Experimental aspects of 2D superconductivity and topology

• Ding Zhang (Tsinghua University)

Superconductivity in highly crystalline 2D materials has become a vibrant field. It not only encompasses emergent quantum phenomena including Ising superconductivity but also helps us deepen the understanding on issues such as quantum phase transitions. This lecture consists of two parts. In the first part, I will take NbSe2 as an example and review the studies over the decade that are related to 2D superconductivity. I will cover two major aspects of ultrathin NbSe2: 1. Ising superconductivity due to strong spin-orbit coupling and intralayer inversion symmetry breaking; 2. Anomalous metal phase due to fragility of superconductivity in the 2D limit. I will also review some recent progresses on finite momentum Cooper pairing in relatively thick NbSe2, as well as Ising superconductivity in bulk NbSe2. In the second part, I will review studies on candidate materials that possess both 2D superconductivity and non-trivial topological bands. The exemplary systems are WTe2 and stanene—a tin analog of graphene. Recently, it has been proposed that twisted cuprate bilayers host high-temperature topological superconductivity. Experimental developments in this field will be reviewed.

Perspectives on the Superconductor-Insulator-Transition

• Christoph Strunk (University of Regensburg)

The interplay of electron-electron interactions and strong disorder superconductor-insulator transition leads to the superconductor-insulator transition (SIT). Beginning with the pioneering experiment of Haviland et al. [1], this phenomenon has remained enigmatic. This begins with the question of what to call an insulator. Very early, scaling theories exploited a duality of Cooper-pairs and vortices in 2D films [2]. Within this picture, the dual of the superconducting state is a vortex superfluid that behaves electrically insulating. This scenario has led to an intense activity, centered around scaling behavior of resistance isotherms as function of a control parameter. In many cases, the temperature dependence of the resistance resembled more a metal with quantum corrections, however. Later, also highly insulating states have been found, e.g., in InOx, TiN, and NbN. Hopping conductance, thermally activated conductance and even finite temperature insulation were observed. Moreover, there can be intermediate metallic-like states, where the resistance eventually saturates as a function of temperature. I will give an overview over these phenomena and discuss different avenues of their interpretation. [1] D. B. Haviland, Y. Liu, A. M. Goldman, Phys. Rev. Lett. 62, 2180 (1989). [2] M. P. A. Fisher, Phys. Rev. Lett. 65, 923 (1990).

Summer School Lecture 1: Introduction to the Superconductor-Insulator Transition

• Mohit Randeria (Ohio State University)

This lecture will be a pedagogical introduction to the theory of the disorder-driven superconductor-to-insulator transition in 2D s-wave superconductors, developed over the years with N. Trivedi and collaborators [1-6]. Predictions for and comparisons with experiments will be emphasized. For students who want to do some background reading, I especially recommend reference [3s] and [4]. [1] N. Trivedi, R. T. Scalettar, and M. Randeria, Phys. Rev. B 54, R3756 (1996) [2] A. Ghosal, M. Randeria, and N. Trivedi, Phys. Rev. Lett. 81, 3940 (1998) [3] A. Ghosal, M. Randeria and N. Trivedi, Phys. Rev. B 65, 014501 (2001) [4] K. Bouadim, Y. L. Loh, M. Randeria, and N. Trivedi, Nature Physics 7, 884 (2011) [5] M. Swanson, Y. L. Loh, M. Randeria, and N. Trivedi, Phys. Rev. X 4, 021007 (2014) [6] Y. L. Loh, M. Randeria, N. Trivedi, C-C. Chang, R. Scalettar, Phys. Rev. X 6, 021029 (2016)

Summer School Lecture 2: Are There Bounds on the Superconducting Transition Temperature?

• Mohit Randeria (Ohio State University)

The question of understanding limits on the superconducting transition temperature Tc is of great fundamental and technological importance. I will begin with a pedagogical introduction to this question and describe recent progress on deriving rigorous upper bounds [1] on the Tc of 2D superconductors applicable to a wide range of quantum materials and to ultracold atomic gases. I will illustrate the usefulness of these bounds by comparing with recent experiments on a variety of systems where standard BCS theory fails. Next, motivated by twisted bilayer graphene, I will generalize our bounds to flat bands with non-trivial topology and obtain rigorous quantum geometric bounds for flat band superconductivity [2]. I will conclude by discussing the open question [3] of obtaining general upper bounds on Tc in 3D. [1] T. Hazra, N. Verma, M. Randeria, Phys. Rev. X 9, 031049 (2019) [2] N. Verma, T. Hazra, M. Randeria, Proc. Nat. Acad. Sci. 118, e2106744118 (2021) [3] M. Randeria in “50 years of RG: In memory of M.E. Fisher”, edited by A. Aharony et al. (World Scientific, 2024); Mod. Phys. Lett. B 38, 2430004 (2024)

Quantum critical collapse of the pinned vortex glass at the superconductor-insulator transition

• Benjamin SACEPE (Institut Néel, CNRS Grenoble)

Superconducting films of amorphous indium oxide (a:InO) undergo a transition to an insulating state upon increasing disorder or magnetic field. The gradual suppression of the critical temperature as the disorder-driven transition is approached has long suggested a continuous collapse of the superfluid density, in line with the conventional picture of a continuous quantum phase transition. In this talk, I will show that this expectation fails: the disorder-tuned transition is instead marked by an abrupt jump of the superfluid density at the critical disorder, revealing a first-order quantum transition [1]. I will then turn to the magnetic-field-driven transition, where superconductivity survives in the form of a pinned vortex glass. Using microwave measurements of the superfluid response, I will show that interaction-driven collective vortex pinning strongly reshapes the field evolution of the stiffness, stabilizing superconductivity over an unexpectedly broad field range before its final collapse into an insulating state [2]. [1] T. Charpentier, D. Perconte, S. Léger, K. Amin, F. Blondelle, F. Gay, O. Buisson, L. Ioffe, A. Khvalyuk, I. Poboiko, M. Feigel’man, N. Roch, B. Sacépé, Nature Physics, 21, 104 (2025) [2] D. Perconte, T. Charpentier, N. Koutsopoulos, K. roy, N. Benchabane, X. Peng, F. Blondelle, F. Gay, M. Feigel’man, V. Kabanov, B. Sacépé, arXiv:2605.23838 (2026)

