Two-leg Ladder Research Articles

Emergent spin-1 Haldane gap and ferroelectricity in a frustrated spin- 12 ladder

We report experimental and theoretical evidence that Rb$_2$Cu$_2$Mo$_3$O$_{12}$ has a nonmagnetic tetramer ground state of a two-leg ladder comprising antiferromagnetically coupled frustrated spin-$1/2$ chains and exhibits a Haldane spin gap of emergent spin-1 pairs. Three spin excitations split from the spin-1 triplet by a Dzyaloshinskii-Moriya interaction are identified in inelastic neutron-scattering and electron spin resonance spectra. A tiny magnetic field generates ferroelectricity without closing the spin gap, indicating a novel class of ferroelectricity induced by a vector spin chirality order.

In-plane ordering of oxygen vacancies in a high- Tc cuprate superconductor with compressed Cu-O octahedrons: An automated cluster expansion study

A recently discovered high-Tc cuprate superconductor Ba2CuO$_{4-\delta}$ exhibits exceptional Jahn-Teller distortion, wherein the CuO6 octahedrons are compressed along the c axis. As a consequence, the O vacancies prefer to reside in the CuO2 plane, but the exact structure is not known. By combining first-principles total energy calculation with the automated structure inversion method, the effective cluster interactions of O vacancies are mapped out. Around $\delta$=0.8, where the 73K superconductivity was observed experimentally, we predict that the ordered O vacancies slice the CuO2 plane into not only 1D chains and but also two-leg ladders. A Monte Carlo simulation is performed based on the effective cluster interaction model, showing that such an ordering pattern is stable up to ~900 K. Our results put forth a concrete structural basis to discuss the underlying superconducting mechanism.

Iron telluride ladder compounds: Predicting the structural and magnetic properties of BaFe2Te3

Since the discovery of pressure-induced superconductivity in the two-leg ladder system BaFe$_2X_3$ ($X$=S, Se), with the 3$d$ iron electronic density $n = 6$, the quasi-one-dimensional iron-based ladders have attracted considerable attention. Here, we use Density Functional Theory (DFT) to predict that the novel $n = 6$ iron ladder BaFe$_2$Te$_3$ could be stable with a similar crystal structure as BaFe$_2$Se$_3$. Our results also indicate that BaFe$_2$Te$_3$ will display the complex 2$\times$2 Block-type magnetic order. Due to the magnetic striction effects of this Block order, BaFe$_2$Te$_3$ should be a magnetic noncollinear ferrielectric system with a net polarization $0.31$ $\mu$C/cm$^2$. Compared with the S- or Se-based iron ladders, the electrons of the Te-based ladders are more localized, implying that the degree of electronic correlation is enhanced for the Te case which may induce additional interesting properties. The physical and structural similarity with BaFe$_2$Se$_3$ also suggests that BaFe$_2$Te$_3$ could become superconducting under high pressure.

The Synthesis of a Quasi-One-Dimensional Iron-Based Telluride with Antiferromagnetic Chains and a Spin Glass State.

The report on the superconductivity of the two-legged spin ladders BaFe2S3 and BaFe2Se3 has established 123-type iron chalcogenides as a novel subgroup in the iron-based superconductor family and has stimulated the continuous exploration of other iron-based materials with new structures and potentially novel properties. In this paper, we report the systematic study of a new quasi-one-dimensional (1D) iron-based compound, Ba9Fe3Te15, including its synthesis and magnetic properties. The high-pressure synthesized Ba9Fe3Te15 crystallized in a hexagonal structure that mainly consisted of face-sharing FeTe6 octahedral chains running along the c axis, with a lattice constant of a = 10.23668 Å; this led to weak interchain coupling and an enhanced one-dimensionality. The systematic static and dynamic magnetic properties were comprehensively studied experimentally. The dc magnetic susceptibility showed typical 1D antiferromagnetic characteristics, with a Tmax at 190 K followed by a spin glass (SG) state with freezing at Tf ≈ 6.0 K, which were also unambiguously proved by ac susceptibility measurements. Additionally, X-ray magnetic circular dichroism (XMCD) experiments revealed an unexpected orbital moment for Fe2+, i.e., 0.84 μB per Fe in Ba9Fe3Te15. The transport property is electrically insulating, with a thermal activation gap of 0.32 eV. These features mark Ba9Fe3Te15 as an alternative type of iron-based compound, providing a diverse candidate for high-pressure studies in order to pursue some emerging physics.

Dynamics of the spin-1/2 Ising two-leg ladder with four-spin plaquette interaction and transverse field.

