Charge Stripe Order Research Articles

Engineering phase competition between stripe order and superconductivity in La1.88Sr0.12CuO4

Unconventional superconductivity often couples to other electronic orders in a cooperative or competing fashion. Identifying external stimuli that tune between these two limits is of fundamental interest. Here, we show that strain perpendicular to the copper-oxide planes couples directly to the competing interaction between charge stripe order and superconductivity in La1.88Sr0.12CuO4 (LSCO). Compressive c-axis pressure amplifies stripe order within the superconducting state, while having no impact on the normal state. By contrast, strain dramatically diminishes the magnetic field enhancement of stripe order in the superconducting state. These results suggest that c-axis strain acts as tuning parameter of the competing interaction between charge stripe order and superconductivity. This interpretation implies a uniaxial pressure-induced ground state in which the competition between charge order and superconductivity is reduced.

Light-induced coherent interlayer transport in stripe-ordered La1.6−xNd0.4SrxCuO4

We have investigated the photoexcited transient responses of stripe-ordered phase in a cuprate superconductor, ${\rm La}_{1.6-x}{\rm Nd}_{0.4}{\rm Sr}_{x}{\rm CuO}_{4}~(x = 0.12)$ using optical-pump terahertz (THz)-probe spectroscopy. Upon the near-infrared photoexcitation with the electric field polarized along the $c$-axis, a clear plasma edge appears in the THz reflection spectrum along the $c$-axis with its position nearly coinciding with the Josephson plasma resonance of similarly doped ${\rm La}_{2-x}{\rm Sr}_{x}{\rm CuO}_{4}~(x = 0.125)$ in the low-temperature superconducting phase. The appearance of light-induced plasma edge sustains up to the onset temperature of the charge-stripe order, indicating the inherent interplay between the light-induced phase and the charge-stripe order. The optical conductivity spectrum of the light-induced state is mostly reproduced by the Drude model with a scattering rate as small as a few meV, and its imaginary part does not exhibit $1/{\omega}$-divergence behavior in any temporal region after the photoexcitation. We discuss the possible origin of the observed coherent interlayer transport behavior as manifested by the narrow Drude response in the THz reflectivity along the $c$-axis.

Quantum Phase Diagram and Spontaneously Emergent Topological Chiral Superconductivity in Doped Triangular-Lattice Mott Insulators.

The topological superconducting state is a highly sought-after quantum state hosting topological order and Majorana excitations. In this Letter, we explore the mechanism to realize the topological superconductivity (TSC) in the doped Mott insulators with time-reversal symmetry (TRS). Through large-scale density matrix renormalization group study of an extended triangular-lattice t-J model on the six- and eight-leg cylinders, we identify a d+id-wave chiral TSC with spontaneous TRS breaking, which is characterized by a Chern number C=2 and quasi-long-range superconducting order. We map out the quantum phase diagram with by tuning the next-nearest-neighbor (NNN) electron hopping and spin interaction. In the weaker NNN-coupling regime, we identify a pseudogaplike phase with a charge stripe order coexisting with fluctuating superconductivity, which can be tuned into d-wave superconductivity by increasing the doping level and system width. The TSC emerges in the intermediate-coupling regime, which has a transition to a d-wave superconducting phase with larger NNN couplings. The emergence of the TSC is driven by geometrical frustrations and hole dynamics which suppress spin correlation and charge order, leading to a topological quantum phase transition.

Atomic-scale imaging of emergent order at a magnetic field-induced Lifshitz transition.

The phenomenology and radical changes seen in material properties traversing a quantum phase transition have captivated condensed matter research over the past decades. Strong electronic correlations lead to exotic electronic ground states, including magnetic order, nematicity, and unconventional superconductivity. Providing a microscopic model for these requires detailed knowledge of the electronic structure in the vicinity of the Fermi energy, promising a complete understanding of the physics of the quantum critical point. Here, we demonstrate such a measurement at the surface of Sr3Ru2O7. Our results show that, even in zero field, the electronic structure is strongly C2 symmetric and that a magnetic field drives a Lifshitz transition and induces a charge-stripe order. We track the changes of the electronic structure as a function of field via quasiparticle interference imaging at ultralow temperatures. Our results provide a complete microscopic picture of the field-induced changes of the electronic structure across the Lifshitz transition.

