Recent observations [A.~Pustogow et al. Nature 574, 72 (2019)] of a drop of the $^{17}$O nuclear magnetic resonance (NMR) Knight shift in the superconducting state of Sr$_2$RuO$_4$ challenged the popular picture of a chiral odd-parity paired state in this compound. Here we use polarized neutron scattering to show that there is a $34 \pm 6$ % drop in the magnetic susceptibility at the ruthenium site below the superconducting transition temperature. Measurements are made at lower fields $H \sim \tfrac{1}{3} H_{c2}$ than a previous study allowing the suppression to be observed. Our results are consistent with the recent NMR observations and rule out the chiral odd-parity $\mathbf{d}=\hat{\mathbf{z}}(k_x\pm ik_y)$ state. The observed susceptibility is consistent with several recent proposals including even-parity $B_{1g}$ and odd-parity helical states.
We study the longitudinal spin susceptibility inside a magnetically ordered phase, which exhibits a superconducting instability leading to a coexistence of the two ordered phases. Inside the magnetic phase, the superconducting gap acquires a linear term in a magnetic field applied along the direction of the magnetic moment. We find that such a linear term generates a jump of the longitudinal spin susceptibility when the superconducting instability occurs via a continuous phase transition. This anomaly at the superconducting instability is a thermodynamic signature of the microscopic coexistenc…
In order to determine the superconducting paring state in the ferromagnetic superconductor UCoGe, ^{59}Co NMR Knight shift, which is directly related to the microscopic spin susceptibility, was measured in the superconducting state under magnetic fields perpendicular to spontaneous magnetization axis: ^{59}K^{a, b}. ^{59}K^{a, b} shows to be constant, but does not decrease below a superconducting transition. These behaviors as well as the invariance of the internal field at the Co site in the superconducting state exclude the spin-singlet pairing, and can be interpreted with the equal-spin pai…
Experiment and theory indicate that UPt3 is a topological superconductor in an odd-parity state, based in part from temperature independence of the NMR Knight shift. However, quasiparticle spin-flip scattering near a surface, where the Knight shift is measured, might be responsible. We use polarized neutron scattering to measure the bulk susceptibility with H||c, finding consistency with the Knight shift but inconsistent with theory for this field orientation. We infer that neither spin susceptibility nor Knight shift are a reliable indication of odd-parity.
The magnetic field dependence of the spin-susceptibility, $χ_{s}$ was measured in the superconducting state of high purity MgB$_{2}$ fine powders below 1.3 T. $χ_{s}$ was determined from the intensity of the conduction electron spin resonance spectra at 3.8, 9.4, and 35 GHz. At the lowest magnetic fields (0.14 T), a gap opens in the density of states at the Fermi energy and, accordingly, $χ_{s}(T)$ is small at low temperatures. Fields above 0.2 T (about 15 % of $H^{c}_{c2}$, the minimum upper critical field), destroy the gap. The field induced $χ_{s}$ is much larger than expected from current …
The heavy fermion superconductor UPt$_3$ is thought to have odd-parity, a state for which the temperature dependence of the spin susceptibility is an important signature. In order to address conflicting reports from two different experiments, the NMR Knight shift and measurements of the anisotropy of the upper critical field, we have measured the bulk susceptibility in a high quality single crystal using polarized-neutron diffraction. A temperature independent susceptibility was observed for $H||a$ through the transitions between the normal state and the superconducting A-, B- and C-phases, co…
We analyze microwave cavity perturbation methods, and show that the technique is an excellent, precision method to study the dynamic magnetic and dielectric response in the $GHz$ frequency range. Using superconducting cavities, we obtain exceptionally high precision and sensitivity for measurements of relative changes. A dynamic electromagnetic susceptibility $\tildeζ(T)=ζ^{\prime}+iζ^{\prime \prime}$ is introduced, which is obtained from the measured parameters: the shift of cavity resonant frequency $δf$ and quality factor $Q$. We focus on the case of a spherical sample placed at the center …
Clear Reduction in Spin Susceptibility and Superconducting Spin Rotation for $H \parallel a$ in the Early-Stage Sample of Spin-Triplet Superconductor UTe$_2$
This paper treats a number of issues of the cuprates, ranging from the spin resonance peak and the linear one-particle scattering rate to the superconducting transition, in the frame of a Fermi liquid model. Recent ARPES expts. by Valla et al., Science vol. 285, 2110 (1999), and e-print cond-mat/0003407, directly support the linearity of the one-particle scattering rate everywhere in the Brillouin zone we obtained here. We show that the origin of this linearity is the strong linear in energy term of the imaginary part of the carrier susceptibility. This result yields directly a linear in tempe…
