Synthesis, Structure, and Magnetic Properties of an Antiferromagnetic Spin-Ladder Complex: Bis(2,3-dimethylpyridinium) Tetrabromocuprate

The complex (2,3-dmpyH)2CuBr4 has been synthesized and its crystal packing determined by single-crystal X-ray diffraction (2,3-dmpyH = 2,3-dimethylpyridinium). The compound crystallizes in the triclinic space group P1. The crystal packing is characterized by the formation of a ladder structure for the CuBr4 anions showing short Br...Br contacts. The rungs of the ladder are formed via a crystallographic inversion center, while the rails are formed via unit cell translations. Variable temperature magnetic susceptibility measurements agree very well with the ladder model [Jrung = -3.10 cm-1 (-4.34 K) and Jrail = -6.02 cm-1 (-8.42 K)]. The assignment as a magnetic ladder is confirmed by first principles bottom-up theoretical calculations which conclude that Jrung = -3.49 cm-1 (-4.89 K) and Jrail = -7.79 cm-1 (-10.9 K), in very good agreement with the experimental values. They also support the absence of additional significant magnetic exchange within the crystals. Thus, (2,3-dmpyH)2CuBr4 represents the second reported example of a weak-exchange limit magnetic ladder (that is, one in which the exchange along the rail is stronger than that across the rung).

In-gap spin excitations and finite triplet lifetimes in the dilute singlet ground state system SrCu(2-x)Mgx(BO3)2

High resolution neutron scattering measurements on a single crystal of SrCu(2-x)Mgx(BO3)2 with x approximately 0.05 reveal the presence of new spin excitations within the gap of this quasi-two-dimensional, singlet ground state system. The application of a magnetic field induces Zeeman-split states associated with S=1/2 unpaired spins which are antiferromagnetically correlated with the bulk singlet. Substantial broadening of both the one- and two-triplet excitations in the doped single crystal is observed, as compared with pure SrCu2(BO3)2. Theoretical calculations using a variational algorithm and a single quenched magnetic vacancy on an infinite lattice are shown to qualitatively account for these effects.

Hopping conductivity in CaCu(2)O(3) single crystals

The resistivity, ρ, of the spin-ladder compound CaCu(2)O(3) is investigated between T∼130-450 K. The ρ(T) data measured for [Formula: see text] (along the Cu-O-Cu leg) and [Formula: see text] (along the Cu-O-Cu rungs), ρ(a)(T)>ρ(b)(T), exhibit an activated dependence, similar in both directions and characterized by a nearest-neighbour hopping followed by a variable-range hopping (VRH) regime when T is decreased. A detailed analysis of ρ(T) demonstrates that conventional d-dimensional models of the hopping conductivity, based on the electron localization in disordered systems, cannot interpret the experimental data at any d = 1, 2 or 3, leading to the mismatch of the characteristic energies and/or unphysical values of the characteristic length scales. The observed VRH conductivity law on the low-temperature interval, lnρ∼T(-3/4), contradicts the models above, too. Instead, it is found that this law can be substantiated and the correct matching of the energy and length scales can be found within a model of Fogler et al (2004 Phys. Rev. B 69 035413) by treating CaCu(2)O(3) as a three-dimensional array of quasi-one-dimensional electron crystals.

Zeeman effect in superconducting two-leg ladders: irrational magnetization plateaus and exceeding the Pauli limit

The effect of a parallel magnetic field on superconducting two-leg ladders is investigated numerically. The magnetization curve displays an irrational plateau at a magnetization equal to the hole density. Remarkably, its stability is fundamentally connected to the existence of a well-known magnetic resonant mode. Once the zero-field spin gap is suppressed by the field, pairs acquire a finite momentum characteristic of a Fulde-Ferrell-Larkin-Ovchinnikov phase. In addition, Sz = 0 triplet superconducting correlations coexist with singlet ones above the irrational plateau. This provides a simple mechanism in which the Pauli limit is exceeded as suggested by recent experiments.

Phonon analysis of the S = 1 quantum spin systems Ni(5)Te(4)O(12)X(2) (X = Cl and Br)

We report our investigations of the electrodynamic response of the S = 1 quantum spin systems Ni(5)Te(4)O(12)X(2) (X = Cl and Br), which develop a magnetic ordered state below 30 K. We measure the optical reflectivity over a broad spectral range extending from the far infrared up to the ultraviolet. Besides identifying the electronic interband transitions, we primarily focus our attention on the lattice dynamics, emphasizing the phonon modes spectrum and its temperature dependence. Our findings do not reveal any direct link between possible structural anomalies and the transition into the magnetically ordered state at low temperatures.