Origin of the superconductor-insulator transition in disordered two-dimensional films

• Christoph Strunk (University of Regensburg)

The superconductor-to-insulator transition (SIT) originates from the competition between Anderson localization, which tends to localize single-particle wavefunctions, and superconductivity, which establishes long-range correlations in the superconducting order parameter. The evolution of the sheet resistance and the superfluid stiffness is monitored in a wide range of disorder strength. We establish that even up to disorder values near the quantum-critical point, the finite-temperature transition from the superconducting into the resistive state remains of BKT type. When disorder approaches the critical value, the zero temperature stiffness is witnessed to vanish rapidly, while the order parameter remains finite, pointing towards quantum fluctuations of the superconducting phase driving the zero-temperature transition.

Conference Talk: On the pairing symmetry of moiré graphene superconductors

• Mohit Randeria (Ohio State University)

Eight years after the discovery of superconductivity in magic-angle twisted bilayer graphene, its pairing symmetry is not definitively established. I will first discuss existing experimental and theoretical constraints on the SC order parameter. I will then focus on Andreev spectroscopy, which is a phase sensitive probe uniquely suited to address this issue. I will describe recent theoretical work [1] which highlights problems in the analysis of existing Andreev experiments and provides a natural explanation of puzzling features in the data that can only be understood in terms of Andreev bound states in a superconductor with an unconventional, sign-changing order parameter. I will end with predictions [2] for Andreev experiments in an in-plane magnetic field that would determine the spin wavefunction of the Cooper pairs and unambiguously distinguish between the allowed pairing symmetries. [1] S. Biswas, S. Suman, M. Randeria, R. Sensarma, PNAS 122, e2509881122 (2025) [2] S. Biswas, R. Sensarma, M. Randeria, arXiv:2606.xxxx (to appear)

Scanning SQUID View of Quantum Materials

• Beena Kalisky (Bar Ilan University)

Competition between electronic orders with similar energy scales can give rise to complex emergent behaviors. Detecting traces of such orders requires versatile probes, which access different aspects of the system, such as conductivity, superconductivity and magnetism. I will describe few material systems where scanning SQUID view uncovered surprising mesoscopic effects. Two polymorphs of Tantalum disulfide: a van-der Waals material, 4Hb-TaS₂, in which we found a hidden magnetic phase and a 1T polymorph, in which we probed a hidden metallic state buried in an insulator. I will also show intriguing new findings in the superconducting state of the Weyl semimetal PtBi₂. These results demonstrate the power of a local phase-sensitive view in probing quantum materials.

Inverse melting of the vortex lattice in a-Re6Zr thin films

• Pratap Raychaudhuri (Tata Institute of Fundamental Research, Mumbai)

Inverse melting refers to a phenomenon where a liquid transforms into a solid with increase in temperature before melting again at a higher temperature. Predicted more than a century ago, inverse melting is rarely observed. In this talk, I will describe low temperature scanning tunneling spectroscopy experiments on a 20 nm thick amorphous Re6Zr (a-Re6Zr) thin films from which we observe direct signatures of inverse melting of the vortex lattice created under the application of a magnetic field[1]. By identifying distinct signatures of these transitions from magnetotransport and magnetic shielding measurements and integrating with scanning tunneling spectroscopy imaging, we construct a comprehensive vortex-state phase diagram in the magnetic field-temperature parameter space. Comparing these results with those on a 5 nm and 50 nm thick a-Re6Zr thin film [2,3] we demonstrate that inverse melting is thickness-dependent: a 5 nm film retains an inhomogeneous liquid state, while a 50 nm film maintains a crystalline solid structure except near the upper critical field. These results suggest that the re-entrant transformations of the vortex lattice are caused by a complex interplay of dimensionality and disorder. [1] Rishabh Duhan, Subhamita Sengupta, John Jesudasan, Somak Basistha, Pratap Raychaudhur, Inverse melting and re-entrant transformations of the vortex lattice in amorphous Re6Zr thin film, Nature Communications 16, 2100 (2025). [2] R. Duhan et al., Structure and dynamics of a pinned vortex liquid in superconducting a-Re{x}Zr (x ~ 6) thin film, Phys. Rev. B 108, L180503 (2023). [3] [ArXiv: 2605.23567] P. Das et al., Phase diagram of the vortex state in an amorphous Re6Zr thin film exhibiting inverse melting

Disordered superconducting nanoporous films – Model systems to explore BKT physics and quantum phase transitions

• Sangita Bose (UM-DAE Centre for Excellence in Basic Sciences)

Conference Talk

Sub-gap modes observed with Kinetic inductance detectors: source of extra-dissipation in disordered thin superconductors?

