CAMBRIDGE, England—A substance 200 times stronger than steel yet as thin as an atom has ignited a global scientific gold rush, sending companies and universities racing to understand, patent and profit from the skinnier, more glamorous cousin of ordinary pencil lead.

The material is graphene, and to demonstrate its potential, Andrea Ferrari recently picked up a sheet of clear plastic, flexed it and then tapped invisible keys, triggering tinkly musical notes.

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