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We study the superconducting order in a two-dimensional square lattice Hubbard model with weak repulsive interactions, subject to a Zeeman field and weak Rashba spin-orbit interactions. Diagonalizing the noninteracting Hamiltonian leads to two separate bands, and by deriving an effective low-energy interaction we find the mean field gap equations for the superconducting order parameter on the bands. Solving the gap equations just below the critical temperature, we find that superconductivity is caused by Kohn-Luttinger-type interaction, while the pairing symmetry of the bands is indirectly affected by the spin-orbit coupling. The dominating attractive momentum channel of the Kohn-Luttinger term depends on the filling fraction $n$ of the system, and it is therefore possible to change the momentum dependence of the order parameter by tuning $n$. Moreover, $n$ also determines which band has the highest critical temperature. Rotating the magnetic field changes the momentum dependence from states that for small momenta reduce to a chiral $p_x\pm i{p}_y$ type state for out-of-plane fields, to a nodal $p$-wave-type state for purely in-plane fields.

Contrary to the expected detrimental influence on superconductivity when applying a magnetic field, we predict that the abrupt onset of such a field can temporarily strongly enhance the superconducting order parameter. Specifically, we find that the supercurrent in a Josephson junction with a normal metal weak link can increase more than twentyfold in this way. The effect can be understood from the interplay between the energy dependence of Andreev reflection and the abrupt spin-dependent shift in the distribution functions for excitations in the system. The duration of the increase depends on the inelastic scattering rate in the system and is estimated to be in the range of nanoseconds. We demonstrate this by developing a method which solves the Usadel equation for an arbitrary time dependence. This enables the study of ultrafast time-dependent physics in heterostructures combining superconductors with different types of materials.

We demonstrate that the current-density functional theory for superconductors (sc-CDFT) can describe the magnetic-field-induced first-order phase transition of aluminum from a superconducting state to a normal state. This is accomplished by introducing a model for the magnetic-field dependence of the attractive interaction between superconducting electrons. This model states that the surface potential well produced by a penetrating magnetic field leads to the magnetic-field dependence of the attractive interaction. Specifically, the electron density near the surface increases with the magnetic field owing to the surface potential well, which causes a reduction in the attractive interaction because of the screening effect. We also develop a calculation scheme to solve the gap equation of the sc-CDFT by considering the magnetic-field dependence of the attractive interaction. The calculation results for the magnetic-field dependence of the superconducting gap are in good agreement with the experimental results of the first-order phase transition.

We report evidence for a reentrant spin glass phase in electron-doped ${\text{EuFe}}_2{\text{As}}_2$ single crystals and first traces of the superconductivity reentrance in optics. In the close-to-optimal doped $\text{Eu}{\left({\text{Fe}}_{0.91}{\text{Ir}}_{0.09}\right)}_2{\text{As}}_2$ and $\text{Eu}{\left({\text{Fe}}_{0.93}{\text{Rh}}_{0.07}\right)}_2{\text{As}}_2$ samples, two magnetic transitions are observed below the superconducting critical temperature $T_c\approx 21$ K: the canted $A$-type antiferromagnetic order of the ${\text{Eu}}^{2+}$ ions sets in around $17\text{K}$ and the spin glass behavior occurs another $2\text{K}$ lower in temperature. In addition, strong evidence for an additional transition is found far below the spin glass temperature. Our extensive optical and magnetic investigations provide important insight into the interplay of local magnetism and superconductivity in these systems and elucidate the effect of the spin glass phase on the reentrant superconducting state.

We theoretically study the behavior of the critical current of a thermally biased tunnel Josephson junction with a particular design, in which the electrodes of the junction are enclosed in two different superconducting loops pierced by independent magnetic fluxes. In this setup, the superconducting gaps can be modified independently through the magnetic fluxes threading the loops. We investigate the response of the device as a function of the magnetic fluxes, by changing the asymmetry parameter, i.e., the ratio between the zero-temperature superconducting gaps $\delta ={\mathrm{\Delta }}_{10}/{\mathrm{\Delta }}_{20}$ and the temperatures of the two rings. We show a magnetically controllable steplike response of the critical current, which emerges even in a symmetric junction, $\delta =1$. Finally, we discuss the optimal working conditions and the high response of the critical current to small changes in the magnetic flux, reporting good performance of a magnetic flux-to-critical current transducer, with a high transfer function that depends on the operating point, the temperature gradient, and the quality of the junction.

We study the localization and oscillation properties of the Majorana fermions that arise in a two-dimensional electron gas (2DEG) with spin-orbit coupling (SOC) and a Zeeman field coupled with a $d$-wave superconductor. Despite the angular dependence of the $d$-wave pairing, localization and oscillation properties are found to be similar to the ones seen in conventional $s$-wave superconductors. In addition, we study a microscopic lattice version of the previous system that can be characterized by a topological invariant. We derive its real space representation that involves nearest and next-to-nearest-neighbors pairing. Finally, we show that the emerging chiral Majorana fermions are indeed robust against static disorder. This analysis has potential applications to quantum simulations and experiments in high-$T_c$ superconductors.

