Charge Stripe Order Research Articles

Moir\xe9 Superstructure and Dimensional Crossover of 2D Electronic States on Nanoscale Lead Quantum Films

We investigate using scanning tunneling microscopy and spectroscopy electronic aspects of Moiré superstructures in nanoscale Pb quantum films grown on IrTe2, which is a unique layered material with charge-order transitions into stripe phases. Pb ultrathin films exhibit a Moiré superstructure due to the lattice mismatch of Pb and IrTe2, which produces strong lateral electronic modulation of hexagonal symmetry and discreet subbands. Moreover, strongly anisotropic or 1D electronic states are formed in Pb films as modulated by the stripe charge order. Present results indicate the controllability of lateral electronic structures of various ultrathin films by extra interfacial potentials due not only to Moiré superstructures but also to novel electronic orderings of substrates.

Evidence for a Nematic Phase in La_{1.75}Sr_{0.25}NiO_{4}.

Determining the nature of electronic states in doped Mott insulators remains a challenging task. In the case of tetragonal La_{2-x}Sr_{x}NiO_{4}, the occurrence of diagonal charge and spin stripe order in the ground state is now well established. In contrast, the nature of the high-temperature "disordered" state from which the stripe order develops has long been a subject of controversy, with considerable speculation regarding a polaronic liquid. Following the recent detection of dynamic charge stripes, we use neutron scattering measurements on an x=0.25 crystal to demonstrate that the dispersion of the charge-stripe excitations is anisotropic. This observation provides compelling evidence for the presence of electronic nematic order.

Cu nuclear magnetic resonance study of charge and spin stripe order inLa1.875Ba0.125CuO4

We present a Cu nuclear magnetic/quadrupole resonance study of the charge stripe ordered phase of LBCO, with detection of previously unobserved ('wiped-out') signal. We show that spin-spin and spin-lattice relaxation rates are strongly enhanced in the charge ordered phase, explaining the apparent signal decrease in earlier investigations. The enhancement is caused by magnetic, rather than charge fluctuations, conclusively confirming the long-suspected assumption that spin fluctuations are responsible for the wipeout effect. Observation of the full Cu signal enables insight into the spin and charge dynamics of the stripe-ordered phase, and measurements in external magnetic fields provide information on the nature and suppression of spin fluctuations associated with charge order. We find glassy spin dynamics, in agreement with previous work, and incommensurate static charge order with charge modulation amplitude similar to other cuprate compounds, suggesting that the amplitude of charge stripes is universal in the cuprates.

Evidence for strong lattice effects as revealed from huge unconventional oxygen isotope effects on the pseudogap temperature in La2−xSrxCuO4

The oxygen isotope ($^{16}$O/$^{18}$O) effect (OIE) on the pseudogap (charge-stripe ordering) temperature $T^{\ast}$ is investigated for the cuprate superconductor La$_{2-x}$Sr$_{x}$CuO$_{4}$ as a function of doping $x$ by means of x-ray absorption near edge structure (XANES) studies. A strong $x$ dependent and sign reversed OIE on $T^{\ast}$ is observed. The OIE exponent $\alpha_{T^{\ast}}$ systematically decreases from $\alpha_{T^{\ast}} = - 0.6(1.3)$ for $x = 0.15$ to $\alpha_{T^{\ast}} = - 4.4(1.1)$ for $x = 0.06$, corresponding to increasing $T^{\ast}$ and decreasing superconducting transition temperature $T_{c}$. Both $T^{\ast}(^{16}{\rm O})$ and $T^{\ast}(^{18}{\rm O})$ exhibit a linear doping dependence with different slopes and critical end points (where $T^{\ast}(^{16}{\rm O})$ and $T^{\ast}(^{18}{\rm O})$ fall to zero) at $x_{c}(^{16}{\rm O}) = 0.201(4)$ and $x_{c}(^{18}{\rm O}) = 0.182(3)$, indicating a large positive OIE of $x_{c}$ with an exponent of $\alpha_{x_{c}} = 0.84(22)$. The remarkably large and strongly doping dependent OIE on $T^{\ast}$ signals a substantial involvement of the lattice in the formation of the pseudogap, consistent with a polaronic approach to cuprate superconductivity and the vibronic character of its ground state.