• Florence LEVY-BERTRAND (CNRS - Institut Néel)

Kinetic inductance detectors (KIDs) are state-of-the-art detectors used for observations in the millimeter-wave range in astrophysics. They are planar resonant circuits consisting of thin superconducting films deposited on an insulating substrate. The photon detection principe consists in monitoring the shift in the resonance frequency, which is proportional to the incident power [1]. Instead of using KIDs made from known materials to study unknown astrophysical sources [2], we use known sources to study the spectroscopic responses of KIDs made from various superconductors. The advantages of this technique over conventional optical spectroscopic techniques are: high sensitivity to variations in superfluid density down to a few tens of broken Cooper pairs, a measurement temperature that can go as low as 100 mK, and statistical control of the response through the simultaneous measurement of a large number of KIDs. The optical dilution refrigerator enables illumination at room temperature using various sources, ranging from a broadband Fourier transform spectrometer to monochromatic sources in the Hz to THz range. First, I will explain how kinetic inductance detectors work and describe the different types of measurements we can perform in the laboratory. I will then present results showing sub-gap modes in granular aluminum [3] and amorphous indium oxide [4]. These sub-gap modes are non-equilibrium phenomena triggered by incident radiation. I will discuss how these modes could explain the additional dissipation observed in disordered thin superconductors [5]. [1] P. K. Day et al, Nature, vol. 425, 817 (2003). [2] A. Monfardini and G. Lagache, Nature Astronomy 5, 970 (2021). [3] F. Levy-Bertrand et al, Phys. Rev. B 99, 094506 (2019). [4] O. Dupré et al, Supercond. Sci. Technol. 30, 04007 (2017). [5] T. Charpentier et al, arXiv:2507.08953 (2025).

Current bistability in insulators with large localization lengths

• Miguel ORTUÑO (Universidad de Murcia)

Beyond a critical disorder, two-dimensional superconductors become insulating at the Superconductor-Insulator Transition (SIT) [1-2]. We present an experimental study on insulating a-YxSi1-x films in the vicinity of the SIT, as well as corresponding numerical simulations of the electrical conductivity [3]. At the lowest temperatures, electronic transport is activated. On the insulating side, our results indicate a bistability in the current-voltage characteristics, with jumps in the current of several orders of magnitude [4,5] and which we analyze in terms of electron-phonon decoupling [6]. We extend the hot-electron model [7] to explain different features of the experimental results. We perform numerical simulations in which grains are at an effective temperature and electron jumps between them are due to the hopping term. These simulations can reproduce the most significant features of the experimental results. We also present experimental results on disordered InSb thin films where apparently similar jumps to those observed in the previous systems take place. However, the hot-electron model is not able to explain these jumps. They seem to be driven by transitions from a rigid phase to a fluid one [8,9]. We analyze and compare the difference between both types of systems. [1] Kapitulnik, A., Kivelson, S. A. & Spivak, B. Colloquium: Anomalous metals: failed superconductors. Rev. Mod. Phys. 91, 011002 (2019). [2] Sacépé, B. et al. Localization of preformed Cooper pairs in disordered superconductors. Nat. Phys. 7, 239–244 (2011). [3] Humbert, V., Ortuno, M., Somoza, A.M., Bergé, L., Dumoulin, L. & Marrache-Kikuchi, C.A. Overactivated transport in the localized phase of the superconductor-insulator transition. Nature Comm., 12, 6733 (2021). [4] Ovadia, M. and Sacepe, B. and Shahar, D. Electron-Phonon Decoupling in Disordered Insulators, Phys. Rev. Lett. 102, 176802 (2009). [5] Ladieu, F. and L'Hote, D. and Tourbot, R. Non-Ohmic hopping transport in a-YSi: From isotropic to directed percolation. Phys. Rev. B 61, 8108 (2000). [6] Altshuler, B. L. and Kravtsov, V. E. and Lerner, I. V. and Aleiner, I. L. Jumps in Current-Voltage Characteristics in Disordered Films, Phys. Rev. Lett. 102, 176803 (2009). [7] Wang, Ning and Wellstood, F. C. and Sadoulet, B. and Haller, E. E. and Beeman, J. Electrical and thermal properties of neutron-transmutation-doped Ge at 20 mK, Phys. Rev. B 41, 3761 (1990). [8] Porrati, F. and Huth, M. Resistive switching in tunable Pt–C granular metals, J. Appl. Phys. 139, 185103 (2026). [9] Shashkina, A.A., Melnikova, M.Yu, and Kravchenko, S.V. Transport evidence for the quantum Wigner solid formation in two-dimensional electron systems, Physica E 168, 116192 (2025).

Controlling magnetic domain walls with supercurrents

• Tero Heikkilä (University of Jyväskylä, Finland)

Establishing a versatile, fast and reliable magnetic memory technology is a giant bottleneck for cryogenic computing since present-day room-temperature solutions either cease to work or consume too much power. The long-term goal of superconducting spintronics has been to overcome this bottleneck by generating magnetic memories with equal-spin triplet supercurrent driven through them to control their magnetization direction. This path has been hampered by the short spin relaxation length and strong anisotropy in ferromagnets. We show [1] how the supercurrent driven generation of spin accumulation in a superconductor/magnetic insulator bilayer, together with Gilbert damping of magnetization lead to a motion of magnetic domain walls. This manifests as a local voltage across the wall, which allows its position to be identified. Associated with this voltage and the current, there is Joule power which is dissipated via the Gilbert damping. The power required to maintain domain wall motion is orders of magnitude smaller than in the normal state, where most of the power is wasted in producing the current. Suitable materials combinations for realizing this effect include hybrids of heavy-metal superconducting thin films and ferromagnetic insulators or hybrid multilayers of 2D materials combining superconductors and ferromagnetic insulators. [1] T. Kokkeler, R. Ojajärvi, F.S. Bergeret and T.T. Heikkilä, arXiv:2606.19078

Recombination of localized quasiparticles in an disordered superconductors probed with resonators

• Pieter de Visser;de Visser (SRON / TU Delft, Netherlands)

Disordered superconductors offer new impedance regimes for quantum circuits, enable a pathway to protected qubits, and can improve superconducting detectors due to their high kinetic inductance and sheet resistance. Our focus is on kinetic inductance detectors for visible- to near-infrared wavelengths, for exoplanet research. The performance of these devices is determined by quasiparticles dynamics – recombination, electron-phonon scattering and the electrodynamics. While experiments have shown that disorder affects the relaxation of quasiparticles drastically, the microscopic mechanisms are still not understood. We measure quasiparticle relaxation in a disordered β-Ta film, which we pattern as the inductor of a microwave resonator. We observe that quasiparticle recombination is governed by the phonon scattering time, and that it is not affected by phonon trapping (using a membrane), both in contrast with the same experiments with an ordered superconductor (aluminium). We interpret the results as recombination of localized quasiparticles, induced by disorder, which first delocalize. We will discuss how this type of measurement, which addresses both the temporal dynamics of the quasiparticle system and its microwave electrodynamics, could experimentally bridge the gap between the observed excess microwave dissipation in disordered supercondcutors and the microscopic interpretation in terms of excess quasiparticles, trapping and recombination.

