Early attempts towards directly harnessing atomistic information in computing gauge fields have been given recently where concepts from discrete differential geometry are used.
In addition, freestanding graphene membranes are naturally rippled, and as a result charge puddles and pseudo-magnetic fields are created. The theory expressed in curved spaces is particularly appealing from a fundamental point of view as it brings a number of concepts from relativistic quantum theory to condensed matter Physics, making graphene a unique tabletop system into which fundamental theories can be verified and applied, and where new and exciting developments are to be expected. The creation of strain and its simultaneous measurement by scanning tunneling microscopy (STM) opens clear opportunities to study the inter- relation among curvature and the electronic structure of graphene membranes. Curvature is routinely created by local probes on suspended graphene membranes. In the cases where the lattice distortion induces curvature there is an alternative description to the usual (tight binding) approach that can be more suited in this description one uses the geometric formalism of coupling quantum fields to curved backgrounds. This development was guided by a first order theory expressed in a continuum media.
The experimental observation of well-defined electronic levels by scanning tunnel microscopy of a strained graphene nanobubble on a metal substrate has fueled an unprecedented interest, as suggested by the recent exponential growth of publications on the subject.
A single graphene layer is one atom thick: Its electronic properties can be modified by mechanical strain thus opening a door for the creation of state-of-the-art ultra sensitive mechanical/electronic transducers.
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