Interlayer transport in high-$T_C$ cuprates is mediated by superconducting tunneling across the CuO$_2$ planes. For this reason, the terahertz frequency optical response is dominated by one or more Josephson plasma resonances and becomes highly nonlinear at fields for which the tunneling supercurrents approach their critical value, $I_C$. These large terahertz nonlinearities are in fact a hallmark of superconducting transport. Surprisingly, however, they have been documented in La$_{2-x}$Ba$_x$CuO$_4$ also above $T_C$ for doping values near $x=1/8$, and interpreted as an indication of superfluidity in the stripe phase. Here, Electric Field Induced Second Harmonic (EFISH) is used to study the dynamics of time-dependent interlayer voltages when La$_{2-x}$Ba$_x$CuO$_4$ is driven with large-amplitude terahertz pulses, in search of other characteristic signatures of Josephson tunnelling in the normal state. We show that this method is sensitive to the voltage anomalies associated with 2$π$ Josephson phase slips, which near $x=1/8$ are observed both below and above $T_C$. These results document a new regime of nonlinear transport that shares features of fluctuating stripes and superconducting phase dynamics.
The striped cuprate La$_{2-x}$Ba$_x$CuO$_4$ ($x=\frac18)$ undergoes several transitions below the charge-ordering temperature $T_{co}$ = 54 K. From Nernst experiments, we find that, below $T_{co}$, there exists a large, anomalous Nernst signal $e_{N,even}(H,T)$ that is symmetric in field $H$, and remains finite as $H\to 0$. The time-reversal violating signal suggests that, below $T_{co}$, vortices of one sign are spontaneously created to relieve interlayer phase frustration.
We report on a thermoelectric investigation of the stripe and superconducting phases of the cuprate La$_{2-x}$Ba$_{x}$CuO$_{4}$ near the $x=1/8$ doping known to host stable stripes. We use the doping and magnetic field dependence of field-symmetric Nernst effect features to delineate the phenomenology of these phases. Our measurements are consistent with prior reports of time-reversal symmetry breaking signatures above the superconducting $T_{\rm c}$, and crucially detect a sharp, robust, field-invariant peak at the stripe charge order temperature, $T_{\rm {\scriptscriptstyle CO}}$. Our observ…
Optical excitation of stripe-ordered La$_{2-x}$Ba$_x$CuO$_4$ has been shown to transiently enhance superconducting tunneling between the CuO$_2$ planes. This effect was revealed by a blue-shift, or by the appearance of a Josephson Plasma Resonance in the terahertz-frequency optical properties. Here, we show that this photo-induced state can be strengthened by the application of high external magnetic fields oriented along the c-axis. For a 7-Tesla field, we observe up to a ten-fold enhancement in the transient interlayer phase correlation length, accompanied by a two-fold increase in the relax…
The interplay between charge order and superconductivity remains one of the central themes of research in quantum materials. In the case of cuprates, the coupling between striped charge fluctuations and local electromagnetic fields is especially important, as it affects transport properties, coherence and dimensionality of superconducting correlations. Here, we study the emission of coherent terahertz radiation in single-layer cuprates of the La$_{2-x}$Ba$_x$CuO$_4$ family, for which this effect is expected to be forbidden by symmetry. We find that emission vanishes for compounds in which the …
The CuO-planes of high-T_c superconductors were found to consist of geometric stripes with alternating superconducting and antiferromagnetic areas. Here we will investigate the repulsive Hubbard model of striped clusters as a possible microscopic description of the superconducting elements. The focus of our attention lies on the superconducting properties. We report in agreement with the square Hubbard model a signal in the d-wave channel and investigate its dependence on system size, cluster shape and interaction strength.