Multiple-spin coupling is a key tool for investigating magnetic quantum systems. In particular, models with four-spin interactions became of great interest since they have been applied to describe material properties such as superconductivity. In this framework, the dynamics of the spin-1/2 Ising two-leg ladder with four-spin plaquette interaction in a transverse field is investigated. By means of the recurrence relations method, the first four recurrants are determined exactly for the general model, while five exact recurrants are calculated for two particular models. In all cases, higher-order recurrants are computed through extrapolation to obtain time-dependent autocorrelation functions and spectral densities in the long-time regime and infinite-temperature limit. It is found that the relaxation functions decay slower than the expected behavior of the one-dimensional transverse Ising model. The spectral lines, characterized by a Lorentzian behavior in the central body and a Gaussian shape in the tails, display exchange narrowing as the coupling intensities increase.

Transport in a long-range Kitaev ladder: Role of Majorana and subgap Andreev states

We study the role of the constituent Majorana fermions and the subgap Andreev states on local and non-local transport across a two-leg long-range Kitaev ladder connected to metallic leads. The double degeneracy of Majorana fermions of the individual legs of the ladder gets lifted by a coupling between the two, resulting in the creation of Andreev bound states. A finite inter-leg hopping can be used to induce this coupling, provided a suitable superconducting phase difference (between the legs) is also applied. Andreev bound states formed strongly enhance local Andreev reflection. When the ladder and normal metal are weakly coupled the non-local nature of Andreev bound states enhances the non-local scattering weakly. When the ladder-normal metal interface is transparent to electron flow, we find that the subgap Andreev states enhance non-local conductance strongly. The features in the local and non-local conductances resemble the spectrum of the isolated ladder. Long-range pairing helps lift the degeneracy of the Majorana modes, makes them less localized, and thus inhibits local transport, while aiding non-local transport.

Spin Gap in β-TeVO4: a Quantum Monte Carlo Study

In this paper, we proposed a two-leg spin ladder model for the description of magnetic properties of the β-TeVO4 compound. Quantum Monte Carlo (QMC) simulation was applied to describe the temperature-dependent magnetic susceptibility data for low temperatures. The two-leg spin ladder model presents a spin gap, and we suggests that β-TeVO4 compound presents such a spin gap also, and therefore, the model proposed here can be experimentally tested by measuring the spin gap of the compound. The susceptibility phase diagram has a rounded peak in the vicinity of T ≈ 12.2 K and obeys Troyer’s law for low temperatures and Curie’s law for high temperatures. We also study the susceptibility diagram in low temperatures and found the spin gap Δ = 8.06 K. The linearization of the equation for susceptibility in low temperatures allows us to obtain the spin gap value, and such a linearization was made with the data from the QMC simulation. In all the results, there is a very good agreement with the experimental data. We also show that the spin gap is null and the susceptibility is proportional to T for low temperatures when relatively high values of the ladders’ coupling is considered. The theoretical results are compared with other studies as well as applied to describe the susceptibility phase diagram of consolidated spin ladder compound, C9H18N2CuBr4.

Emergence of orbital-selective marginal Fermi liquidness in compressed RbFe2Te3

Driving a Mott insulator towards an orbital-selective metal with coexisting Mott localized and marginal Fermi liquid electronic states remains central to understanding various correlated emergent phenomena. Here, using density functional dynamical mean-field theory we explore correlation and hole-doping-induced electronic reconstruction in ${\mathrm{RbFe}}_{2}{\mathrm{Te}}_{3}$, a potential two-leg ladder system for hole carrier superconductivity under pressure. We stress the importance of multiorbital Coulomb interactions in concert with band structure calculations for a consistent understanding of intrinsic Mott localization at ambient pressure. We elucidate the nature of pressure-induced Mottness upon tuning the correlation to bandwidth ratio away from the Mott boundary. As a by-product of our analysis, a quantum critical phenomenon with coexisting Mott localized and marginal Fermi liquid electrons is predicted to exist in compressed ${\mathrm{RbFe}}_{2}{\mathrm{Te}}_{3}$ metal.

Multiparticle Interactions for Ultracold Atoms in Optical Tweezers: Cyclic Ring-Exchange Terms.

Dominant multiparticle interactions can give rise to exotic physical phases with anyonic excitations and phase transitions without local order parameters. In spin systems with a global SU(N) symmetry, cyclic ring-exchange couplings constitute the first higher-order interaction in this class. In this Letter, we propose a protocol showing how SU(N)-invariant multibody interactions can be implemented in optical tweezer arrays. We utilize the flexibility to rearrange the tweezer configuration on short timescales compared to the typical lifetimes, in combination with strong nonlocal Rydberg interactions. As a specific example, we demonstrate how a chiral cyclic ring-exchange Hamiltonian can be implemented in a two-leg ladder geometry. We study its phase diagram using density-matrix renormalization group simulations and identify phases with dominant vector chirality, a ferromagnet, and an emergent spin-1 Haldane phase. We also discuss how the proposed protocol can be utilized to implement the strongly frustrated J-Q model, acandidate for hosting a deconfined quantum critical point.