Unconventional charge order in a co-doped high-Tc superconductor.

Charge-stripe order has recently been established as an important aspect of cuprate high-Tc superconductors. However, owing to the complex interplay between competing phases and the influence of disorder, it is unclear how it emerges from the parent high-temperature state. Here we report on the discovery of an unconventional ordered phase between charge-stripe order and (pseudogapped) metal in the cuprate La1.8−xEu0.2SrxCuO4. We use three complementary experiments—nuclear quadrupole resonance, nonlinear conductivity and specific heat—to demonstrate that the order appears through a sharp phase transition and exists in a dome-shaped region of the phase diagram. Our results imply that the new phase is a state, which preserves translational symmetry: a charge nematic. We thus resolve the process of charge-stripe development in cuprates, show that this nematic phase is distinct from high-temperature pseudogap and establish a link with other strongly correlated electronic materials with prominent nematic order.

D-Density Wave Scenario Description of the New Hidden Charge Order in Cuprates

In this paper, we show that the theory of high $T_c$ superconductivity based on a microscopic model with $d$-density wave (DDW) scenario in the pseudogap phase is able to reproduce some of the most important features of the recent experimentally discovered hidden charge order in several families of Cuprates. In particular, by computing and comparing energies of charge orders of different modulation directions derived from a full microscopic theory with $d$-density wave scenario, the axial charge order $\phi_{X(Y)}$ with wavevector $\mathbf{Q}=(Q_0,0)((0,Q_0))$ is shown to be unambiguously energetically more favorable over the diagonal charge order $\phi_{X\pm Y}$ with wavevector $\mathbf{Q}=(Q_0,\pm Q_0)$ at least in commensurate limit, to be expected also to hold even to more general incommensurate case, in agreement with experiment. The two types of axial charge order $\phi_X$ and $\phi_Y$ are degenerate by symmetry. We find that within the superconducting background, biaxial (checkerboard) charge order is energetically more favorable than uniaxial (stripe) charge order, and therefore checkerboard axial charge order should be the one observed in experiments, assuming a single domain of charge ordered state on each CuO$_2$ plane.

Nanoscale Superconducting Honeycomb Charge Order in IrTe2.

Entanglement of charge orderings and other electronic orders such as superconductivity is in the core of challenging physics issues of complex materials including high temperature superconductivity. Here, we report on the observation of a unique nanometer scale honeycomb charge ordering of the cleaved IrTe2 surface, which hosts a superconducting state. IrTe2 was recently established to exhibit an intriguing cascade of stripe charge orders. The stripe phases coexist with a hexagonal phase, which is formed locally and falls into a superconducting state below 3 K. The atomic and electronic structures of the honeycomb and hexagon pattern of this phase are consistent with the charge order nature, but the superconductivity does not survive on neighboring stripe charge order domains. The present work provides an intriguing physics issue and a new direction of functionalization for two-dimensional materials.

Multiple broken symmetries in stripedLa2−xBaxCuO4detected by the field-symmetric Nernst effect

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 observations suggest the onset of a nontrivial charge ordered phase at $T_{{\rm {\scriptscriptstyle CO}}}$, and the subsequent presence of spontaneously generated vortices over a broad temperature range before the emergence of bulk superconductivity in LBCO.

Neutron scattering study of spin ordering and stripe pinning in superconductingLa1.93Sr0.07CuO4

The relationships among charge order, spin fluctuations, and superconductivity in underdoped cuprates remain controversial. We use neutron scattering techniques to study these phenomena in La$_{1.93}$Sr$_{0.07}$CuO$_4$, a superconductor with a transition temperature of $T_c = 20$~K. At $T\ll T_c$, we find incommensurate spin fluctuations with a quasielastic energy spectrum and no sign of a gap within the energy range from 0.2 to 15 meV. A weak elastic magnetic component grows below $\sim10$~K, consistent with results from local probes. Regarding the atomic lattice, we have discovered unexpectedly strong fluctuations of the CuO$_6$ octahedra about Cu-O bonds, which are associated with inequivalent O sites within the CuO$_2$ planes. Furthermore, we observed a weak elastic $(3\bar{3}0)$ superlattice peak that implies a reduced lattice symmetry. The presence of inequivalent O sites rationalizes various pieces of evidence for charge stripe order in underdoped \lsco. The coexistence of superconductivity with quasi-static spin-stripe order suggests the presence of intertwined orders; however, the rotation of the stripe orientation away from the Cu-O bonds might be connected with evidence for a finite gap at the nodal points of the superconducting gap function.