Lithium intercalation induces superconductivity with anomalous metal phase, resistance/gap oscillations, and even ferromagnetism

• Ding Zhang (Tsinghua University)

Lithium intercalation is a powerful approach to realizing emergent quantum phenomena in a variety of material systems. Here we report our recent studies of lithium intercalated superconductors by utilizing a solid lithium-ion conductor. We transfer exfoliated materials such as TiSe2 [1,2], Bi2Sr2CaCu2O8+x (Bi-2212) [3], and FeSe [4] on this conductor. The exfoliated flakes can be intercalated with lithium by applying a positive gate voltage to the backside of the solid ion conductor. Such a simple method allows us to explore intriguing superconducting properties. In TiSe2, we realize a superconducting dome by lithium doping. Anomalous metal phase emerges around the optimally doped regime. Tunneling spectroscopy reveals a symmetric gap even in this anomalous metal phase. Furthermore, both resistance measurements and tunneling spectroscopy show oscillations with a perpendicular magnetic field, suggesting a spontaneously formed superconducting network. We confirm the similar resistance oscillations in Bi-2212 in the underdoped regime. This finding indicates that superconducting networks emerge in different material systems. In FeSe, we observe that lithium intercalation brings together both high-temperature superconductivity and ferromagnetism. The coexistence of two usually antagonistic phenomena suggests possible formation of spin triplet Cooper pairing. References: [1] M. Liao, et al., Nat. Commun. 12, 5342 (2021). [2] J.-Y. Ji, et al., Nano Lett. 25, 10641 (2025). [3] M. Liao, et al., Nat. Commun. 13, 1316 (2022). [4] Y. Hu, et al., Nat. Commun. 16, 7305 (2025).

Anomalous metal states in cuprate, Fe-based, and nickelate superconducting films

• Jian Wang (Peking University)

Governed by the fundamental Heisenberg uncertainty principle, two ground states are expected in two-dimensional (2D) Cooper pair systems: the zero-resistance superconducting state with phase-coherent Cooper pairs and the insulating state with localized Cooper pairs. Whether an intermediate metallic ground state exists in 2D superconducting system has been a long debate. In the thin films of three high-Tc superconducting families, we observe the ubiquitous emergence of anomalous metal state (i.e., quantum metal or Bose metal), which is characterized by resistance saturations approaching the zero-temperature limit. In high-Tc superconducting YBCO films patterned with triangular array of nanoholes, we detected a robust intervening anomalous metal state [1]. The suppressed Hall coefficient and the charge-2e quantum oscillations reveal the bosonic nature of this metallic ground state. Then, in the ultrathin crystalline FeSe films grown on SrTiO3, we observed a high-temperature anomalous metal state, which persists up to an exceptionally high temperature of 20 K [2]. Furthermore, a linear-in-temperature resistance is observed below onset superconducting critical temperature, uncovering a bosonic strange metallic behaviour. We also develop a microscopic model for the anomalous metal state based on the ohmic dissipation-influenced quantum tunnelling of vortices, which gives a quantitative explanation for the temperature dependence of resistance. Recently, in the nanoholes patterned infinite-layer nickelate Nd0.8Sr0.2NiO2 films, we uncover the direct correlation between the ground-state resistance saturation and the saturation of phase coherence length among Cooper pairs [3]. The modulation on the macroscopic superconducting phase further drives an anomalous reversal of superconducting anisotropy, where the in-plane critical fields become even below the out-of-plane values ("B" _"c∥" <"B" _("c" ⟂)). Our findings uncover the ubiquitous existence of anomalous quantum metallic ground states in 2D high-Tc superconducting systems [4]. More broadly, our works highlight the critical role of phase coherence in determining the macroscopic superconducting states in two dimensions, and establish a general methodology by nano-fabrication. [1] C. Yang et al., Science 366, 1505-1509 (2019) [2] Y. Li et al., Phys. Rev. Lett. 132, 226003 (2024) [3] H. Ji et al., arXiv: 2603.00670 (2026) [4] Z. Wang et al., Rep. Prog. Phys. 87, 014502 (2024)

From Majorana to Andreev and Back

• Ramon AGUADO SOLA (Quantum Advanced Research Center (QuARC) and Institute of Materials Science Madrid (ICMM), Spanish Research Council (CSIC))