Topological phases in two-legged Heisenberg ladders with alternating interactions

We analyze the possible existence of topological phases in two-legged spin ladders considering a staggered interaction in both chains. When the staggered interaction in one chain is shifted by one site with respect to the other chain, the model can be mapped, in the continuum limit, into a non linear sigma model NL$\sigma$M plus a topological term which is nonvanishing when the number of legs is two. This implies the existence of a critical point which distinguishes two phases. We perform a numerical analysis of energy levels, parity and string non-local order parameters, correlation functions between $x,y,z$ components of spins at the edges of an open ladder, the degeneracy of the entanglement spectrum and the entanglement entropy in order to characterize these two different phases. Finally, we identify one phase with a Mott insulator and the other one with a Haldane insulator.

Solitons in two-leg bosonic ladder subject to an artificial magnetic field

SynopsisThe nonlinear dynamics in two-leg ladder system subject to an artificial magnetic field are discussed in detail. The critical conditions for the formation of soliton and for the transition from diffusion to self-trapping are presented, and confirmed by the numerical simulations of the full discrete nonlinear Schrödinger equation.

Phase transitions and critical behaviors of XXZ ladders

We study the phase transitions and critical behaviors of the two-leg dimerized XXZ ladders by extensive Monte Carlo simulations and finite-size scaling analysis. For the Heisenberg model on the staggered ladder, we verify that the phase transition between the two topological phases belongs to the four-state Potts universality class; for the XY case (), the phase diagram is similar to the Heisenberg case, but the critical behavior belongs to a new universality class; for the Ising case (), we find three topological phases, in which one of them has both the topological orders and the local magnetic order; the two phase transitions associated with these phases also belong to the Ising universality class. On the columnar ladder, we have not found any phase transition for all the three cases. Furthermore, we find that the magnetic field can also induce phase transitions for both the staggered and columnar models, and the topological phases are in certain magnetic plateaux. For the staggered model, we study the phase transition associated with the plateau of zero magnetization; we find that the critical behavior of the string order parameter belongs to the 2D classical Ising model, and the scaling behavior of the uniform magnetization is different from the Dzhaparidze–Nersesyan–Pokrovsky–Talapov universality class. For the columnar model, we study the phase transition associated with the plateau whose magnetization is half of the saturation value, which has fractional quantized Berry phase; in this case, the conventional string order parameters are not applicable as order parameters, we determine the critical point of this phase transition by the scaling behavior of the uniform magnetization which is also different from the Dzhaparidze–Nersesyan–Pokrovsky–Talapov universality class.

Quantum phases of biased bosonic ladders subject to a magnetic field

SynopsisThe quantum phase transition of the Plane Wave I phase, the Plane Wave II phase, and interestingly, a new phase named Moving Biased Vortex phase are revealed in the biased bosonic two-leg ladder system.

Creutz ladder in a resonantly shaken 1D optical lattice

We report the experimental realization of a Creutz ladder for ultracold fermionic atoms in a resonantly driven 1D optical lattice. The two-leg ladder consists of the two lowest orbital states of the optical lattice and the cross inter-leg links are generated via two-photon resonant coupling between the orbitals by periodic lattice shaking. The characteristic pseudo-spin winding structure in the energy bands of the ladder system is demonstrated using momentum-resolved Ramsey-type interferometric measurements. We discuss a two-tone driving method to extend the inter-leg link control and propose a topological charge pumping scheme for the Creutz ladder system.

Emergent bosons in the fermionic two-leg flux ladder

We study the emergence of bosonic pairs in a system of two coupled one-dimensional fermionic chains subject to a gauge flux (two-leg flux ladder), with both attractive and repulsive interaction. In the presence of strong attractive nearest-neighbor interaction and repulsive next-to-nearest-neighbor interaction, the system crosses into a regime in which fermions form tightly bound pairs, which behave as bosonic entities. By means of numerical simulations based on the density-matrix-renormalization-group (DMRG) method, we show in particular that in the strongly paired regime, the gauge flux induces a quantum phase transition of the Ising type from vortex density wave (VDW) to a charge density wave (CDW), characteristic of bosonic systems.

Strongly Enhanced Superconductivity Due to Finite Energy Spin Fluctuations Induced by an Incipient Band: A FLEX Study on the Bilayer Hubbard Model with Vertical and Diagonal Interlayer Hoppings

We study the spin-fluctuation-mediated $s\pm$-wave superconductivity in the bilayer Hubbard model with vertical and diagonal interlayer hoppings. As in the two-leg ladder model with diagonal hoppings, studied previously by the present authors, superconductivity is strongly enhanced when one of the bands lies just below (or touches) the Fermi level, that is, when the band is incipient. The strong enhancement of superconductivity is because large weight of the spin fluctuations lies in an appropriate energy range, whereas the low energy, pair-breaking spin fluctuations are suppressed. The optimized eigenvalue of the linearized Eliashberg equation, a measure for the strength of superconductivity, is not strongly affected by the bare width of the incipient band, but the parameter regime where superconductivity is optimized is wide when the incipient band is narrow, and in this sense, the coexistence of narrow and wide bands is favorable for superconductivity.

