The Instituto de Ciencia de Materiales de Madrid (ICMM) is an institute of the Consejo Superior de Investigaciones Cientificas (CSIC) (Spanish National Research Council) founded in December 1986, that belongs to the Area of Science and Technology of Materials, one of the eight Areas in which the CSIC divides its research activities.


Our mission is to create new fundamental and applied knowledge in materials of high technological impact, their processing and their transfer to the productive sectors at local, national and European scales (the true value of materials is in their use), the training of new professionals, and the dissemination of the scientific knowledge.

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Forthcoming Events


Molecular Sieves: What are we doing and
what do we want to do?

Sibele Pergher  read more


Quantum Hall ferromagnetism in multicomponent systems
Angelika Knothe  read more


Líquidos Iónicos en Tribología e Ingeniería de Superficies
María Dolores Bermúdez Olivares  read more

Topologically Enforced Bifurcations in Superconducting Circuits

G. Engelhardt, M. Benito, G. Platero, and T. Brandes

The relationship of topological insulators and superconductors and the field of nonlinear dynamics is widely unexplored. To address this subject, we adopt the linear coupling geometry of the Su-Schrieffer-Heeger model, a paradigmatic example for a topological insulator, and render it nonlinearly in the context of superconducting circuits. As a consequence, the system exhibits topologically enforced bifurcations as a function of the topological control parameter, which finally gives rise to chaotic dynamics, separating phases that exhibit clear topological features.

Phys. Rev. Lett.

(a) Phase diagram for the order parameter κ defined in Eq. (7). Parameters are as in Fig. 2. Black lines depict the phase boundary obtained by the generalized force functionals Eq. (10). (b) Phase diagram of the topological order parameter Δ. (c) Level sets G1=0(solid line) and G2=0 (dashed line) of Eq. (10) for fixed, but optimized a3 for Iac=4t0. The corresponding parameters are marked in (a) by colored dots. The vanishing of the stable attractor at α ≈0.25t0 triggers the chaotic dynamics observed in the central region of the phase diagram.

Publications Highlights

ICMM-2017 - Sor Juana Inés de la Cruz, 3, Cantoblanco, 28049 Madrid, Spain. Tel: +34 91 334 9000. Fax: +34 91 372 0623. info@icmm.csic.es