Incipient Bands Research Articles

Emergent Fano-Feshbach resonance in two-band superconductors with an incipient quasiflat band: Enhanced critical temperature evading particle-hole fluctuations

Emergent Fano-Feshbach resonance in two-band superconductors with an incipient quasiflat band: Enhanced critical temperature evading particle-hole fluctuations

Superplastic deformation inside the knife-sharp shear bands in mid-crustal granites

We examined the microstructures of three ductile shear bands of granitic composition that deformed under mid-to-upper greenschist facies. These shear bands, from the Bundelkhand Craton, India, are 0.8–4.4 mm thick with 20–30 μm median grain sizes and share sharp contacts with the host granite. Comminution of the rheologically stronger feldspars increased permeability, promoted fluid influx, and allowed strain localisation in the incipient shear bands. The major components, quartz and feldspars, deformed via phase-specific crystal plastic deformation mechanisms. Quartz in the monomineralic bands deformed predominantly via dislocation creep, while the feldspars deformed via diffusion creep. Finer quartz grains, which occur at plagioclase triple junctions, resulted from myrmekitisation – also evident from the anti-clustered distribution of quartz-plagioclase phase boundaries and CPO inheritance. The weak CPOs and high mean misorientation angles of the fine plagioclase and K-feldspar grains and yet a high shear strain (γ = 16–37) suggest a significant contribution of grain boundary sliding (GBS) in strain localisation inside the ductile shear bands. Since intracrystalline slip alone cannot explain the high ductile strain in the shear bands, we suggest that GBS controlled the deformation and maturation of the shear bands and promoted superplasticity to accommodate further shearing.

In situ characterisation of the strain fields of intragranular slip bands in ferrite by high-resolution electron backscatter diffraction

High angular resolution electron backscatter diffraction has been used to quantify the local elastic field at the tip of mechanically loaded intragranular slip bands observed in situ in the ferrite grains of an age-hardened duplex stainless steel (Zeron 100). The surface elastic strain field was integrated to calculate in-plane and out-of-plane surface displacements. This allowed the elastic fields to be parameterised in a finite element analysis, which used the displacement field as the boundary conditions, to obtain the potential strain energy release rate (J-integral) and three-dimensional stress intensity factors (KI,II,III).This new analysis method is demonstrated by examining the elastic fields around the tip of an incipient slip band, an array of slip bands and the loading of a slip band. Direct measurement of the stress tensor in the grain identified the active slip systems with the highest Schmid factor. The stress intensity factors ahead of the slip band, measured under load, were directly affected by the magnitude of loading and the inclination angle of the slip band to the observed surface.

Pseudogap and strong pairing induced by incipient and shallow bands in quasi-two-dimensional KCa2Fe4As4F2

The optical properties of $\mathrm{K}{\mathrm{Ca}}_{2}{\mathrm{Fe}}_{4}{\mathrm{As}}_{4}{\mathrm{F}}_{2}$ (K12442, ${T}_{c}=33.5$ K) and $\mathrm{K}{\mathrm{Ca}}_{2}{({\mathrm{Fe}}_{0.95}{\mathrm{Ni}}_{0.05})}_{4}{\mathrm{As}}_{4}{\mathrm{F}}_{2}$ (Ni-K12442, ${T}_{c}=29$ K) have been examined at a large number of temperatures. For both samples, a nodeless superconducting gap is clearly observed in the optical conductivity at 5 K. The superconducting gap $\mathrm{\ensuremath{\Delta}}\ensuremath{\simeq}8.7$ meV ($2\mathrm{\ensuremath{\Delta}}/{k}_{\text{B}}{T}_{c}\ensuremath{\simeq}6.03$) in K12442, pointing towards strong-coupling Cooper pairs, but in sharp contrast, $\mathrm{\ensuremath{\Delta}}\ensuremath{\simeq}4.6$ meV ($2\mathrm{\ensuremath{\Delta}}/{k}_{\text{B}}{T}_{c}\ensuremath{\simeq}3.68$) in Ni-K12442, which agrees with the BCS weak-coupling pairing state. More intriguingly, below ${T}^{*}\ensuremath{\simeq}75$ K, the optical conductivity of K12442 reveals a pseudogap that smoothly evolves into the superconducting gap below ${T}_{c}$, while no such behavior is detected in the electron-doped Ni-K12442. The comparison between the two samples suggests that the pseudogap and strong-coupling Cooper pairs in K12442 may be intimately related to the shallow and incipient bands. We provide arguments supporting a preformed pairing mechanism of the pseudogap, but at the moment a magnetic scenario cannot yet be excluded.

