The upcoming Evolved Laser Interferometer Space Antenna could help verify string theory's predictions of gravity waves. Three spacecraft will orbit around the sun and measure tiny ripples in space-time via sensitive lasers [credit: AEI/MM/EXOZET]. Inset: A 2D slice of the 6D Calabi-Yau quintic manifold. Andrew J. Hanson, Indiana University. [CC BY-SA 3.0 or Attribution], via Wikimedia Commons.
Fig. 2: BLG domain size and stacking order control*
[Reprinted by permission from Macmillan Publishers Ltd: Nature Nanotechnology ©2016]
Bernal (AB)-stacked bilayer graphene (BLG) is a semiconductor whose bandgap can be tuned by a transverse electric field, making it a unique material for a number of electronic and photonic devices. A scalable approach to synthesize high-quality BLG is therefore critical and requires minimal crystalline defects in both graphene layers and maximal area of Bernal stacking, which is necessary for bandgap tunability.
Fig. 1b: Wilson lines and effectively degenerate Bloch bands.* [Reprinted with permission from AAAS ©2016.]
Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high-energy theories, quantum information, and condensed-matter physics. In condensed-matter systems, a wide range of phenomena stem from the geometry of the band eigenstates, which is encoded in the matrix-valued Wilson line for general multiband systems.