Condensed Matter Seminar: Engineering flat electronic bands from first mathematical principles

The concept of flat electronic bands is a change of paradigm in condensed matter physics. In this talk, I will address the origin of band flatness and its connection to the quantum geometry of electronic states.1 My work focuses on engineering the flat topological bands from the first mathematical principles, namely the Riemannian metrics and quantum geometry, with consequent holomorphicity and meromorphicity of the flat band states,1,2,3 enforced with accurate atomistic compu¬ tations, DFT and tight binding with lattice relaxation effects.4,5 It provides deep insights on the origin of band flatness, which should be looked for in the real space (rather than in momentum space as conventionally it had been). In the complicated and messy domain of band structure computations, the developed approach provides an aesthetical tool for engineering flat electronic bands in realistic materials4 with consequent experimental confirmation.6,7 Time permitting, I will address the novel formalism of flat-band quantum transport built on the concepts of quantum geometry.8 

References:

[1] A. Kruchkov, Origin of band flatness and constraints of higher Chern numbers, arXiv 2105.14672 (2021).

[2.] G. Tarnopolsky, A. J. Kruchkov, A. Vishwanath, Origin of magic angles in twisted bilayer graphene, Physical Review Letters 122, 106405 (2019).

[3.] E. Khalaf, A. J. Kruchkov, G. Tarnopolsky, A. Vishwanath, Magic angle hierarchy in twisted graphene multilayers, Physical Review B 100, 085109 (2019).

[4.] S. Carr, C. Li, Z. Zhu, E. Kaxiras, S. Sachdev, A.J. Kruchkov, Ultraheavy and ultrarelativistic Dirac quasiparticles in sandwiched graphenes, Nano Letters (2020).

[5.] F. Haddadi, Q. Wu, A. J. Kruchkov, O.V. Yazyev, Moiré flat bands in twisted double bilayer graphene, Nano Letters (2020).

[6.] J.M. Park, Y. Cao, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene, Nature volume 590, (2021).

[7.] Z. Hao, A. M. Zimmerman, P. Ledwith, E Khalaf, D. Najafabadi, K. Watanabe, T. Taniguchi, A. Vishwanath, P. Kim, Electric field–tunable superconductivity in alternating-twist magic-angle trilayer graphene, Science 371, 6534 (2021).

[8.] A. Kruchkov, Quantum transport in dispersionless electronic bands, in preparation (2021).