Observation of bands with dxy orbital character near the Fermi level in NdFeAs1−xPxO0.9F0.1 using angle-resolved photoemission spectroscopy

We studied the band structure of NdFeAs$_{1-x}$P$_{x}$O$_{0.9}$F$_{0.1}$ ($x$ = 0, 0.2, 0.4 and 0.6) using angle-resolved photoemission spectroscopy (ARPES) measurements. Two of the hole bands, ${\alpha}_1$ $(d_{xz})$ and ${\alpha}_3$ $(d_{z^2})$, were observed at the Brillouin zone center in the $P$-polarized light configuration, while the other two hole bands, ${\alpha}_2$ $(d_{yz})$ and ${\gamma}$ $(d_{xy})$, were observed in the $S$-polarized alternative. The observed ${\gamma}$ band shifts downwards as $x$ increases, which is consistent with the theoretical prediction for the change in bond angle of As/P-Fe-As/P. Furthermore, a small amount of the $d_{xy}$ orbital component was observed at the same binding energy as that of the top of the ${\alpha}_1$ band, thus indicating the band reconstruction of the originally degenerate ${\alpha}_1$ and ${\alpha}_2$ $(d_{xz}/d_{yz})$ bands by the unoccupied $d_{xy}$ band. The change in the energy level of the ${\alpha}_1$ band top with $d_{xy}$ orbital character is accompanied by a $T_{c}$ upturn at $0.2 < x < 0.4$. The $T_{c}$ continues to increase as the ${\alpha}_1$ band shifts downward, crossing the Fermi level. The incipient band with the $d_{xy}$ orbital character on its top could be an important ingredient for high $T_{c}$ 1111-type iron-based superconductors.

Resonant pair-exchange scattering and BCS-BEC crossover in a system composed of dispersive and heavy incipient bands: A Feshbach analogy

We theoretically show that a two-band system with very different masses harbors a resonant pair scattering that leads to novel pairing properties, as highlighted by the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. Most importantly, the interband pair-exchange coupling induces an effective intraband attraction in each band, enhancing the superfluidity/superconductivity. The effect, a kind of Suhl-Kondo mechanism, is specifically enhanced when the second band has a heavy mass and is incipient (lying close to, but just above, the chemical potential, $\mu$), which we call a resonant pair scattering. By elucidating the dependence of the effective interactions and gap functions on $\mu$, we can draw an analogy between the resonant pair scattering and the Feshbach resonance.

A Technique for High-Speed Microscopic Imaging of Dynamic Failure Events and Its Application to Shear Band Initiation in Polycarbonate

Abstract An experimental technique is reported, which can image the deformation fields associated with dynamic failure events at high spatial and temporal resolutions simultaneously. The technique is demonstrated at a spatial resolution of ∼1 µm and a temporal resolution of 250 ns, while maintaining a relatively large field of view (≈1.11 mm × 0.63 mm). As a demonstration, the technique is used to image the deformation field near a notch tip during initiation of a shear instability in polycarbonate. An ordered array of 10 µm diameter speckles with 20 µm pitch, and deposited on the specimen surface near the notch tip helps track evolution of the deformation field. Experimental results show that the width of the shear band (SB) in polycarbonate is approximately 75 µm near the notch tip within resolution limits of the experiments. The measurements also reveal formation of two incipient localization bands near the crack tip, one of which subsequently becomes the dominant band while the other is suppressed. Computational simulation of the experiment was conducted using a thermomechanically coupled rate-dependent constitutive model of polycarbonate to gain further insight into the experimental observations enabled by the combination of high spatial and temporal resolutions. The simulation results show reasonable agreement with the experimentally observed kinematic field and features near the notch tip, while also pointing to the need for further refinement of constitutive models that are calibrated at high strain rates (∼105/s) and also account for damage evolution.