The promise of Majorana zero modes (MZMs) for fault-tolerant topological quantum computing stems from their unique non-Abelian statistics and inherent topological protection from local decoherence [1]. However, after fifteen years of research, distinguishing MZMs from near-zero-energy Andreev bound states (ABSs) in hybrid devices remains a key challenge. This “Majorana versus Andreev” challenge [2] has revealed that, rather than being a disadvantage,ABSs can serve as a foundation for novel qubit designs. One promising approach encodes a qubit in the spin of a quasiparticle residing in an ABS of a quantum dot [3]. Embedding such a superconducting spin qubit into a transmon circuit provides an intrinsic spin-supercurrent coupling, enabling an effective interface with circuit quantum electrodynamics for coherent control, readout, and strong qubit-qubit coupling [4]. Alternatively, a minimal Kitaev chain implemented in quantum dots coupled via superconductors [5] is a promising platform. Even a minimal chain of two dots can host a pair of Majorana modes and store quantum information in their joint parity. Recent quantum capacitance measurements on such platforms have enabled single-shot parity readout and demonstrated parity lifetimes exceeding 1 millisecond [6]. These results establish essential readout capabilities and resolve a long-standing experimental challenge, paving the way for time-domain control of Majorana-based qubits. [1] Majorana qubits for topological quantum computing, Ramón Aguado, Leo P Kouwenhoven, Physics Today 73, 44 (2020). [2] From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires, Elsa Prada, Pablo San-Jose, Michiel WA de Moor, Attila Geresdi, Eduardo JH Lee, Jelena Klinovaja, Daniel Loss, Jesper Nygård, Ramón Aguado, Leo P Kouwenhoven, Nature Review Physics,2, 575–594 (2020). [3] Spectroscopy of Spin-Split Andreev Levels in a Quantum Dot with Superconducting Leads, Arno Bargerbos, Marta Pita-Vidal, Rok Žitko, Lukas J Splitthoff, Lukas Grünhaupt, Jaap J Wesdorp, Yu Liu, Leo P Kouwenhoven, Ramón Aguado, Christian Kraglund Andersen, Angela Kou, Bernard Van Heck, Phys. Rev. Lett. 131, 097001 (2023) [4] Direct manipulation of a superconducting spin qubit strongly coupled to a transmon qubit, Marta Pita-Vidal, Arno Bargerbos, Rok Žitko, Lukas J Splitthoff, Lukas Grünhaupt, Jaap J Wesdorp, Yu Liu, Leo P Kouwenhoven, Ramón Aguado, Bernard van Heck, Angela Kou, Christian Kraglund Andersen, Nature Physics, 19, 1110 (2023) [5] Optimal Majoranas in Mesoscopic Kitaev Chains, M Alvarado, R Seoane Souto, María José Calderón, Ramón Aguado, arXiv preprint arXiv:2604.13945. [6] Single-shot parity readout of a minimal Kitaev chain, Nick van Loo, Francesco Zatelli, Gorm O Steffensen, Bart Roovers, Guanzhong Wang, Thomas Van Caekenberghe, Alberto Bordin, David van Driel, Yining Zhang, Wietze D Huisman, Ghada Badawy, Erik PAM Bakkers, Grzegorz P Mazur, Ramón Aguado, Leo P Kouwenhoven, Nature 650, 334-339 (2026)

Search for spin-triplet superconductivity in van der Waals hybrid systems

• Elke Scheer (University of Konstanz)

Hybrid structures combining a superconductor (S) with a magnetically inhomogeneous material (F) are known to generate long-range, spin-polarized (spin-triplet) Cooper pairs [1]. The magnetic inhomogeneity at S/F interfaces converts singlet and zero-spin-triplet Cooper pairs into fully polarized spin-triplet Cooper pairs. Experimental support for this mechanism has been obtained from studies of thin-film multilayers [2], and evidence of a similar phenomenon has been reported for van der Waals heterostructures combining the 2D superconductor NbS$_2$ with the intercalated helimagnetic metal Cr$_{1/3}$NbS$_2$ [3]. In this talk, multiple S/F stacks consisting of the transition metal dichalcogenide superconductor NbSe2 and various helimagnetic materials Cr$_{1/3}$NbS$_2$, Cr$_{1/3}$TaS$_2$, Mn$_{1/3}$NbS$_2$ [4-5], exfoliated down to roughly 10 to 20 nm are investigated. A strong modulation of the critical temperature of NbSe$_2$ under an applied magnetic field is observed, depending on the paired helimagnet. First results on VdW spin-valves (F/S/F’) and Josephson junctions (S/F/S) are also shown, with the perspective of direct evidence of involvement of fully polarized spin-triplets. [1] F. S. Bergeret et al, Long-Range Proximity Effects in Superconductor-Ferromagnet Structures, Phys. Rev. Lett. **86**, 4096 (2001) [2] J.W.A. Robinson et al, Controlled Injection of Spin-Triplet Supercurrents into a Strong Ferromagnet, Science **329**, 59-61 (2010) [3] A. Spuri et al, Signature of long-ranged spin triplets across a two-dimensional superconductor/helimagnet van der Waals interface, Phys. Rev. Research **6**, L012046 (2024) [4] C. Zhang et al, Magnetic soliton confinement and discretization effects in Cr$_{1/3}$TaS$_2$ nanoflakes. Rare Metals **41**, 3005-3011 (2022). [5] S.A. Osorio et al, Chiral helimagnetism and stability of magnetic textures in MnNb$_3$S$_6$, Phys. Rev. B **108**, 054414 (2023)

Misfit compounds as a platform for engineering topological superconductivity

• Tristan Cren (INSP, CNRS - Sorbonne University)

In the current quest of innovative materials which combine two-dimensionality, strong spin-orbit, valley physics, superconductivity, charge density waves, quantum-spin Hall effect, the transition metal dichalcogenides (TMD) misfit materials appear as extremely promising. They are constituted by sandwiching rocksalt layers, such as LaSe, and TMD layers such as NbSe$_2$. A very large combination of materials is achievable by playing on the stacking. TMD misfits are a new platform that allows achieving unprecedented high doping levels in TMD materials [1,2]. We will show how we have succeeded adjusting finely the chemical potential over a very wide range in NbSe2 using a Pb$_x$La$_{1-x}$ rocksalt [2], and how this can used for stabilizing several charge density wave orders (2 × 2, 3 × 3, √3 × √3) and tuning the superconducting transition temperature over a wide range. Superconductivity in these compounds exhibits a huge in- plane critical field which is much higher than the paramagnetic limit [3,4] due to a very strong Ising spin-orbit coupling. It was predicted that this huge spin-orbit coupling could lead to non-conventional chiral superconductivity. We will show some hint of a topological superconducting transition in the misfit compounds: on one side of the transition, we observe a conventional s-wave superconductivity immune to disorder, while, on the other side, we observe a fragile superconductivity that exhibits in-gap edge states at step-edges. References: [1] R.T. Leriche et al. Advanced Functional Materials 31, 2007706 (2021). [2] L. Zullo, G. Marini, T. Cren, M. Calandra. Nano Letters 23, 6658 (2023). [3] P. Samuely et al. Phys. Rev. B 104, 224507 (2021). [4] T. Samuely et al. Physical Review B 108, L220501 (2023).

