Open research questions in Advanced Condensed Matter Physics
99 gap statements mined from Advanced Condensed Matter Physics papers in our 4.5M-paper local library, which holds 789 papers on the topic — drawn mostly from each paper's own stated research gap, future-work, challenge and limitation notes, and its abstract. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one.
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What the literature leaves open
While our symmetry-based framework inherently covers all symmetry-allowed mechanisms in the presence of helimagnetism—including uniform magnetization mediated by spin or orbital Edelstein effects34,35, spin-transfer torque8,36,37, or chirality- induced spin selectivity (CISS)38–42—identifying the dominant microscopic mechanism remains to be clarified. The types of defect dynamics relevant to the polarity- dependent q switching remain an open and interesting question. Although the motion of defects with a nonquantized topological charge can contribute to current-polarity-independent q switching26, such a mechanism does not account for the polarity-dependent switching observed in the present study.
Reversible reorientation of the helimagnetic q-director in a cubic chiral magnet by electric-current polarity · 2026 · DOIIn this study, we performed ultrasonic measurements on the unconventional superconductor Sr2RuO4. We found that the ultrasonic attenuation coefficient αT for the in-plane trans- verse ultrasonic waves associated with the elastic constant CT = (C11 − C12) /2 exhibits an anomalous increase at low temperatures, while the elastic softening of CT expected from the Kramers-Kronig relation is absent. Based on the Landau- Khalatnikov theory, we found that fluctuations of the elec- tronic degrees of freedom show slowing down, reaching a re- laxation time of τ ∼ 0.14 × 10−9 s (τ−1 ∼ 7.1 GHz) at the superconducting transition temperature of Tc = 1.42 K. This slowing down follows the Ising universality with a critical exponent product zν = 1 as expected from mean-field the- ory. Group-theoretical considerations suggest that the electric hexadecapole Hα z with the irrep A2g in the point group D4h is the electronic degree of freedom responsible for the slowing down. Our ultrasonic measurements also demonstrated that the rotation ωxy introduced by the in-plane transverse waves plays an essential role in Sr2RuO4 in addition to the strains. These results establish ultrasonic attenuation measurements as a powerful probe of dynamical electronic multipole fluctu- ations and provide new constraints on the symmetry and mi- croscopic nature of superconductivity in Sr2RuO4.
In this work we presented a general framework for studying anomalies of non-invertible symmetries in 3+1d, using a corresponding 4+1d Abelian 2-form gauge theory with a 0-form symmetry. We found that for the particular example of Kramers-Wannier like symmetries, certain symmetries are anomalous due to a quantity that generalizes the 2+1d FS indicator. These provide anomalies beyond those studied in Refs. [28,39,65]. We also uncovered a family of non-invertible time-reversal symmetries in 2+1d and presented some lattice models with these non-invertible symmetries. Let us comment on some future directions which we would like to revisit: • It would be interesting to study how non-invertible symmetries might fractionalize in 3+1d. This was studied in depth in e.g. [113, 144, 159, 160] for invertible symmetries. • We can generalize to study topological defects of other dimensions including those related to continuous symmetries. As a particular example, the anomaly field theory that describes mixed anomaly of U (1) higher form symmetries with is given by the analogue of Chern-Simons term for the gauge fields. It would be interesting to study the possible gapped or gapless boundaries of such examples from this point of view. • In principle, our discussion does not need to assume Poincar´e invariance, and should apply also to condensed matter systems. For instance, the anomaly field theory is Witt 40 ˜X+˜X˜X˜X+˜Z+˜Z˜Z˜Z+ equivalent to the ZN two-form gauge theory described by the loop toric code model in 4+1d. This is unlike the argument in [65]. It would be interesting to apply our results to a more broad class of systems with less spacetime symmetry. • The discussion can be generalized to defects that generate gauging a subsystem symmetry. See e.g. [161, 162] for examples of non-invertible subsystem symmetries. • A natural future direction is to study other non-invertible symmetries in 3+1d by using different 0-form symmetry enriched 2-form Abelian gauge theories in 4+1d. For example, we can study anomalies of ST n symmetries in 3+1d. We already studied the first level obstructions in Section 2.2, but we did not systematically study anomalies from FS indicators. We did give an example in Section 3.5.1 showing that ST n symmetry may have obstructions to symmetric TQFTs related to beyond-cohomology SPTs not encountered for S symmetry. • The 0-form symmetry enriching the Abelian gauge theory can also be non-Abelian. For example, it can be a permutation