Crossband versus intraband pairing in superconductors: Signatures and consequences of the interplay

Porta S., Privitera L., Ziani N.T., Sassetti M., Cavaliere F., Trauzettel B.

Recently, it has been proposed that a mechanism for the appearance of non-equilibrium superconductivity in a resonantly driven semiconductor with repulsive interband interactions exists.~\cite{Goldstein_PRB15} The underlying microscopic model relies on the appearance of a specific fermionic dissipation mechanism and the careful simultaneous tailoring of the electronic dispersion relation and electron-electron interactions. We, instead, show that the phenomenon is rather general and does not need a special fine tuning of parameters. By considering a pair of bands with locally the same sign of concavity, we demonstrate that interband pairing arises under the natural assumption of the presence of phononic baths and radiative recombination. In light of these findings, we demonstrate how the emergence of superconductivity can be understood in terms of standard equilibrium interband BCS theory.

Singh G., Jouan A., Herranz G., Scigaj M., Sánchez F., Benfatto L., Caprara S., Grilli M., Saiz G., Couëdo F., Feuillet-Palma C., Lesueur J., Bergeal N.

In multi-orbital materials, superconductivity can exhibit several coupled condensates. In this context, quantum confinement in two-dimensional superconducting oxide interfaces offers new degrees of freedom to engineer the band structure and selectively control the occupancy of 3d orbitals by electrostatic doping. Here, we use resonant microwave transport to extract the superfluid stiffness of the (110)-oriented LaAlO3/SrTiO3 interface in the entire phase diagram. We provide evidence of a transition from single-condensate to two-condensate superconductivity driven by continuous and reversible electrostatic doping, which we relate to the Lifshitz transition between 3d bands based on numerical simulations of the quantum well. We find that the superconducting gap is suppressed while the second band is populated, challenging Bardeen–Cooper–Schrieffer theory. We ascribe this behaviour to the existence of superconducting order parameters with opposite signs in the two condensates due to repulsive coupling. Our findings offer an innovative perspective on the possibility to tune and control multiple-orbital physics in superconducting interfaces. Electrostatic doping drives a transition from single condensate to two condensate superconductivity at the (110)-oriented LaAlO3/SrTiO3 interface.

Hanaguri T., Kasahara S., Böker J., Eremin I., Shibauchi T., Matsuda Y.

FeSe is argued as a superconductor in the Bardeen-Cooper-Schrieffer Bose-Einstein-condensation crossover regime where the superconducting-gap size and the superconducting transition temperature Tc are comparable to the Fermi energy. In this regime, vortex bound states should be well quantized and the preformed pairs above Tc may yield a pseudogap in the quasiparticle-excitation spectrum. We performed spectroscopic-imaging scanning tunneling microscopy to search for these features. We found Friedel-like oscillations near the vortex, which manifest the quantized levels, whereas the pseudogap was not detected. These apparently conflicting observations may be related to the multi-band nature of FeSe.

Piatti E., Romanin D., Gonnelli R.S.

Gate-induced superconductivity at the surface of nanolayers of semiconducting transition metal dichalcogenides (TMDs) has attracted a lot of attention in recent years, thanks to the sizeable transition temperature, robustness against in-plane magnetic fields beyond the Pauli limit, and hints to a non-conventional nature of the pairing. A key information necessary to unveil its microscopic origin is the geometry of the Fermi surface hosting the Cooper pairs as a function of field-effect doping, which is dictated by the filling of the inequivalent valleys at the K/K$^{\prime}$ and Q/Q$^{\prime}$ points of the Brillouin Zone. Here, we achieve this by combining Density Functional Theory calculations of the bandstructure with transport measurements on ion-gated 2H-MoS$_{2}$ nanolayers. We show that, when the number of layers and the amount of strain are set to their experimental values, the Fermi level crosses the bottom of the high-energy valleys at Q/Q$^{\prime}$ at doping levels where characteristic kinks in the transconductance are experimentally detected. We also develop a simple 2D model which is able to quantitatively describe the broadening of the kinks observed upon increasing temperature. We demonstrate that this combined approach can be employed to map the dependence of the Fermi surface of TMD nanolayers on field-effect doping, detect Lifshitz transitions, and provide a method to determine the amount of strain and spin-orbit splitting between sub-bands from electric transport measurements in real devices.

