We consider the intrinsic fluctuation conductivity in metals with multiply sheeted Fermi surfaces approaching a superconducting critical point. Restricting our attention to extreme type-II multicomponent superconductors motivates focusing on the ultraclean limit. Using functional-integral techniques, we derive the Gaussian fluctuation action from which we obtain the gauge-invariant electromagnetic linear response kernel. This allows us to compute the optical conductivity tensor. We identify essential conditions required for a nonzero dissipative part of the longitudinal conductivity in a disorder-free and translationally invariant system. Specifically, this derives indirectly from the multicomponent character of the incipient superconducting order and the parent metallic state. Under these conditions, the enhancement of the DC conductivity due to fluctuations close to the critical point follows the same critical behavior as in the diffusive limit.

We study an unconventional phase transition in ferroelectrics where the polarization field is constrained to be divergence-free, allowing only looplike configurations. This local constraint fundamentally alters the critical behavior, driving the system beyond the Landau-Ginzburg-Wilson paradigm. A renormalization group analysis shows that the polarization acquires an unusually large anomalous dimension, η≈0.239 in three dimensions, far exceeding the typical values in O(3)-invariant systems. We attribute this effect to a naturally induced gauge symmetry originating from the zero-divergence constraint. Such constraint-induced gauge-field behavior is reminiscent of fractionalized phases, revealing a fundamental connection between constrained ferroelectrics and emergent gauge phenomena in correlated matter.

We employ optical pump-THz probe spectroscopy to chart the ultrafast superconductivity suppression in NbN over a broad range of excitation fluences. Our measurements uncover a pronounced lengthening of the superconductivity quenching time when the absorbed optical energy is close to the condensation energy of the superconductor, which constitutes a non-equilibrium analog of critical slowing-down on a timescale comparable to that of superconducting fluctuations. Time-dependent Ginzburg-Landau simulations reproduce this behavior and ascribe it to the flattening of the free energy landscape at the dynamical phase transition boundary. Our findings represent a direct observation in real time of slowed-down superconductivity dynamics in proximity to a critical point and open a pathway for investigating out-of-equilibrium critical phenomena with time-resolved THz spectroscopy.

We present a comprehensive theoretical analysis of magnetic heterostructures composed of ferromagnetic (FM) layers interfaced with three-dimensional topological insulators (TIs). Integrating out the topological surface states and computing the spin determinant to second order in spins, we derive the effective generalized Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interactions mediated by topological surface states. These interactions inherently incorporate spin-momentum locking and anisotropic spin susceptibilities stemming from the Dirac-like dispersion of the TI surface electrons. The analysis reveals that the interplay between the spin-orbit coupling intrinsic to the TI and the magnetization in the FM layer induces highly nonlocal and retarded, chiral, and Dzyaloshinskii-Moriya (DM)-like contributions to the effective spin Hamiltonian. Furthermore, the spin dynamics is studied through a derivation of the LLG equation for this problem. The induced interactions renormalize many of the FM's intrinsic properties, but a new term in the LLG equation is induced that is related to the rate of change of the magnetization's curl, which is relevant to skyrmion dynamics. The magnon dispersion exhibits modifications due to the TI-mediated interactions, including a softened inertial spin-wave mode and tunable magnon gaps, sensitive to a tunable chemical potential and interfacial exchange coupling strength. The results also apply to finite temperatures. They elucidate topologically induced magnetic phenomena and pave the way for engineering exotic spin textures, such as skyrmions and chiral domain walls, in TI-FM hybrid systems with tunable interactions.

We show that the spin conductivity of a metal approaching a ferromagnetic quantum critical point exhibits divergent fluctuation corrections. This effect arises from critical spin fluctuations and constitutes a spin analog of the Aslamazov-Larkin theory of paraconductivity in superconductors. The spin current is derived in linear response within a Gaussian-level treatment of the effective action for a system with easy-plane magnetic anisotropy. We demonstrate the consistency of our spin transport theory by showing that it (i) fulfills the Ward identity and (ii) yields vanishing spin stiffness in the normal state. The critical enhancement of the spin conductivity is interpreted as incipient spin superfluidity in the quantum critical region. This is further supported by an intuitive picture based on the current-loop representation of the easy-plane ferromagnet.

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.

We investigate many-body effects on the spin-split electron bands in altermagnets by computing the electron self-energy arising from interactions with magnons, phonons, and hybridized magnon-phonon modes. These interactions lead to band broadening, which can obscure the intrinsic spin-splitting in spectroscopic measurements. We consider a d-wave Lieb lattice altermagnet as a representative example. Our results reveal that the spin-splitting remains spectroscopically resolvable and provide theoretical estimates of lifetime effects relevant for experimental detection. For electron-magnon coupling, we find a distinct difference between spectral function broadening for up and down spins close to the Fermi surface, which is not present in the case of electron-phonon coupling. We relate it to the spin splitting of the magnon modes in altermagnets. The results, including magneto-elastic coupling, are very similar to the pure magnon case. This provides insights into quasiparticle dynamics in altermagnets and contributes to the broader understanding of many-body interactions in spin-split systems. By including the temperature dependence of the self-energies, we also quantify how thermal fluctuations influence the broadening of the electronic states.