Magnetic phase diagram of a spin S = 1/2 antiferromagnetic two-leg ladder with modulated along legs Dzyaloshinskii-Moriya interaction

We study the ground-state magnetic phase diagram of a spin S=1/2 antiferromagnetic two-leg ladder in the presence of period two lattice units modulated, Dzyaloshinskii-Moriya (DM) interaction along the legs. We consider the case of collinear DM vectors and strong rung exchange and magnetic field. In this limit we map the initial ladder model onto the effective spin $\sigma=1/2$ XXZ chain and study the latter using the continuum-limit bosonization approach. We identified four quantum phase transitions and corresponding critical magnetic fields, which mark transitions from the spin gapped regimes into the gapless quantum spin-liquid regimes. In the gapped phases the magnetization curve of the system shows plateaus at magnetisation M=0 and to its saturation value per rung M=1. We have shown that the very presence of alternating DM interaction leads to opening of a gap in the excitation spectrum at magnetization M=0.5. The width of the magnetization plateau at M=0.5, is determined by the associated with the dynamical generation of a gap in the spectrum is calculated and is shown that its length scales as $(D_{0}D_{1}/J^{2})^{\alpha}$ where $D_{0},D_{1}$ are uniform and staggered components of the DM term, $J$ is the intraleg exchange and $\alpha \leq 3/4$ and weakly depends on the DM couplings.

Magnetic states of iron-based two-leg ladder tellurides

The recent discovery of superconductivity at high pressure in the two-leg ladder compounds BaFe$_2X_3$ ($X$=S, Se) started the novel field of quasi-one-dimensional iron-based superconductors. In this publication, we use Density Functional Theory (DFT) to predict that the previously barely explored ladder compound RbFe$_2$Te$_3$ should be magnetic with a CX-type arrangement involving ferromagnetic rungs and antiferromagnetic legs, at the realistic density of $n=5.5$ electrons per iron. The magnetic state similarity with BaFe$_2$S$_3$ suggests that RbFe$_2$Te$_3$ could also become superconducting under pressure. Moreover, at $n=6.0$ our DFT phase diagrams (with and without lattice tetramerization) reveal that the stable magnetic states could be either a 2$\times$2 magnetic Block-type, as for $X$=Se, or a previously never observed before CY-type state, with ferromagnetic legs and antiferromagnetic rungs. In the Te-based studies, electrons are more localized than in S, implying that the degree of electronic correlation is enhanced for the Te case.

Iron-Based Chalcogenide Spin Ladder BaFe2X3 (X = Se,S)

The relevance of magnetic, structural, orbital, and charge degrees of freedom in the iron-based superconductors (FeSCs) and related materials occupies a central focus in condensed matter physics. While the majority of iron-based materials exhibit the same two-dimensional iron square lattice structural motif, a family of AFe2X3 (X = Se,S) compounds introduces a quasi-one-dimensional (1D) ladder motif, which resembles the two-legged spin ladder copper oxide materials. Furthermore, unlike most parent compounds of FeSCs, the members of this spin ladder family are insulators. Recently, a superconducting transition has been observed under pressure with Tc up to 24 K, similar to the pressure-induced superconductivity in the copper oxide ladder Sr14−xCaxCu24O41 material, stimulating much interest. Here, we review the magnetic, structural, and electronic properties in this family, particularly in the BaFe2X3 series tuned by pressure and by chemical substitution. The established pressure-temperature (P-T) and carrier concentration-temperature (x-T) phase diagrams in related materials provide useful information to extend the variety of high-temperature superconductors and compare with other FeSCs. We also review some essential information about analogous square lattice FeSCs.

Inter-layer modified -wave superconductivity in an effectively doped spin-1 ladder

We construct a four-leg spin-1/2 t–J type model to simulate a doped two-leg spin-1 antiferromagnetic Heisenberg ladder. Employing renormalized mean-field theory with simple Gutzwiller factors, we obtain three degenerate superconducting states with different pairing symmetry. Through improving the Gutzwiller factors, we find that the state C with inter-layer modified -wave pairing has the lowest energy in a large doping range. Besides, we use the density matrix renormalization group method to solve the model. The negative binding energy reveals the pairing tendency, and the pair–pair correlation functions exhibit a slowly decaying behavior on certain types of bonds. From the pair correlations, we confirm the inter-layer modified -wave superconducting state as the ground state of the model.