Gate-tunable Rashba-like edge modes versus quantum spin Hall channels in Bi2Se3 nanoplates

• Chuan Li (University of Twente)

Feike van Veen1, Jara Vliem2, Femke Witmans3, Daniel Vanmaeckelberg4, Alexander Brinkman1, and Chuan Li1 1 MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands 2 Institute of Physical and Theoretical Chemistry, University of T¨ubingen, D-72076 T¨ubingen, Germany 3 II. Physikalisches Institut, Universit¨at zu Koln, D-50937 Koln, Germany and 4 Debye Institute for Nanomaterials Science, Utrecht University, 3584 CC Utrecht, The Netherlands * Email: chuan.li@utwente.nl A limited number of material platforms hosting topologically protected edge channels have been experimentally confirmed since the first observation of the quantum spin Hall effect two decades ago. As the realization of topologically protected Majorana bound states remains elusive, the search for novel candidate quantum spin Hall insulators continues to attract significant interest. One promising route toward two-dimensional topological insulators, and ultimately Majorana physics, is offered by ultrathin three-dimensional topological insulators[1-3]. Recent scanning tunnelling spectroscopy measurements on ultrathin colloidal Bi2Se3 nanoplatelets revealed the presence of edge states [4]. Here, we report a superconducting transport study of this system, providing evidence for one-dimensional channels localized at the perimeter of the nanoplatelets. By tuning the back-gate voltage, we identify an insulating regime that is interpreted as a topologically trivial signature, and we discuss a possible Rashba-band origin of these edge channels. Nevertheless, the remarkable robustness of the states against magnetic field and their intriguingly narrow spatial extent remain fundamentally interesting and call for further investigation. [1]. Liu, C.-X. et al. Phys. Rev. B 81, 041307 (2010) [2]. Lu, H.-Z., Niu, Q., Shen, S.-Q, et al., Phys. Rev. B 81, 115407 (2010). [3]. Linder, J., Yokoyama, T. & Sudbø, A. Phys. Rev. B 80, 205401 (2009). [4]. Moes, J. R. et al., Nano Lett. 3c04460 (2024).

Tunnelling spectroscopy of few-monolayer NbSe2: possible magnetism, and nonequilibirum effects

• Jericho Narvasa (Laboratoire de Physique des Solides (Universite Paris-Saclay))
• Charis Quay (Université Paris-Saclay)

Superconducting transition metal dichalcogenides in the few- and monolayer limit, such as NbSe2, can sustain high in-plane magnetic fields, due to their Ising (or valley Zeeman) spin-orbit coupling (ISOC), which pins the internal spin axis of Cooper pairs out-of-plane. The interplay of the Ising field and the in-plane magnetic field has been predicted to give rise to non-conventional superconducting phases such as odd-parity equal-spin triplet pairs (ESTPs), the orbital FFLO (Fulde-Ferrell-Larkon-Ovchinnikov) phase, pair density waves, striped phases etc. [1] Using van der Waals tunnel junctions, we perform spectroscopy of superconducting NbSe2 flakes, of thicknesses ranging from 2--25 monolayers, measuring the quasiparticle density of states as a function of applied in-plane magnetic field up to 33T, the first spectroscopy measurements on TMDs at these fields. In flakes up to ~15 monolayers thick, we find that the density of states is well-described by a single band superconductor. In these thin samples, the magnetic field acts primarily on the spin (vs orbital) degree of freedom of the electrons, and superconductivity is further protected by ISOC. We extract the superconducting energy gap as a function of the applied magnetic field from our tunnelling data. In bilayer NbSe2, close to the critical field (up to 30T, much larger than the Pauli limit), superconductivity appears to be even more robust than expected if only ISOC is considered. Our data are well-explained by the above-mentioned equal-spin triplet pairs. These ESTPs are revealed by the magnetic field, which also couples them to the dominant singlet order parameter [2, 3]. We have also fabricated a new generation of devices, featuring multiple tunnel junctions to few-layer NbSe2, forming SIS’ (superconductor-insulator-superconductor) Josephson junctions. We’ll briefly discuss non-local and out-of-equilibrium phenomena as well as possible emergent magnetism from these devices.

Layer-selective Cooper pairing in an alternately stacked transition metal dichalcogenide

• Miguel Ugeda (Donostia International Physics Center (DIPC))

Materials exhibiting multiple superconducting phases are exceptionally rare in nature. The few known examples of multiphase superconductors display complex phase diagrams, where distinct phases can be independently induced by means of external stimuli such as pressure or magnetic fields. Here we report the coexistence of two superconducting condensates with different spatial localization in the van der Waals 4Hb-TaSSe polytype. Its layered structure consisting of alternating layers of the T-type and H-type polymorphs enables the development of two effectively decoupled superconducting phases with marked distinct microscopic properties. Using high-resolution quasiparticle tunneling and Andreev reflection spectroscopy in the two polymorph layers, we identify two different superconducting gaps in size in each layer, with signatures compatible with weakly coupled condensates, potentially of different pairing symmetry. The coexistence of these condensates is further corroborated by our measured critical temperatures and upper critical magnetic fields, which significantly differ in each polymorph layer. We explore the possible superconducting ground states using a minimal model based on ab initio calculations that captures many of the experimental features (1). Lastly, I will compare this phenomenology with that occurring in related layered compounds showing conventional superconductivity (2). Our results challenge the current understanding of superconductivity in low-dimensional superconductors and open new pathways for customizable superconducting devices that could independently operate several superconducting states. References (1) H. Guo, S. Sajan, et al. Arxiv:2507.15647 (2025). (2) S. Sajan, H. Guo, et al. Nano Letters 25, 6654 (2025).

