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1. Topological chiral superconductivity beyond pairing in a Fermi liquid

   https://doi.org/10.1103/PhysRevB.111.014508  

   Kim, Minho; Timmel, Abigail; Ju, Long; Wen, Xiao-Gang (January 2025, Physical Review B)

   We investigate a mechanism to produce superconductivity by strong purely repulsive interactions for flat dispersion $$\veps \sim k^4$$, without using pairing instability in Fermi-liquid. The resulting superconductors break both time-reversal and reflection symmetries in the orbital motion of electrons, and exhibit non-trivial topological order. Our findings suggest that this topological chiral superconductivity is more likely to emerge near or between fully spin-valley polarized metallic phase and Wigner crystal phase. These topological chiral superconductors can be fully or partially spin-valley polarized. For partial spin-valley polarization, the ratios of electron densities associated with different spin-valley quantum numbers are quantized as simple rational numbers. Furthermore, many of these topological chiral superconductors exhibit charge-4 or higher condensation, neutral quasiparticles with fractional statistics, and/or gapless chiral edge states. Two of the topological chiral superconductors are in the same phases as the ``spin''-triplet or spinless $$p+ \textrm{i} p$$ BCS superconductor, while others are in different phases than any BCS superconductors. The same mechanism is also used to produce anyon superconductivity between fractional anomalous quantum Hall states in the presence of a periodic potential. 

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2. Topology meets time-reversal symmetry breaking in FeSe1−xTex superconductors

   https://doi.org/10.1038/s41467-025-61651-y  

   Roppongi, Masaki; Cai, Yipeng; Ogawa, Koki; Liu, Supeng; Zhao, Guoqiang; Oudah, Mohamed; Fujii, Takenori; Imamura, Kumpei; Fang, Shengjie; Ishihara, Kota; et al (December 2025, Nature Communications)

   Time-reversal symmetry breaking (TRSB) in magnetic topological insulators induces a Dirac gap in the topological surface state (TSS), leading to exotic phenomena such as the quantum anomalous Hall effect. Yet, the interplay between TRSB and topology in superconductors remains underexplored due to limited suitable materials. Here we employ zero-fieldmuon spin relaxation (μSR) as a sensitive probe of TRSB to map out the electronic phase diagrams of iron-chalcogenide superconductors FeSe1−xTex. For the Te composition x = 0.64 with the highest superconducting transition temperature Tc = 14.5K, which is known to host a TSS and Majorana zero modes within vortices, we detect spontaneous magnetic fields below Tc distinct from a magnetic order. This signifies a TRSB superconducting state in the bulk, revealing the convergence of unconventional TRSB superconductivity with topologically nontrivial electronic structures in FeSe1−xTex. Given the relatively high Tc and the tunability of the Fermi level through chemical substitution, iron-chalcogenide superconductors offer an intriguing platform for investigating the synergy between topological superconductivity and TRSB. 

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3. Anyon superconductivity from topological criticality in a Hofstadter–Hubbard model

   https://doi.org/10.1073/pnas.2426680122  

   Divic, Stefan; Crépel, Valentin; Soejima, Tomohiro; Song, Xue-Yang; Millis, Andrew J; Zaletel, Michael P; Vishwanath, Ashvin (August 2025, Proceedings of the National Academy of Sciences)

   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. 

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4. Quantum Spin Hall Effects in Van der Waals Materials

   https://doi.org/10.1002/qute.202500327  

   Tang, Jian; Ding, Thomas Siyuan; Wang, Chengdong; Mao, Ning; Belosevich, Vsevolod; Zhang, Yang; Qian, Xiaofeng; Ma, Qiong (November 2025, Advanced Quantum Technologies)

   The quantum spin Hall (QSH) effect, first predicted in graphene by Kane and Mele in 2004, has become a key platform for exploring spin–orbit coupling, topology, and electronic interactions. Initially demonstrated in quantum wells, the field has expanded with the emergence of van der Waals (vdW) materials. This review focuses on vdW systems, which provide unique advantages: exposed surfaces allow comprehensive spectroscopic and microscopic detection of the QSH state; mechanical stacking enables symmetry tuning and proximity effects; and moiré engineering introduces new topology and strong correlations. We highlight two monolayer families, 1T'‐MX2and , represented by WTe2 and TaIrTe4, respectively, which host QSH phases in close proximity to other quantum states including excitonic insulators, charge density waves, and superconductivity. Their low symmetry and topology produce rich quantum geometrical responses, from nonlinear Hall to circular photogalvanic effects. We also discuss moiré systems that combine topology with flatband physics, enabling spontaneous symmetry breaking and transitions from QSH to quantum anomalous Hall (QAH) states. Recent observations of fractionalized QAH and QSH states mark a major advance in condensed matter physics. Finally, we outline potential applications, such as nonlinear Hall–based microwave rectification and fractional states for topological quantum computing. 

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5. Colossal magnetoresistance in the multiple wave vector charge density wave regime of an antiferromagnetic Dirac semimetal

   https://doi.org/10.1126/sciadv.adh0145  

   Singha, Ratnadwip; Dalgaard, Kirstine J.; Marchenko, Dmitry; Krivenkov, Maxim; Rienks, Emile D.; Jovanovic, Milena; Teicher, Samuel M.; Hu, Jiayi; Salters, Tyger H.; Lin, Jingjing; et al (October 2023, Science Advances)

   Colossal negative magnetoresistance is a well-known phenomenon, notably observed in hole-doped ferromagnetic manganites. It remains a major research topic due to its potential in technological applications. In contrast, topological semimetals show large but positive magnetoresistance, originated from the high-mobility charge carriers. Here, we show that in the highly electron-doped region, the Dirac semimetal CeSbTe demonstrates similar properties as the manganites. CeSb_0.11Te_1.90hosts multiple charge density wave modulation vectors and has a complex magnetic phase diagram. We confirm that this compound is an antiferromagnetic Dirac semimetal. Despite having a metallic Fermi surface, the electronic transport properties are semiconductor-like and deviate from known theoretical models. An external magnetic field induces a semiconductor metal–like transition, which results in a colossal negative magnetoresistance. Moreover, signatures of the coupling between the charge density wave and a spin modulation are observed in resistivity. This spin modulation also produces a giant anomalous Hall response. 

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