A characteristic feature of magnetic impurities in superconductors is the existence of a spin- and parity-changing quantum phase transition (known as “0-$\pi$” transition) which has been observed in scanning tunneling microscopy (STM) and quantum transport experiments. Using the Abelian bosonization technique, here we analyze the ground-state properties and the quantum phase diagram of an artificial “Shiba impurity” in a one-dimensional superconductor. Within the bosonization framework, the ground-state properties are determined by simple solitonlike solutions of the classical equations of motion of the bosonic fields, whose topological charge is related to the spin and fermion-parity quantum numbers. Interestingly, the same theoretical framework can be used in the case of a bulk superconductor, where previous results can be rederived in an elegant fashion. Our results indicate that the quantum phase diagram of a magnetic impurity in the superconductor can be strongly affected by geometrical and dimensional effects. Exploiting this fact, in the one-dimensional case we propose an experimental superconducting setup in which a novel parity-preserving, spin-changing “0-0” transition is predicted.

Heterostructures allow the realization of electronic states that are difficult to obtain in isolated uniform systems. Exemplary is the case of quasi-one-dimensional heterostructures formed by a superconductor and a semiconductor with spin-orbit coupling in which Majorana zero-energy modes can be realized. We study the effect of a single impurity on the energy spectrum of superconducting heterostructures. We find that the coupling between the superconductor and the semiconductor can strongly affect the impurity-induced states and may induce additional subgap bound states that are not present in isolated uniform superconductors. For the case of quasi-one-dimensional superconductor/semiconductor heterostructures we obtain the conditions for which the low-energy impurity-induced bound states appear.

We study a two-orbital $t\text{−}{J}_1\text{−}{J}_2$ model, originally developed to describe iron-based superconductors at low energies, in the presence of bond disorder (via next-nearest-neighbor $J_2$-bond dilution). By using the Bogoliubov–de Gennes approach, we self-consistently calculate the local pairing amplitudes and the corresponding density of states, which demonstrate a change of dominant pairing symmetry from $s_{\pm }$ wave to $d$ wave when increasing disorder strength as long as $J_1\lesssim J_2$. Moreover, the combined pairing interaction and strong bond disorder lead to the formation of $s_{\pm }$-wave “islands” with length scale of the superconducting coherence length embedded in a $d$-wave “sea.” This picture is further complemented by the disorder-averaged pair-pair correlation functions, distinct from the case with potential disorder, where the “sea” is insulating. Due to this inevitable formation of spatial inhomogeneity, the superconducting $T_c$ determined by the superfluid density ${\rho }_s\left(T\right)$ obviously deviates from the value predicted by the conventional Abrikosov-Gorkov theory, where the pairing amplitudes are viewed as uniformly suppressed as the disorder increases.

We describe a method for calculating the resonant inelastic x-ray scattering (RIXS) response—including the dynamics of the transient core hole—of many-body systems with nontrivial gap structure encoded in their single particle Green's function. Our approach introduces auxiliary fermions in order to obtain a form amenable to the determinant method of Benjamin et al., [Phys. Rev. Lett. 112, 247002 (2014)], and is applicable to systems where interactions are most strongly felt through a renormalization of the single particle propagator. As a test case we consider the Yang-Rice-Zhang ansatz for cuprate phenomena in the underdoped “pseudogap” regime, which remains a popular tool for interpreting the results of experimental probes. We show that taking the core hole dynamics into account for a system described by this ansatz pushes the RIXS peaks towards higher energy transfer, improving agreement with experiments.

We have varied the oxygen defect concentration in ${\mathrm{Pr}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_{4+\delta }$ and characterized the mean-free path length $\ell$ and the superconducting coherence length $\xi$ of ${\mathrm{Pr}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_{4+\delta }$ by means of low-temperature transport measurements. Concomitant with the clean-to-dirty crossover around $\ell \approx \xi$ we find the emergence of linear resistivity behavior being persistent far into the clean limit $\left(\ell \gg \xi \right)$. We find a violation of Matthiessen's rule that can be explained by a model of $\sigma$ involving a defect-assisted interlayer channel which acts in parallel with the bandlike conductivity. We observe an unusual dependence of $T_c$ on residual resistivity, inconsistent with the generalized Abrikosov-Gor'kov theory for an order parameter with a single component, providing an important constraint on models of the superconductivity in this material system.