Electron scattering, charge order, and pseudogap physics inLa1.6−xNd0.4SrxCuO4: An angle-resolved photoemission spectroscopy study

We report an angle-resolved photoemission study of the charge stripe ordered La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ system. A comparative and quantitative line shape analysis is presented as the system evolves from the overdoped regime into the charge ordered phase. On the overdoped side ($x=0.20$), a normal state anti-nodal spectral gap opens upon cooling below ~ 80 K. In this process spectral weight is preserved but redistributed to larger energies. A correlation between this spectral gap and electron scattering is found. A different lineshape is observed in the antinodal region of charge ordered Nd-LSCO $x=1/8$. Significant low-energy spectral weight appears to be lost. These observations are discussed in terms of spectral weight redistribution and gapping %of spectral weight originating from charge stripe ordering.

Hour-glass magnetic excitations induced by nanoscopic phase separation in cobalt oxides.

The magnetic excitations in the cuprate superconductors might be essential for an understanding of high-temperature superconductivity. In these cuprate superconductors the magnetic excitation spectrum resembles an hour-glass and certain resonant magnetic excitations within are believed to be connected to the pairing mechanism, which is corroborated by the observation of a universal linear scaling of superconducting gap and magnetic resonance energy. So far, charge stripes are widely believed to be involved in the physics of hour-glass spectra. Here we study an isostructural cobaltate that also exhibits an hour-glass magnetic spectrum. Instead of the expected charge stripe order we observe nano phase separation and unravel a microscopically split origin of hour-glass spectra on the nano scale pointing to a connection between the magnetic resonance peak and the spin gap originating in islands of the antiferromagnetic parent insulator. Our findings open new ways to theories of magnetic excitations and superconductivity in cuprate superconductors.

Rotated stripe order and its competition with superconductivity inLa1.88Sr0.12CuO4

We report the observation of a bulk charge modulation in La$_{1.88}$Sr$_{0.12}$CuO$_4$ (LSCO) with a characteristic in-plane wave-vector of (0.236, $\pm \delta$), with $\delta$=0.011 r.l.u. The transverse shift of the ordering wave-vector indicates the presence of rotated charge-stripe ordering, demonstrating that the charge ordering is not pinned to the Cu-O bond direction. On cooling through the superconducting transition, we find an abrupt change in the growth of the charge correlations and a suppression of the charge order parameter indicating competition between the two orderings. Orthorhombic LSCO thus helps bridge the apparent disparities between the behavior previously observed in the tetragonal "214" cuprates and the orthorhombic yttrium and bismuth-based cuprates and thus lends strong support to the idea that there is a common motif to charge order in all cuprate families.

Competing charge, spin, and superconducting orders in underdopedYBa2Cu3Oy

To explore the doping dependence of the recently discovered charge density wave (CDW) order in YBa2Cu3Oy, we present a bulk-sensitive high-energy x-ray study for several oxygen concentrations, including strongly underdoped YBa2Cu3O6.44. Combined with previous data around the so-called 1/8 doping, we show that bulk CDW order exists at least for hole concentrations (p) in the CuO2 planes of 0.078 <~ p <~ 0.132. This implies that CDW order exists in close vicinity to the quantum critical point for spin density wave (SDW) order. In contrast to the pseudogap temperature T*, the onset temperature of CDW order decreases with underdoping to T_CDW ~ 90K in YBa2Cu3O6.44. Together with a weakened order parameter this suggests a competition between CDW and SDW orders. In addition, the CDW order in YBa2Cu3O6.44 shows the same type of competition with superconductivity as a function of temperature and magnetic field as samples closer to p = 1/8. At low p the CDW incommensurability continues the previously reported linear increasing trend with underdoping. In the entire doping range the in-plane correlation length of the CDW order in b-axis direction depends only very weakly on the hole concentration, and appears independent of the type and correlation length of the oxygen-chain order. The onset temperature of the CDW order is remarkably close to a temperature T^\dagger that marks the maximum of 1/(T_1T) in planar 63^Cu NQR/NMR experiments, potentially indicating a response of the spin dynamics to the formation of the CDW. Our discussion of these findings includes a detailed comparison to the charge stripe order in La2-xBaxCuO4.

