A PQM PhD project offered by Dr Gunnar Möller - description with more background information
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Project Background
A plethora of new phenomena can be generated when materials are driven into a regime where electrons are half-way between localised orbitals and delocalised waves. We can think of this as a manifestation of the particle-wave duality in materials, whereby local orbitals effectively capture the particle-like nature of electrons, while electrons propagating through a material are wave-like. Simultaneously, the Coulomb force applies further frustration to these competing tendencies. When the contributions to the energy stemming from band dispersion and interactions are both of similar magnitude, the material may enter a strongly correlated regime in which many electrons become strongly intertwined with each other and can form complex collective orders.
The simplest model displaying such phenomena, known as the Hubbard model, has been understood in many regimes – although it still awaits final solution after more than 50 years investigation. The Hubbard model assumes that electrons move on a regular lattice consisting of atomic sites with a single atomic orbital each, and there is an energy penalty when two electrons occupy the same site. This simple model is believed to provide a minimal description of the high-temperature superconductors (although definite proof of this remains lacking).
In practice, many materials have a more complex structure with multiple atomic orbitals in the unit cell, which can lead to many more exotic collective states. A prime example of this can be found in twisted graphene multilayers, which have been heralded for the discovery of new types of correlated insulators [1] and superconducting phases [2]. This has triggered a wave of excitement in the community leading to many investigations into this spectacular new regime of strong correlation physics. A small twist between layers leads to huge unit cells with many 1000s of atoms. However, only few orbitals are relevant at the lowest energies, with eight flat bands near the magic twist angle – that furthermore have interesting features in terms of non-trivial topology with a finite Chern number. Simpler examples include models of superconductors with several orbitals, as are relevant for the iron pnictides [3] or the scenario of non-unitary triplet superconductivity in a two-orbital model of LaNiGa2 [4].
Methods
To unravel strong correlation physics in multi-band models, my group deploys a range of high-performance numerical techniques. Here, we propose to generalise the connected determinantal Monte-Carlo (cDet) approach [5], which has already shown potential to yield definite answers for many regimes of the Hubbard model physics [6,7], and then provides a genuinely unbiased solution. We propose to deploy the recursive approach of Ref. [5] to construct perturbation expansions in multi-band models. During the project, we will first benchmark the approach on simple limiting cases, and then proceed to more realistic two-band models and later to analyse more advanced applications from among the families of multi-orbital materials discussed above. The work will build on an established code-base for diagrammatic Monte-Carlo algorithms developed in Dr Möller’s group.
Team and Collaborators
Dr Gunnar Möller is a Royal Society University Research Fellow / Senior Lecturer in the PQM group and leads a team focusing on topology and interactions in condensed matter many-body systems. His group deploys advanced numerical methods, and you can find an overview and a list of publications on his directory page. The project will benefit from established national and international collaborations, including with Dr E. Kozik (King’s College London) and Dr Leni Bascones (CSIC Madrid).
Bibliography
[1] Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
[2] Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
[3] Stewart, G. R. Superconductivity in iron compounds. Rev. Mod. Phys. 83, 1589 (2011).
[4] Weng, Z. F. et al. Two-Gap Superconductivity in LaNiGa2 with Nonunitary Triplet Pairing and Even Parity Gap Symmetry. Phys. Rev. Lett. 117, 027001 (2016).
[5] Rossi, R. Determinant diagrammatic Monte-Carlo algorithm in the thermodynamic limit. Physical Review Letters 119, 045701 (2017).
[6] Fedor Šimkovic, I. V. et al. Extended crossover from a Fermi liquid to a quasi-antiferro-magnet in the half-filled 2D Hubbard model. Physical Review Letters 124, 017003 (2020).
[7] Spada, G. et al. High-order expansion around BCS theory. arxiv:2103.12038 (2021).
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