Superconductivity in the bilayer Hubbard model: Two Fermi surfaces are better than one

Fully occupied or unoccupied bands in a solid are often considered inert and irrelevant to a material's low-energy properties. But the discovery of enhanced superconductivity in heavily electron-doped FeSe-derived superconductors poses questions about the possible role of incipient bands (those laying close to but not crossing the Fermi level) in pairing. To answer this question, researchers have studied pairing correlations in the bilayer Hubbard model, which has an incipient band for large interlayer hopping ${t}_{\ensuremath{\perp}}$, using many-body perturbation theory and variational methods. They have generally found that superconductivity is enhanced as one of the bands approaches the Lifshitz transition and even when it becomes incipient. Here we address this question using the nonperturbative quantum Monte Carlo (QMC) dynamical cluster approximation (DCA) to study the bilayer Hubbard model's pairing correlations. We find that the model has robust ${s}^{\ifmmode\pm\else\textpm\fi{}}$ pairing correlations in the large ${t}_{\ensuremath{\perp}}$ limit, which can become stronger as one band is made incipient. While this behavior is linked to changes in the effective interaction, we further find that it is counteracted by a suppression of the intrinsic pair-field susceptibility and does not translate to an increased ${T}_{c}$. Our results demonstrate that the highest achievable transition temperatures in the bilayer Hubbard model occur when the system has two bands crossing the Fermi level.

Atomic Line Defects and Topological Superconductivity in Unconventional Superconductors

Topological superconductors (TSCs) are correlated quantum states with simultaneous off-diagonal long-range order and nontrivial topological invariants. They produce gapless or zero energy boundary excitations, including Majorana zero modes and chiral Majorana edge states with topologically protected phase coherence essential for fault-tolerant quantum computing. Candidate TSCs are very rare in nature. Here, we propose a novel route toward emergent quasi-one-dimensional (1D) TSCs in naturally embedded quantum structures such as atomic line defects in unconventional spin-singlet $s$-wave and $d$-wave superconductors. We show that inversion symmetry breaking and charge transfer due to the missing atoms lead to the occupation of incipient impurity bands and mixed parity spin singlet and triplet Cooper pairing of neighboring electrons traversing the line defect. Nontrivial topological invariants arise and occupy a large part of the parameter space, including the time reversal symmetry breaking Zeeman coupling due to applied magnetic field or defect-induced magnetism, creating TSCs in different topological classes with robust Majorana zero modes at both ends of the line defect. Beyond providing a novel mechanism for the recent discovery of zero-energy bound states at both ends of an atomic line defect in monolayer Fe(Te,Se) superconductors, the findings pave the way for new material realizations of the simplest and most robust 1D TSCs using embedded quantum structures in unconventional superconductors with large pairing energy gaps and high transition temperatures.

Designing nickelate superconductors with d8 configuration exploiting mixed-anion strategy

Inspired by a recently proposed superconducting mechanism for a new cuprate superconductor Ba$_2$CuO$_{3+\delta}$, we theoretically design an unconventional nickelate superconductor with $d^8$ electron configuration. Our strategy is to enlarge the on-site energy difference between $3d_{x^2-y^2}$ and other $3d$ orbitals by adopting halogens or hydrogen as out-of-plane anions, so that the $3d$ bands other than $d_{x^-y^2}$ lie just below the Fermi level for the $d^8$ configuration, acting as incipient bands that enhance superconductivity. We also discuss a possible relevance of the present proposal to the recently discovered superconductor (Nd,Sr)NiO$_2$.

Raman Study of Cooper Pairing Instabilities in (Li_{1-x}Fe_{x})OHFeSe.