We report $^{115}$In nuclear magnetic resonance (NMR) measurements of the heavy-fermion superconductor CeCoIn$_5$ in the vicinity of the superconducting critical field $H_{c2}$ for a magnetic field applied perpendicular to the $\hat c$-axis. A possible inhomogeneous superconducting state, Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), is stabilized in this part of the phase diagram. In 11 T applied magnetic field, we observe clear signatures of the two phase transitions: the higher temperature one to the homogeneous superconducting state and the lower temperature phase transition to a FFLO state. It …
We have grown a single crystal of La_2-x_Sr_x_CuO_4_ in which the Sr concentration, x, continuously changes from 0.24 to 0.29 in the overdoped regime and obtained many pieces of single crystals with different x values by slicing the single crystal. From detailed measurements of the magnetic susceptibility, chi, of each piece, it has been found that the absolute value of chi at the measured lowest temperature 2 K, |chi_2K_|, on field cooling rapidly decreases with increasing x as well as the superconducting (SC) transition temperature. As the value of |chi_2K_| is regarded as corresponding to t…
We measure the ac susceptibility of single-crystal CeCoIn5 in dc field parallel to the c axis and find further evidence for a high-field phase transition within the superconducting phase in this orientation. We apply up to 2.3 kbar uniaxial pressure along the c axis and discuss the pressure dependence of the high-field phase. We also report the behavior of Hc2 under uniaxial pressure for field along c.
We have investigated the ac susceptibility of the spin triplet superconductor Sr$_2$RuO$_4$ as a function of magnetic field in various directions at temperatures down to 60 mK. We have focused on the in-plane field configuration (polar angle $θ\simeq 90^{\circ}$), which is a prerequisite for inducing multiple superconducting phases in Sr$_2$RuO$_4$. We have found that the previous attribution of a pronounced feature in the ac susceptibility to the second superconducting transition itself is not in accord with recent measurements of the thermal conductivity or of the specific heat. We propose t…
Taking advantage of a novel multiprobe setup we have measured, on a unique sample, the ac-magnetic susceptibility, the resistivity, the ac-specific heat and the thermopower of the superconductor heavy fermion CeCu$_{2}$Si$_{2}$ under pressure up to 5.1 GPa. At the superconducting transition temperature $T_c$, the Meissner signal corresponds to that expected for the sample volume and coincides with the specific heat jump and the resistive transition completion temperatures. Differing from previous observations, here the susceptibility measurements did not reveal any anomaly in the vicinity of t…
We analyze the two-dimensional {\it d-p} model, considering both antiferromagnetic spin fluctuation and $d_{x^2-y^2}$-wave superconducting fluctuation. We adopt the fluctuation-exchange approximation in order to derive both normal and anomalous vertices composed only of the renormalized {\it d}-electron Green function and the on-site repulsive interaction among the {\it d}-electrons. Using these vertices, we derive a $t$-matrix as a superconducting fluctuation propagator. Then, we obtain self-consistent solutions in which the system is close to antiferromagnetic instability. In our solutions, …
Old susceptibility data, measured in superconducting materials at low-frequency, are shown to be accounted for consistently within the framework of a recently published\cite{sz1} analysis of the skin effect. Their main merit is to emphasize the significance of the skin-depth measurements, performed \textit{just beneath} the critical temperature $T_c$, in order to disprove an assumption, which thwarted any understanding of the skin-depth data, achieved so far by conventional high-frequency methods, so that those data might, from now on, give access to the temperature dependence of the concentra…
$^{63}$Cu and $^{199}$Hg NMR shifts for an optimally and underdoped HgBa$_{2}$CuO$_{4+δ}$ single crystal are reported, and the temperature dependence dictates a two-component description of the uniform spin susceptibility. The first component, associated with the pseudogap phenomenon in the NMR shifts, decreases already at room temperature and continues to drop as the temperature is lowered, without a drastic change at the transition temperature into the superconducting state. The second component is temperature independent above the superconducting transition temperature and vanishes rapidly …
To investigate spin susceptibility in a superconducting (SC) state, we measured the $^{125}$Te-nuclear magnetic resonance (NMR) Knight shifts at magnetic fields ($H$) up to 6.5 T along the $b$ and $c$ axes of single-crystal UTe$_2$, a promising candidate for a spin-triplet superconductor. In the SC state, the Knight shifts along the $b$ and $c$ axes ($K_b$ and $K_c$, respectively) decreased slightly and the decrease in $K_b$ was almost constant up to 6.5 T. The reduction in $K_c$ decreased with increasing $H$, and $K_c$ was unchanged through the SC transition temperature at 5.5 T, excluding th…
