Several models of the strange-metal state of the cuprate superconductors postulate the existence of strong inelastic forward scattering of the electrons, but direct evidence of such scattering is missing. Here, we show that angle-resolved photoemission spectroscopy (ARPES) provides a unique tool which can address this issue. We propose a two-lifetime phenomenological model of the superconducting state of the cuprates, and we show that it explains several salient low-energy features of the measured ARPES spectra. The model enables discrimination between forward- and large-angle scattering and, in addition, gives access to the magnitude of the gap function away from the Fermi surface.

Nowadays Nb-based superconducting radio frequency (SRF) cavities represent fundamental tools used for (Standard Model) particle acceleration, (beyond Standard Model) particle probing, and long-lifetime photon preservation. We study the SRF frequency shift in the vicinity of the critical temperature $T_c$ and the quality factor mainly at low temperatures within the Dynes superconductor model. We scrutinize and use the local limit response to the external electromagnetic field. Our approach allows for a finer analysis of the peculiar behavior of the resonant frequency shift immensely close to $T_c$, observed in recent experiments. In several regimes, we analytically elaborate on the width and depth of the resulting dip. Studying the sign of the slope of the resonant frequency shift at $T_c$ in the moderately clean regime clarifies the role of the pair-breaking and pair-conserving disorder. Next, to find the relevance of our description, we compare and also fit our results with the recent experimental data from the N-doped Nb sample presented in [arXiv:2307.07905]. Our analysis complies with the experimental findings, especially concerning the dip width. We offer a straightforward, homogeneous-disorder-based interpretation within the moderately clean regime. Comparative analysis for three other cavities with different resonant frequencies reported in [arXiv:2207.14236] points towards a similar regime. Assuming the same regime at low temperatures, we address details of the high-quality plateaus. Summing all up, this work presents (and studies the limits of) the simple, effective description of the complex problem corresponding to the electromagnetic response in the superconductors, combining homogeneous conventional pairing and two different kinds of disorder scattering.

photon preservation. We study the superconducting radio-frequency shift in the vicinity of the critical temperature Tc and the quality factor mainly at low temperatures within the Dynes superconductor model. We scrutinize and use the local limit response to the external electromagnetic field. Our approach allows for a finer analysis of the peculiar behavior of the resonant frequency shift immensely close to Tc, observed in recent experiments. In several regimes, we analytically elaborate on the width and depth of the resulting dip. Studying the sign of the slope of the resonant frequency shift at Tc in the moderately clean regime clarifies the role of the pair-breaking and pair-conserving disorder. Next, to find the relevance of our description, we compare and also fit our results with the recent experimental data from the N-doped Nb sample presented by Zarea et al. [Front. Supercond. Mater. 3, 1 (2023)]. Our analysis complies with the experimental findings, especially concerning the dip width. We offer a straightforward, homogeneousdisorder-based interpretation within the moderately clean regime. Comparative analysis for three other cavities with different resonant frequencies reported by Ueki et al. [Prog. Theor. Exp. Phys. 5, 053I02 (2025)] points toward a similar regime. Assuming the same regime at low temperatures, we address details of the high-quality plateaus. Summing all up, this work presents (and studies the limits of) the simple, effective description of the complex problem corresponding to the electromagnetic response in the superconductors, combining homogeneous conventional pairing and two different kinds of disorder scattering.

We investigate the terahertz conductivity of conventional superconductors in Voigt and Faraday magneto-optical configurations. First, we review theoretical approaches describing the fundamental processes of suppression of superconductivity in magnetic field and how the in-gap states are filled. In the Voigt geometry, thin superconducting films are fully penetrated by the magnetic field which interacts with the spin, thus modifying the magnitudes of the optical gap and of the density of the condensate. In this configuration, we provide an alternative description of the recent experiments showing the gapless conductivity of a Nb film measured by Lee et al. [Nat. Commun. 14,2737 (2023)], which better fits their data for magnetic fields above 1 T. In the Faraday geometry, we measured and analyzed the terahertz conductivity of three NbN films with varying thicknesses using the Maxwell-Garnett model, treating vortices as normal-state inclusions within a superconducting matrix. In both geometries, the optical conductivity can be comprehensively described by the model of Herman and Hlubina [Phys. Rev. B 96, 014509 (2017)] involving pair-conserving, and magnetic-field-dependent pair-breaking disorder scattering processes.