We consider a one-dimensional model for a p-wave magnet within the bosonization framework. The model consists of itinerant electrons described by an extended Hubbard model coupled to a chain of localized moments through the Kondo exchange. The classical ground state of the local-moment system captures the salient features of an odd-parity magnet. By bosonizing the coupled system, a description in terms of coupled Luttinger liquids follows, giving rise to a rich weak-coupling phase diagram. It is shown that the spin chain develops quasi long-range order consistent with the combined time-reversal and translation symmetry defining the p-wave magnet. We highlight the peculiar role played by this order in establishing a commensurability condition on the electronic filling under which additional interactions appear in the bosonic field theory. It is demonstrated that these interactions endow the electron spectral function with a pronounced p-wave character. Away from commensurate filling, these interactions are rendered irrelevant and the ensuing p-wave character is lost.

Topological defects are the key feature mediating 2D phase transitions. However, both resolution and tunability have been lacking to access the dynamics of the transitions. With dynamic Kerr microscopy, we directly capture the melting of a confined 2D magnetic skyrmion lattice with high resolution in real-time and -space. Skyrmions in magnetic thin films are two-dimensional, topologically non-trivial quasi-particles that provide rich dynamics as well as unique tunability as an essential ingredient for controlling phase behavior: We tune the skyrmion size and effective temperature on the fly to drive the two-step melting through an intermediate hexatic regime between the solid lattice and the isotropic liquid. We quantify the characteristic occurrence of topological defects mediating the transitions and reveal the so-far inaccessible dynamics of the lattice dislocations. The full real-time and -space imaging reveals the diffusion coefficient of the dislocations, which we find to be orders of magnitudes higher than that of the skyrmions.

The term altermagnetism has recently been introduced to describe the N & eacute;el order of a class of materials whose magnetic sublattices are neither related by translation nor inversion. While these materials arguably have large technological potential, little effort has been devoted to studying the universal distinction of this phase of matter compared to collinear antiferromagnetism. Employing a recently proposed minimal microscopic model, we explicitly derive a nonlinear sigma model describing long-wavelength fluctuations of the staggered magnetization in this system, including quantum effects to leading order. The term that distinguishes the altermagnetic nonlinear sigma model from its antiferromagnetic counterpart is an interaction term that derives directly from the Berry phase of the microscopic spin degrees of freedom. Its effects on the one-loop renormalization group flow in d = 2 + 1 dimensions are examined. Extending the theory to describe the fermionic excitations of the metallic altermagnet, we find an effective low-energy model of d-wave spin-split Dirac fermions interacting with the magnetic fluctuations. Using a Dyson-Schwinger approach, we derive the many-body effects on the dynamical critical scaling due to the competition between the long-range Coulomb interaction and the fluctuations of the staggered magnetization.

Topological defects are the key feature mediating two-dimensional phase transitions. However, both resolution and tunability have been lacking to access the dynamics of these transitions in the various two-dimensional systems explored. Skyrmions in magnetic thin films are two-dimensional, topologically non-trivial quasi-particles that provide rich dynamics as well as tunability as an essential ingredient for the control of their phase behaviour. With dynamic Kerr microscopy, we directly capture the melting of a confined two-dimensional magnetic skyrmion lattice in a Ta/CoFeB/Ta/MgO/Ta magnetic multilayer system with high resolution in real time and real space. By the applied magnetic field, we tune the skyrmion size and effective temperature on the fly to drive the two-step melting through an intermediate hexatic regime between the solid lattice and the isotropic liquid. We quantify the characteristic occurrence of topological defects mediating the transitions and reveal the dynamics of the lattice dislocations. The full real-time and real-space imaging reveals the diffusion coefficient of dislocations, which is two orders of magnitude higher than that of skyrmions.

We study the critical behavior of a Landau-type theory for ferroelectrics in which the polarization order parameter P⃗ is subject to a divergence-free constraint, such that only loop-like polarization configurations contribute to the partition function. This constraint forces the number of components of the field P⃗ to equal the spatial dimensionality D, allowing a natural extension of the present theory to O(N) models with N=D. Renormalization group analysis reveals critical behavior beyond the conventional Landau-Ginzburg-Wilson paradigm. In particular, the order parameter acquires a remarkably large anomalous dimension, with η≈ 0.239 in three dimensions – significantly exceeding the value η≈ 0.034 typical of the O(3) universality class. This is due to an emergent gauge symmetry originating with the local constraint.

Quantum geometry provides important information about the structure and topology of quantum states in various forms of quantum matter. The information contained therein has profound effects on observable quantities such as superconducting weight, Drude weight, and optical responses. Motivated by the recent advances in flat-band interacting systems, we investigate the role of interaction effects on the quantum metric. By using the fermionic Creutz ladder as a representative system, we show that the repulsive Hubbard interaction monotonically suppresses the quantum metric. While the eigenstates and their overlap quantifying the quantum metric can be obtained exactly in the presence of interactions through exact diagonalization, this method is limited to small system sizes. Alternatively, two theoretical proposals, the generalized quantum metric and the dressed quantum metric, suggest using renormalized Green's functions to define the interacting quantum metric. By comparing these analytical approaches with results from exact diagonalization, we show that the dressed quantum metric provides a better fit to the exact diagonalization results. Our conclusion holds for both flat-band and dispersive systems.