Giorgianni F., Cea T., Vicario C., Hauri C.P., Withanage W.K., Xi X., Benfatto L.

The discovery of symmetry-broken phases that host multiple order parameters, such as multiband superconductors1,2, has triggered an enormous interest in condensed matter physics. However, many challenges continue to hinder the fundamental understanding of how to control the collective modes corresponding to these multiple order parameters3,4. Here we demonstrate that, in full analogy with phonons, Raman-active electronic collective modes can be manipulated by intense light pulses. By tuning a sum-frequency excitation process, we selectively trigger collective excitations that can be ascribed to the relative phase fluctuations between two superconducting order parameters—the so-called Leggett mode—in the multiband superconductor MgB2. The excellent comparison between experiments and theory establishes a general protocol for the advanced control of Raman-active electronic modes in symmetry-broken quantum phases of matter. There has latterly been a renewed interest in collective excitations in condensed matter systems. Now, spectroscopic evidence for the so-called Leggett mode is revealed in the superconductor MgB2.

Yu R., Zhu J., Si Q.

Motivated by the recent low-tempearture experiments on bulk FeSe, we study the electron correlation effects in a multiorbital model for this compound in the nematic phase using the U(1) slave-spin theory. We find that a finite nematic order helps to stabilize an orbital selective Mott phase. Moreover, we propose that when the d- and s-wave bond nematic orders are combined with the ferro-orbital order, there exists a surprisingly large orbital selectivity between the xz and yz orbitals even though the associated band splitting is relatively small. Our results explain the seemingly unusual observation of strong orbital selectivity in the nematic phase of FeSe, and uncover new clues on the nature of the nematic order, and sets the stage to elucidate the interplay between superconductivity and nematicity in iron-based superconductors.

Li Y., An C., Hua C., Chen X., Zhou Y., Zhou Y., Zhang R., Park C., Wang Z., Lu Y., Zheng Y., Yang Z., Xu Z.

Topological superconductivity with Majorana bound states, which are critical to implement nonabelian quantum computation, may be realized in three-dimensional semimetals with nontrivial topological feature, when superconducting transition occurs in the bulk. Here, we report pressure-induced superconductivity in a transition-metal dipnictide NbAs2. The emergence of superconductivity is not accompanied by any structural phase transition up to the maximum experimental pressure of 29.8 GPa, as supported by pressure-dependent synchrotron X-ray diffraction and Raman spectroscopy. Intriguingly, the Raman study reveals rapid phonon mode hardening and broadening above 10 GPa, in coincident with the superconducting transition. Using first-principle calculations, we determine Fermi surface change induced by pressure, which steadily increases the density of states without breaking the electron–hole compensation. Noticeably, the main hole pocket of NbAs2 encloses one time-reversal-invariant momenta of the monoclinic lattice, suggesting NbAs2 as a candidate of topological superconductors. Superconductivity is observed in NbAs2, indicating that this predicted topological material could host Majorana fermions. Using transport measurements, researchers led by Zhu-An Xu from Zhejiang University and Zhaorong Yang from the National High Magnetic field Laboratory in Hefei have demonstrated a superconducting transition when this compound is placed under high pressure. X-ray diffraction shows that no structural transition accompanies the onset of superconductivity, but Raman scattering and density functional theory calculations suggest that the pressure induces changes in the electron–phonon coupling and electronic density of states that facilitate the superconductivity. The band structure of NbAs2 is predicted to host topological features, indicating that transition metal dipnictides such as this could be time reversal invariant topological superconductors, and may feature Majorana edge modes that can be utilized in fault-tolerant quantum computing.