Melting of charge stripes in vibrationally driven La(1.875)Ba(0.125)CuO4: assessing the respective roles of electronic and lattice order in frustrated superconductors.

We report femtosecond resonant soft x-ray diffraction measurements of the dynamics of the charge order and of the crystal lattice in nonsuperconducting, stripe-ordered La1.875Ba0.125CuO4. Excitation of the in-plane Cu-O stretching phonon with a midinfrared pulse has been previously shown to induce a transient superconducting state in the closely related compound La1.675Eu0.2Sr0.125CuO4. In La1.875Ba0.125CuO4, we find that the charge stripe order melts promptly on a subpicosecond time scale. Surprisingly, the low temperature tetragonal (LTT) distortion is only weakly reduced, reacting on significantly longer time scales that do not correlate with light-induced superconductivity. This experiment suggests that charge modulations alone, and not the LTT distortion, prevent superconductivity in equilibrium.

Comparison of charge modulations in La1.875Ba0.125CuO4and YBa2Cu3O6.6

A charge modulation has recently been reported in (Y,Nd)Ba$_2$Cu$_3$O$_{6+x}$ [Ghiringhelli {\em et al.} Science 337, 821 (2013)]. Here we report Cu $L_3$ edge soft x-ray scattering studies comparing the lattice modulation associated with the charge modulation in YBa$_2$Cu$_3$O$_{6.6}$ with that associated with the well known charge and spin stripe order in La$_{1.875}$Ba$_{0.125}$CuO$_4$. We find that the correlation length in the CuO$_2$ plane is isotropic in both cases, and is $259 \pm 9$ \AA for La$_{1.875}$Ba$_{0.125}$CuO$_4$ and $55 \pm 15$ \AA for YBa$_2$Cu$_3$O$_{6.6}$. Assuming weak inter-planar correlations of the charge ordering in both compounds, we conclude that the order parameters of the lattice modulations in La$_{1.875}$Ba$_{0.125}$CuO$_4$ and YBa$_2$Cu$_3$O$_{6.6}$ are of the same order of magnitude.

Berry phase mechanism for optical gyrotropy in stripe-ordered cuprates

Optical gyrotropy, the lifting of degeneracy between left and right circularly polarized light, can be generated by either time-reversal or chiral symmetry breaking. In the high-${T}_{c}$ superconductor La${}_{2\ensuremath{-}x}$Ba${}_{x}$CuO${}_{4}$ (LBCO), gyrotropy onsets at the same temperature as charge stripe order, suggesting that the rotation of the stripe direction from one plane to the next generates a helical pattern that breaks chiral symmetry. In order to further test this chiral stacking hypothesis it is necessary to develop an understanding of the physical mechanisms by which chirality generates gyrotropy. In this paper we show that, in chiral metals, optical gyrotropy is a consequence of Berry curvature in momentum space. We describe a physical picture showing that gyrotropy in chiral metals is closely related to the anomalous Hall effect in itinerant ferromagnets. We then calculate the magnitude of the gyrotropic response for a given Berry curvature using the semiclassical picture of anomalous velocity and Boltzmann transport theory. To connect this physical picture with experiment, we calculate the Berry curvature in two tight-binding models. The first model is motivated by the structure of LBCO and illustrates how gyrotropy is created when stripe perturbations are added to a simple cubic model. In the second model, we examine the dramatic enhancement of the gyrotropic coefficient when Rashba spin-orbit coupling is introduced. The magnitude of the rotation of polarization on reflection expected based on these models is calculated and compared with experimental data.

