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Interaction-driven competing instabilities in two-dimensional checkerboard quadratic band crossing semimetals

Year: 2026
Type: preprint
Abstract: Two-dimensional quadratic band crossing point (QBCP) semimetals serve as a fertile platform for interaction-driven quantum criticality, nevertheless, the role of the complete fermion-fermion interactions remains largely unexplored. To address this, we systematically investigate the low-energy physics of a spin-1/2 checkerboard-lattice QBCP semimetal by considering all 16 marginally short-range fermion-fermion interactions. Using the momentum-shell renormalization group, we derive the coupled flow equations, which reveal that the low-energy physics is governed by a series of fixed points. Depending on the initial conditions, the system may exhibit a single stable fixed point, several discrete fixed points, or three continuous groups of fixed points parameterized by a few variables. By introducing source terms and evaluating susceptibilities, we identify the dominant and subdominant instabilities. The leading phases include nematic spin-nematic (NSN), quantum anomalous Hall (QAH), chiral superconducting ($\mathrm{SC}_1$), and quantum spin Hall (QSH) orders. Moreover, several features distinguish our findings from previous simplified models. Off-diagonal interactions generate terms that promote orders absent in such models, the continuous groups allow systematic tuning of the leading instability, and trajectory-dependent instabilities emerge where the full RG flow, rather than the fixed point alone, determines the dominant state. These results offer a comprehensive theoretical understanding of low-energy quantum critical behaviors and phase instabilities in two-dimensional QBCP semimetals and related electron systems.
DOI: 10.48550/arxiv.2610.25046
Language: English
Open Access status: green
OpenAlex ID: W7223060378
Cites: 2
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Related to: 10