Unveiling Novel Aspects of Superconductivity in Twisted Trilayer Graphene

• Mitali Banerjee (Ecole Polytechnique Federal de Lausanne)

Twisted trilayer graphene (TTG) has emerged as a particularly intriguing platform for studying moiré superconductivity. Its flat-band physics closely resembles that of twisted bilayer graphene, yet TTG offers an additional degree of tunability in its band structure, providing a valuable handle for uncovering the mechanisms of moiré superconductivity. In addition, the interference between the two moiré lattices in mirror-symmetry-broken TTG gives rise to a supermoiré lattice, introducing a new degree of freedom for exploring correlated electronic phenomena. In the first part, we report the first transport observation of gate-tunable double-dome superconductivity in MATTG. We found that superconductivity is supressed near v=-2.6 in a small displacement field region. Through temperature, magnetic field and current bias dependence, we reveal the distinct transport behavior of the right and left dome superconductivities, as well as their corresponding normal states. In the second part, we report the existence of the supermoiré lattice in the mirror-symmetry-broken TTG, elucidating its role in generating mini flat bands and mini Dirac bands. We also demonstrate interaction-induced symmetry-broken phases in the supermoiré mini flat bands alongside the cascade of multiple superconductor-insulator transitions enabled by the supermoiré lattice. Our work provides new insights into moiré graphene superconductivity and highlights the importance of the supermoiré lattice as an additional degree of freedom for tuning the electronic properties of twisted multilayer systems.

Upper critical field and pairing symmetry in 2D Ising superconducting materials

• Lena Engstrom

Lena Engström1*, Ludovica Zullo2, Tristan Cren3, Andrej Mesaros1, Pascal Simon1 1 Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France 2 Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden, Universität Würzburg, 97074 Würzburg, Germany 3Sorbonne Université, CNRS, Institut des Nanosciences de Paris, UMR7588, F-75252 Paris, France *E-mail:lena.engstrom@universite-paris-saclay.fr Abstract Several conflicting predictions have been made for the symmetry of the pairing in transition metal dichalcogenide (TMD) superconductors. An indication of if singlet or triplet pairing is present can be given by the upper critical field (Hc2), the magnetic field required to fully suppress superconductivity. Monolayer 1H-NbSe2 and 1H-TaS2 have extremely large critical fields, due to a large Ising spin-orbit coupling (SOC) [1], yet their Hc2 values do not scale with SOC and temperature as expected for other TMDs [2]. In our recent work on few-layer 2H-stacked TMDs [3,4], we highlight that the Ising SOC has nodal lines in the Brillouin zone imposed by symmetry. By deriving the susceptibility, we have found that the scaling of the critical field can be traced back to whether the Fermi surface intersects with these lines or not. Reinterpreting existing experimental data, we find that a predominantly singlet order is consistent with the measured Hc2. We propose two experiments where a signature of spin-singlet pairing would be visible, while discussing the possibility of mixed-parity pairing. References [1] Frigeri, P.A., et al., New J. Phys. 6 115 (2004). [2] de la Barrera, S.C., Sinko, M.R., Gopalan, D.P. et al., Nat Commun 9, 1427 (2018). [3] Engström, L., Zullo, L., Cren, T., Mesaros, A. and Simon, P., Phys. Rev. Lett. 135, 236004 (2025). [4] Engström, Mesaros, A. and Simon, P., arXiv:2602.14210

Controlling topological superconducting phases in TMD heterostructure

• Dganit MEIDAN (SPMS/CentraleSupelec)

Transition metal dichalcogenides (TMDs) offer a highly tunable platform for investigating topological phases and unconventional superconductivity. In this talk, I will focus on hexagonally structured monolayers, where the heavy transition metal and the broken inversion symmetry give rise to Ising spin orbit coupling. I will begin by discussing a topological nodal superconducting phase predicted to appear under strong in-plane magnetic field. This phase hosts Majorana flat bands and leaves a distinctive imprint on the Josephson current-phase relation. I will then turn to the role of Rashba spin–orbit coupling, whose strength can be tuned experimentally via gates. Although it breaks the chiral symmetry that protects the nodal phase, a residual mirror symmetry stabilizes a nodal crystalline superconducting phase with its own topological character. Finally, I will present a topological superconducting phase arising in bilayer structures, where the topology can be controlled through an interlayer current. Taken together, these examples highlight the rich interplay between symmetry, topology, and tunability in TMD-based superconductors.

Pressure Induced Anomalous Metal in the Vicinity of the Superconductor Insulator Transition

• Roy Cohen (Bar Ilan university)

The Superconductor-to-Insulator Transition (SIT) in two-dimensional superconductors occurs due to a competition between superconductivity, quantum interferences, Coulomb interactions, and disorder. Despite extensive theoretical and experimental investigation, the SIT remains an active research area due to the potential for exotic phases near the transition. One such phase is the Anomalous Metal, which has been claimed to exist between the insulating and superconducting states. This elusive phase, which is not consistent with current theories, is under heavy deliberations nowadays. In my talk, I will present an experimental study of the effect of high pressure on thin films of amorphous indium oxide. Our results show that pressure induces a series of transitions from a Bose insulator through a superconducting phase, metallic phases and finally to a conventional insulator. I will suggest that our findings reaffirm the existence of a two-dimensional metal close to the SIT and show that its occurrence requires relatively strong coupling between regions that are weakly superconducting.

