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\subsubsection{\texorpdfstring{Structural and electronic properties of schwarzite}{Structural and electronic properties of schwarzite}}
\label{sec:structural_and_electronic_properties_of_schwarzite}


We have studied the stability, elastic properties and electronic
structure of sp\textsuperscript{2} carbon minimal surfaces with negative
Gaussian curvature, called schwarzites. We focused on two systems with
cubic unit cells containing 152 and 200 carbon  atoms, which are
metallic and very rigid. The porous schwarzite structure allows for
efficient and reversible doping by electrondonors and acceptors,
amking it a promising candidate for the next generation of alkali ion
batteries. We identified schwarzite structures that act as arrays of
interconnected spin quantum dots or become magnetic when doped. We
introduced two interpenetrating scwarzite structures that may find
their use as the ultimate super-capacitor.

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