group. It would be interesting to study anomalies of symmetries in 3+1d related to more general 0-form symmetries of the 4+1d Abelian gauge theory. • In Section 3.6.2, we uncovered an infinite family of theories with non-invertible time reversal, originating from theories where the time-reversal had a mixed anomaly with charge conjugation. This method of obtaining a non-invertible time reversal symmetry from an anomalous time reversal symmetry is very general; we will discuss this and present many more examples in forthcoming work. [154] • It would be very interesting to find realistic examples (beyond stacking constructions) where the FS indicators ω, ωf are nontrivial. It should also be possible to construct lattice models where ω is nontrivial. The lattice models we presented, like the Ising model, have trivial ω. Furthermore, we restricted to bosonic models, but it should also be possible to construct fermionic models, especially with nontrivial ωf , for N even. • As mentioned in Section 4.3, the lattice models we constructed have predictable dynamics for p = 0. However, for p ̸= 0, and in particular for p ∼ N , our models for large N seem have very different dynamics. It would be interesting to study the phase diagram numerically, to confirm our hypothesized phase diagram in Figure 6. It would also be interesting to study the phase diagram for p2 = −1 mod N , where the bulk does not need to undergo a phase transition. √ • If the phase diagrams for N, p where p2 = −1 mod N demonstrate that the J0 = J1 point is gapless, it would be interesting to study what symmetric perturbations can be used to take the system into a trivially gapped phase. • There are many remaining questions related to the subtleties of gauging 1-form symme- tries on the lattice. This is especially true for ST n gauging (see Section 4.4). We plan 41 to study the gauging, and recover the fusion rules (modified by translations) in future work.
A Non-invertible fusion rules from Aut(K) symmetry A.1 Example: ZN two-form gauge theory . . . . . . . . . . . . . . . . . . . . . . B Generalized Frobenius Schur-indicator and statistics C Trivializing the anomaly by symmetry extension 40 42 43 44 45
An important open problem is to investigate how the energy gap varies with the distance between the visons.
Research on CVO thin films remains scarce to date, probably hindered by the complex synthesis of CVO stoichiometric targets necessary for their deposition.
Further development of the source-free xc functional. Application of the functional to other complex magnetic phenomena. Comparison with other methods for describing non-collinear magnetism.
First-principles calculations of magnetic states in pyrochlores using a source-free exchange and correlation functional · 2026 · DOIThe conventional LSDA is limited in its ability to describe non-collinear magnetism. The development of a fully relativistic treatment is necessary to incorporate spin-orbit coupling. The accuracy of functionals for non-collinear magnetism is a major challenge.
First-principles calculations of magnetic states in pyrochlores using a source-free exchange and correlation functional · 2026 · DOIInvestigating the diverse and intriguing physics of Mn-based kagome lattices, - Exploring novel topological phases in this material class, - Further studies on the magnetic properties of ScMn6(Sn0.78Ga0.22)6
Complex electronic topography and magnetotransport in an in-plane ferromagnetic kagome metal · 2026 · DOIThe lack of understanding of the magnetic properties of kagome metals, particularly the interplay between flat bands, Dirac cones, and magnetism. The need to control and modulate the magnetic phases in these materials. The gap in knowledge about the electronic structure of magnetic kagome materials.
Complex electronic topography and magnetotransport in an in-plane ferromagnetic kagome metal · 2026 · DOIThe complex interplay between the strong SOC and Coulomb repulsion in 5d compounds. The limited understanding of the superexchange interactions in Y2NiIrO6. The difficulty in predicting the behavior of Y2NiIrO6 under physical pressure.
The study does not provide a comprehensive analysis of the magnetic frustration in Y2NiIrO6. The calculations are limited to the evolution of crystal structure under physical pressures.
The paper only considers a theoretical model and does not provide experimental results. The numerical simulations are limited to a 3 × 4 cluster with periodic boundary conditions.
Ferromagnetic superconductivity with excitonic Cooper pairs: Application to Γ-valley twisted semiconductors · 2026 · DOIThe Kohn-Luttinger-type theories yield weak-coupling superconductivity, which has a transition temperature much smaller than the Fermi energy. A novel mechanism for superconductivity from repulsive interaction is needed for multiband systems.
Ferromagnetic superconductivity with excitonic Cooper pairs: Application to Γ-valley twisted semiconductors · 2026 · DOIThe lack of a controlled framework for distinguishing gapless and gapped phases in frustrated spin systems. The need for a sensitive probe of frustrated quantum spin liquids.