Evolution of superconducting correlations within magnetic-field-decoupled La2−xBaxCuO4(x=0.095)

We explore the evolution of superconductivity in La(2-x)Ba(x)CuO(4) with x=0.095 in magnetic fields of up to 35 T applied perpendicular to the CuO(2) planes. Previous work on this material has shown that perpendicular fields enhance both charge and spin stripe order within the planes. We present measurements of the resistivity parallel and perpendicular to the planes, as well as the Hall effect. Measurements of magnetic susceptibility for fields of up to 15 T applied both parallel and perpendicular to the planes provide complementary measures of the superconductivity. We show that fields sufficient to destroy pair tunneling between the planes do not disrupt the superconducting correlations within the planes. In fact, we observe an onset of large amplitude but phase disordered superconductivity within the planes at approximately 30 K that is remarkably insensitive to field. With further cooling, we observe a phase-transition-like drop in the in-plane resistivity to an apparent state of superconductivity, despite the lack of phase coherence between the layers. These observations raise interesting questions concerning the identification of the upper critical field, where pairing is destroyed, in underdoped cuprates.

Checkerboard to stripe charge ordering transition in TbBaFe2O5

A combined neutron and x-ray diffraction study of TbBaFe2O5 reveals a rare checkerboard to charge ordering transition. TbBaFe2O5 is a mixed valent compound where Fe2+/Fe3+ ions are known to arrange into a stripe charge-ordered state below TV = 291 K, that consists of alternating Fe2+/Fe3+ stripes in the basal plane running along the b direction. Our measurements reveal that the stripe charge-ordering is preceded by a checkerboard charge-ordered phase between TV < T < T* = 308 K. The checkerboard ordering is stabilized by inter-site coulomb interactions which give way to a stripe state stabilized by orbital ordering.

Quantum phase transition from triangular to stripe charge order in NbSe 2

The competition between proximate electronic phases produces a complex phenomenology in strongly correlated systems. In particular, fluctuations associated with periodic charge or spin modulations, known as density waves, may lead to exotic superconductivity in several correlated materials. However, density waves have been difficult to isolate in the presence of chemical disorder, and the suspected causal link between competing density wave orders and high-temperature superconductivity is not understood. Here we used scanning tunneling microscopy to image a previously unknown unidirectional (stripe) charge-density wave (CDW) smoothly interfacing with the familiar tridirectional (triangular) CDW on the surface of the stoichiometric superconductor NbSe(2). Our low-temperature measurements rule out thermal fluctuations and point to local strain as the tuning parameter for this quantum phase transition. We use this quantum interface to resolve two longstanding debates about the anomalous spectroscopic gap and the role of Fermi surface nesting in the CDW phase of NbSe(2). Our results highlight the importance of local strain in governing phase transitions and competing phenomena, and suggest a promising direction of inquiry for resolving similarly longstanding debates in cuprate superconductors and other strongly correlated materials.

Enhanced charge stripe order of superconducting La2−xBaxCuO4in a magnetic field

The effect of a magnetic field on the charge stripe order in ${\mathrm{La}}_{2\ensuremath{-}\mathit{x}}{\mathrm{Ba}}_{\mathit{x}}{\mathrm{CuO}}_{4}$ has been studied by means of high-energy (100 keV) x-ray diffraction for charge carrier concentrations ranging from strongly underdoped to optimally doped. We find that charge stripe order can be significantly enhanced by a magnetic field applied along the $c$ axis, but only at temperatures and dopings where it coexists with bulk superconductivity at zero field. The field also increases stripe correlations between the planes, which can result in an enhanced frustration of the interlayer Josephson coupling. Close to the famous $x=\frac{1}{8}$ compound, where zero field stripe order is pronounced and bulk superconductivity is suppressed, charge stripe order is independent of a magnetic field. The results for ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Ba}}_{x}{\mathrm{CuO}}_{4}$ resemble recent observations in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+\ensuremath{\delta}}$ and, independent of potential differences in the microscopic origin of charge order in these two compounds, imply a very similar competition with three-dimensionally coherent superconductivity.