Unlike de Haas–van Alphen measurements, heat-capacity magneto-quantum oscillations directly probe the oscillatory bulk quasiparticle density of states. Here, we report the observation of MQOs in V_2Ga_5 single crystals studied via highly sensitive ac calorimetry. The strongest MQO signal is observed for a magnetic field applied along the vanadium chains, in excellent agreement with de Haas–van Alphen magnetization data. A single dominant frequency of 126.6 T resolved by fast Fourier transform confirms the true bulk origin of the elliptical γ Fermi-surface pocket located near the Z point of the Brillouin zone. The angular dependence of the FFT frequency closely tracks the anisotropy of the γ pocket, as supported by first-principles calculations. Analysis of the temperature- and field-dependent MQO amplitudes allows the precise determination of the effective cyclotron mass, Dingle temperature, quantum relaxation time, carrier mobility, and electron mean free path. Furthermore, we demonstrate that the net Berry flux is invariant with respect to the magnetic-field orientation, as a consequence of a conserved hybridization phase twist within the γ pocket. These findings establish ac calorimetry as a powerful macroscopic probe of topological orbital hybridization in complex intermetallics.

Ising superconductivity allows in-plane upper critical magnetic fields to vastly surpass Pauli limit by locking the antiparallel electron spins of Cooper pairs in the out-of-plane direction. It was first explicitly demonstrated in fully two-dimensional monolayers of transition metal dichalcogenides with large spin-orbit coupling and broken inversion symmetry. Since then, several studies have shown that it can be present in layered bulk materials, too. In our previous study, we have clarified the underlying microscopic mechanism of Ising superconductivity in bulk, based on a reduced electronic coupling between superconducting layers due to intercalation by insulating layers and restricted inversion symmetry. But earlier studies suggest that in some transition metal dichalcogenide polytypes Pauli paramagnetic limit is violated even without intercalation. Here, using heat capacity measurements we unambiguously demonstrate, that the pristine noncentrosymmetric bulk 4Ha-NbSe2 polytype significantly violates the Pauli limit. The band structure parameters obtained from ab initio calculations using the experimentally determined crystal structure are used in the theoretical model which provides the microscopic mechanism of the Ising protection based solely on broken inversion symmetry.

In 2025, the Year of Quantum Science and Technology ( https://quantum2025.org/ ), we celebrate a century of quantum mechanics, witnessing a surge in activities that illuminate its inherent strangeness and drive technological innovation. Superconductivity, discovered 114 years ago, stands as a prime example, offering direct and compelling evidence of macroscopic quantum phenomena. Beyond its ability to conduct immense currents without loss, superconductivity reveals the quantum realm operating on a scale we can directly observe and manipulate. The macroscopic quantum coherence, where an ensemble of particles is described by a single wave function, leads to remarkable consequences: dissipation-less current and flux quantization—the basic properties exploited in superconducting quantum circuit fabrication. This Roadmap has been inspired by intensive discussions and collaborations emerging from the European Cooperation in Science & Technology COST-Action CA21144 (SuperQuMap—Superconducting Nanodevices and Quantum Materials for Coherent Manipulation). The aim of the COST Action SuperQuMap is to establish a strong European network centered on macroscopic quantum behavior in superconductors, bringing together groups of different backgrounds and more than 30 countries. The roadmap outlines the network’s concrete activities, driving advancements in superconductor-based quantum technologies and charting future directions. Spanning fundamental research to practical applications, the roadmap incorporates insights from industry partners developing quantum computation. It begins by exploring quantum materials, highlighting how topology and electronic correlations could catalyze a quantum leap in technology. We then delve into manipulating the superconducting phase, leveraging advancements in magnetism, 3D fabrication, and tunable correlations. Further, we showcase the advanced microscopy techniques—such as angle-resolved photoemission spectroscopy and scanning probes—used to visualize quantum behavior. Finally, and crucially, we detail the quantum devices developed within the network, and their transformative impact on modern quantum computing approaches.

Multiband superconductors with structural anisotropy offer a fertile ground for exploring unconventional quantum states, yet disentangling their directional pairing characteristics remains a formidable challenge. Here, we present a comprehensive thermodynamic and spectroscopic study of the tetragonal intermetallic superconductor V_2Ga_5 (T_ c≈ 3.5 K), combining first-principles electronic structure calculations with highly sensitive AC calorimetry and directional low-temperature scanning tunneling spectroscopy. By constructing a self-consistent, anisotropic multiband singlet s-wave pairing model within the fully symmetric A_1g representation, we successfully reconcile the experimental specific heat and upper critical field anomalies. Crucially, we reveal that the apparent reversal of bulk gap hierarchies in directional tunneling experiments is a direct consequence of band-selective tunneling. This effect is governed by an elegant interplay between localized Fermi velocity 'hot spots' and specific Fermi surface topologies, rather than raw thermodynamic gap magnitudes alone. Our findings provide a clear microscopic picture of direction-dependent, band-selective tunneling in a highly uniaxial anisotropic superconductor, demonstrating how orientation-dependent transport constraints shape the observable signatures of multiband quantum condensates.