Doped spin liquid: Luttinger sum rule and low temperature order

We analyze a model of two-leg Hubbard ladders weakly coupled by interladder tunneling. At half filling a semimetallic state with small Fermi pockets is induced beyond a threshold tunneling strength. The sign changes in the single electron Green's function relevant for the Luttinger sum rule now take place at surfaces with both zeros and infinities with important consequences for the interpretation of angle-resolved photoemission spectroscopy experiments. Residual interactions between electron and holelike quasiparticles cause a transition to long range order at low temperatures. The theory can be extended to small doping leading to superconducting order.

Gadolinium and Neodymium Citrates: Evidence for Weak Ferromagnetic Exchange between Gadolinium(III) Cations

A new lanthanide citrate motif of general formula [Ln(Hcit)(H2O)2.H2O]n, where Ln = Gd (1) and Nd (2) and Hcit3- = C(OH)(COO-)(CH2COO-)2, has been synthesized hydrothermally from Ln2O3 and citric acid at 100 degrees C and characterized by elemental analysis, IR, TG-DTA, single-crystal X-ray diffraction, and magnetic measurements. The structures can be seen as "ladder chains" along the a axis, with dinuclear Ln2O2 units serving as "steps" and R-COO groups as "uprights", which are connected by H bonds. The magnetic susceptibility between 2 and 300 K and the magnetization at 2 K, as a function of magnetic field between 0 and 5 T, were measured for both compounds. By modeling the magnetic behavior of the Gd compound with a dinuclear Hamiltonian [symbol: see text](S) = gmu(B)(S(A) + S(B))B(o) - J(o)S(A)S(B) (S(A) = S(B) = 7/2), a ferromagnetic exchange interaction J(o) = 0.039 cm(-1) was evaluated between Gd ions situated at d(o) = 4.321 angstroms in dinuclear units bridged by two symmetry-related tridentate carboxylate oxygens. The EPR spectrum of the Gd compound is discussed. The temperature dependence of the susceptibility of the Nd compound is caused by the depopulation of the excited crystal-field levels when the temperature decreases. The magnetic-field dependence of the magnetization of 2 is attributed to the ground-state Kramers' doublet populated at 2 K. The g factor of this ground-state doublet is calculated from the data and compared with values for other compounds reported in the literature.

La4Cu(3-x)Zn(x)MoO12: zinc-doped cuprates with Kagomé lattices

Two solid solutions, La4Cu(3-x)Zn(x)MoO12 (0.05 < or = x < or = 0.20, SS1) and La4Cu(3-x)Zn(x)MoO12 (0.30 < or = x < or = 2.40, SS2), were synthesized at ambient pressure and at temperatures from 1025 to 1200 degrees C by traditional solid-state reactions. Their structures were determined from X-ray powder diffraction with the help of electron and neutron diffraction. The atomic arrangements of SS1 and SS2 are similar, but their space groups are different, Pmnm for SS1 and P-1 for SS2, respectively. The copper, zinc, and molybdenum are coordinated by oxygen in corner-sharing trigonal bipyramids that are sandwiched between layers of lanthanum cations. In the transition metal cations layer of SS2, the copper and zinc cations order into a Kagomé-like lattice of triangular clusters. The magnetism has been measured from 2 to 300 K and is highly influenced by the geometric arrangement of the Cu(II) and Zn(II) cations. The number of free electrons per three Cu atoms is close to one for all samples in SS1 and SS2 indicating that the system can be well expressed by independent Cu(II)3 clusters. Spontaneous magnetization was observed in the system.

Complexity in Strongly Correlated Electronic Systems

A wide variety of experimental results and theoretical investigations in recent years have convincingly demonstrated that several transition metal oxides and other materials have dominant states that are not spatially homogeneous. This occurs in cases in which several physical interactions-spin, charge, lattice, and/or orbital-are simultaneously active. This phenomenon causes interesting effects, such as colossal magnetoresistance, and it also appears crucial to understand the high-temperature superconductors. The spontaneous emergence of electronic nanometer-scale structures in transition metal oxides, and the existence of many competing states, are properties often associated with complex matter where nonlinearities dominate, such as soft materials and biological systems. This electronic complexity could have potential consequences for applications of correlated electronic materials, because not only charge (semiconducting electronic), or charge and spin (spintronics) are of relevance, but in addition the lattice and orbital degrees of freedom are active, leading to giant responses to small perturbations. Moreover, several metallic and insulating phases compete, increasing the potential for novel behavior.