Benfatto L., Valenzuela B., Fanfarillo L.

FeSe is an intriguing iron-based superconductor. It presents an unusual nematic state without magnetism and can be tuned to increase the critical superconducting temperature. Recently it has been observed a noteworthy anisotropy of the superconducting gaps. Its explanation is intimately related to the understanding of the nematic transition itself. Here, we show that the spin-nematic scenario driven by orbital-selective spin fluctuations provides a simple scheme to understand both phenomena. The pairing mediated by anisotropic spin modes is not only orbital selective but also nematic, leading to stronger pair scattering across the hole and X electron pocket. The delicate balance between orbital ordering and nematic pairing points also to a marked kz dependence of the hole–gap anisotropy. FeSe is a high-temperature superconductor displaying a complex interplay between structure, magnetism and superconductivity; new theoretical results might now shed light on its pairing mechanism. FeSe is widely studied because its superconducting critical temperature can be tuned over a wide range by chemical intercalation or pressure. Superconductivity appears in a phase that is called nematic, which breaks rotational symmetry but preserves translational symmetry. Experimental measurements show that the superconducting gaps are anisotropic: this is probably related to the nematic transition, in which spin fluctuations seem to play a part. Laura Fanfarillo from the International School for Advanced Studies, Italy, and colleagues present a model suggesting that orbital-selective spin fluctuations provide the pairing mechanism, which is at the same time orbital selective and nematic. This explains both the anisotropy of the gaps and its connection to the nematic transition.

Wang D., Kong L., Fan P., Chen H., Zhu S., Liu W., Cao L., Sun Y., Du S., Schneeloch J., Zhong R., Gu G., Fu L., Ding H., Gao H.

An iron home for Majoranas The surface of the iron-based superconductor FeTe 0.55 Se 0.45 has been identified as a potential topological superconductor and is expected to host exotic quasiparticles called the Majorana bound states (MBSs). Wang et al. looked for signatures of MBSs in this material by using scanning tunneling spectroscopy on the vortex cores formed by the application of a magnetic field. In addition to conventional states, they observed the characteristic zero-bias peaks associated with MBSs and were able to distinguish between the two, owing to the favorable ratios of energy scales in the system. Science , this issue p. 333

Trevisan T.V., Schütt M., Fernandes R.M.

Although discovered many decades ago, superconductivity in doped SrTiO$_{3}$ remains a topic of intense research. Recent experiments revealed that, upon increasing the carrier concentration, multiple bands cross the Fermi level, signaling the onset of Lifshitz transitions. Interestingly, $T_{c}$ was observed to be suppressed across the Lifshitz transition of oxygen-deficient SrTiO$_{3}$; a similar behavior was also observed in gated LaAlO$_{3}$/SrTiO$_{3}$ interfaces. Such a behavior is difficult to explain in the clean theory of two-band superconductivity, as the additional electronic states provided by the second band should enhance $T_{c}$. Here, we show that this unexpected behavior can be explained by the strong pair-breaking effect promoted by disorder, which takes place if the inter-band pairing interaction is subleading and repulsive. A consequence of this scenario is that, upon moving away from the Lifshitz transition, the two-band superconducting state changes from opposite-sign gaps to same-sign gaps.

Herbrych J., Kaushal N., Nocera A., Alvarez G., Moreo A., Dagotto E.

Iron-based superconductors display a variety of magnetic phases originating in the competition between electronic, orbital, and spin degrees of freedom. Previous theoretical investigations of the multi-orbital Hubbard model in one-dimension revealed the existence of an orbital-selective Mott phase (OSMP) with block spin order. Recent inelastic neutron scattering (INS) experiments on the BaFe2Se3 ladder compound confirmed the relevance of the block-OSMP. Moreover, the powder INS spectrum revealed an unexpected structure, containing both low-energy acoustic and high-energy optical modes. Here we present the theoretical prediction for the dynamical spin structure factor within a block-OSMP regime using the density-matrix renormalization-group method. In agreement with experiments, we find two dominant features: low-energy dispersive and high-energy dispersionless modes. We argue that the former represents the spin-wave-like dynamics of the block ferromagnetic islands, while the latter is attributed to a novel type of local on-site spin excitations controlled by the Hund coupling. Exploring the orbital-selective Mott phase (OSMP) addresses the central issue of electron correlations in the iron-based superconductors. Here the authors theoretically study the dynamical spin structure factor in the block-OSMP regime and unveil momentum dependent characteristics for different spin excitation modes.