Percolation and (super)conduction: 2d superconductors with correlated disorder

• Giulia Venditti

Two-dimensional superconductors should exhibit a Berezinskii–Kosterlitz–Thouless (BKT) transition, and the 𝑇-dependence of the superfluid stiffness should distinguish between nodal or gapped order parameter symmetries. However, this picture dramatically changes when large scale inhomogeneities and spatially correlated disorder are taken into account, washing out BKT signatures. At the same time, superconducting percolative transitions can give rise to apparent unconventional features. Random resistor and random impedance network (RRN/RIN) [1,2] models capture this phenomenology, naturally explaining features such as residual resistivity [1], non-linear IV characteristics [3], and unconventional stiffness [4,5]. In twisted multilayer graphene, we use elasticity theory to show how single site impurities can generate twist angle inhomogeneities. By mapping them into their corresponding local critical temperatures, we compute their finite-frequency conductance with the RIN. Our calculations are consistent with recent microwave transport experiments [6,7,8] and gives a quantitative explanation of the reproducibility issues reported in twisted bilayer graphene devices [9]. Moreover, we identify the real part of the conductivity to be a key diagnostic observable to probe the relevance of correlated disorder. References: [1] G. Venditti, I. Maccari, M. Grilli, and S. Caprara, Condens. Mat. 5(2) (2020) [2] G. Venditti, I. Maccari, M. Grilli, and S. Caprara, Nanomat. 11(8) (2021) [3] G. Venditti, J. Biscaras, S. Hurand, N. Bergeal, J. Lesueur, A. Dogra, R. C. Budhani, Mintu Mondal, John Jesudasan, Pratap Raychaudhuri, S. Caprara, and L. Benfatto, Phys. Rev. B 100 (2019) 064506. [4] G. Venditti, I. Maccari, A. Jouan, G. Singh, R. C. Budhani, C. Feuillet-Palma, J. Lesueur, N. Bergeal, S. Caprara, M. Grilli, SciPost Phys. 15 239 (2023) [5] I. Maccari, L. Rademaker, G. Venditti, How twist angle inhomogeneity masks the BKT transition and the order parameter symmetry, arXiv: 2606.17191 (2026) [6] J. M. Park et al., Science 10.1126/science.adv8376 (2025) [7] Banerjee et al,Nature 638, 93–98 (2025) [8] Mukherjee et al, Nature Materials 24, 1400–1406 (2025) [9] Chun Ning Lau et al, Nature 602 41-50 (2022)

Bulk Localized Collective Excitations in Strongly Disordered Superconductors

• Anton KHVALYUK (Laboratoire de Physique de l'ENS de Lyon, CNRS)

Macroscopic electromagnetic response of a superconductor is described by a finite superfluid stiffness $\theta$, which underlies hallmark phenomena such as dissipationless current flow. In conventional superconductors, these properties persist at finite temperature $T$ and frequency $\omega$ due to a hard superconducting gap. The conventional Mattis‑Bardeen framework further predicts that increasing disorder reduces $\theta$—a desirable trait for microwave-device applications. However, strongly disordered superconductors (amorphous indium oxide, niobium nitride, titanium nitride) run counter to the conventional theory of superconductivity. Tunneling spectroscopy reveals a hard “pseudogap” persisting above the transition temperature. Furthermore, the suppression of $\theta$ with $T$ follows an unexpected power law spanning more than a decade of $T$ [1], and microwave dissipation shows a non‑monotonic $T$ trend that cannot be explained by conventional means [2, 3]. This talk presents a theoretical framework that consistently addresses these observations. A combination of custom numerical simulations and theoretical analysis links macroscopic electromagnetic response to disorder‑induced spatial inhomogeneity of the superconducting state—a key feature of strong disorder. By analytically characterizing the statistical order parameter distribution, we derive expressions for both $\theta$ and low-$\omega$ dissipation that agree with experimental data [1, 3]. The analysis further identifies the relevant low‑energy collective excitations that are phenomenologically similar to two-level systems [3]. The steep profile of the spectral density of these excitations suggests a strong $\omega$ dependence of dissipation. Finally, these insights help explain the non‑monotonic shape of the superconducting transition line in the temperature–disorder plane [2]. References: [1] AVK et al., Phys. Rev. B 109, 144501 (2024) [2] T. Charpentier et al., Nature Physics 21, 104-109 (2025) [3] AVK and M. V. Feigel'man, Phys. Rev. Lett. 136, 256001 (2026)

AC Josephson effect in graphene for quantum metrology

• Nicolas Aparicio Da Silva (LNE)

Quantum electrical standards in the International System of units (SI) are challenging to put in practice together as their working conditions are nowadays intrinsically incompatible. The magnetic field required to realize the quantum Hall effect for the primary resistance standard prevents superconductivity, which is at the core of the quantum voltage standard through the AC Josephson effect. Considerable efforts are being made to simplify access to SI units through the development of a quantum multimeter. Here we explore the potential of devices made from graphene encapsulated in hexagonal boron nitride (h-BN) as a promising platform to host the two quantum effects. High mobilily quantum Hall devices have been shown to allow the Hall resistance quantization at low magnetic field (~ 1 T). We first characterise the graphene junction in its DC regime, and then observe particularly resilient phase-locked Shapiro plateaus under RF illumination at temperatures from 7 mK up to above 1.5 K [1]. Half-integer Shapiro steps also manifest at fRF = 8.8 GHz, which may indicate a nonsinusoidal current-phase relation (CPR) and thus a highly transparent junction [2]. We present our efforts into identifying limiting factors of the accuracy of the n = 1 Shapiro plateau as a function of experimental parameters (such as RF power, temperature, DC current bias, time and measurement setup).