We study the energy gap within the Dynes superconductor theory. This model generalizes the Bardeen-Cooper-Schrieffer (BCS) approach by including the pair-breaking scattering, introducing the tunneling in-gap states up to a Fermi level. We analytically solve the energy gap equation in various limit cases. The solution provides simple tools for further studies, compared to more complex numerics, and highlights the basic characteristics of the theory. First, in the critical limit of pair-breaking scattering, we derive an analytical form of zero-temperature gap to transition temperature ratio. Next, we derive the dependence of the energy gap close to critical temperature and look at its behavior for general and critical pair-breaking scattering rate. Furthermore, we compare our result with the numerical solution of the gap equation assuming general temperature. We show the range of temperatures, for which the analytical approximation is valid. In the end, we provide the approximative formula of the gap, assuming general pair-breaking scattering, emphasizing its exact behavior close to transition temperature.

We investigate the terahertz conductivity of conventional superconductors in Voigt and Faraday magneto-optical configurations. In the Voigt geometry, an ultrathin superconducting film is fully penetrated by the magnetic field which interacts with the spin, thus modifying the magnitudes of the optical gap and of the density of the condensate. We provide an alternative interpretation of the recent experiments showing the gapless conductivity of a Nb film measured by Lee et al. [1] which describes better their data for magnetic field above 1 T. In the Faraday geometry, we analyze the terahertz conductivity of three NbN films with varying thicknesses using the Maxwell-Garnett model, treating vortices as normal-state inclusions within a superconducting matrix. Moreover, we effectively account for ubiquitous pair-conserving and magnetic-field-dependent pair-breaking disorder scattering processes using the model of Herman and Hlubina [2].

The size of the Cooper pair $\xi_{\rm pair}$ is one of the basic characteristics of a superconductor, but it is not possible to measure it directly. It might be argued that $\xi_{\rm pair}$ can be determined from the value $\xi_{\rm slope}$ extracted from the measurement of the slope of $H_{c2}$ close to $T_c$. Taking into account both pair-conserving and pair-breaking scattering on impurities within the recently developed theory of Dynes superconductors, we perform an explicit calculation of $\xi_{\rm pair}$ and $\xi_{\rm slope}$. We show that the two quantities agree only in clean superconductors. In particular, when the pair-breaking disorder approaches the quantum critical point, $\xi_{\rm pair}$ stays finite, whereas $\xi_{\rm slope}$ diverges.

Bilayer graphene is a nanomaterial that allows for well-defined, separated quantum states to be defined by electrostatic gating and, therefore, provides an attractive platform to construct tunable quantum dots. When a magnetic field perpendicular to the graphene layers is applied, the graphene valley degeneracy is lifted, and splitting of the energy levels of the dot is observed. Given the experimental ability to engineer this energy valley splitting, bilayer graphene quantum dots have a great potential for hosting robust qubits. Although bilayer graphene quantum dots have been recently realized in experiments, it is critically important to devise robust methods that can identify the observed quantum states from accessible measurement data. Here, we develop an efficient algorithm for extracting the model parameters needed to characterize the states of a bilayer graphene quantum dot completely. We introduce a Hamiltonian-guided random search method and demonstrate robust identification of quantum states on both simulated and experimental data.

