Inhomogeneous superconductivity in LuxZr1-xB12 dodecaborides with dynamic charge stripes
A. Azarevich, A. Bogach, V. Glushkov, S. Demishev, A. Khoroshilov, K. Krasikov, V. Voronov, N. Shitsevalova, V. Filipov, S. Gabani, K. Flachbart, A. Kuznetsov, … 展开作者
A. Azarevich, A. Bogach, V. Glushkov, S. Demishev, A. Khoroshilov, K. Krasikov, V. Voronov, N. Shitsevalova, V. Filipov, S. Gabani, K. Flachbart, A. Kuznetsov, S. Gavrilkin, K. Mitsen, S. J. Blundell, N. Sluchanko
We have studied the normal and superconductive state characteristics (resistivity, Hall coefficient, heat capacity and magnetization) of model strongly correlated electronic systems LuxZr1-xB12 with cooperative Jahn-Teller instability of the boron rigid cage and with dynamic charge stripes. It was found that these metals are s-wave dirty limit superconductors with a small mean free path of charge carriers l = 5 - 140 A and with a Cooper pair size changing non-monotonously in the range 450 - 4000 A. The parent ZrB12 and LuB12 borides are type-I superconductors, and Zr to Lu substitution induces a type-I - type-II phase transition providing a variation of the Ginzburg-Landau-Maki parameter in the limits 0.65 < kappa1,2 < 6. We argue in favor of the two-band scenario of superconductivity in LuxZr1-xB12 with gap values Delta_1 ~ 14 K and Delta_2 ~ 6 - 8 K, with pairing corresponding to strong coupling limit (lambda_e-ph ~ 1) in the upper band, and to weak coupling (lambda_e-ph ~ 0.1 - 0.4) in the lower one. A pseudogap Delta_ps-gap ~ 60 - 110 K is observed in LuxZr1-xB12 above Tc. We discuss also the possibility of anisotropic single-band superconductivity with stripe-induced both pair-breaking and anisotropy, and analyze the origin of unique enhanced surface superconductivity detected in these model compounds.
We report $^{139}$La nuclear magnetic resonance (NMR) measurements on La$_{2-x}$Sr$_x$CuO$_4$ ($0.07\leq x \leq 0.15$) and La$_{2-x}$Ba$_x$CuO$_4$ ($x=1/8$) single crystals, focusing on the spin freezing observed in 1/8-doped lanthanum cuprates. Charge stripe order seems to induce the inhomogeneous slowing down of spin fluctuations toward spin order and compete with superconductivity.
We propose a unified approach for describing the carrier localization, metal-insulator transitions (MITs) and stripe formation in high-$T_c$ cuprates. The ground-state energy of a carrier interacting with a defect and with lattice vibrations is calculated within the continuum model and adiabatic approximation. At low doping levels, hole carriers in $\rm{La}$-based systems with large-radius dopants are localized near the dopants with the formation of hydrogenic impurity centers.
We study competitions between charge uniform and inhomogeneous states in two-dimensional Hubbard models by using a variational Monte Carlo method. At realistic parameters for cuprate superconductors, emergent effective attraction of carriers generated from repulsive Coulomb interaction leads to charge/spin stripe ground states, which severely compete with uniform superconducting excited states in the energy scale of 10 K for the cuprates. Stripe period increases with decreasing hole doping $δ$, which agrees with the experiments for La-based cuprates at $δ$ = 1/8. For lower $δ$, we find a phase…
We carry out the variational Monte Carlo calculation to examine spatially inhomogeneous states in hole- and electron-doped cuprates. By using Gutzwiller approximation, we consider the excitations, arising from charge density, spin density and pair field, of the mean-field ground state of the t-J model. It leads to the stripe patterns we have found numerically in a generalized t-J-type model including mass renormalization from the electron-phonon coupling. In the hole-doped side, a robust d-wave superconducting order results in the formation of the half-doped antiferromagnetic resonating-valenc…
We studied electronic states in vortex cores of slightly overdoped Bi2Sr2CaCu2Ox by scanning tunneling spectroscopy. We have found that they have stripe structures with a 4a0 width extending along the Cu-O bond directions. Vortex core states are observed as two peaks at particle-hole symmetric positions in the energy gap. Along a stripe, the peak positions of vortex core states are constant and not influenced by the spatial variation of the energy gap Δ. Outer stripes have a larger energy than inner stripes. A mazelike pattern in the electronic states at E = +-Δhas been observed all over the s…
We study nickelate-centered and oxygen-centered stripe phases in doped La$_{2}$NiO$_{4}$ materials. We use an inhomogeneous Hartree-Fock and random-phase approximation approach including both electron-electron and electron-lattice(e-l) coupling for a layer of La$_{2}$NiO$_{4}$. We find that whether the ground state after commensurate hole doping comprises Ni-centered or O-centered charge-localized stripes depends sensitively on the e-l interaction. With increasing e-l interaction strength, a continuous transition from an O-centered stripe phase to a Ni-centered one is found. Various low- and h…
