A single graphene layer is one atom thick: Its electronic properties can be modified by mechanical strain [1] thus opening a door for the creation of state-of-the-art ultra sensitive mechanical/electronic transducers. The experimental observation of well-defined electronic levels by scanning tunnel microscopy of a strained graphene nanobubble on a metal substrate [2,3] has fueled an unprecedented interest, as suggested by the recent exponential growth of publications on the subject.

This development was guided by a first order theory expressed in a continuum media. 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 [4]. Curvature is routinely created by local probes on suspended graphene membranes [5]. The creation of strain and its simultaneous measurement by scanning tunneling microscopy (STM) [6] opens clear opportunities to study the inter- relation among curvature and the electronic structure of graphene membranes. 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. In addition, freestanding graphene membranes are naturally rippled [7,8], and as a result charge puddles and pseudo-magnetic fields [9,10] are created. Early attempts towards directly harnessing atomistic information in computing gauge fields have been given recently [11] where concepts from discrete differential geometry are used.

We explicitly identify six areas of opportunity and further exploration: (i) As the fields created by mechanical strain can in principle be much larger (> 100 Tesla) than currently achievable magnetic fields (~100 Tesla), electron-electron interactions may be expected to be large; strain engineering could then provide a playground the Physics of highly-correlated electrons and novel Hall effects, which remains virtually wide open. (ii) So far most theories are static: How would the electronic response be modified if the mechanical load is time-dependent? (iii) There are opportunities for exploration of analogue systems such as "molecular graphene" [12]. (iv) Can non-abelian gauge fields [13,14] be facilitated by mechanical strain? (v) Can the theory developed so far be applied to other novel two-dimensional materials such as few-layer topological insulators and transition metal dichalcogenides? (vi) How strain can help realize the goal of graphene valleytronics [15]?

Scientific computation and the creation of novel numerical and geometrical methods to study the interrelation among mechanics and the electronic structure is to play an important role in moving the field forward. Concepts such as metric and curvature tensors have been proposed in the context of carbon nanotubes by the Mechanics Community [16]: Clearly, opportunities for translating such methods directly to graphene membranes will lead to a large leap in the field.

Contact e-mail: gse14.cecam@gmail.com

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## CECAM Workshop on graphene's strain engineering: Establishing connections between Condensed Matter Physics, Relativistic Quantum Field Theory, and Computational Mechanics

#### CECAM-ETHZ, Zurich, Switzerland

## References

**Netherlands**

Mikhail I. Katsnelson ( Radboud University Nijmegen ) - Organiser & speaker

**Spain**

Maria Vozmediano ( Spanish National Research Council (CSIC) ) - Organiser

**United States**

Salvador Barraza-Lopez ( University of Arkansas ) - Organiser & speaker