Ghigo G., Torsello D., Ummarino G. ., Gozzelino L., Tanatar M. ., Prozorov R., Canfield P. .

Microwave measurements of the London penetration depth and critical temperature T_{c} were used to show evidence of a disordered-driven transition from s_{±} to s_{++} order parameter symmetry in optimally doped Ba(Fe_{1-x}Rh_{x})_{2}As_{2} single crystals, where disorder was induced by means of 3.5 MeV proton irradiation. Signatures of such a transition, as theoretically predicted [V. D. Efremov et al., Phys. Rev. B 84, 180512(R) (2011)PRBMDO1098-012110.1103/PhysRevB.84.180512], are found as a drop in the low-temperature values of the London penetration depth and a virtually disorder-independent superconducting T_{c}. We show how these experimental observations can be described by multiband Eliashberg calculations in which the effect of disorder is accounted for in a suitable way. To this aim, an effective two-band approach is adopted, allowing us to treat disorder in a range between the Born approximation and the unitary limit.

Flammia L., Zhang L.-., Covaci L., Perali A., Milošević M.V.

Extended defects are known to strongly affect nanoscale superconductors. Here we report the properties of superconducting nanoribbons with a constriction formed between two adjacent step-edges, by solving the Bogoliubov-de Gennes equations self-consistently in the regime where quantum confinement is important. Since the quantum resonances of the superconducting gap in the constricted area are different from the rest of the nanoribbon, such constriction forms a quantum-confined S-S'-S Josephson junction, with a broadly tunable performance depending on the length and width of the constriction with respect to the nanoribbon, and possible gating. These findings provide an intriguing approach to further tailor superconducting quantum devices where Josephson effect is of use.

Continenza A., Profeta G.

We present a comparative and detailed study of transition metal doping in CaFe2As2. Comparing with several experimental results and carefully analyzing how the states at the Fermi level are affected by doping we show that: i) simulation of real doping and considering induces structural relaxations are crucial to correctly address the physical mechanisms induced by transition metal substitutions; ii) different dopant concentration induces changes on the band structure that can not be described within a simple rigid-band picture; iii) careful comparison with the available ARPES results shows that the main effects on band filling and symmetry can be caught within DFT.

Matt C.E., Sutter D., Cook A.M., Sassa Y., Månsson M., Tjernberg O., Das L., Horio M., Destraz D., Fatuzzo C.G., Hauser K., Shi M., Kobayashi M., Strocov V.N., Schmitt T., et. al.

The minimal ingredients to explain the essential physics of layered copper-oxide (cuprates) materials remains heavily debated. Effective low-energy single-band models of the copper–oxygen orbitals are widely used because there exists no strong experimental evidence supporting multi-band structures. Here, we report angle-resolved photoelectron spectroscopy experiments on La-based cuprates that provide direct observation of a two-band structure. This electronic structure, qualitatively consistent with density functional theory, is parametrised by a two-orbital ( $$d_{x^2 - y^2}$$ and $$d_{z^2}$$ ) tight-binding model. We quantify the orbital hybridisation which provides an explanation for the Fermi surface topology and the proximity of the van-Hove singularity to the Fermi level. Our analysis leads to a unification of electronic hopping parameters for single-layer cuprates and we conclude that hybridisation, restraining d-wave pairing, is an important optimisation element for superconductivity. The essential physics of cuprate superconductors is often described by single-band models. Here, Matt et al. report direct observation of a two-band electronic structure in La-based cuprates.