Striped high-$T_{\rm c}$ superconductors such as La$_{2-y-x}$Nd$_{y}$Sr$_x$CuO$_4$ and La$_{2-x}$Ba$_{x}$CuO$_4$ near $x=1/8$ show a fascinating competition between spin and charge order and superconductivity. A theory for these systems therefore has to capture both the spin correlations of an antiferromagnet and the pair correlations of a superconductor. For this purpose we present here an effective Hartree-Fock theory incorporating both electron pairing with finite center-of-mass momentum and antiferromagnetism. We show that this theory reproduces the key experimental features such as the fo…
Recent transport experiments in the original cuprate high temperature superconductor, {La$_{2-x}$Ba$_x$CuO$_4$}, have revealed a remarkable sequence of transitions and crossovers which give rise to a form of dynamical dimensional reduction, in which a bulk crystal becomes essentially superconducting in two directions while it remains poorly metallic in the third. We identify these phenomena as arising from a distinct new superconducting state, the "striped superconductor," in which the superconducting order is spatially modulated, so that its volume average value is zero. Here, in addition to …
We present results of magnetic neutron diffraction experiments on the co-doped super-oxygenated La(2-x)Sr(x)CuO(4+y) (LSCO+O) system with x=0.09. The spin-density wave has been studied and we find long-range incommensurate antiferromagnetic order below T_N coinciding with the superconducting ordering temperature T_c=40 K. The incommensurability value is consistent with a hole-doping of n_h~1/8, but in contrast to non-superoxygenated La(2-x)Sr(x)CuO(4) with hole-doping close to n_h ~ 1/8 the magnetic order parameter is not field-dependent. We attribute this to the magnetic order being fully dev…
In a very interesting recent Letter\cite{berg}, the authors suggested that a novel form of superconducting state is realized in La$_{2-x}$Ba$_x$CuO$_4$ with $x$ close to 1/8. This suggestion was based on experiments\cite{li} on this compound which found predominantly two-dimensional (2D) characters of the superconducting state, with extremely weak interplane coupling. Later this specific form of superconducting state was termed striped superconductors\cite{berg08}. The purpose of this note is to point out that the suggested form\cite{berg} of the superconducting order parameter can be detected…
The interplay of charge orders with superconductivity in underdoped cuprates at high magnetic fields ($H$) is an open question, and even the value of the upper critical field ($H_{c2}$), a measure of the strength of superconductivity, has been the subject of a long-term debate. We combined three complementary transport techniques on underdoped La$_{1.8-x}$Eu$_{0.2}$Sr$_{x}$CuO$_{4}$ with a "striped" charge order and a low $H=0$ transition temperature $T_{c}^{0}$, to establish the $T-H$ phase diagram and reveal the ground states in CuO$_2$ planes: a superconductor, a wide regime of superconduct…
By in-situ change of polarization a small splitting of the Zhang-Rice singlet state band near the Fermi level has been resolved for optimum doped (x=0.4) Bi$_{2}$Sr$_{2-x}$La$_{x}$CuO$_{6+δ}$ at the (pi,0)-point (R.Manzke et al. PRB 63, R100504 (2001). Here we treat the momentum dependence and lineshape of the split band by photoemission in the EDC-mode with very high angular and energy resolution. The splitting into two destinct emissions could also be observed over a large portion of the major symmetry line $Γ$M, giving the dispersion for the individual contributions. Since bi-layer effects …
A model of an anti-phase modulated d-wave superconductor has been proposed to describe the decoupling between Cu-O planes in 1/8 doped La$_{2-x}$Ba$_{x}$CuO$_{4}$. Unlike a uniform d-wave superconductor, this model exhibits an extended Fermi surface. Within Bogoliubov-de Gennes theory, we study the mixed state of this model and compare it to the case of a uniform d-wave superconductor. We find a periodic structure of the low-energy density of states, with a period that is proportional to $B$, corresponding to Landau levels that are a coherent mixture of particles and holes. These results are a…
We address the kinetic competition between charge striped order and superconductivity in La$_{1.675}$Eu$_{0.2}$Sr$_{0.125}$CuO$_{4}$. Ultrafast optical excitation is tuned to a mid-infrared vibrational resonance that destroys charge order and promptly establishes transient coherent interlayer coupling in this material. This effect is evidenced by the appearance of a longitudinal plasma mode reminiscent of a Josephson plasma resonance. We find that coherent interlayer coupling can be generated up to the charge order transition $T_{CO} \approx$ 80 K, far above the equilibrium superconducting tra…
We present a combined magnetic neutron scattering and muon spin rotation study of the nature of the magnetic and superconducting phases in electronically phase separated La(2-x)Sr(x)CuO(4+y), x = 0.04, 065, 0.09. For all samples, we find long-range modulated magnetic order below T_N ~ T_c = 39 K. In sharp contrast wit oxygen-stoichiometric La(2-x)Sr(x)CuO(4), we find that the magnetic propagation vector as well as the ordered magnetic moment is independent of Sr content and consistent with that of the 'striped' cuprates. Our study provides direct proof that superoxygenation in La(2-x)Sr(x)CuO(…
We show, using density matrix renormalization group calculations complemented by field theoretic arguments, that the spin gapped phase of the one dimensional Kondo-Heisenberg model exhibits quasi-long range superconducting correlations {\it only} at a non-zero momentum. The local correlations in this phase resemble those of the pair density wave state which was recently proposed to describe the phenomenology of the striped ordered high temperature superconductor {La$_{2-x}$Ba$_x$% CuO$_4$}, in which the spin, charge, and superconducting orders are strongly intertwined.