The superconducting parameters and upper critical field of the noncentrosymmetric superconductor BiPd have proven contentious. This material is of particular interest because it is a rare example of a $4f$-electron-free noncentrosymmetric superconductor of which crystals may be grown and cleaved, enabling surface-sensitive spectroscopies. Here, using bulk probes augmented by tunneling data on defects, we establish that the lower of the previously reported upper critical fields corresponds to the bulk transition. The material behaves as a nearly weak-coupled BCS $s$-wave superconductor, and we report its superconducting parameters as drawn from the bulk upper critical field. Possible reasons behind the order-of-magnitude discrepancy in the reported upper critical fields are discussed.

Using intrinsic multiple Andreev reflections effect spectroscopy, we studied SnS contacts in the layered oxypnictide superconductors ${\mathrm{Sm}}_{1-x}{\mathrm{Th}}_x\mathrm{OFeAs}$ with various thorium doping and critical temperatures $T_C=21–54$ K. We observe a scaling between both superconducting gaps and $T_C$. The determined BCS ratio for the large gap $2{\mathrm{\Delta }}_L/k_B{T}_C=5.0–5.7$ and its eigen-BCS ratio (in a hypothetical case of zero interband coupling) $2{\mathrm{\Delta }}_L/k_B{T}_C^L=4.1–4.6$ both exceeding the weak-coupling limit 3.52, and for the small gap $2{\mathrm{\Delta }}_S/k_B{T}_C=1.2–1.6$, remain nearly constant within all the $T_C$ range studied. The temperature dependences ${\mathrm{\Delta }}_{L,S}\left(T\right)$ agree well with a two-band BCS-like Moskalenko and Suhl model. We prove intraband coupling to be stronger than interband coupling, whereas Coulomb repulsion constants ${\mu }^{*}$ are finite in Sm-based oxypnictides.

The influence of a rotating magnetic field (in the $ab$ plane) on the density of states has been investigated in the superconducting state of the nematic FeSe superconductor using high sensitivity specific heat measurements. As expected for (quasi-)nodal superconductors, oscillations in the specific heat $C$ associated with the Doppler energy shift of Cooper pairs with momenta close to the gap minima are observed. In the $T_c=9$ K crystal, $C(\varphi$) displays a twofold symmetry at low temperature and low magnetic field confirming the nematic character of FeSe from thermodynamical measurements. As expected, a $\pi /2$ phase shift is observed for increasing temperatures (at $H=1$ T) but our measurements suggest that the gap structure abruptly changes above $\approx 1$ K in this sample. At low temperature, the maxima observed for $H\left|\right|a$ axis at low $H$ split into lobes at $\pm {45}^{\circ }$ when the magnetic field is increased, which can be accounted for by assuming that the electron gap rapidly closes with field.

The possible superconducting states of strontium ruthenate $\left({\mathrm{Sr}}_2{\mathrm{RuO}}_4\right)$ are organized into irreducible representations of the point group $D_{4h}$, with a special emphasis on nodes occurring within the superconducting gap. Our analysis covers the cases with and without spin-orbit coupling and takes into account the possibility of interorbital pairing within a three-band, tight-binding description of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. No dynamical treatment if performed: We are confining ourselves to a group-theoretical analysis. We nevertheless adopt an intermediate-coupling point of view by working in the orbital basis instead of the band basis. The case of uniaxial deformations, under which the point group symmetry is reduced to $D_{2h}$, is also covered. It turns out that nodal lines, in particular equatorial nodal lines, occur in most representations. We also highlight some results specific to multiorbital superconductivity. Among other things, we find that odd interorbital pairing allows us to combine singlet and triplet superconductivity within the same irreducible representation, that pure interorbital superconductivity leads to nodal surfaces and that the notion of nodes imposed by symmetry is not clearly defined.

Using multiple Andreev reflection spectroscopy, we studied superconductor–normal metal–superconductor semiballistic contacts with incoherent transport in overdoped pnictide superconductors ${\mathrm{BaFe}}_{1.86}{\mathrm{Ni}}_{0.14}{\mathrm{As}}_2$ with critical temperature $T_c\approx 12\mathrm{K}$. We directly determined an anisotropic large gap with the characteristic ratios $2{\mathrm{\Delta }}_L^{\mathrm{out}}\left(0\right)/k_B{T}_c\approx 6$ and $2{\mathrm{\Delta }}_L^{\mathrm{in}}\left(0\right)/k_B{T}_c\approx 4$, almost isotropic small gap with $2{\mathrm{\Delta }}_S\left(0\right)/k_B{T}_c\approx 2$, and the temperature dependence of the resolved superconducting order parameters. Above the large gap position $2{\mathrm{\Delta }}_L$, a fine $dI\left(V\right)/dV$ structure fully vanishing at $T_c$ and possibly caused by a resonant coupling with a bosonic mode was observed.