Ji H., Yuan N.F.

Inspired by the recent experiments in monolayer iron-based superconductors, we theoretically investigate the properties of a two-dimensional multiband superconductor under magnetic fields, focusing on two aspects. First, for vortex bound states under out-of-plane magnetic fields, the spatial anisotropy and positions of electron density peaks are associated with interband couplings. Second, under in-plane magnetic fields, even with inversion symmetry, a Ising-type spin-orbit coupling is allowed, leading to an enhanced in-plane upper critical field. Applications to other two-dimensional multiband superconductors are also discussed. Published by the American Physical Society 2025

Valletta A., Bianconi A., Perali A., Logvenov G., Campi G.

Kopasov A.A., Mel'nikov A.S.

Paramasivam S.K., Gangadharan S.P., Milošević M.V., Perali A.

Holst M.F., Sigrist M., Samokhin K.V.

We study the effects of interband pairing in two-band s-wave and d-wave superconductors with D4h symmetry in both time-reversal invariant as well as time-reversal symmetry-breaking states. The presence of interband pairing qualitatively changes the nodal structure of the superconductor: nodes can (dis)appear, merge, and leave high-symmetry locations when interband pairing is tuned. Furthermore, in the d-wave case, we find that also the boundary modes change qualitatively when interband pairing increases: flat zero-energy Andreev bound states gap out and transition to helical edge states. Published by the American Physical Society 2024

Midei G., Perali A.

Abstract Two-dimensional superconductors and electron-hole superfluids in van der Waals heterostructures having tunable valence and conduction bands in the electronic spectrum are emerging as rich platforms to investigate novel quantum phases and topological phase transitions. In this work, by adopting a mean-field approach considering multiple-channel pairings and the Kosterlitz-Nelson criterion, we demonstrate giant amplifications of the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature and a shrinking of the pseudogap for small energy separations between the conduction and valence bands and small density of carriers in the conduction band. The presence of the holes in the valence band, generated by intra-band and pair-exchange couplings, contributes constructively to the phase stiffness of the total system, adding up to the phase stiffness of the conduction band electrons that is boosted as well, due to the presence of the valence band electrons. This strong cooperative effect avoids the suppression of the BKT transition temperature for low density of carriers, that occurs in single-band superconductors where only the conduction band is present. Thus, we predict that in this regime, multi-band superconducting and superfluid systems with valence and conduction bands can exhibit much larger BKT critical temperatures with respect to single-band and single-condensate systems.

Núñez J.J., Schmidt A.A., Tifrea I.

We analyze the superconducting state properties for the case of a two-band self-consistent BCS model that considers an electron band structure suitable for iron based superconducting materials. The superconducting gap parameters corresponding to each component electron band, $$|\Delta _{11}(T)|$$ and $$|\Delta _{22}(T)|$$ , are investigated as function of temperature, T, inter-orbital hopping parameter, $$t_4$$ , and electron doping, N. The values of the two ratios $$2|\Delta ^0_{11}|/T_c$$ and $$2|\Delta ^0_{22}|/T_c$$ are not universal, and they are strongly dependent on the value of the hopping parameter, $$t_4$$ . In the case of $$s^\pm $$ -wave symmetry, the superconducting state in the system exists only at certain electron doping concentrations, leading to a complex superconducting phase diagram for iron based superconducting materials.

Aase N.H., Johnsen C.S., Sudbø A.

We consider superconductivity in a system with $N$ Fermi surfaces, including intraband and interband effective electron-electron interactions. The effective interaction is described by an $N\ifmmode\times\else\texttimes\fi{}N$ matrix whose elements are assumed to be constant in thin momentum shells around each Fermi surface, giving rise to $s$-wave superconductivity. Starting with attractive intraband interactions in all $N$ bands, we show that too strong interband interactions are detrimental to sustaining $N$ nonzero components of the superconducting order parameter. We find similar results in systems with repulsive intraband interactions. The dimensionality reduction of the order-parameter space is given by the number of nonpositive eigenvalues of the interaction matrix. Using general models and models for superconducting transition metal dichalcogenides and iron pnictides frequently employed in the literature, we show that constraints must be imposed on the order parameter to ensure a lower bound on the free energy and that subsequent higher-order expansions around the global minimum are thermodynamically stable. We also demonstrate that similar considerations are necessary for unconventional pairing symmetries.