Inhomogeneous superconductivity in the high quality single crystals of ZrB12 (Tc = 6 K) has been studied using the heat capacity and x-ray diffraction (XRD) data. Evidence of two-band superconductivity with two branches of upper critical field Hc2(Tc) is obtained in a magnetic field applied along the [110] axis of the crystal. On the contrary, at H //[100], the only dependence Hc2(Tc) is observed. This finding is supplemented with the checkerboard-type patterns of the charge stripes in ZrB12 deduced from the detailed analysis of XRD data. These patterns are compared to the structure of the cha…
We investigate the structure of the pairing potential in the stripe phase of the two-dimensional Hubbard model. Based on the random phase approximation we discuss in detail the interactions in the charge- and spin channel and compare our calculations with related considerations in commensurate antiferromagnets. Our main finding is that due to the incommensurate charge-density wave formation the exchange of collective modes in the charge channel is significantly enhanced with respect to the spin bag approach whereas due to the inhomogeneous charge distribution the coupling to transverse spin fl…
Striped superconductivity with lattice distortions is investigated based on the three-band Hubbard model for high-Tc cuprates. A stable inhomogeneous striped state is determined in the low-temperature tetragonal (LTT) phase with lattice distortions using a quantum variational Monte Carlo method. The ground state has vertical or horizontal hole-rich arrays coexisting with incommensurate magnetism and superconductivity induced by several percent lattice distortions. The superconductivity order parameter oscillates according to the inhomogeneity in the antiferromagnetic background with its maxima…
We study a two-dimensional t-J model close to the Ising limit in which charge inhomogeneity is stabilized by an on-site potential e_s, by using diagonalization in a restricted Hilbert space and finite temperature Quantum Monte Carlo. Both site and bond centered stripes are considered and their similitudes and differences are analyzed. The amplitude of charge inhomogeneity is studied as e_s -> 0. Moreover, we show that the anti-phase domain ordering occurs at a much lower temperature than the formation of charge inhomogeneities and charge localization. Hole-hole correlations indicate a metallic…
We study inhomogeneous solutions of a 3+1-dimensional Einstein-Maxwell-scalar theory. Our results provide a holographic model of superconductivity in the presence of a charge density wave sourced by a modulated chemical potential. We find that below a critical temperature superconducting stripes develop. We show that they are thermodynamically favored over the normal state by computing the grand canonical potential. We investigate the dependence of the critical temperature on the modulation's wave vector, which characterizes the inhomogeneity. We find that it is qualitatively similar to that e…
We present a minimal model of a doped Mott insulator that simultaneously supports antiferromagnetic stripes and d-wave superconductivity. We explore the implications for the global phase diagram of the superconducting cuprates. At the unrestricted mean-field level, the various phases of the cuprates, including weak and strong pseudogap phases, and two different types of superconductivity in the underdoped and the overdoped regimes, find a natural interpretation. We argue that on the underdoped side, the superconductor is intrinsically inhomogeneous -- striped coexistence of of superconductivit…
We consider 2D surface superconductivity in high magnetic fields parallel to the surface. We demonstrate that the spin-orbit interaction at the surface changes the properties of the inhomogeneous superconducting Larkin-Ovchinnikov-Fulde-Ferrell state that develops above fields given by the paramagnetic criterion. Strong spin-orbit interaction significantly broadens the range of existence of the LOFF phase, which takes the form of periodic superconducting stripes running along the field direction on the surface, leading to the anisotropy of its properties. In connection with experiments by J.H.…
In this review we examine the experimental evidence for dynamic inhomogeneity, defining the length, time and energy scales of the relevant elementary excitations. The dynamics of the objects below and above Tc are examined in detail with femtosecond spectroscopy and compared with magnetic and other measurements. The dynamically inhomogeneous state is described theoretically by considering an interaction between electrons, spins and the lattice. By symmetry, only electrons in degenerate states can couple to the lattice and spins to give an anisotropic, d-wave symmetry interaction. The proposed …
We present a percolation theory for the high-$T_c$ oxides pseudogap and $T_c$ dependence on the hole level. The doping dependent inhomogeneous charge structure is modeled by a distribution which may represent the stripe morphology and yield a spatial distribution of local $T_c(r)$. The temperature onset of spatial dependent superconducting gap is identified with the vanishing of the pseudogap temperature $T^*$. The transition to a superconducting state corresponds to the percolation threshold among regions of different $T_c$. As a paradigm we use a Hubbard Hamiltonian with a mean field approxi…