Cooperative density wave and giant spin gap in the quarter-filled zigzag electron ladder

Strong cooperative interactions occur between four different broken symmetries involving charge ordering and bond distortions in the quarter-filled correlated zigzag electron ladder. The ground state is singlet, with spin gap several times larger than in the spin-Peierls state of the one-dimensional quarter-filled chain with the same parameters. We propose the quarter-filled zigzag electron ladder model for several different organic charge transfer solids with coupled pairs of quasi-one-dimensional stacks, in which the spin-gap transition temperatures are unusually high.

Quantum percolation in two-dimensional antiferromagnets

The interplay of geometric randomness and strong quantum fluctuations is an exciting topic in quantum many-body physics, leading to the emergence of novel quantum phases in strongly correlated electron systems. Recent investigations have focused on the case of homogeneous site and bond dilution in the quantum antiferromagnet on the square lattice, reporting a classical geometric percolation transition between magnetic order and disorder. In this study we show how inhomogeneous bond dilution leads to percolative quantum phase transitions, which we have studied extensively by quantum Monte Carlo simulations. Quantum percolation introduces a new class of two-dimensional spin liquids, characterized by an infinite percolating network with vanishing antiferromagnetic order parameter.

Wigner crystallization in Na3Cu2O4 and Na8Cu5O10 chain compounds

We report the synthesis of novel edge-sharing chain systems Na(3)Cu(2)O(4) and Na(8)Cu(5)O(10), which form insulating states with commensurate charge order. We identify these systems as one-dimensional Wigner lattices, where the charge order is determined by long-range Coulomb interaction and the number of holes in the d shell of Cu. Our interpretation is supported by x-ray structure data as well as by an analysis of magnetic susceptibility and specific heat data. Remarkably, due to large second neighbor Cu-Cu hopping, these systems allow for a distinction between the (classical) Wigner lattice and the 4k(F) charge-density wave of quantum mechanical origin.

Structural, Magnetic, and Electrical Characterization of New Polycrystalline Phases of Nickel- and Platinum-Doped [(DT-TTF)n][Au(mnt)2] (n = 1, 2)

Doping of spin-ladder systems by isostructural paramagnetic complexes was attempted. Despite the close isostructural nature of the pure (DT-TTF)2[M(mnt)2] (M = Au, Ni, Pt) end-members, which present a ladder structure, doping of the spin-ladder (DT-TTF)2[Au(mnt)2] with either 5% or 25% [M(mnt)2]- (M = Ni, Pt) generates two (metrically) new phases. Their markedly different crystal structures have been determined using laboratory X-ray powder diffraction data. (DT-TTF)2[Au0.75Ni0.25(mnt)2] consists of a mixed-valence compound (of triclinic symmetry), which was only detected, pure or in a mixture of phases, when [Ni(mnt)2]- was used as a dopant. Differently, the stoichiometric 1:1 [DT-TTF][Au0.75Pt0.25(mnt)2] monoclinic phase was found when [Pt(mnt)2]- (in 5% and 25%) was employed as the doping agent. Remarkably, only in the 5% Pt doping experiment, the major component of the mixture was the ladder structure compound (DT-TTF)2[Au(mnt)2] doped with minor amounts of Pt. This 5% Pt-doped specimen shows an EPR signal (g = 2.0115, DeltaHpp = 114 G at 300 K) wider than the pure compound (DT-TTF)2[Au(mnt)2], denoting exchange between the donor spins and Pt(mnt)2- centers. The electrical transport properties of the 5% Pt-doped composition at high temperatures are comparable to those of (DT-TTF)2[Au(mnt)2] with room-temperature conductivity sigma300K = 13 S/cm and thermopower S300K = 46 microV/K, with a sharp transition at 223 K similar to that previously observed in the Cu analogue at 235 K.

Pressure-induced quantum phase transition in the spin-liquid TlCuCl3

The condensation of magnetic quasiparticles into the nonmagnetic ground state has been used to explain novel magnetic ordering phenomena observed in quantum spin systems. We present neutron scattering results across the pressure-induced quantum phase transition and for the novel ordered phase of the magnetic insulator TlCuCl3, which are consistent with the theoretically predicted two degenerate gapless Goldstone modes, similar to the low-energy spin excitations in the field-induced case. These novel experimental findings complete the field-induced Bose-Einstein condensate picture and support the recently proposed field-pressure phase diagram common for quantum spin systems with an energy gap of singlet-triplet nature.