Transition-metal dichalcogenides (TMDs) offer an extremely rich material platform in the exploration of unconventional superconductivity. The unconventional aspects include exotic coupling mechanisms such as the Ising pairing, a complex interplay with other electronic orders such as charge-density waves (CDWs), symmetry-breaking and topological effects, and non-trivial gap structures such as multi-gap and possible nodal phases. Among TMDs, titanium diselenide (1T-TiSe2) is one of the most studied and debated cases. Hints to an anomalous structure of its superconducting order parameter have emerged over the years, possibly linked to its texturing in real and reciprocal space due to the presence of a 2x2x2 CDW phase, or to a pressure-driven multi-band Fermi surface. However, direct evidence for an unconventional structure of the superconducting gap in this material is still lacking. In this work, the combination of the temperature dependence of the upper critical field with point-contact Andreev reflection and scanning tunneling spectroscopy measurements all consistently indicate the existence of two distinct superconducting gaps in the recently-discovered H-intercalated TiSe2 superconductor. These results provide unambiguous evidence for a non-trivial superconducting phase in TiSe2 and stimulate further research aimed at clarifying its connection with the orbital character and its interplay with the underlying CDW order.

Atomically thin layered materials are systems with zero limit bulk-to-surface ratio. Their physical properties are determined by two-dimensionality and strongly affected by interfacing with other systems. Therefore, they represent an accessible platform for the abundance of quantum effects that can be engineered by combining them into vertical stacks. Two types of layered systems are considered here - artificially prepared (exfoliated) van der Waals nanostructures, and naturally layered systems showing quasi 2D behaviour already in a bulk form. A special class of naturally layered materials is misfit structures combining atomic layers of hexagonal transition metal dichalcogenides and slabs of tetragonal ionic rare-earth monochalcogenides in the same superlattice. Both types of layered systems feature a new state of quantum matter, the Ising superconductivity extremely resilient to external magnetic field. A giant electron doping, natural to the misfit structures, can lead to topological superconductivity. Both systems can also be assembled into heterostructures combining different constituents. Layered 2D heterostructures have a large number of implications for many potential applications in solid-state devices.

Point-contact Andreev reflection spectroscopy at low temperatures and high magnetic fields has been performed on a noncentrosymmetric La3Se4 superconductor with a critical temperature T c = 8 K. Two superconducting energy gaps A 1 and A 2 , with 2A1/kBTc similar to 5.8 and 2A2/kBTc similar to 2.3, are directly observed in some of the spectra. The temperature and magnetic field effects help to resolve a two-gap structure even on the most frequent spectra where at low temperatures only a single gap is apparent, reflected in a pair of maxima around the zero bias. Two-gap superconductivity consistently with the point contact Andreev reflection spectroscopy is also supported by the heat capacity and the Hall probe magnetization measurements.

Superconductor-insulator transition (SIT) driven by disorder and transverse magnetic field has been investigated in ultrathin MoN films by means of transport measurements and scanning tunneling microscopy and spectroscopy. Upon decreasing thickness, the homogeneously disordered films show increasing sheet resistance Rs, shift of the superconducting transition Tc to lower temperatures with the 3 nm MoN being the last superconducting film and thinner films already insulating. Fermionic scenario of SIT is evidenced by applicability of the Finkelsteins model, by the fact that Tc and the superconducting gap are coupled with a constant ratio, and by the spatial homogeneity of the superconducting and electronic characteristics. The logarithmic anomaly found in the tunneling spectra of the non-superconducting films is further enhanced in increased magnetic field due to the Zeeman spin effects driving the system deeper into the insulating state and pointing also to fermionic SIT.

