Towards Ab Initio Simulations of High-Temperature Superconductivity

Citation

Cui, Zhi-Hao (2023) Towards Ab Initio Simulations of High-Temperature Superconductivity. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/y2qf-1f77. https://resolver.caltech.edu/CaltechTHESIS:11022022-092201743

Abstract

High-temperature superconductors have been discovered for more than three decades. Nonetheless, the theoretical understanding of their microscopic properties remains unclear with substantial difficulties in linking the observed phenomena to material composition and structures. This thesis aims to establish a theoretical hierarchy (from lattice models to realistic materials) for faithful simulations of high temperature superconductivity.

We start with the lattice models of superconductors by using quantum embedding theory, whose self-consistency allows magnetic and superconducting phases to emerge. We extended the density matrix embedding theory (DMET) with improved self-consistency algorithms and determined the ground-state phase diagrams for both one-band [Chap. 3] the three-band Hubbard models [Chap. 4]. In particular, in the three-band model, we explored the atomic-scale nature of the antiferromagnetic and superconducting orders for different model parametrizations, and highlighted the role of the oxygen degrees of freedom beyond the one-band picture.

To go beyond the models, we therefore extended the original theory [DMET and dynamical mean-field theory (DMFT)] to ab initio realistic solids [Chap. 5]. The methods, namely the full-cell quantum embedding, are distinct from other embedding schemes in three aspects: (i) all local orbitals in a unit cell are included in the embedding problem whereas the bath orbitals are truncated according the atomic valence characters; (ii) The embedding Hamiltonian is of full quartic fermionic form rather simplified Hubbard like Hamiltonians; (iii) Many-body quantum chemistry solvers such as coupled cluster (CC) are used to generate embedding density matrix and Green’s functions. As demonstrated across a variety of semiconducting and insulating materials, the full-cell quantum embedding provides accurate energy, equation of state, spin-spin correlation functions and excited-state band structures.

We then applied our ab initio quantum embedding methods to the parent state of a series of cuprate superconductors [Chap. 6]. We uncovered microscopic trends in the electron correlations and revealed the link between the material composition and magnetic energy scales via a many-body picture of excitation processes involving the buffer layers. We found the competition between the in-plane superexchange and the CuO₂-buffer layer excitations, which explains the magnetic coupling difference among a series of superconducting materials.

Finally, we investigated the doped cuprates, where the superconducting orders enter into the phase diagram [Chap. 7]. We generalized our ab initio framework to allow the particle-number symmetry breaking states such that the superconducting orders can spontaneously emerge during the self-consistency. We showed that the d-wave superconducting magnitude increases with the pressure applied to crystals and the trend connects to the superexchange coupling J . Furthermore, we also studied the layer effect on superconductivity. Unlike the pressure effect, the layer effect between different compounds is affected by more factors - both magnetic coupling J and charge distribution matters. The work provides a promising route to study the material-specific physics in high-temperature superconductivity.

The aforementioned applications also relied on (i) the development and adaptation of many-body solvers, including the CC singles and doubles (CCSD) with Newton-Krylov method for better numerical convergence, and active-space quantum chemistry techniques with large-scale density matrix renormalization group. (ii) projection-based orbital localizations for metallic systems, frozen core techniques and symmetry adaptations. These contents are discussed in Chap. 2 and Appendices, including their efficient implementation and parallelization.

In the concluding remarks [Chap. 8], we summarized the current status and limitations of the high-temperature superconductivity studies. In addition, we proposed several possible directions to address the challenges in electronic correlation and atomic modelling of other exotic phases from an ab initio perspective.

Thesis Files