Spin stripe fluctuations in antiferromagnetic Pr2−xSrxNiO4+δ

We report inelastic neutron scattering study of the antiferromagnetic spin stripe fluctuations above the spin stripe melting temperature ${\mathrm{T}}_{so}\ensuremath{\approx}190\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ in the hole doped ${\mathrm{Pr}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{NiO}}_{4+\ensuremath{\delta}}$ with stripe incommensurability $\ensuremath{\epsilon}=0.33$. The fluctuations are nondispersive and detected upto 10 meV at the incommensurate wave vector indicating a persisting instantaneous spin and charge stripe correlation above ${\mathrm{T}}_{so}$, while they are strongly diminished already below the charge stripe melting temperature ${\mathrm{T}}_{co}\ensuremath{\approx}255\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, which indicates that static charge stripe order is essential for the dynamical spin stripe correlation to exist. Furthermore, it also suggests that the presence of spin stripe fluctuations is not a prerequisite for the formation of static charge stripes.

Crystal symmetry of stripe-ordered La1.88Sr0.12CuO4

We present a combined x-ray and neutron diffraction study of the stripe-ordered superconductor ${\mathrm{La}}_{1.88}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_{4}$. The average crystal structure is consistent with the orthorhombic $Bmab$ space group as commonly reported in the literature. This structure, however, is not symmetry compatible with a second-order phase transition into the stripe order phase, and as we report here, numerous Bragg peaks forbidden in the $Bmab$ space group are observed. We have studied and analyzed these $Bmab$-forbidden Bragg reflections. Fitting of the diffraction intensities yields monoclinic lattice distortions that are symmetry consistent with charge stripe order.

Unveiling Unequivocal Charge Stripe Order in a Prototypical Cuprate Superconductor.

In the cuprates, high-temperature superconductivity, spin-density-wave order, and charge-density-wave (CDW) order are intertwined, and symmetry determination is challenging due to domain formation. We investigated the CDW in the prototypical cuprate La_{1.88}Sr_{0.12}CuO_{4} via x-ray diffraction employing uniaxial pressure as a domain-selective stimulus to establish the unidirectional nature of the CDW unambiguously. A fivefold enhancement of the CDW amplitude is found when homogeneous superconductivity is partially suppressed by magnetic field. This field-induced state provides an ideal search environment for a putative pair-density-wave state.

Intertwined spin, charge, and pair correlations in the two-dimensional Hubbard model in the thermodynamic limit

The high-temperature superconducting cuprates are governed by intertwined spin, charge, and superconducting orders. While various state-of-the-art numerical methods have demonstrated that these phases also manifest themselves in doped Hubbard models, they differ on which is the actual ground state. Finite-cluster methods typically indicate that stripe order dominates, while embedded quantum-cluster methods, which access the thermodynamic limit by treating long-range correlations with a dynamical mean field, conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in the doped single-band Hubbard model using a quantum Monte Carlo dynamical cluster approximation (DCA) method. By resolving both the fluctuating spin and charge orders using DCA, we demonstrate that they survive in the doped Hubbard model in the thermodynamic limit. This discovery also provides an opportunity to study the influence of fluctuating stripe correlations on the model's pairing correlations within a unified numerical framework. Using this approach, we also find evidence for pair-density-wave correlations whose strength is correlated with that of the stripes.

Superconductivity from Charge Order in Cuprates

Superconductivity in layered cuprates is induced by doping holes into a parent antiferromagnetic insulator. It is now recognized that another common emergent order involves charge stripes, and our understanding of the relationship between charge stripes and superconductivity has been evolving. Here we review studies of 214 cuprate families obtained by doping La$_2$CuO$_4$. Charge-stripe order tends to compete with bulk superconductivity; nevertheless, there is plentiful evidence that it coexists with two-dimensional superconductivity. This has been interpreted in terms of pair-density-wave superconductivity, and the perspective has shifted from competing to intertwined orders. In fact, a new picture of superconductivity based on pairing within charge stripes has been proposed, as we discuss.