Angle resolved photoemission spectroscopy (ARPES) provides a detailed view of the renormalized band structure and, consequently, is a key to the self-energy and the single-particle Green's function. Here we summarize the ARPES data accumulated over the whole Brillouin zone for the optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8-δ}$ into a parametric model of the Green's function, which we use for calculating the itinerant component of the dynamic spin susceptibility in absolute units with many-body effects taken into account. By comparison with inelastic neutron scattering (INS) data we show that th…
Starting from the generalized t-J-G model Hamiltonian, we analyze the spin response in the superconducting cuprates taking into account both local and itinerant spin components which are coupled to each other self-consistently. Derived expression reproduces the basic observations of neutron scattering data in YBa2Cu3O6+y compounds near the optimal doping level.
We use inelastic neutron scattering with spin polarization analysis to study the magnetic excitations in the normal and superconducting states of YBa2Cu3O6.9. Polarization analysis allows us to determine the spin polarization of the magnetic excitations and to separate them from phonon scattering. In the normal state, we find unambiguous evidence of magnetic excitations over the 10-60meV range of the experiment with little polarization dependence to the excitations. In the superconducting state, the magnetic response is enhanced near the "resonance energy" and above. At lower energies, 10<E<30…
The electronic spin susceptibility of YBa_2Cu_3O_{6.95} has been measured with high precision up to 24 Tesla with 17O nuclear magnetic resonance. Its temperature dependence can be accounted for by superconducting fluctuations that result in a smooth crossover from the normal to the vortex liquid state. A magnetic field-temperature phase diagram for this crossover has been established having strong upward curvature.
We report complex ac magnetic susceptibility measurements of a superconducting transition in very high-quality single-crystal alpha-uranium using microfabricated coplanar magnetometers. We identify an onset of superconductivity at T~0.7 K in both the real and imaginary components of the susceptibility which is confirmed by resistivity data. A superconducting volume fraction argument, based on a comparison with a calibration YBCO sample, indicates that the superconductivity in these samples may be filamentary. Our data also demonstrate the sensitivity of the coplanar micro-magnetometers, which …
The temperature dependence of ac susceptibility of YBCO thin film was measured as a function of frequency and ac field amplitude in a field perpendicular to the film plane. We show that all measured ac susceptibility curves can be caled into a single curve using the peak temperature (Tp) of its imaginary part as the scaling parameter. The frequency effect on ac susceptibility was also measured. As the frequency increases,(Tp)shifts to higher temperature.This effect can be interpreted in terms of flux creep. The temperature T,and field,Hac, dependence of the activation energy obtained from the …
We investigate characteristic features in the spin response of doped three-dimensional topological insulators with odd-parity unequal-spin superconducting pairing, which are predicted to have gapless Majorana surface modes. These Majorana modes contribute to the local spin susceptibility, giving rise to a characteristic temperature behavior of the Knight shift and the spin-lattice relaxation time in magnetic resonance experiments. Because of their different decay lengths, the Majorana modes can be observed and clearly distinguished from the Dirac modes of the topological insulator by local pro…
Magnetic susceptibility of non-ellipsoidal samples is a long-standing problem in experimental studies of magnetism and superconductivity. Here the quantitative description of the Meissner-London response (no Abrikosov vortices) of right circular cylinders in an axial magnetic field is given. The three-dimensional adaptive finite-element modeling was used to calculate the total magnetic moment, m, in a wide range of London penetration depth, λ, to sample size ratios. By fitting the numerical data, the closed-form universal magnetic susceptibility is formulated involving only sample dimensions a…
We report a systematic investigation of Ba[Fe(1-x)Co(x)]2As2 based on transport and 75-As NMR measurements, and establish the electronic phase diagram. We demonstrate that doping progressively suppresses the uniform spin susceptibility and low frequency spin fluctuations. The optimum superconducting phase emerges at x_c~0.08 when the tendency toward spin ordering completely diminishes. Our findings point toward the presence of a quantum critical point near x_c between the SDW (spin density wave) and superconducting phases.
