Many-body paradigm in quantum moiré material research

Professor Meng, Zi Yang   (Principal Investigator (PI))

JÄCK Berthold   (Co-Investigator)

Professor Wang Ning   (Co-Investigator)

Liu Junwei   (Co-Investigator)

Professor Cui Xiaodong   (Collaborator)

Professor Ki Dongkeun   (Co-principal investigator)

Po Hoi Chun   (Co-Investigator)

Dai Xi   (Co-Investigator)

36

2023-03-01

5464800

Many-body paradigm in quantum moiré material research

Many-body paradigm, quantum moiré material research

Physical Sciences

C7037-22G

Collaborative Research Fund (CRF) - Group Research Project 2022/2023

2022

On-going

1.Characterizing and modeling moiré systems by extracting better effective system parameters via theoretical and experimental analysis and designing accurate models for various quantum moiré systems. [Justifications: The small lattice mismatch in a moiré system generates a moiré length scale an order of magnitude bigger than the microscopic lattice constants. This necessitates a departure from the conventional modeling of solid-state systems in which the atomic orbitals form the natural ingredient. Instead, existing and successful methods rely on effective theories derived from a single-particle momentum-space perspective, where one inputs the correlation effects from the microscopic scale and derives effective interaction on the moiré scale. It is challenging to quantify how the effective interaction has been renormalized in the process. Here, we seek to integrate experimental and theoretical analysis to directly probe the interaction parameters in moiré systems at their moiré length scales. Experimentally, we will extract information on the moiré potential, global and local electron density profile, and energy scales of the correlated phases, by combining transport measurement of the ensemble-averaged global electronic properties (NW and DKK) and scanning tunneling spectroscopy of the local properties with high spatial resolution (BJ). Theoretically, we (XD, HCP, ZYM) will consider the relation between flat bands and remote bands, the nature of the long-range Coulomb interactions and to balance the topological quantum metric of the flat band wavefunction and the long-range interaction, and compare the gaps, spectra, and compressibility with the experimental results such that the novel correlated phases can be properly characterized.]2.Developing theoretical and computational techniques to solve the models and reveal the mechanism behind novel correlated states in moiré materials. [Justifications: XD will develop constrained RPA, LDA+Gutzwiller, and dynamical mean-field theory based on quantum Monte Carlo approaches, which have been developed in his group for over a decade. Specifically, XD’s team will develop two new variational methods that can treat effective interactions among electrons in flat bands by numerically computing effective Landau Fermi liquid parameters. These methods consider local correlations and extend well beyond simple RPA or Hartree-Fock methods. The formalism behind these methods is extremely general and can be applied to most symmetry-breaking phases of interest. ZYM will develop highperformance computation schemes such as quantum Monte Carlo, thermal tensor-network, and explainable-AI techniques that can incorporate the key model parameters in Objective 1. ZYM developed the momentum space quantum Monte Carlo method that could fully consider the long-range Coulomb interaction in flat band models without approximation, and can calculate various collective excitations. Team members (XD, HCP, JWL, ZYM) will make use of the advanced theoretical understanding and powerful numerical tools to compute the ground state, finite temperature, global and local electronic and spectral properties for various moiré materials and provide explanation and guidance for experiments.]3.Combining different experimental techniques to obtain a conclusive understanding of the phase diagram (e.g., lowering inter-sample variability). [Justifications: Moiré superlattice structures exhibit unconventional superconductivity, magnetism, correlated insulating phases, and quantum anomalous and non-linear Hall states. To understand such systems with diverse electronic phases, we (NW, DKK, BJ) will combine electron transport and local tunnelling spectroscopy techniques. From electron transport, we can determine the phase diagram of the system in temperature, electron density, and magnetic field. Local spectroscopy with the scanning tunnelling microscope provides spatially resolved information on the local electronic density of states, the magnetic and superconducting order parameters, and other spectral gaps as a function of electron density, temperature, and magnetic field. To have a coherent result, we will design samples that can be used in different types of experiments. We can cover the sample with an hBN monolayer not only to protect the sample for the high-quality transport measurement but also to facilitate scanning tunnelling microscopy of the buried moiré heterostructure. Our team members are experts in the relevant fields; NW and DKK in quantum transport and heterostructure assembly and BJ in local spectroscopy with the scanning tunnelling microscope.] 4.Integrating the improved understanding of the existing moiré structures to propose and make new generation moiré material with improved properties. [Justifications: Quantum moiré materials offer a new paradigm to precisely control and manipulate the many-body effects in electrons at a much higher level than the traditional strongly correlated materials. Based on the theoretical and experimental results in the above 3 objectives, the team will propose and identify new generation moiré materials with improved properties, such that the engineering of the density of states, or the in-situ tuning of correlated topological phases can be realized. Examples are possible heavy Fermion states originating from Kondo effect and non-linear optical signature of the many-body states in moiré systems. In this way, the unique correlation effects (flat-band, long-range Coulomb, topology and superconductivity) can be understood and amplified to more accessible experimental conditions, and a new paradigm of many-body theory, computation, and experiment research of moiré materials will be firmly established.]