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.6 MoreReceived 31 August 2020Revised 17 December 2020Accepted 12 May 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023180Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAntiferroelectricityCharge density wavesEdge statesElectrical propertiesMagnetic orderPhase transitionsQuasicrystalline structurePhysical Systems2-dimensional systemsQuasicrystalsTechniquesHubbard modelMean field theoryRenormalization groupSecond quantizationSymmetries in condensed matterTight-binding modelCondensed Matter, Materials & Applied Physics
Highlights
The discovery of quasicrystals has triggered exciting, pioneering experimental [1,2,3,4,5,6,7] and theoretical [8,9,10,11,12,13,14,15,16,17] research on the topic
We systematically study the electronic instabilities of the quasicrystalline Penrose model employing such a beyond-MF method, i.e., the real-space truncated unity functional renormalization group (TUFRG) developed here [30,31]
For U U, an antiferrromagnetic spin density wave (SDW) instability prevails with a similar ordering pattern to the ordering pattern at half filling without nearest-neighbor interactions (U = 0) [42]
Summary
The discovery of quasicrystals has triggered exciting, pioneering experimental [1,2,3,4,5,6,7] and theoretical [8,9,10,11,12,13,14,15,16,17] research on the topic. In experimental studies, superconductivity [18] as well as antiferromagnetic ordering [19] were observed in quasicrystalline systems and their approximants, which are large clusters of quasicrystalline tilings as periodically repeated unit cells. These new experimental findings, especially the reported superconductivity, cannot be explained by our current theory and, new theoretical approaches are needed. For the study of translation symmetry-broken models, such as quasicrystals, and scales favorably enough to reach the thermodynamic limit Utilizing this advance, we unveil the surprisingly rich ordering behavior of quasicrystals expanding significantly on what is realized in crystals. We expand the catalog of how phases of matter emerge in quasicrystals and show that in general, one requires an unbiased, beyondMF approach to capture the intricate nature and interplay of orderings in these systems
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