Magnetic skyrmions are chiral spin structures with non-trivial topology that comprise two-dimensional quasi-particles and are promising information carriers for data storage and processing devices. Skyrmion lattices in magnetic thin films exhibit Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) phase transitions and have garnered significant interest for studying emergent 2D phase behavior. In experimental skyrmion lattices, the main factor limiting the quasi-long-range order in thin films has been the non-flat energy landscape - often referred to as pinning effects. We demonstrate direct control of the skyrmion lattice order by effectively tuning the energy landscape employing magnetic field oscillations. By quantifying lattice order and dynamics, we explore how domain boundaries form and evolve due to pinning effects in Kerr microscopy experiments and in Brownian dynamics simulations, offering a pathway to control and study emergent skyrmion lattice properties and 2D phase behavior.

We consider the spin dynamics of a normal metal-ferromagnet heterostructure, with emphasis on spin-nutation terms arising from a dynamical Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. We find that the spin-nutation term is anisotropic in spin space due to the broken time-reversal symmetry of the ferromagnet. This contrasts with what one obtains in the paramagnetic state, where the nutation term is isotropic in spin space. We compute the effects this has on the magnetization dynamics derived from a Landau-Lifshitz-Gilbert equation. In particular, due to broken time-reversal symmetry, we predict a third ferromagnetic resonance due to nutational spin dynamics. This resonance frequency is tunable by applying an external magnetic field. We propose this as a strong indicator for the existence of nutation in spin systems.

Magnetic skyrmions forming two-dimensional (2D) lattices provide a versatile platform for investigating phase transitions predicted by Kosterlitz–Thouless–Halperin–Nelson–Young theory. While 2D melting in skyrmion systems has been demonstrated, achieving controlled ordering in skyrmion lattices remains challenging due to pinning effects from a non-uniform energy landscape, which often results in polycrystalline structures. Skyrmions in thin films, however, offer thermal diffusion with high tunability and can be directly imaged via Kerr microscopy, enabling real-time observation of their dynamics. To regulate lattice order in such flexible systems, we introduce geometric confinements of varying shapes. Combining Kerr microscopy experiments with Thiele model simulations, we demonstrate that confinement geometry critically influences lattice order. Specifically, hexagonal confinements commensurate with the skyrmion lattice stabilize monodomain hexagonal ordering, while incommensurate geometries induce domain formation and reduce overall order. Understanding these boundary-driven effects is essential for advancing the study of 2D phase behavior and for the design of skyrmion-based spintronic applications, ranging from memory devices to unconventional computing architectures.

We compute magnon Hall conductivities in a minimal model of a two-dimensional altermagnet. To do so, we derive an analytic expression for the relevant quantum geometric tensor describing two-band bosonic Bogoliubov Hamiltonians, providing insight into the geometric, topological, and transport properties. The magnon thermal Hall and spin Nernst conductivities are shown to directly depend on the altermagnetic parameter, which may serve as an experimental probe of altermagnetism.

Two-dimensional quantum antiferromagnets are believed to host phases of matter whose excitations are more fundamental than those of the ordered phases. When combining two such spin systems in a bilayer, strong interaction between the emergent excitations can produce phases not realized in either of its subsystems. We show that the critical fluctuations of a two-dimensional spin-liquid state can induce a deconfined quantum critical point in a proximate antiferromagnet. The most relevant coupling between the associated effective field theories is given by a mixed Chern-Simons term of the emergent gauge fields in each layer. This describes a topological current-current interaction. In contrast to the local spin-spin interaction, it strongly modifies the renormalization group flow of the theory describing the N & eacute;el-valence-bond-solid transition of the antiferromagnet. In particular, the protected coupling constant associated with it implies nontrivial quantum critical scaling characterized by a nonuniversal power-law divergence of the correlation length in the critical domain and Berezinskii-KosterlitzThouless divergence approaching it.

We consider the possibility of phonon-mediated unconventional superconductivity in a recently discovered new class of antiferromagnets, dubbed altermagnets. Within a weak-coupling approach, and using a minimal Lieb lattice model for altermagnets, we find a dominant superconducting instability odd in momentum and even in spin with spin-polarized Cooper pairs. We discuss the origin of this unusual result in terms of the spin-structure of the altermagnetic Fermi surface, in combination with the momentum-space structure of the effective phonon-mediated electron-electron interactions on the Fermi surface.

We study the effective low-energy fermionic theory of the Kondo-Kitaev model to leading order in the Kondo coupling. Our main goal is to understand the nature of the superconducting instability induced in the proximate metal due to its coupling to spin fluctuations of the spin liquid. The special combination of the low-energy modes of a graphene-like metal and the form of the interaction induced by the Majorana excitations of the spin liquid furnish chiral superconducting order with p x + i p y symmetry. Computing its response to a U(1) gauge field moreover shows that this superconducting state is topologically nontrivial, characterized by a first Chern number of + 2.