Striped phases, in which spin, charge, and pairing correlations vary inhomogeneously in the CuO_2 planes, are a known experimental feature of cuprate superconductors, and are also found in a variety of numerical treatments of the two dimensional Hubbard Hamiltonian. In this paper we use determinant Quantum Monte Carlo to show that if a stripe density pattern is imposed on the model, the d-wave pairing vertex is significantly enhanced. We attribute this enhancement to an increase in antiferromagnetic order which is caused by the appearence of more nearly half-filled regions when the doped holes…
Low-valent nickelates R$_{n+1}$Ni$_n$O$_{2n+2}$ (R = rare earth) containing Ni$^{1+}$ (d$^{9}$) with a quasi-two-dimensional (quasi-2D) square planar coordination geometry possess structural and electronic properties that are similar to those of high-Tc cuprates, including superconductivity itself in the doped infinite layer ($n = \infty$) RNiO$_2$ system. Within this R$_{n+1}$Ni$_n$O$_{2n+2}$ nickelate family, the crystallographic isomorphs Pr$_4$Ni$_3$O$_8$ and La$_4$Ni$_3$O$_8$ exhibit singularly different ground states: Pr$_4$Ni$_3$O$_8$ is metallic and La$_4$Ni$_3$O$_8$ is a charge- and s…
We investigate the microscopic mechanism of charge instabilities and the formation of inhomogeneous states in systems with strong electron correlations. It is demonstrated that within a strong coupling expansion the single-band Hubbard model shows an instability towards phase separation and extend the approach also for an analysis of phase separation in the Hubbard-Kanamori hamiltonian as a prototypical multiband model. We study the pairing fluctuations on top of an inhomogeneous stripe state where superconducting correlations in the extended s-wave and d-wave channels correspond to (anti)boun…
The discovery of charge- and spin-density-wave (CDW/SDW) orders in superconducting cuprates has altered our perspective on the nature of high-temperature superconductivity (SC). However, it has proven difficult to fully elucidate the relationship between the density wave orders and SC. Here using resonant soft X-ray scattering we study the archetypal cuprate, La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) over a broad doping range. We reveal the existence of two types of CDW orders in LSCO, namely CDW stripe order and CDW short-range order (SRO). While the CDW-SRO is suppressed by SC, it is partially transfor…
Inhomogeneous s-wave superconductivity is studied in the two-dimensional, square lattice attractive Hubbard Hamiltonian using the Bogoliubov-de Gennes (BdG) mean field approximation. We find that at weak coupling, and for densities mainly below half-filling, an inhomogeneous interaction in which the on-site interaction $U_i$ takes on two values, $U_i=0, 2U$ results in a larger zero temperature pairing amplitude, and that the superconducting $T_c$ can also be significantly increased, relative to a uniform system with $U_i=U$ on all sites. These effects are observed for stripe, checkerboard, and…
Several recent experiments have revealed that the charge density $ρ$ in a given compound (mostly underdoped) is intrinsic inhomogeneous with large nanoscale spatial variations. Therefore it is appropriate to define a local charge density $ρ(r)$. These differences in the local charge concentration yield insulator and metallic regions, either in an intrinsic granular or in a stripe morphology. In the metallic region, the inhomogeneous charge density produces spatial or local distributions of superconducting critical temperatures $T_c(r)$ and zero temperature gap $Δ_0(r)$. We propose that the sup…
We studied experimentally the effect of a stripe-like domain structure in a ferromagnetic BaFe_{12}O_{19} substrate on the magnetoresistance of a superconducting Pb microbridge. The system was designed in such a way that the bridge is oriented perpendicular to the domain walls. It is demonstrated that depending on the ratio between the amplitude of the nonuniform magnetic field B_0, induced by the ferromagnet, and the upper critical field H_{c2} of the superconducting material, the regions of the reverse-domain superconductivity in the H-T plane can be isolated or can overlap (H is the externa…
We study s-wave superconductivity in the two-dimensional square lattice attractive Hubbard Hamiltonian for various inhomogeneous patterns of interacting sites. Using the Bogoliubov-de Gennes (BdG) mean field approximation, we obtain the phase diagram for inhomogeneous patterns in which the on-site attractive interaction U_i between the electrons takes on two values, U_i=0 and -U/(1-f) (with f the concentration of non-interacting sites) as a function of average electron occupation per site n, and study the evolution of the phase diagram as f varies. In certain regions of the phase diagram, inho…
We propose a general theory for the critical $T_c$ and pseudogap $T^*$ temperature dependence on the doping concentration for high-$T_c$ oxides, taking into account the charge inhomogeneities in the $CuO_2$ planes. The well measured experimental inhomogeneous charge density in a given compound is assumed to produce a spatial distribution of local $ρ(r)$. These differences in the local charge concentration is assumed to yield insulator and metallic regions, possibly in a stripe morphology. In the metallic region, the inhomogeneous charge density yields also spatial distributions of superconduct…