Implementation of spin Hamiltonians in optical lattices

We propose an optical lattice setup to investigate spin chains and ladders. Electric and magnetic fields allow us to vary at will the coupling constants, producing a variety of quantum phases including the Haldane phase, critical phases, quantum dimers, etc. Numerical simulations are presented showing how ground states can be prepared adiabatically. We also propose ways to measure a number of observables, like energy gap, staggered magnetization, end-chain spins effects, spin correlations, and the string-order parameter.

Theoretical study of encapsulated alkali metal atoms in nanoporous channels of ITQ-4 zeolite: one-dimensional metals and inorganic electrides

Electronic structure calculations within density-functional theory have been carried out in a class of novel inorganic electrides M-ITQ-4 zeolite (M = Na, K, Rb, Cs) to understand the competing effects of guest-guest (M-M) and guest-host (M-ITQ-4) interactions. We find that Na forms a nearly perfect 1D metal undergoing Peierls distortion whereas Cs couples rather strongly to the host accompanied by a large charge transfer. In addition to the guest-host high energy charge transfer excitations we find a new far infrared excitation peak in Na at approximately 0.35 eV that can be ascribed to the Peierls distortion.

Crystallization of charge holes in the spin ladder of Sr14Cu24O41

Determining the nature of the electronic phases that compete with superconductivity in high-transition-temperature (high-T(c)) superconductors is one of the deepest problems in condensed matter physics. One candidate is the 'stripe' phase, in which the charge carriers (holes) condense into rivers of charge that separate regions of antiferromagnetism. A related but lesser known system is the 'spin ladder', which consists of two coupled chains of magnetic ions forming an array of rungs. A doped ladder can be thought of as a high-T(c) material with lower dimensionality, and has been predicted to exhibit both superconductivity and an insulating 'hole crystal' phase in which the carriers are localized through many-body interactions. The competition between the two resembles that believed to operate between stripes and superconductivity in high-T(c) materials. Here we report the existence of a hole crystal in the doped spin ladder of Sr14Cu24O41 using a resonant X-ray scattering technique. This phase exists without a detectable distortion in the structural lattice, indicating that it arises from many-body electronic effects. Our measurements confirm theoretical predictions, and support the picture that proximity to charge ordered states is a general property of superconductivity in copper oxides.

Spin-liquid versus dimerized ground states in a frustrated Heisenberg antiferromagnet

We present a density matrix renormalization group study of the ground-state properties of spin-1/2 frustrated J1-J3 Heisenberg n(l)-leg ladders (with n(l) up to 8). For strong frustration (J(3)/J(1) approximately 0.5), both even-leg and odd-leg ladders display a finite gap to spin excitations, which we argue remains finite in the two-dimensional limit. In this regime, on odd-leg ladders the ground state is spontaneously dimerized, in agreement with the Lieb-Schultz-Mattis prediction, while on even-leg ladders the dimer correlations decay exponentially. The magnitude of the dimer order parameter decreases as the number of legs increases, consistent with a two-dimensional spin-liquid ground state.

Dispersive excitations in the high-temperature superconductor La2-xSrxCuO4

High-resolution neutron scattering experiments on optimally doped La2-xSrxCuO4 (x=0.16) reveal that the magnetic excitations are dispersive. The dispersion is the same as in YBa2Cu3O6.85, and is quantitatively related to that observed with charge sensitive probes. The associated velocity in La2-xSrxCuO4 is only weakly dependent on doping with a value close to the spin-wave velocity of the insulating (x=0) parent compound. In contrast with the insulator, the excitations broaden rapidly with increasing energy, forming a continuum at higher energy and bear a remarkable resemblance to multiparticle excitations observed in 1D S=1/2 antiferromagnets. The magnetic correlations are 2D, and so rule out the simplest scenarios where the copper oxide planes are subdivided into weakly interacting 1D magnets.

Spin-charge separation in Aharonov-Bohm rings of interacting electrons

We investigate the properties of strongly correlated electronic models on a flux-threaded ring connected to semi-infinite free-electron leads. The interference pattern of such an Aharonov-Bohm ring shows sharp dips at certain flux values, determined by the filling, which are a consequence of spin-charge separation in a nanoscopic system.