An advanced theoretical framework is introduced and examined. Its main idea is to extract properties of the superconducting pairing gap function Δ(ω) in the conventional, nearly localized superconductors. To test the approach, we present an experimentally relevant benchmark model with defined normal and superconducting sectors. The developed reverse engineering framework consists of two logic steps. First, dismantle the superconducting density of states into the effects coming from the superconducting pairing and effects inherited from the normal state. Second, extract and reconstruct properties of Δ(ω) and compare it to the superconducting sector of the defined benchmark model. Applying this approach, we can: (i) simulate extraction from the actual experimental low-temperature tunneling data and comment on their required properties, and (ii) maintain absolute control above the reconstructed Cooper-pair-influencing properties during ameliorating the individual steps of the method.

The gap function $\Delta(\omega)$ carries essential information on both, the pairing glue as well as the pair-breaking processes in a superconductor. Unfortunately, in nearly localized superconductors with a non-constant density of states in the normal state, the standard procedure for extraction of $\Delta(\omega)$ cannot be applied. Here, we introduce a model-independent method that makes it possible to extract $\Delta(\omega)$ also in this case. The feasibility of the procedure is demonstrated on the tunneling data for the disordered thin films of TiN. We find an unconventional feature of $\Delta(\omega)$ which suggests that the electrons in TiN are coupled to a very soft pair-breaking mode.

Tuning of electronic density-of-states singularities is a common route to unconventional metal physics. Conceptually, van Hove singularities are realized only in clean two-dimensional systems. Little attention has therefore been given to the disordered (dirty) limit. Here, we provide a magnetotransport study of the dirty metamagnetic system calcium-doped strontium ruthenate. Fermi liquid properties persist across the metamagnetic transition, but with an unusually strong variation of the Kadowaki-Woods ratio. This is revealed by a strong decoupling of inelastic electron scattering and electronic mass inferred from density-of-state probes. We discuss this Fermi liquid behavior in terms of a magnetic field tunable van Hove singularity in the presence of disorder. More generally, we show how dimensionality and disorder control the fate of transport properties across metamagnetic transitions. Strongly correlated materials can exhibit deviations from Fermi-liquid behavior partly due to anomalies in the density of states at the Fermi level, such as van Hove singularities. Here, the authors investigate the unusual Fermi liquid behavior of calcium-doped strontium ruthenate and find an unusual variation of the Kadowaki-Woods ratio which may originate from disorder.

Recent exploration of the commensurate structure in the turbostratic double layer graphene shows that the large angle twisting can be treated by the decrease of the effective velocity within the energy spectra of the single layer graphene. Within our work, we use this result as a starting point, aiming towards understanding the physics of by a large angle twisted double layer graphene (i.e. Moire) quantum dot systems. We show that within this simple approach using the language of the first quantization, yet another so far unrealized (not up to our knowledge), illustrative property of the commutation relation appears in the graphene physics. Intriguingly, large twisting angles show to be a suitable tunning knob of the position symmetry in the graphene systems. Complete overview of the large angle twisting on the considered dot systems is provided.

Surface impedance of type-II superconductors is determined by their local optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$. Standard BCS-like theoretical descriptions of $\ensuremath{\sigma}(\ensuremath{\omega})$, due to Mattis and Bardeen [Phys. Rev. 111, 412 (1958)] or Zimmermann et al. [Physica C 183, 99 (1991)], do not take pair-breaking processes into account. Therefore they do not provide a quantitative explanation of the microwave response, and in particular, they cannot predict the magnitude of the coherence peak. Here, based on the recently developed concept of Dynes superconductors, which does take also the pair-breaking scattering into account, we provide a simple but complete description of the microwave response of type-II superconductors, concentrating on the unexpected properties of clean superconductors which are often used as cavity materials.