Robust d-Wave Superconductivity in the Square-Lattice t-J Model.

Unravelling competing orders emergent in doped Mott insulators and their interplay with unconventional superconductivity is one of the major challenges in condensed matter physics. To explore the possible superconducting state in a doped Mott insulator, we study the square-lattice t-J model with both the nearest-neighbor and next-nearest-neighbor electron hoppings and spin interactions. By using the state-of-the-art density matrix renormalization group calculation with imposing charge U(1) and spin SU(2) symmetries on the six-leg cylinders, we establish a quantum phase diagram including three phases: a stripe charge density wave phase, a superconducting phase without static charge order, and a superconducting phase coexistent with a weak charge stripe order. Crucially, we demonstrate that the superconducting phase has a power-law pairing correlation that decays much slower than the charge density and spin correlations, which is a quasi-1D descendant of the uniform d-wave superconductor in two dimensions. These findings reveal that enhanced charge and spin fluctuations with optimal doping is able to produce robust d-wave superconductivity in doped Mott insulators, providing a foundation for connecting theories of superconductivity to models of strongly correlated systems.

Superconductivity emerging from a stripe charge order in IrTe2 nanoflakes

Superconductivity in the vicinity of a competing electronic order often manifests itself with a superconducting dome, centered at a presumed quantum critical point in the phase diagram. This common feature, found in many unconventional superconductors, has supported a prevalent scenario in which fluctuations or partial melting of a parent order are essential for inducing or enhancing superconductivity. Here we present a contrary example, found in IrTe2 nanoflakes of which the superconducting dome is identified well inside the parent stripe charge ordering phase in the thickness-dependent phase diagram. The coexisting stripe charge order in IrTe2 nanoflakes significantly increases the out-of-plane coherence length and the coupling strength of superconductivity, in contrast to the doped bulk IrTe2. These findings clarify that the inherent instabilities of the parent stripe phase are sufficient to induce superconductivity in IrTe2 without its complete or partial melting. Our study highlights the thickness control as an effective means to unveil intrinsic phase diagrams of correlated van der Waals materials.

Thermoelectric properties of the stripe-charge ordering phases in IrTe2

We investigate the effects of stripe-charge ordering on the thermoelectric power of ${\mathrm{IrTe}}_{2}$, together with other transport properties, including the resistivity, thermal conductivity, and Hall effect. At the stripe-charge ordering transitions, clear transport anomalies such as abrupt changes in the thermoelectric power and Hall effect are observed and attributed to multiband conduction due to stripe-order-driven Fermi surface (FS) reconstruction. This FS reconstruction depends sensitively on intralayer charge modulations and interlayer staircaselike arrangements, leading to complex sign changes in the thermoelectric power. These results are in good agreement with the Boltzmann transport calculations based on the reconstructed FS and confirm the strong impact of the stripe charge order on the intrinsic charge conduction in ${\mathrm{IrTe}}_{2}$.

Antiferromagnetism, charge ordering and stretched Ni–O bond in Ln4Ni3O8 (Ln = La, Nd)

Superconductivity was recently observed in Sr-doped NdNiO2 film after a long pursuit, which inspires us to investigate another Ruddlesden–Popper-based nickelate Nd4Ni3O8 which may hold an antiferromagnetic order and a charge stripe order. Through ab initio calculations, we find that the obtained results turn out to be similar to those of La4Ni3O8. However, we propose that Ni1+ ions in the charge stripe order observed in La4Ni3O8 are in fact antiferromagnetically coupled through a twofold double-exchange mediated by the intermediate Ni2+ ion and the stretched Ni1+–O bond. Under high pressure, the extension of the stretched Ni1+–O bond is not favored and the system will be pushed into a meta-stable insulating state. Our picture can successfully explain the temperature dependence of resistivity under high pressure of La4Ni3O8, and shows also consistency with the insulating behavior of Nd4Ni3O8 observed in recent experiment. Considering a +1.33 average valence of Ni in Nd4Ni3O8, which is very close to that of the Sr-doped NdNiO2, our results support the earlier proposal that a possible way leading to metallicity and even superconductivity is to suppress the existing antiferromagnetism and charge ordering.