Diamagnetic susceptibility measurements under high hydrostatic pressure (up to 1.03 GPa) were carried out on the newly discovered Fe-based superconductor LaO_{1-x}F_{x}FeAs(x=0.11). The transition temperature T_c, defined as the point at the maximum slope of superconducting transition, was enhanced almost linearly by hydrostatic pressure, yielding a dT_c/dP of about 1.2 K/GPa. Differential diamagnetic susceptibility curves indicate that the underlying superconducting state is complicated. It is suggested that pressure plays an important role on pushing low T_c superconducting phase toward the …
We synthesized tetragonal alpha-FeSe by melting a powder mixture of iron and selenium at high pressure. Subsequent annealing at normal pressure results in removing traces of hexagonal beta- FeSe, formation of a rather sharp transition to superconducting state at Tc ~ 7 K, and the appearance of a magnetic transition near Tm = 120 K. Resistivity and ac-susceptibility were measured on the annealed sample at hydrostatic pressure up to 4.5 GPa. A magnetic transition visible in ac-susceptibility shifts down under pressure and the resistive anomaly typical for a spin density wave (SDW) antiferromagne…
We have measured magnetic response of second-generation high temperature superconductor YBa2Cu3Ox wire and Nb thin film in perpendicular ac field as a function of temperature. We compare experimental complex ac susceptibility to the calculated susceptibility based on the model of Bean's critical-state response in two-dimensional (2D) disk in perpendicular field. The harmonic analysis is needed for comparison between the model and the experimental data. We present a method of linking model and experimental susceptibility. Good agreement of experimental susceptibility with model susceptibility o…
Literature and experimental data about practical determination of phase composition and structure of BiHTSC ceramics from results of measurements of temperature dependence of magnetic susceptibility are presented. It is shown that Bi2223 to Bi2212 phases ratio, calculated by XRD-analysis results, does not correlate precisely with magnetic susceptibility - temperature dependence. Phase, which is present in smaller amount, especially Bi2212 phase with lower critical temperature, appears less pronouncedly at the magnetic susceptibility - temperature dependence. Besides, limiting parts of Meissner…
We scrutinize the enhanced superconducting performance of melt quench Bismuth based Bi2Sr2CaCu2O8 (Bi-2212) superconductor. The superconducting properties of melt quenched Bi-2212 (Bi2212-MQ) sample are compared with non-melted Bi2212-NM and Bi1.4Pb0.6Sr2Ca2Cu3O10 (Bi-2223). Crystal structure and morphology of the samples are studied using X-ray diffraction and Scanning Electron Microscopy (SEM) techniques. The high field (14T) magneto-transport and DC/AC magnetic susceptibility techniques are extensively used to study the superconducting properties of the investigated samples. The superconduc…
We report 29Si-NMR study on a single crystal of the heavy-fermion superconductor CeIrSi3 without an inversion symmetry along the c-axis. The 29Si-Knight shift measurements under pressure have revealed that the spin susceptibility for the ab-plane decreases slightly below Tc, whereas along the c-axis it does not change at all. The result can be accounted for by the spin susceptibility in the superconducting state being dominated by the strong antisymmetric (Rashba-type) spin-orbit interaction that originates from the absence of an inversion center along the c-axis and it being much larger than …
We systematically analyze the influence of the superconducting gap symmetry and the electronic structure on the dynamical spin susceptibility in superconducting Na_xCoO_2$\cdot y$H_2O within a three different models: the single a_{1g}-band model with nearest-neighbor hoppings, the realistic three-band t_{2g}-model with, and without e'_g pockets present at the Fermi surface. We show that the magnetic response in the normal state is dominated by the incommensurate antiferromagnetic spin density wave fluctuations at large momenta in agreement with experimental temperature dependence of the spin-l…
We theoretically investigate how the spin susceptibility of a planar Josephson junction is affected when the system transits into the topological superconducting state. We show that the magnetic flux and magnetic field dependence of the spin susceptibility closely maps the phase diagram of the system. In the absence of an external magnetic flux the system can self-tune into the topological superconducting state by minimizing its free energy. Self-tuned topological transitions are accompanied by sharp peaks in the spin susceptibility, which can therefore be use as measurable fingerprints for de…