Recent angle-resolved $c$-axis resistivity measurements of the stripe-ordered La$_{2-x}$Ba$_x$CuO$_4$ (LBCO) with $x=1/8$ revealed an unexpected dependence on the direction of the in-plane magnetic field. We argue that these and other available data for the $c$-axis transport point to the existence of superconducting pairs of two different types in the $x=1/8$ LBCO below the stripe ordering temperature. The pairs of one type carry finite momentum and are confined to the Cu-O planes; the pairs of other type (probably the conventional $d$-wave with zero momentum) propagate along narrow conductin…
New advances in x-ray diffraction, extended x-ray absorption fine structure EXAFS and x-ray absorption near edge structure XANES using synchrotron radiation have now provided compelling evidence for a short range charge density wave phase (CDW) called striped phase in the CuO2 plane of all cuprate high temperature superconductors. The CDW is associated with a bond order wave (BOW) and an orbital density wave (ODW) forming nanoscale puddles which coexist with superconducting puddles below Tc. The electronic CDW crystalline phase occurs around the hole doping 0.125 between the Mott charge transf…
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…
Even before the experimental discovery of spin- and charge-stripe order in La$_{2-x-y}$Nd$_y$Sr$_x$CuO$_4$ and La$_{2-x}$Ba$_x$CuO$_4$ at x = 1/8, stripe formation was predicted from theoretical considerations. Nevertheless, a consistent description of the complex coexistence of stripe order with superconductivity has remained a challenge. Here we introduce a Hartree-Fock decoupling scheme which unifies previous approaches and allows for a detailed analysis of the competition between antiferromagnetism and superconductivity in real and momentum space. We identify two distinct parameter regimes…
Grain boundary bicrystal Josephson junctions of the electron-doped infinite-layer superconductor Sr$_{1-x}$La$_x$CuO$_2$ ($x = 0.15$) were grown by pulsed laser deposition. BaTiO$_3$-buffered $24\,^\circ$ [001]-tilt symmetric SrTiO$_3$ bicrystals were used as substrates. We examined both Cooper pair (CP) and quasiparticle (QP) tunneling by electric transport measurements at temperatures down to 4.2\,K. CP tunneling revealed an extraordinary high critical current density for electron-doped cuprates of $j_c > 10^3\,$A/cm$^2$ at 4.2\,K. Thermally activated phase slippage was observed as dissipati…
Understanding the electron pairing in hole-doped cuprate superconductors has been a challenge, in particular because the "normal" state from which it evolves is unprecedented. Now, after three and a half decades of research, involving a wide range of experimental characterizations, it is possible to delineate a clear and consistent cuprate story. It starts with doping holes into a charge-transfer insulator, resulting in in-gap states. These states exhibit a pseudogap resulting from the competition between antiferromagnetic superexchange $J$ between nearest-neighbor Cu atoms (a real-space inter…
We analyze the pump wavelength dependence for the photo-induced enhancement of interlayer coupling in La1.885Ba0.115CuO4, which is promoted by optical melting of the stripe order. In the equilibrium superconducting state (T < Tc = 13 K), in which stripes and superconductivity coexist, time-domain THz spectroscopy reveals a photo-induced blue-shift of the Josephson Plasma Resonance after excitation with optical pulses polarized perpendicular to the CuO2 planes. In the striped, non-superconducting state (Tc < T < T_SO = 40 K) a transient plasma resonance similar to that seen below Tc appears fro…