Charge-stripe order, antiferromagnetism, and spin dynamics in the cuprate-analog nickelate La4Ni3O8

We report a muon spin rotation ($\mu$SR) study of the cuprate-analog nickelate La$_4$Ni$_3$O$_8$, which undergoes a transition at 105 K to a low-temperature phase with charge-stripe and antiferromagnetic (AFM) order on square planar NiO$_2$ layers. Zero-field $\mu$SR shows that this transition is abrupt and that the AFM configuration is commensurate. Comparison of observed muon precession frequencies with Ni dipolar field calculations yields Ni moments $\lesssim 0.5\mu_B$. Dynamic muon spin relaxation above 105 K suggests critical slowing of Ni spin fluctuations, but is inconsistent with corresponding $^{139}$La NMR results. Critical slowing and an abrupt transition are also observed in the planar cuprate AFM La$_2$CuO$_{4+\delta}$, where they are evidence for weakly interplanar-coupled two-dimensional AFM spin fluctuations, but our $\mu$SR data do not agree quantitatively with theoretical predictions for this scenario.

Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene

Bilayer graphene can be modified by rotating (twisting) one layer with respect to the other. The interlayer twist gives rise to a moiré superlattice that affects the electronic motion and alters the band structure1-4. Near a 'magic angle' of twist2,4, where the emergence of a flat band causes the charge carriers to slow down3, correlated electronic phases including Mott-like insulators and superconductors were recently discovered5-8 by using electronic transport. These measurements revealed an intriguing similarity between magic-angle twisted bilayer graphene and high-temperature superconductors, which spurred intensive research into the underlying physical mechanism9-14. Essential clues to this puzzle, such as the symmetry and spatial distribution of the spectral function, can be accessed through scanning tunnelling spectroscopy. Here we use scanning tunnelling microscopy and spectroscopy to visualize the local density of states and charge distribution in magic-angle twisted bilayer graphene. Doping the sample to partially fill the flat band, we observe a pseudogap phase accompanied by a global stripe charge order that breaks the rotational symmetry of the moiré superlattice. Both the pseudogap and the stripe charge order disappear when the band is either empty or full. The close resemblance to similar observations in high-temperature superconductors15-21 provides new evidence of a deeper link underlying the phenomenology of these systems.

Spin Stripe Order in a Square Planar Trilayer Nickelate.

Trilayer nickelates, which exhibit a high degree of orbital polarization combined with an electron count (d^{8.67}) corresponding to overdoped cuprates, have been identified as a promising candidate platform for achieving high-T_{c} superconductivity. One such material, La_{4}Ni_{3}O_{8}, undergoes a semiconductor-insulator transition at ∼105 K, which was recently shown to arise from the formation of charge stripes. However, an outstanding issue has been the origin of an anomaly in the magnetic susceptibility at the transition and whether it signifies the formation of spin stripes akin to single layer nickelates. Here we report single crystal neutron diffraction measurements (both polarized and unpolarized) that establish that the ground state is indeed magnetic. The ordering is modeled as antiferromagnetic spin stripes that are commensurate with the charge stripes, the magnetic ordering occurring in individual trilayers that are essentially uncorrelated along the crystallographic c axis. A comparison of the charge and spin stripe order parameters reveals that, in contrast to single-layer nickelates such as La_{2-x}Sr_{x}NiO_{4} as well as related quasi-2D oxides including manganites, cobaltates, and cuprates, these orders uniquely appear simultaneously, thus demonstrating a stronger coupling between spin and charge than in these related low-dimensional correlated oxides.

Charge-stripe crystal phase in an insulating cuprate.