Experimental realization of spin supersolids is challenging due to the need for highly frustrated magnetic systems. Theoretical modeling of spin supersolids is challenging due to the complexity of the underlying physics.
Further experimental and theoretical studies are needed to fully understand the properties of spin supersolids. The potential applications of spin supersolids in highly efficient demagnetization cooling and spin transport need to be explored further.
Further study of the interplay between LC order and superconductivity is needed. Experimental verification of the proposed mechanism is necessary.
The correspondence between experiments and theoretical calculations has yet to be clarified due to the complexity of the spin Hamiltonian. The study aims to address this gap by exploring the thermal transport in honeycomb antiferromagnet MnPS$_{3}$.
Anomalies in the thermal conductivity of honeycomb antiferromagnet MnPS$_{3}$ · 2026The $J_{1}$-$J_{2}$ antiferromagnetic XY model's phase diagram is not yet completely settled. New findings on the subject continue to appear.
Magnetic phases in the $J_{1}$-$J_{2}$ antiferromagnetic XY model on the honeycomb lattice · 2026experimental realization of the chiral spin liquid, - investigation of the non-universal properties of the domain wall, - study of the gapless edge modes and their contribution to the domain wall theory
The Chern-Simons theory does not capture the symmetry-breaking properties of a chiral spin liquid. The theory does not capture non-universal but experimentally important features of the system. The paper identifies the need to incorporate amplitude fluctuations of spinon hoppings into an effective field theoretic framework.
The understanding of the relationship between lattice geometry and symmetry and the topological character of quantum materials is still limited. The development of high-quality single crystals is essential for advancing our understanding of quantum phenomena. The study of topological quantum materials is crucial for advancing our understanding of quantum phenomena.
The study faces the challenge of simulating the behavior of a complex many-body system. The work must overcome the difficulty of charting the full surrounding phase diagram. The research needs to address the complexity of understanding the role of van Hove singularities in driving correlated phases.
The study is based on simulations and does not include experimental results. The phase diagram is computed for a limited range of interaction strengths and carrier densities.
Most-cited papers in Advanced Condensed Matter Physics
- The Resonating Valence Bond State in La 2 CuO 4 and Superconductivity · Science · 1987 · 7,313 citations
- Spin liquids in frustrated magnets · Nature · 2010 · 4,050 citations
- Probing topological spin liquids on a programmable quantum simulator · Science · 2021 · 719 citations
- Time-reversal symmetry-breaking charge order in a kagome superconductor · Nature · 2022 · 478 citations
- Concurrence of anomalous Hall effect and charge density wave in a superconducting topological kagome metal · Physical review. B./Physical review. B · 2021 · 371 citations
- Kitaev materials · Physics Reports · 2022 · 321 citations
- Half-integer quantized anomalous thermal Hall effect in the Kitaev material candidate α-RuCl 3 · Science · 2021 · 294 citations
- Electronic instabilities of kagome metals: Saddle points and Landau theory · Physical review. B./Physical review. B · 2021 · 250 citations
- Multiband Superconductivity with Sign-Preserving Order Parameter in Kagome Superconductor CsV 3 Sb 5 · Physical Review Letters · 2021 · 207 citations
- The Néel Theory of Ferrimagnetism · American Journal of Physics · 1955 · 205 citations
Most recent work
- Altermagnetic Proximity Effect · Physical Review Letters · 2026
- Anomalies of coset non-invertible symmetries · SciPost Physics · 2026
- Direct evidence of a near-ideal J eff = 1 / 2 ground state in triangular-lattice Na 2 BaCo ( PO 4 ) 2 · Physical Review Materials · 2026
- All-Altermagnetic Tunnel Junction of RuO 2 /NiF 2 /RuO 2 · Chinese Physics Letters · 2026
- Surface-localized magnetic order in RuO2 thin films revealed by low-energy muon probes · Applied Physics Letters · 2026
- Magnetic phase transitions driven by quantum geometry · Physical Review Research · 2026
- Intertwined orders in a quantum-entangled metal · Nature Materials · 2026
- Micromagnetics of conical-helix textures in thin films with different kinds of Dzyaloshinskii-Moriya interactions · npj Computational Materials · 2026
- Emergent Spin Supersolids in Frustrated Quantum Materials · Advanced Materials · 2026
- T -square electric resistivity and its thermal counterpart in RuO 2 · Physical Review Materials · 2026
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