Topological Gapped Phases in Twisted Bilayer Systems - Emil Prodan

Explore the fascinating world of topological gapped phases in twisted bilayer systems through this comprehensive lecture. Delve into explicit examples of periodic mass-spring systems under periodic potential with twisted lattices. Discover how phonon resonant spectra exhibit Hofstadter characteristics when mapped against twist angles. Examine the intriguing relationship between integrated density of states within spectral gaps and twist angles across various lattices and potential forms. Gain insights into the connection between tight-binding Hamiltonians of double layer systems and the non-commutative 4-torus algebra. Learn about the enumeration of gapped topological phases supported by such lattices and uncover new physical effects, including quantized non-linear transport coefficients related to 2nd Chern numbers and edge spectral flow quantization induced by layer sliding. Enhance your understanding of advanced concepts in condensed matter physics and topological materials.