High-temperature (high-Tc) superconductivity in cuprates arises from carrier doping of an antiferromagnetic Mott insulator. This carrier doping leads to the formation of electronic liquid-crystal phases1. The insulating charge-stripe crystal phase is predicted to form when a small density of holes is doped into the charge-transfer insulator state1-3, but this phase is yet to be observed experimentally. Here, we use surface annealing to extend the accessible doping range in Bi-based cuprates and realize the lightly doped charge-transfer insulating state of the cuprate Bi2Sr2CaCu2O8+x. In this insulating state with a charge transfer gap on the order of ~1 eV, our spectroscopic imaging scanning tunnelling microscopy measurements provide strong evidence for a unidirectional charge-stripe order with a commensurate 4a0 period along the Cu-O-Cu bond. Notably, this insulating charge-stripe crystal phase develops before the onset of the pseudogap and formation of the Fermi surface. Our work provides fresh insight into the microscopic origin of electronic inhomogeneity in high-Tc cuprates.

Revisiting Cu63 NMR evidence for charge order in superconducting La1.885Sr0.115CuO4

The presence of charge and spin stripe order in the La2CuO4-based family of superconductors continues to lead to new insight on the unusual ground state properties of high Tc cuprates. Soon after the discovery of charge stripe order at T(charge)=65K in Nd3+ co-doped LSCO ($T_{c}\simeq6$~K) [Tranquada et al., Nature {\bf 375} (1995) 561], Hunt et al. demonstrated that La$_{1.48}$Nd$_{0.4}$Sr$_{0.12}$CuO$_4$ and superconducting LSCO with x~1/8 (Tc ~ 30K) share nearly identical NMR anomalies near $T_{charge}$ of the former [Phys. Rev. Lett. {\bf 82} (1999) 4300]. Their inevitable conclusion that LSCO also undergoes charge order at a comparable temperature became controversial, because diffraction measurements at the time were unable to detect Bragg peaks associated with charge order. Recent advances in x-ray diffraction techniques finally led to definitive confirmations of the charge order Bragg peaks in LSCO with an onset at as high as T(charge)=80K. Meanwhile, improved instrumental technology has enabled routine NMR measurements that were not feasible two decades ago. Motivated by these new developments, we revisit the charge order transition of a LSCO single crystal based on 63Cu NMR techniques. We demonstrate that 63Cu NMR properties of the nuclear spin $I_{z}$ = -1/2 to +1/2 central transition below T(charge) exhibit unprecedentedly strong dependence on the measurement time scale set by the NMR pulse separation time $\tau$; a new kind of anomalous, very broad wing-like 63Cu NMR signals gradually emerge below T(charge) only for extremely short $\tau \lesssim 4~\mu$s, while the spectral weight of the normal NMR signals is progressively wiped out. The NMR linewidth and relaxation rates depend strongly on $\tau$ below T(charge), and their enhancement in the charge ordered state indicates that charge order turns on strong but inhomogeneous growth of Cu spin-spin correlations.

Charge-Stripe Order and Superconductivity in Ir1\u2212xPtxTe2

A combined resistivity and hard x-ray diffraction study of superconductivity and charge ordering in Ir Ir1−xPtxTe2, as a function of Pt substitution and externally applied hydrostatic pressure, is presented. Experiments are focused on samples near the critical composition xc ~ 0.045 where competition and switching between charge order and superconductivity is established. We show that charge order as a function of pressure in Ir0.95Pt0.05Te2 is preempted — and hence triggered — by a structural transition. Charge ordering appears uniaxially along the short crystallographic (1, 0, 1) domain axis with a (1/5, 0, 1/5) modulation. Based on these results we draw a charge-order phase diagram and discuss the relation between stripe ordering and superconductivity.

Stability of charge-stripe ordered La2−xSrxNiO4+δ at one third doping

The stability of charge ordered phases is doping dependent, with different materials having particularly stable ordered phases. In the half filled charge ordered phases of the cuprates this occurs at one eighth doping, whereas in charge-stripe ordered La2−xSrxNiO4+δ there is enhanced stability at one third doping. In this paper we discuss the known details of the charge-stripe order in La2−x SrxNiO4+δ, and how these properties lead to the one third doping stability.