Flux Period, Spin Gap, and Pairing in the One-Dimensional t-J-J' Model

Using the factorization of the wave function in the t-J-J' model at small exchange couplings, we demonstrate the connection between the existence of a spin gap and an hc/2e flux periodicity of the ground state energy. We conjecture that all spin-gapped SU(2)-invariant Luttinger liquids have hc/2e flux periodicity, and that this is connected to the fact that a gapped spin-1/2 chain always breaks translational symmetry by doubling the unit cell.

Magnon-hole scattering and charge order in Sr14-xCaxCu24O41

The magnon thermal conductivity kappa(mag) of the hole-doped spin ladders in Sr14-xCaxCu24O41 has been investigated at low doping levels x. The analysis of kappa(mag) reveals a strong doping and temperature dependence of the magnon mean free path l(mag), which is a local probe for the interaction of magnons with the doped holes in the ladders. In particular, this novel approach to studying charge degrees of freedom via spin excitations shows that charge ordering of the holes in the ladders leads to a freezing out of magnon-hole scattering processes.

Pressure-Induced Buckling of Spin Ladder in SrCu2O3

Pressure-induced structural phase transition of spin ladder compound SrCu2O3 was investigated by synchrotron X-ray powder diffraction with a diamond anvil cell (DAC). The change was characterized by a buckling of the Cu2O3 plane in the rung direction of the ladder. The structure of the high-pressure phase was found to be essentially the same as that of CaCu2O3. Application of an external pressure of 3.4 GPa therefore affected the structure in the same manner that the chemical (internal) pressure does.

Quantum magnetic excitations from stripes in copper oxide superconductors

In the copper oxide parent compounds of the high-transition-temperature superconductors the valence electrons are localized--one per copper site--by strong intra-atomic Coulomb repulsion. A symptom of this localization is antiferromagnetism, where the spins of localized electrons alternate between up and down. Superconductivity appears when mobile 'holes' are doped into this insulating state, and it coexists with antiferromagnetic fluctuations. In one approach to describing the coexistence, the holes are believed to self-organize into 'stripes' that alternate with antiferromagnetic (insulating) regions within copper oxide planes, which would necessitate an unconventional mechanism of superconductivity. There is an apparent problem with this picture, however: measurements of magnetic excitations in superconducting YBa2Cu3O6+x near optimum doping are incompatible with the naive expectations for a material with stripes. Here we report neutron scattering measurements on stripe-ordered La1.875Ba0.125CuO4. We show that the measured excitations are, surprisingly, quite similar to those in YBa2Cu3O6+x (refs 9, 10) (that is, the predicted spectrum of magnetic excitations is wrong). We find instead that the observed spectrum can be understood within a stripe model by taking account of quantum excitations. Our results support the concept that stripe correlations are essential to high-transition-temperature superconductivity.

Structure and Magnetism of a Spin Ladder System: (C5H9NH3)2CuBr4

The crystal structure of bis(cyclopentylammonium)tetrabromocuprate(II) has been determined at room temperature and at -70 degrees C. The room temperature structure is orthorhombic, space group Pn2(1)a, with a = 12.092(6) A, b = 8.134(4) A, and c = 18.698(10) A. The low temperature structure is also orthorhombic, space group Pna2(1), with a = 24.111(5) A, b = 8.089(2) A, and c = 18.448(4) A. DSC studies reveal the presence of a weak endotherm at -13 degrees C. The structures of the two phases are very similar, differing only in the relative orientations of the cyclopentyl rings of the organic cations and slight displacements of the anionic tetrahedra. The CuBr(4)(2)(-) anions in the low temperature phase are arranged to define a spin ladder system through Cu-Br.Br-Cu two-halide exchange pathways. Magnetic susceptibility data have been analyzed and yield antiferromagnetic exchange strengths 2J(rail)/k = -11.6 K and 2J(rung)/k = -5.5 K with a singlet-triplet gap energy Delta/k(B) = 2.3 K. This is the first report of a spin ladder with a stronger interaction along the axis of the ladder than along the rungs.

Paramagnetic cp/dithiolene complexes as molecular hinges: interplay of metal/ligand electronic delocalization and solid-state magnetic behavior

Paramagnetic, flexible organometallic dithiolene complexes associating cyclopentadienyl (Cp) and dithiolate (dt) ligands, such as CpM(dt), Cp2M(dt), or CpM(dt)2, are investigated in the solid state through their structural and magnetic properties. The degree of delocalization of the spin density between the metal and the dithiolene fragments in a given complex, its varying molecular geometry and frontier orbitals, and the structures adopted in the solid state are intimately correlated and adapt mutually to each other. A variety of magnetic structures follows, from noninteracting spins to dyads, spin chains, spin ladders, or antiferromagnetic ground state, the detailed properties of which are highly sensitive to "minor" molecular modifications.