Salamone T., Hugdal H.G., Jacobsen S.H., Amundsen M.

We present a mechanism allowing for superconductivity at high magnetic fields, beyond the Pauli-Chandrasekhar-Clogston limit. We consider spin splitting induced by an in-plane external magnetic field in a superconductor with two relevant bands close to the Fermi level. The magnetic field therefore controls which bands are available for Cooper pair formation. The presence of interband superconducting pairing, i.e., Cooper pairs formed by electrons with different band indices, produces high-field reentrant superconducting domains, whose critical magnetic field violates the Pauli-Chandrasekhar-Clogston limit. We analyze how the interband superconducting domains are influenced by the band parameters, and show that, for a certain range of parameters, the system presents two separate superconducting regions, for low and high magnetic field.

Midei G., Perali A.

Two-band electronic structures with a valence and a conduction band separated by a tunable energy gap and with pairing of electrons in different channels can be relevant to investigate the properties of two-dimensional multiband superconductors and electron-hole superfluids, such as monolayer FeSe, recently discovered superconducting bilayer graphene, and double-bilayer graphene electron-hole systems. This electronic configuration also allows us to study the coexistence of superconductivity and charge-density waves in connection with underdoped cuprates and transition metal dichalcogenides. By using a mean-field approach to study the system mentioned above, we have obtained numerical results for superconducting gaps, chemical potential, condensate fractions, coherence lengths, and superconducting mean-field critical temperature, considering a tunable band gap and different fillings of the conduction band, for a parametric choice of the pairing interactions. By tuning these quantities, the electrons redistribute among valence and conduction band in a complex way, leading to a new physics with respect to single-band superconductors, such as density-induced and band-selective BCS-BEC crossover, quantum phase transitions, and hidden criticalities. At finite temperature, this phenomenon is also responsible for the nonmonotonic behavior of the superconducting gaps resulting in a superconducting-normal state reentrant transition, without the need of disorder or magnetic effects.

Chapai R., Reddy P.V., Xing L., Graf D.E., Karki A.B., Chang T., Jin R.

AbstractPdTe is a superconductor with Tc ~ 4.25 K. Recently, evidence for bulk-nodal and surface-nodeless gap features has been reported in PdTe. Here, we investigate the physical properties of PdTe in both the normal and superconducting states via specific heat and magnetic torque measurements and first-principles calculations. Below Tc, the electronic specific heat initially decreases in T3 behavior (1.5 K < T < Tc) then exponentially decays. Using the two-band model, the superconducting specific heat can be well described with two energy gaps: one is 0.372 meV and another 1.93 meV. The calculated bulk band structure consists of two electron bands (α and β) and two hole bands (γ and η) at the Fermi level. Experimental detection of the de Haas-van Alphen (dHvA) oscillations allows us to identify four frequencies (Fα = 65 T, Fβ = 658 T, Fγ = 1154 T, and Fη = 1867 T for H // a), consistent with theoretical predictions. Nontrivial α and β bands are further identified via both calculations and the angle dependence of the dHvA oscillations. Our results suggest that PdTe is a candidate for unconventional superconductivity.

Pasek W.J., Degani M.H., Maialle M.Z.