Recent experiments revealed non-Fermi-liquid resistivity in the unconventional superconductor Sr_2RuO_4 when strain pushes one of the Fermi surfaces close to a van Hove singularity. The origin of this behavior and whether it can be understood from a picture of well defined quasiparticles is unclear. We employ a Boltzmann transport analysis beyond the single relaxation-time approximation based on a single band which undergoes a Lifshitz transition, where the Fermi surface crosses a van Hove singularity, either due to uni-axial or epitaxial strain. First analytically investigating impurity scattering, we clarify the role of the diverging density of states together with the locally flat band at the point of the Lifshitz transition. Additionally including electron-electron scattering numerically, we find good qualitative agreement with resistivity measurements on uni-axially strained Sr_2RuO_4, including the temperature scaling and the temperature dependence of the resistivity peak. Our results imply that even close to the Lifshitz transition, a description starting from well-defined quasiparticles holds. To test the validity of Boltzmann transport theory near a van Hove singularity, we provide further experimentally accessible parameters, such as thermal transport, the Seebeck coefficient, and Hall resistivity and compare different strain scenarios.

In bilayer graphene, electrostatic confinement can be realized by a suitable design of top and back gate electrodes. We measure electronic transport through a bilayer graphene quantum dot, which is laterally confined by gapped regions and connected to the leads via p-n junctions. Single electron and hole occupancy is realized and charge carriers $n = 1, 2,\dots 50$ can be filled successively into the quantum system with charging energies exceeding $10 \ \mathrm{meV}$. For the lowest quantum states, we can clearly observe valley and Zeeman splittings with a spin g-factor of $g_{s}\approx 2$. In the low field-limit, the valley splitting depends linearly on the perpendicular magnetic field and is in qualitative agreement with calculations.

The tunneling density of states in dirty superconductors is often well described by the phenomenological Dynes formula. Recently we have shown that this formula can be derived, within the coherent potential approximation, for superconductors with simultaneously present pair-conserving and pair-breaking impurity scattering. Here we demonstrate that the theory of such so-called Dynes superconductors is thermodynamically consistent. We calculate the specific heat and critical field of the Dynes superconductors, and we show that their gap parameter, specific heat, critical field, and penetration depth exhibit power-law scaling with temperature in the low-temperature limit. We also show that, in the vicinity of a coupling constant-controlled superconductor to normal metal transition, the Homes law is replaced by a different, pair-breaking dominated scaling law.

Recently it has been found that models with at least two lifetimes have to be considered when analyzing the angle resolved photoemission data in the nodal region of the cuprates [T. Kondo et al., Nat. Commun. 6, 7699 (2015)]. In this paper we compare two such models. First we show that the phenomenological model used by Kondo et al. violates the sum rule for the occupation number. Next we consider the recently proposed model of the so-called Dynes superconductors, wherein the two lifetimes measure the strengths of pair-conserving and pair-breaking processes. We demonstrate that the model of the Dynes superconductors is fully consistent with known exact results and we study in detail the resulting spectral functions. Finally, we show that the spectral functions in the nodal region of the cuprates can be fitted well by the model of the Dynes superconductors.

Recently, a generic model was proposed for the single-particle properties of gapless superconductors with simultaneously present pair-conserving and pair-breaking impurity scatterings (the so-called Dynes superconductors). Here we calculate the optical conductivity of the Dynes superconductors. Our approach is applicable for all disorder strengths from the clean limit up to the dirty limit and for all relative ratios of the two types of scattering; nevertheless, the complexity of our description is equivalent to that of the widely used Mattis-Bardeen theory. We identify two optical fingerprints of the Dynes superconductors: (i) the presence of two absorption edges and (ii) finite absorption at vanishing frequencies even at the lowest temperatures. We demonstrate that the recent anomalous optical data on thin MoN films can be reasonably fitted by our theory.

Excellent fits of the tunneling density of states in disordered superconductors can be often achieved making use of the phenomenological Dynes formula. However, no consistent derivation of this formula has been available so far. The Dynes formula can be interpreted by the simplest causal frequency-dependent gap function $\mathrm{\ensuremath{\Delta}}(\ensuremath{\omega})$ with a vanishing gap at the Fermi level. Here we show, within the coherent potential approximation, that precisely such a gap function describes superconductors with a Lorentzian distribution of pair-breaking fields and arbitrary potential disorder. We predict spectral and thermodynamic properties of such superconductors.