The Topological Background of Schwarzite Physics

  • Giorgio Benedek
  • Marco Bernasconi
  • Eugenio Cinquanta
  • Luca D’Alessio
  • Marzio De Corato
Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 4)


About 10 years ago the synthesis of random carbon schwarzites by supersonic cluster beam deposition has endowed the rich sp2 carbon family with its three-dimensional member. Its reluctance to grow as a three-periodic minimal surface according to topological and physical predictions still prevents schwarzites from being a hot topic, although spongy carbon is already having countless applications. Understanding the links between topology and quantum structure, possibly with the help of large-scale quantum molecular dynamics simulations should trace the route to the synthesis of periodic schwarzites. In this perspective, after a brief account on the growth and characterization of spongy carbon, we review the elementary topology of schwarzites, their stability and growth conditions as derived from pure topological arguments, the electronic structure and the electron-phonon interaction of the smallest periodic schwarzites and what can be learnt by the topological monitoring of quantum molecular dynamics.


Minimal Surface Graphene Sheet Cyclic Boundary Condition Negative Gauss Curvature Periodic Minimal Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



One of us (GB) gratefully acknowledges the Ikerbasque Foundation for support within the project ABSIDES. We acknowledge many stimulating discussions with Prof. Paolo Milani (University of Milano).


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Copyright information

© Springer Netherlands 2011

Authors and Affiliations

  • Giorgio Benedek
    • 1
    • 2
  • Marco Bernasconi
    • 2
  • Eugenio Cinquanta
    • 2
  • Luca D’Alessio
    • 2
    • 3
  • Marzio De Corato
    • 2
  1. 1.Donostia International Physics Centre (DIPC)Donostia-San SebastiánSpain
  2. 2.Dipartimento di Scienza dei MaterialiUniversitá di Milano-BicoccaMilanoItaly
  3. 3.Department of PhysicsBoston UniversityBostonUSA

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