Chiral spin liquid wave function and the Lieb-Schultz-Mattis theorem

We study a chiral spin liquid wave function defined as a Gutzwiller projected BCS state with a complex pairing function. After projection, spontaneous dimerization is found for any odd but finite number of chains, thus satisfying the Lieb-Schultz-Mattis theorem, whereas for an even number of chains there is no dimerization. The two-dimensional thermodynamic limit is consistently reached for a large number of chains since the dimer order parameter vanishes in this limit. This property clearly supports the possibility of a spin liquid ground state in two dimensions with a gap to all physical excitations and with no broken translation symmetry.

Exact duality relations in correlated electron systems

Using gauge transformations on electron bond operators, we derive exact duality relations between various order parameters for correlated electron systems. Applying these transformations, we find two duality relations in the generalized two-leg Hubbard ladder at arbitrary filling. The relations show that unconventional density-wave orders such as staggered flux or circulating spin current are dual to conventional density-wave orders and there are direct mappings between dual phases. Several exact results on the phase diagram are also concluded.

Exact results for the thermal and magnetic properties of strong coupling ladder compounds

We investigate the thermal and magnetic properties of the integrable su(4) ladder model by means of the quantum transfer matrix method. The magnetic susceptibility, specific heat, magnetic entropy, and high field magnetization are evaluated from the free energy derived via the recently proposed method of high temperature expansion for exactly solved models. We show that the integrable model can be used to describe the physics of the strong coupling ladder compounds. Excellent agreement is seen between the theoretical results and the experimental data for the known ladder compounds (5IAP)2CuBr4.2H(2)O, Cu2(C5H12N2)2Cl4, etc.

Short-Range and Long-Range Magnetic Ordering in SrCuP2O7 and PbCuP2O7

Magnetic properties of SrCuP2O7 and PbCu(1-x)ZnxP2O7 (x=0, 0.1, and 0.5) were studied by magnetic susceptibility, chiT, and specific heat, Cp(T). Both data showed that magnetism of SrCuP2O7 and PbCuP2O7 can be described by the one-dimensional (1D) uniform chain model despite the structural features suggesting the presence of zigzag chains with next-nearest-neighbor interactions. The chiT data were fitted by the Bonner-Fisher curve (plus temperature independent and Curie-Weiss terms) with g=2.20 and J/kB=9.38 K for SrCuP2O7 and g=2.17 and J/kB=8.41 K for PbCuP2O7 (Hamiltonian H=J SigmaSiS(i+1)). Magnetic specific heat, Cm(T), exhibited one broad maximum due to short-range ordering and one sharp peak at TN=1.64 K for SrCuP2O7 and TN=1.15 K for PbCuP2O7 due to long-range antiferromagnetic ordering. The characteristic values of the broad maxima on the Cm(T) curves (Cmax and TC(max)) were in good agreement with the theoretical calculations for the uniform 1D S=1/2 Heisenberg chain. Magnetic properties of PbCu0.9Zn0.1P2O7 still obeyed the 1D uniform chain model but those of PbCu0.5Zn0.5P2O7 did not. In air, SrCuP2O7 was stable at least up to 1373 K while PbCuP2O7 melted incongruently above 1180 K.

Superconducting gap for a two-leg t-J ladder

Single-particle diagonal and off-diagonal Green's functions of a two-leg t-J ladder at 1/8 doping are investigated by exact diagonalizations techniques. A numerically tractable expression for the superconducting gap is proposed and the frequency dependence of the real and imaginary parts of the gap are determined. The role of the low-energy gapped spin modes, whose energies are computed by a (one-step) contractor renormalization procedure, is discussed.

Collective density-wave excitations in two-leg Sr14-xCaxCu24O41 ladders

Raman measurements in the 1.5-20 cm(-1) energy range were performed on single crystals of Sr14-xCaxCu24O41. A quasielastic scattering peak (QEP) which softens with cooling is observed only in the polarization parallel to the ladder direction for samples with x=0, 8, and 12. The QEP is a Raman fingerprint of pinned collective density wave excitations screened by uncondensed carriers in the ladder structures. Our results suggest that transport in metallic samples, which is similar to transport in underdoped high-T(c) cuprates, is driven by a collective electronic response.