We studied the electronic Raman spectra of (Li_{1-x}Fe_{x})OHFeSe as a function of light polarization and temperature. In the B_{1g} spectra alone we observe the redistribution of spectral weight expected for a superconductor and two well-resolved peaks below T_{c}. The nearly resolution-limited peak at 110 cm^{-1} (13.6meV) is identified as a collective mode. The peak at 190 cm^{-1} (23.6meV) is presumably another collective mode since the line is symmetric and its energy is significantly below the gap energy observed by single-particle spectroscopies. Given the experimental band structure of (Li_{1-x}Fe_{x})OHFeSe, the most plausible explanations include conventional spin-fluctuation pairing between the electron bands and the incipient hole band and pairing between the hybridized electron bands. The absence of gap features in A_{1g} and B_{2g} symmetry favors the second case. Thus, in spite of various differences between the pnictides and chalcogenides, this Letter demonstrates the proximity of pairing states and the importance of band structure effects in the Fe-based compounds.

Superconducting mechanism for the cuprate Ba2CuO3+δ based on a multiorbital Lieb lattice model

For the recently discovered cuprate superconductor $\mathrm{Ba_{2}CuO_{3+\delta}}$, we propose a lattice structure which resembles the model considered by Lieb to represent the vastly oxygen-deficient material. We first investigate the stability of the Lieb-lattice structure, and then construct a multiorbital Hubbard model based on first-principles calculation. By applying the fluctuation-exchange approximation to the model and solving the linearized Eliashberg equation, we show that $s$-wave and $d$-wave pairings closely compete with each other, and, more interestingly, that the intra-orbital and inter-orbital pairings coexist. We further show that, if the energy of the $d_{3z^2-r^2}$ band is raised to make it "incipient" with the lower edge of the band close to the Fermi level within a realistic band filling regime, $s\pm$-wave superconductivity is strongly enhanced. We reveal an intriguing relation between the Lieb model and the two-orbital model for the usual K$_2$NiF$_4$ structure where a close competition between $s-$ and $d-$wave pairings is known to occur. The enhanced superconductivity in the present model is further shown to be related to an enhancement found previously in the bilayer Hubbard model with an incipient band.

Many-variable variational Monte Carlo study of superconductivity in two-band Hubbard models with an incipient band

We study superconductivity in two-band models where one of the bands does or does not intersect the Fermi level depending on the parameter values. Applying a many-variable variational Monte-Carlo method for a Hubbard model on two-leg ladder and bilayer square lattices, we show that superconductivity can be enhanced in a parameter regime where the edge of one of the bands is near the Fermi energy, that is, when the band is incipient. The resemblence of the present results to those obtained by a weak coupling method in a recent study suggests that, even in the large $U$ regime, the suppression of the near-zero-energy spin fluctuations and the development of finite energy spin fluctuations are the key factors for the enhancement of superconductivity by an incipient band.

Strongly Enhanced Superconductivity Due to Finite Energy Spin Fluctuations Induced by an Incipient Band: A FLEX Study on the Bilayer Hubbard Model with Vertical and Diagonal Interlayer Hoppings

We study the spin-fluctuation-mediated $s\pm$-wave superconductivity in the bilayer Hubbard model with vertical and diagonal interlayer hoppings. As in the two-leg ladder model with diagonal hoppings, studied previously by the present authors, superconductivity is strongly enhanced when one of the bands lies just below (or touches) the Fermi level, that is, when the band is incipient. The strong enhancement of superconductivity is because large weight of the spin fluctuations lies in an appropriate energy range, whereas the low energy, pair-breaking spin fluctuations are suppressed. The optimized eigenvalue of the linearized Eliashberg equation, a measure for the strength of superconductivity, is not strongly affected by the bare width of the incipient band, but the parameter regime where superconductivity is optimized is wide when the incipient band is narrow, and in this sense, the coexistence of narrow and wide bands is favorable for superconductivity.

Effective pairing interaction in a system with an incipient band

The nature and mechanism of superconductivity in the extremely electron-doped FeSe based superconductors continues to be a matter of debate. In these systems, the hole-like band has moved below the Fermi energy, and various spin-fluctuation theories involving pairing between states near the electron Fermi surface and states of this incipient band have been proposed. Here, using a dynamic cluster quantum Monte Carlo calculation for a bilayer Hubbard model we show that the pairing in these systems can be understood in terms of an effective retarded attractive interaction between electrons near the electron Fermi surface.