This modelling work concerns the effects of the interference between two partial subband condensates in a quasi-one-dimensional superconducting superlattice. The iterative under-relaxation with phase control method is used to solve Bogoliubov–de Gennes equations in the envelope ansatz. This method—easily generalisable to a wide class of multiband superconducting systems—allows us to obtain both the constructive and the destructive interference solution. The discussion is centred on the latter case, with one of the condensates collapsing with increased inter-subband coupling strength, due to the other—the dominating one—imposing its symmetry on the overall order parameter. The in-depth qualitative analysis is made of underlying intra-subband and inter-subband dynamics, such as the possible factors determining the dominant subband condensate or the ones determining the region where the destructive solution coexists with the constructive one. A comprehensive discussion with the recent works concerning inter-band coupling effects follows, pointing that the destructive solution is nearly universally omitted.

Blinov I.V., MacDonald A.H.

We investigate the possibility and implications of interlayer coherence in electrically isolated superconducting bilayers. We find that in a mean-field approximation bilayers can have superconducting and excitonic order simultaneously if repulsive interactions between layers are sufficiently strong. The excitonic order implies interlayer phase coherence and can be studied in a representation of symmetric and antisymmetric bilayer states. When both orders are present we find several solutions of the mean-field equations with different values of the the symmetric and antisymmetric state pair amplitudes. The mixed state necessarily has nonzero pair amplitudes for electrons in different layers in spite of the repulsive interlayer interactions, and these are responsible for spatially indirect Andreev reflection processes in which an incoming electron in one layer can be reflected as a hole in the opposite layer. We evaluate layer diagonal and off-diagonal current-voltage relationships that can be used to identify this state experimentally.

Mazziotti M.V., Bianconi A., Raimondi R., Campi G., Valletta A.

While it is known that a resonant amplification of [Formula: see text] in two-gap superconductors can be driven by using the Fano–Feshbach resonance tuning the chemical potential near a Lifshitz transition, little is known on tuning the [Formula: see text] resonance by cooperative interplay of the Rashba spin–orbit coupling (RSOC) joint with phonon mediated (e-ph) pairing at selected k-space spots. Here, we present first-principles quantum calculation of superconductivity in an artificial heterostructure of metallic quantum wells with 3 nm period where quantum size effects give two-gap superconductivity with RSOC controlled by the internal electric field at the interface between the nanoscale metallic layers intercalated by insulating spacer layers. The key results of this work show that fundamental quantum mechanics effects including RSCO at the nanoscale [Mazziotti et al., Phys. Rev. B, 103, 024523 (2021)] provide key tools in applied physics for quantitative material design of unconventional high temperature superconductors at ambient pressure. We discuss the superconducting domes where [Formula: see text] is a function of either the Lifshitz parameter ([Formula: see text]) measuring the distance from the topological Lifshitz transition for the appearing of a new small Fermi surface due to quantum size effects with finite spin–orbit coupling and the variable e-ph coupling [Formula: see text] in the appearing second Fermi surface linked with the energy softening of the cut off [Formula: see text].

Núñez J.J., Schmidt A.A., Tifrea I.

We present a possible phase diagram for the superconductivity state in a two-band scenario that includes contributions from the inter-orbital off-diagonal hopping term. Our model accounts for intra-band attractive electron–electron interactions that leads to the formation of superconducting Cooper pairs in each component band and for an inter-band attractive electron–electron interaction responsible for a single superconductive transition temperature $$T_\textrm{c}$$ in the model. Using a mean field approximation, we obtained an analytical equation for the superconducting critical temperature that includes contributions from a hybridization term due to the mixing of the two electron bands. For a numerical solution of this equation, we considered a band structure that reproduced as much as possible the situation in the Ba $$_{1-x}$$ K $$_x$$ Fe $$_2$$ As $$_2$$ pnictide superconductor material. Our possible phase diagram $$T_\textrm{c}$$ vs. N is obtained assuming that Cooper pairs in both electron bands have either s-wave or $$s^\pm $$ -wave symmetry. The main result of our calculation is the existence of a complex phase diagram that at different inter-orbital hopping strengths can have one or two local maxima for the transition critical temperature $$T_\textrm{c}$$ . The electron concentration at which these maxima occur in the phase diagram can be tuned using the inter-orbital off-diagonal hopping term.