In a previous study (2017 Phys. Rev. B 96 144501), a strong variation in the superconducting transition temperature T c of YB 6 differing by a factor of two has been explained by a change in the density of yttrium and boron vacancies tuning the electron–phonon interaction. Here, by using an array of miniature Hall probes, we address the penetration of the magnetic field, pinning, and critical current density on a series of YB 6 single crystals with T c variation between 4.25 and 7.35 K. The analysis of the superconducting and normal-state specific heat characteristics allowed us to determine T c and the stoichiometry of our samples. We observed almost no pinning in the most stoichiometric YB 6 crystal with the lowest T c . Upon increasing the number of vacancies weak pinning appears, and the critical current density is enhanced following the increased transition temperature in a linear variation. We argue that such an increase is, within weak collective pinning theory, consistent with the increasing number of vacancies that serve as pinning centers.

Low-dimensional materials have remarkable properties that are distinct from their bulk counterparts. A paradigmatic example is Ising superconductivity that occurs in monolayer materials such as NbSe2 which show a strong violation of the Pauli limit. In monolayers, this occurs due to a combination of broken inversion symmetry and spin-orbit coupling that locks the spins of the electrons out-of-plane. Bulk NbSe2 is centrosymmetric and is therefore not an Ising superconductor. We show that bulk misfit compound superconductors, (LaSe)1.14(NbSe2) and (LaSe)1.14(NbSe2)2, comprised of monolayers and bilayers of NbSe2, exhibit unexpected Ising protection with a Pauli-limit violation comparable to monolayer NbSe2, despite formally having inversion symmetry. We study these misfit compounds using complementary experimental methods in combination with first-principles calculations. We propose theoretical mechanisms of how the Ising protection can survive in bulk materials. We show how some of these mechanisms operate in these bulk compounds due to a concerted effect of charge-transfer, defects, reduction of interlayer hopping, and stacking. This highlights how Ising superconductivity can, unexpectedly, arise in bulk materials, and possibly enable the design of bulk superconductors that are resilient to magnetic fields.

Point-contact spectroscopy offers a unique straightforward possibility to study the electronic properties of metals. Soon after the invention of this technique by Igor Yanson in the B. Verkin Institute for Low Temperature Physics and Engineering of the NAS of Ukraine [Sov. Phys. JETP39, 506 (1974)], multiple laboratories adopted this technique and applied it to various topical problems in modern solid-state physics. Here, we offer a brief review of how point-contact spectroscopy has been developed and used in the Centre of Low Temperature Physics Košice. By this technique, we were able to obtain for example the spectrum of the electron-phonon interaction in an unprecedented large energy scale up to 160 meV in LaB6. The Zeeman splitting of the Pr3+ ion levels in the crystal-electric field has been detected for the first time in PrNi5. “Inverse” point-contact spectra of the electron-phonon interaction found in semimetallic arsenic were explained by the weak localization in the point-contact area. The point-contact Andreev reflection spectroscopy enabled to detect not only the superconducting energy gap in YB6, but also the Einstein-like phonon mode responsible for superconductivity. The first spectroscopic evidence of the two-gap superconductivity in MgB2 has been provided in our experiments. High spin polarization in Co2FeSn Heusler nanowires for spintronics has been obtained.

We investigated the vortex phase diagram of needle shaped high quality NiBi3 single crystals by transport measurements. The current is applied along the crystalline b-axis of this intermetallic quasi-1D BCS superconductor. The single crystals show a Ginzburg-Levanchuk (Gi) parameter few orders of magnitude larger than other low Tc BCS superconductors. Vortex phase diagram, critical currents and pinning forces have been extracted from the experimental data. The main findings are: 1) Enhancement of the vortex liquid phase in comparison with low Tc superconductors, 2) reentrance of the liquid phase at low fields and 3) deviation of the pinning force vs field from the usual pinning mechanisms. The interplay between weak pinning, due to quenched disorder, and the quasi-1D character of the material could be a hint to explain the lack of a single pinning mechanism.

A strong disorder characterized by a small product of the Fermi vector kF and the electron mean free l drives superconductors towards insulating state. Such disorder can be introduced by making the films very thin. Here, we present 3-nm Mo2N film with k_F*l ~ 2 with a resistive superconducting transition temperature Tc = 2 K heavily suppressed in comparison with the bulk Tc. Superconducting density of states (DOS) with smeared gap-like peaks and in-gap states, so called Dynes DOS, is observed by the low temperature tunneling spectroscopy despite a sharp resistive transition. By scanning tunneling microscope the spectral maps are obtained and related to the surface topography. The maps show a spatial variation of the superconducting energy gap on the order of 20 % which is not accidental but well correlates with the surface corrugation: protrusions reveal larger gap, smaller spectral smearing and smaller in-gap states. In agreement with our previous measurements on ultrathin MoC films we suggest that the film-substrate interface introducing the local pair-breaking is responsible for the observed effects and generally for the suppression of the superconductivity in these ultrathin films.