We report the effect of silver addition on superconducting performance of bulk YBCO (YBa2Cu3O7) superconductor. All the studied samples are prepared by conventional solid-state reaction method. Rietveld fitted X-ray diffraction data confirmed the single phase formation for all the studied samples. Detailed AC susceptibility measurements as a function of driven AC amplitude (1Oe-17Oe) of these samples revealed the enhancement of grains coupling with increasing Ag content in YBCO+Agx composite system. 10wt% Ag added YBCO superconductors exhibited the optimum inter granular coupling. The Scanning…
In 2007, type-I superconductivity in heavily boron-doped silicon carbide was discovered. The question arose, if it is possible to achieve a superconducting phase by introducing dopants different from boron. Recently, aluminum-doped silicon carbide was successfully found to superconduct by means of resistivity and DC magnetization measurements. In contrast to boron-doped silicon carbide, the aluminum doped system is treated as a type-II superconductor because of the absence of an hysteresis in data measured upon decreasing and increasing temperature in finite magnetic fields. In this paper, res…
We measured the resistivity and magnetic susceptibility to map out the phase diagram of single crystalline NaFe$_{1-x}$Co$_x$As. Replacement of Fe by Co suppresses both the structural and magnetic transition, while enhances the superconducting transition temperature ($T_{\rm c}$) and superconducting component fraction. Magnetic susceptibility exhibits temperature-linear dependence in the high temperatures up to 500 K for all the superconducting samples, but such behavior suddenly breaks down for the non-superconducting overdoped crystal, suggesting that the superconductivity is closely related…
Magnetic properties of the novel layered superconductor, Na$_{0.35}$CoO$_{2}$$\cdot$1.3H$_{2}$O have been investigated. From the temperature dependence and field dependence of the magnetization, the superconducting transition temperature, as well as upper- and lower-critical fields have been estimated to be $T_{C}=4.6$ K, $H_{C2}(0)=61.0$ T and $H_{C1}(0)=28.1$ Oe. These values give quite unusual phenomenological parameters, \textit{i.e.}, coherent length, penetration depth and Ginzburg-Landau parameter of $ξ=2.32$ nm, $λ=5.68\times 10^{3}$ Å and $κ\equivλ/ξ=244$, suggesting an unconventional …
The superconducting state of NaxCoO2.yH2O with three CoO2 layers in a unit cell has been studied by 59Co-NMR. The Knight shift measured for a peak of the NMR spectra corresponding to the external magnetic field H along one of the principal directions within the CoO2 plane, exhibits a rapid decrease with decreasing temperature T below the superconducting transition temperature Tc, indicating that the spin susceptibility is suppressed in the superconducting phase, at least, for this field direction. Because differences of the superconducting properties are rather small between this three-layer N…
ARPES measurements on HiTc superconductors such as BiSrCaCuO reveal a quasiparticle peak, a broad background and a dip. The background may originate from inelastic spin fluctuation emission. Calculations of the spectral weight are presented incorporating these inelastic processes. Superconducting correlations have been included in the magnetic susceptibility. The dip feature in the spectral weight is evidence for a spin gap in the superconducting state.
Static spin susceptibility of superconductors with spin-orbit relaxation has been calculated in the seminal work of A.A. Abrikosov and L.P. Gor'kov [Sov. Phys. JETP, {\bf 15}, 752 (1962)]. Surprisingly the generalization of this result to finite frequencies has not been done despite being quite important for the modern topic of superconducting spintronics. The present paper fills this gap by deriving the analytical expression for spin susceptibility. The time-dependent spin response is shown to be captured by the quasiclassical Eilenberger equation with collision integrals corresponding to the…
We use the density matrix formalism to analyze the interaction of interferometer-type superconducting qubits with a high quality tank circuit, which frequency is well below the gap frequency of a qubit. We start with the ground state characterization of the superconducting flux and charge qubits. Then, by making use of a dressed state approach we describe the qubits' spectroscopy when the qubit is irradiated by a microwave field which is tuned to the gap frequency. The last section of the paper is devoted to continuous monitoring of qubit states by using a DC SQUID in the inductive mode.
