近日，美国哈佛大学Ashvin Vishwanath团队研究了霍夫施塔特-哈伯德模型拓扑临界下的任意子超导性。该项研究成果发表在2025年8月12日出版的《美国科学院院刊》杂志上。

研究组认为强排斥相互作用和强磁场的结合可以产生电子配对和超导性。受莫尔材料的大晶格常数的启发，这使得在实验室领域可以获得每单位晶胞的大通量，研究组分析了每个晶胞四分之一通量量子的三角晶格Hofstadter–Hubbard模型，其中之前的文献认为，手性自旋液体以每个位点一个电子的密度将弱耦合整数量子霍尔相和强耦合拓扑平凡的反铁磁绝缘体分开。

研究组认为在整数量子霍尔到手性自旋液体跃迁附近掺杂会产生拓扑超导性。他们采用精确对角化和密度矩阵重整化群方法来检验这一理论情景，并发现电子配对确实发生在临界的两侧，且在非常广泛的相互作用强度范围内。在手性自旋液体侧，他们的结果为长期假设的任意子超导机制提供了一个具体的模型实现。该研究建立了一条超越巴丁-库珀-施里弗的路线，在一个可控的极限内实现电子配对，这在很大程度上依赖于电子关联和能带拓扑之间的相互作用。

附：英文原文

Title: Anyon superconductivity from topological criticality in a Hofstadter–Hubbard model

Author: Divic, Stefan, Crépel, Valentin, Soejima, Tomohiro, Song, Xue-Yang, Millis, Andrew J., Zaletel, Michael P., Vishwanath, Ashvin

Issue&Volume: 2025-8-12

Abstract: We argue that the combination of strong repulsive interactions and high magnetic fields can generate electron pairing and superconductivity. Inspired by the large lattice constants of moiré materials, which make large flux per unit cell accessible at laboratory fields, we study the triangular lattice Hofstadter–Hubbard model at one-quarter flux quantum per plaquette, where previous literature has argued that a chiral spin liquid separates a weak-coupling integer quantum Hall phase and a strong-coupling topologically trivial antiferromagnetic insulator at a density of one electron per site. We argue that topological superconductivity emerges upon doping in the vicinity of the integer quantum Hall to chiral spin liquid transition. We employ exact diagonalization and density matrix renormalization group methods to examine this theoretical scenario and find that electronic pairing indeed occurs on both sides of criticality over a remarkably broad range of interaction strengths. On the chiral spin liquid side, our results provide a concrete model realization of the long-hypothesized mechanism of anyon superconductivity. Our study thus establishes a beyond-Bardeen-Cooper-Schrieffer route to electron pairing in a well-controlled limit, relying crucially on the interplay between electron correlations and band topology.

DOI: 10.1073/pnas.2426680122

Source: https://www.pnas.org/doi/abs/10.1073/pnas.2426680122