.Strong frustration arises when the dominant energy scales of theproblem do not select a unique ground state, i.e.,when a hierarchy of energy scales is present such thatthe ground state manifold is extensively degenerate in the approximation by which only the dominant energy scales are accounted for.Prototypical examples of strong frustration are:1.The triangular lattice on which sites effectiveIsing degrees of freedom are localized and interact through a nearest-neighbor antiferromagnetic exchange coupling.2. A network of corner sharing tetrahedra on which vertices effective Ising degrees of freedom are localized and interact through a nearest-neighbor antiferromagnetic exchange coupling.3. The fractional quantum Hall effect in suspended graphene.In Examples 1 and 2, the largest energy scales in the problem are, to leading order, the crystal field responsible for selecting these effective Ising degrees as the only low-energy degrees of freedom that survive at sufficiently low temperatures and, to the first subleading order, the nearest-neighbor antiferromagnetic exchange coupling.In example 3, the largest energy scale in the problem is the magnetic field. In all examples, these dominant energy scales do not select a unique ground state(classical for Examples 1 and 2, quantum for Example 3).Rather, there exists a manifold of ground states that scales fast enough with the system size. This macroscopic degeneracy is lifted by the subdominant energy scales(interlayer or longer-range intralayer exchange couplings,disorder, and quantum perturbations for Example 1, dipolar interaction and disorder for Example 2, the electronic Coulomb interaction and disorder for Example 3).When disorder is sufficiently weak,this selection of a finite number of ground states can produce a ground state thatsupports some long-range order with a local order parameterby breaking spontaneously a symmetry of the model in the limit of no disorder. It can also select a ground state that does not break spontaneously any symmetry but still entails some correlations. This ground state can be thought of as a cooperative paramagnet for classical magnets, or a topologically ordered statein the quantum case. The terminology of a correlated liquid isalso used. Such exotic liquid-like ground states are possible because they emerge from an extensively degenerate manifold of states that all obey the constraints enforced by the dominant energy scales. Even if the selected ground state breaks spontaneously a symmetry, the ordering temperature might be substantiallyreduced by the strength of the fluctuations. The strength of these fluctuations is controlled by the ratio between the dominant energy scales and the subdominant energy scale that selects the ground state(s). This implies a significantly large windowof temperature for which the physics of strong frustration has measurable consequences. The theoretical challenge is thus to explore the signatures of strong frustrationin magnets, for itinerant electrons, or, more generally,whenever magnetism and itinerant electrons coexist.There are many experimental groups at the Paul Scherrer Institute involved in the characterization of materials displaying the smoking guns of strong frustration.The material Ca3Co2O6 (see Example 1)is being studied with neutrons by Kruno Prsa from the laboratory of Joel Mesot. The material Tb2Ti2O7 (see Example 2)is being studied with neutrons by Tom Fennellfrom the laboratory of Christian Rueeggand has been studied with mu-SR by the laboratoryof Elvezio Morenzoni. In all cases, their data are unexplained by existing theories. My last student, Titus Neupert, now a postdoc in Princeton,and I have given a proof by principle that fractional topological insulatorsare possible in two dimensional space (see Example 3).