A theory of tunneling conductance in ferromagnetic metal/insulator/triplet - supercondcutor junctions is presented for unitary and non-unitary spin triplet pairing states which are promising candidates for the superconducting paring symmetry of Sr2RuO4. As the magnitude of the exchange interaction in the ferromagnetic metal is increased, the conductance for the unitary pairing state below the energy gap is reduced in contrast to the case for the non-unitary pairing state.
We study the properties of a one-dimensional (1D) gas of fermions trapped in a lattice by means of the density matrix renormalization group method, focusing on the case of unequal spin populations, and strong attractive interaction. In the low density regime, the system phase-separates into a well defined superconducting core and a fully polarized metallic cloud surrounding it. We argue that the superconducting phase corresponds to a 1D analogue of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, with a quasi-condensate of tightly bound bosonic pairs with a finite center-of-mass momentum tha…
Substitution of isovalent non-magnetic defects, such as Zn, in CuO2 plane strongly modifies the magnetic properties of strongly electron correlated hole doped cuprate superconductors. The reason for enhanced uniform magnetic susceptibility, \c{hi}, in Zn substituted cuprates is debatable. So far, the observed magnetic behavior has been analyzed mainly in terms of two somewhat contrasting scenarios, (a) that due to independent localized moments appearing in the vicinity of Zn arising because of the strong electronic/magnetic correlations present in the host compound and (b) that due to transfer…
We report a comprehensive polarized and unpolarized neutron scattering study of the evolution of the dynamical spin susceptibility with temperature and doping in three underdoped single crystals of the \YBCO{6+x} high temperature superconductor: \YBCO{6.5} (Tc = 52 K), \YBCO{6.7} (Tc = 67 K), and \YBCO{6.85} (T_c = 87 K). Theoretical implications of these data are discussed, and a critique of recent attempts to relate the spin excitations to the thermodynamics of high temperature superconductors is given.
We have performed magnetic susceptibility measurements in Mo$_{(1-x)}$Ge$_x$ amorphous thin films biased with an electrical current using anisotropic coils. We tested the symmetry of the vortex response changing the relative orientation between the bias current and the susceptibility coils. We found a region in the DC current - temperature phase diagram where the dynamical vortex structures behave anisotropically. In this region the shielding capability of the superconducting currents measured by the susceptibility coils is less effective along the direction of vortex motion compared to the tr…
We study the orbital-dependent superconducting pairing in a five-orbital t-J1-J2 model for iron pnictides. Depending on the orbital selectivity of electron correlations and the orbital characters along the Fermi surface, the superconducting gap in an A_{1g} pairing state may exhibit anisotropy. This anisotropy varies with the degree of J1-J2 magnetic frustration. We have also calculated the dynamical spin susceptibility in the superconducting state. The frequency dependence of the susceptibility at the antiferromagnetic wavevector (π,0) shows a resonance, whose width is enhanced by the orbital…
Following the discovery of topological insulators, there has been a renewed interest in superconducting systems that have strong spin-orbit (SO) coupling. Here we address the fundamental question of how the spin properties of a otherwise spin-singlet superconducting ground state evolve with increasing SO impurity density. We have mapped out the Zeeman critical field phase diagram of superconducting Al films that were deposited over random Pb cluster arrays of varying density. These phase diagrams give a direct measure of the Fermi liquid spin renormalization, as well as the spin orbit scatteri…
We have measured and modeled, using three different approaches, the tunneling current in a Nb/NbxOy/Ni planar tunnel junction. The experimental data could be fitted and the correct current polarization could be extracted using a simple quasiclassical model, even in the absence of an applied magnetic field. We also discuss the microscopic structure of the barrier.
Experiments on the iron-pnictide superconductors appear to show some materials where the ground state is fully gapped, and others where low-energy excitations dominate, possibly indicative of gap nodes. Within the framework of a 5-orbital spin fluctuation theory for these systems, we discuss how changes in the doping, the electronic structure or interaction parameters can tune the system from a fully gapped to nodal sign-changing gap with s-wave ($A_{1g}$) symmetry ($s^\pm$). In particular we focus on the role of the hole pocket at the $(π,π)$ point of the unfolded Brillouin zone identified as…