Electronic instabilities in Penrose quasicrystals: Competition, coexistence, 
and collaboration of order

Hauck, J. B.; Honerkamp, C.; Achilles, S.; Kennes, D. M.

doi:10.1103/PhysRevResearch.3.023180

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Electronic instabilities in Penrose quasicrystals: Competition, coexistence, and collaboration of order

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Kennes, D. M.
Institut für Theorie der Statistischen Physik, RWTH Aachen;
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free Electron Laser Science;

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https://dx.doi.org/10.1103/PhysRevResearch.3.023180
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https://arxiv.org/abs/2008.13667
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Citation

Hauck, J. B., Honerkamp, C., Achilles, S., & Kennes, D. M. (2021). Electronic instabilities in Penrose quasicrystals: Competition, coexistence, and collaboration of order. Physical Review Research, 3(2): 023180. doi:10.1103/PhysRevResearch.3.023180.

Cite as: https://hdl.handle.net/21.11116/0000-0008-CC15-B

Abstract

Quasicrystals lack translational symmetry, but can still exhibit long-range order, promoting them to candidates for unconventional physics beyond the paradigm of crystals. Here, we apply a real-space functional renormalization group approach to the prototypical quasicrystalline Penrose tiling Hubbard model treating competing electronic instabilities in an unbiased, beyond-mean-field fashion. Our work reveals a delicate interplay between charge and spin degrees of freedom in quasicrystals. Depending on the range of interactions and hopping amplitudes, we unveil a rich phase diagram including antiferromagnetic orderings, charge density waves, and subleading, superconducting pairing tendencies. For certain parameter regimes, we find a competition of phases, which is also common in crystals, but additionally encounter phases coexisting in a spatially separated fashion and ordering tendencies which mutually collaborate to enhance their strength. We therefore establish that quasicrystalline structures open up a route towards this rich ordering behavior uncommon to crystals and that an unbiased, beyond-mean-field approach is essential to describe this physics of quasicrystals correctly.