TQM: Twisted Quantum Mechanics
Abstract
TQM: Twisted Quantum MechanicsWe propose an integrated approach to tackle new fundamental problems in quantum physics: the emergence of new many-body strong-coupling states of matter in flat bands (e.g. moire lattices), and the interplay between strong interactions, topology and disorder in such systems. The products of thisresearch will be (1) The calculation and prediction of single particle flat topological bands in Moire bilayer and many-layer systems, and the prediction of new electron, magnon and phonon topological bands with emergent symmetries in these systems. (2) The design of experiments to measurethe esoteric topological states predicted in Moire sytems. (3) The development of ab-initio codes of remarkable power based on new ideas such as mixing Lanczos exact diagonalization with ab-initio; computing the electronic structures of Moire patterns containing >10000 atoms, not attainable usingcurrent ab-initio codes. (4) The prediction of new Hofstaeder Topological Insulators as a new type of topology that can exist in Moire patterns due to the large magnetic flux now possible per Moire unit cell. (5) Critical analysis of the mechanism of superconductivity in the flat bands and of the effects of topology on superconductivity. (6) Development of renormalization group methodson the momentum-shell lattice of twisted materials, which would give rise to effective k p models. (7) Mean-field analysis and phase diagram of the Moire systems when Coulomb interactions are introduced in a perturbative way, including the collective modes of these interactions. (8) A completeunderstanding of interactions and phases in Moire systems by exact diagonalization of Coulomb Hamiltonians, and a mapping of the phase diagram of Moire systems by combining ab-initio codes and many-body numerics. (9) Experimental collaborations with several experimental groups in Moiresystem including the Ali Yazdani, Dmitry Efetov, Emanuel Tutuc and Sanfeng Wu labs.Currently new fields of research have emerged in which topological quantum phenomena mix with strong interactions and material engineering. Many of the most interesting materials in these fields have layered or two-dimensional structures, ranging from atomically engineered magnetic superlatticesto single crystalline Heusler compounds with non-collinear spin textures and field-inducedWeyl nodes, to Majorana states formed at the interfaces between low dimensional magnetic structures and superconductors. Recently, Van der Waals (VdW) heterostructures emerged as a platform for the discoveryof exotic states of matter. These heterostructures are composed by 2D sheets stacked on top of each other and held together by weak VdW interactions, artificially creating heterostructures without the requirements of lattice matching. This results in an infinite number of LEGO-like combinations for tailoring the physical properties of heterostructures, which will be analyzed in the grant.These are ambitious goals. The PI has already set up the necessary infrastructure for these advances by developing a unique array of methods (group-theory/topological data, many-body diagonalization, ab-initio, detection of ground-states of matter techniques) to attack the complicated problemsof engineered heterostructures. Our new ab-initio methods can be used to predict the single-particle spectrum of heterostructures, the full formalism of Topological Quantum Chemistry can be used to detect their topological phase and many-body exact diagnonalization can be used to obtain the interactingquantum ground-states of these topological states, and the project can hit the ground running.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 29, 2020
- Source ID
- N000142012303
Entities
People
- Andrei Bernevig
Organizations
- Office of Naval Research
- Trustees of Princeton University
- United States Navy