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Larkin-Ovchinnikov superconducting state has spontaneous modulation of Cooper pair density, while Fulde-Ferrell state has a spontaneous modulation in the phase of the order parameter. We report that a quasi-two-dimensional Dirac metal, under certain conditions has principally different inhomogeneous superconducting states that by contrast have spontaneous modulation in a submanifold of a multiple-symmetries-breaking order parameter. The first state we find can be viewed as a nematic superconductor where the nematicity vector spontaneously breaks rotational and translational symmetries due to spatial modulation. The other demonstrated state is a chiral superconductor with spontaneously broken time-reversal and translational symmetries. It is characterized by an order parameter, which forms a lattice pattern of alternating chiralities.
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To address the issues of superconducting and charge properties in high-T$_c$ cuprates, we perform a quantum Monte Carlo study of an extended three-band Emery model, which explicitly includes attractive interaction $V_{OO}$ between oxygen orbitals. In the physically relevant parameter range, we find that $V_{OO}$ acts to strongly enhance the long-range part of d-wave pairing correlation, with a clear tendency to form long-range superconducting order in the thermodynamic limit. Simultaneously, increasing $|V_{OO}|$ renders a rapid increase of the nematic charge structure factor at most of wavevectors, especially near $textbf{q}=(0,0)$, indicating a dramatic enhancement of nematicity and charge density waves. Our findings suggest that the attraction between oxygen orbitals in high-T$_c$ cuprates is a common thread linking their superconducting and charge properties.
Study of Fe based compounds have drawn much attention due to the discovery of superconductivity as well as many other exotic electronic properties. Here, we review some of our works in these materials carried out employing density functional theory and angle resolved photoemission spectroscopy. The results presented here indicate that the dimensionality of the underlying electronic structure plays important role in deriving their interesting electronic properties. The nematicity found in most of these materials appears to be related to the magnetic long range order. We argue that the exoticity in the electronic properties are related to the subtlety in competing structural and magnetic instabilities present in these materials.
Elucidating the microscopic origin of nematic order in iron-based superconducting materials is important because the interactions that drive nematic order may also mediate the Cooper pairing. Nematic order breaks fourfold rotational symmetry in the iron plane, which is believed to be driven by either orbital or spin degrees of freedom. However, as the nematic phase often develops at a temperature just above or coincides with a stripe magnetic phase transition, experimentally determining the dominant driving force of nematic order is difficult. Here, we use neutron scattering to study structurally the simplest iron-based superconductor FeSe, which displays a nematic (orthorhombic) phase transition at $T_s=90$ K, but does not order antiferromagnetically. Our data reveal substantial stripe spin fluctuations, which are coupled with orthorhombicity and are enhanced abruptly on cooling to below $T_s$. Moreover, a sharp spin resonance develops in the superconducting state, whose energy (~4 meV) is consistent with an electron boson coupling mode revealed by scanning tunneling spectroscopy, thereby suggesting a spin fluctuation-mediated sign-changing pairing symmetry. By normalizing the dynamic susceptibility into absolute units, we show that the magnetic spectral weight in FeSe is comparable to that of the iron arsenides. Our findings support recent theoretical proposals that both nematicity and superconductivity are driven by spin fluctuations.
Strain is a powerful experimental tool to explore new electronic states and understand unconventional superconductivity. Here, we investigate the effect of uniaxial strain on the nematic and superconducting phase of single crystal FeSe using magnetotransport measurements. We find that the resistivity response to the strain is strongly temperature dependent and it correlates with the sign change in the Hall coefficient being driven by scattering, coupling with the lattice and multiband phenomena. Band structure calculations suggest that under strain the electron pockets develop a large in-plane anisotropy as compared with the hole pocket. Magnetotransport studies at low temperatures indicate that the mobility of the dominant carriers increases with tensile strain. Close to the critical temperature, all resistivity curves at constant strain cross in a single point, indicating a universal critical exponent linked to a strain-induced phase transition. Our results indicate that the superconducting state is enhanced under compressive strain and suppressed under tensile strain, in agreement with the trends observed in FeSe thin films and overdoped pnictides, whereas the nematic phase seems to be affected in the opposite way by the uniaxial strain. By comparing the enhanced superconductivity under strain of different systems, our results suggest that strain on its own cannot account for the enhanced high $T_c$ superconductivity of FeSe systems.
The cuprate superconductors are characterized by numerous ordering tendencies, with the nematic order being the most distinct form of order. Here the intertwinement of the electronic nematicity with superconductivity in cuprate superconductors is studied based on the kinetic-energy-driven superconductivity. It is shown that the optimized Tc takes a dome-like shape with the weak and strong strength regions on each side of the optimal strength of the electronic nematicity, where the optimized Tc reaches its maximum. This dome-like shape nematic-order strength dependence of Tc indicates that the electronic nematicity enhances superconductivity. Moreover, this nematic order induces the anisotropy of the electron Fermi surface (EFS), where although the original EFS with the four-fold rotation symmetry is broken up into that with a residual two-fold rotation symmetry, this EFS with the two-fold rotation symmetry still is truncated to form the Fermi arcs with the most spectral weight that locates at the tips of the Fermi arcs. Concomitantly, these tips of the Fermi arcs connected by the wave vectors ${bf q}_{i}$ construct an octet scattering model, however, the partial wave vectors and their respective symmetry-corresponding partners occur with unequal amplitudes, leading to these ordered states being broken both rotation and translation symmetries. As a natural consequence, the electronic structure is inequivalent between the $k_{x}$ and $k_{y}$ directions. These anisotropic features of the electronic structure are also confirmed via the result of the autocorrelation of the single-particle excitation spectra, where the breaking of the rotation symmetry is verified by the inequivalence on the average of the electronic structure at the two Bragg scattering sites. Furthermore, the strong energy dependence of the order parameter of the electronic nematicity is also discussed.
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