Phonon Boost Effect on the S\xb1-wave Superconductor with Incipient Band

We showed that the all phonons – not only forward-scattering phonon but also local (all-momentum-scattering) phonon – contribute to boosting Tc of the S±-wave pairing state in the incipient band model. In particular, when the incipient band sinks deeper, the phonon boost effect of the local phonon increases and becomes as effective as the one of the forward-scattering phonon. Our finding implies that all interface phonons from the SrTiO3 substrate – not only the 90 meV Fuchs-Kliewer (F-K) phonon but also the 60 meV F-K phonon – as well as all intrinsic phonons of the FeSe monolayer itself, regardless of their degree of “forwardness”, should contribute to increase Tc of the FeSe/STO monolayer system. This all-phonon boost mechanism should universally work in all heavily doped (either by holes or by electrons) Iron-based superconductors.

Possible Pairing Symmetry in the FeSe-Based Superconductors Determined by Quasiparticle Interference

We study the momentum-integrated quasiparticle interference (QPI) in the FeSe-based superconductors. This method was recently proposed theoretically and has been applied to determine the pairing symmetry in these materials experimentally. Our findings suggest that, if the incipient bands and the superconducting (SC) pairing on them are taken into consideration, then the experimentally measured bound states and momentum-integrated QPI can be well fitted, even if the SC order parameter does not change sign on the Fermi surfaces. Therefore, we offer an alternative explanation to the experimental data, calling for more careful identification of the pairing symmetry that is important for the pairing mechanism.

Short-time dynamics in s+is -wave superconductor with incipient bands

Motivated by the recent observation of the time-reversal symmetry broken state in K-doped BaFe$_2$As$_2$ superconducting alloys, we theoretically study the collective modes and the short time dynamics of the superconducting state with $s+is$-wave order parameter using an effective four-band model with two hole and two electron pockets. The superconducting $s+is$ state emerges for incipient electron bands as a result of hole doping and appears as an intermediate state between $s^{\pm}$ (high number of holes) and $s^{++}$ (low number of holes). The amplitude and phase modes are coupled giving rise to a variety of collective modes. In the $s^{\pm}$ state, we find the Higgs mode at frequencies similar to a two-band model with an absent Leggett mode, while in the $s+is$ and $s^{++}$ state, we uncover a new coupled collective soft mode. Finally we compare our results with the $s+id$ solution and find similar behaviour of the collective modes.

In-gap bound states induced by a single nonmagnetic impurity in sign-preserving s -wave superconductors with incipient bands

We have investigated the in-gap bound states (IGBS) induced by a single nonmagnetic impurity in multiband superconductors with incipient bands. Contrary to the naive expectation, we found that even if the superconducting (SC) order parameter is a sign-preserving $s$ wave on the Fermi surfaces, the incipient bands may still affect the appearance and locations of the IGBS, although the gap between the incipient bands and the Fermi level is much larger than the SC gap. Therefore in scanning tunneling microscopy experiments, the IGBS induced by a single nonmagnetic impurity are not the definitive evidence for the sign-changing order parameter on the Fermi surfaces. Our findings have special implications for the experimental determination of the pairing symmetry in the FeSe-based superconductors.

Possible high- Tc superconductivity due to incipient narrow bands originating from hidden ladders in Ruddlesden-Popper compounds

We introduce a concept of hidden ladders for the bilayer Ruddlesden-Popper type compounds: While the crystal structure is bilayer, $d_{xz}$ ($d_{yz}$) orbitals in the relevant $t_{2g}$ sector of the transition metal form a two-leg ladder along $x$ ($y$), since the $d_{xz}$ ($d_{yz}$) electrons primarily hop along the leg direction $x$ ($y$) on top of the rung $z$ direction. We predict that Sr$_3$Mo$_2$O$_7$ and Sr$_3$Cr$_2$O$_7$ are candidates for the hidden-ladder material with a right position of $E_F$, from a first-principles band calculation. Based on the analysis of Eliashberg equation for these systems, we propose a possible occurrence of high temperature superconductivity in these materials arising from the interband pair scattering processes between the wide and "incipient" narrow bands on the ladder.