We have observed superconductivity in heavy p-doped Ge by measuring of differential resistance dV/dI(V) of Ge - PtIr point contacts. The superconducting (SC) features disappear above 6 K or above 1 T, what can be taken as the critical temperature and the critical magnetic field, respectively. The observed dV/dI(V) spectrum with Andreev reflection like features was fitted within one-gap Blonder-Tinkham-Klapwijk model. The extracted SC gap demonstrates Bardeen-Cooper-Schrieffer-like behavior with 2 Delta/kBTc = 10+/-1 ratio, which is much higher that expected for conventional superconductors. Magnetic field suppresses Andreev reflection features, but the SC gap moderately decreases in magnetic field similarly as it was observed previously for the type-II superconductors, including nickel borocarbide and iron-based superconductors. Curiously, we have not yet observed superconductivity in n-doped Ge with a similar dopant concentration.

Centre of Low Temperature Physics, Institute of Experimental Physics, Slovak Academy of Sciences, 04001 Košice, Slovakia Centre of Low Temperature Physics, Faculty of Science, P. J. Šafárik University, 04001 Košice, Slovakia Institut des Matériaux Jean Rouxel, Université de Nantes and CNRS-UMR 6502, Nantes 44322, France Universté Grenoble Alpes, CEA, Grenoble INP, IRIG, PHELIQS, F-38000 Grenoble, France Laboratoire National des Champs Magnétiques Intenses (LNCMI-EMFL), CNRS, UGA, F-38042 Grenoble, France Institut des NanoSciences de Paris, Sorbonne Université and CNRS-UMR 7588, Paris 75005, France

The magnetization properties of the endohedral cluster superconductor Mo 8 Ga 41 are studied by sensitive Hall-probe magnetometry. The temperature dependence of the lower critical magnetic field H c 1 is obtained and compared to theoretical models accounting for single-gap and two-gap superconductivity. Data can be described by both models with minor differences. These results are confronted with our previous measurements which evidence that the system is inherently single-gap s -wave superconductor but minor additional phases are present also in seemingly perfect samples. We discuss how presence of such additional phases with varying size of the penetration depth and H c 1 field is reflected in magnetization measurements which could lead to misinterpretation of the multigap superconductivity in Mo 8 Ga 41 .

Extreme in-plane upper critical magnetic fields $B_{c2//ab}$ strongly violating the Pauli paramagnetic limit have been observed in the misfit layer $(LaSe)_{1.14}(NbSe_2)$ and $(LaSe)_{1.14}(NbSe_2)_2$ single crystals with $T_c$ = 1.23 K and 5.7 K, respectively. The crystals show a two-dimensional to three-dimensional transition at temperatures slightly below $T_c$ with an upturn in the temperature dependence of $B_{c2//ab}$, a temperature dependent huge superconducting anisotropy and a cusplike behavior of the angular dependence of $B_{c2}$. Both misfits are characterized by a strong charge transfer from LaSe to $NbSe_2$. As shown in our previous work, $(LaSe)_{1.14}(NbSe_2)$ is electronically equivalent to the highly doped $NbSe_2$ monolayers. Then, the strong upper critical field can be attributed to the Ising coupling recently discovered in atomically thin transition metal dichalcogenides with strong spin-orbit coupling and a lack of inversion symmetry. A very similar behavior is found in $(LaSe)_{1.14}(NbSe_2)_2$, where the charge transfer is nominally twice as big, which could eventually lead to complete filling of the $NbSe_2$ conduction band and opening superconductivity in LaSe. Whatever the particular superconducting mechanism would be, a common denominator in both misfits is that they behave as a stack of almost decoupled superconducting atomic layers, proving that Ising superconductivity can also exist in bulk materials.

Superconductor insulator transition in transverse magnetic field is studied in the highly disordered MoC film with the product of the Fermi momentum and the mean free path $k_F*l$ close to unity. Surprisingly, the Zeeman paramagnetic effects dominate over orbital coupling on both sides of the transition. In superconducting state it is evidenced by a high upper critical magnetic field $B_{c2}$, by its square root dependence on temperature, as well as by the Zeeman splitting of the quasiparticle density of states (DOS) measured by scanning tunneling microscopy. At $B_{c2}$ a logarithmic anomaly in DOS is observed. This anomaly is further enhanced in increasing magnetic field, which is explained by the Zeeman splitting of the Altshuler-Aronov DOS driving the system into a more insulating or resistive state. Spin dependent Altshuler-Aronov correction is also needed to explain the transport behavior above $B_{c2}$.