We show using bosonization methods that extended Hubbard-Heisenberg models on two types of two leg ladders (without flux and with flux $π$ per plaquette) have commensurate pair-density wave (PDW) phases. In the case of the conventional (flux-less) ladder the PDW arises when certain filling fractions for which commensurability conditions are met.
For the flux $π$ ladder the PDW phase is generally present. The PDW phase is characterized by a finite spin gap and a superconducting order parameter with a finite (commensurate in this case) wave vector and power-law superconducting correlations. In this phase the uniform superconducting order parameter, the $2k_F$ charge-density-wave (CDW) order parameter and the spin-density- wave Néel order parameter exhibit short range (exponentially decaying) correlations. We discuss in detail the case in which the bonding band of the ladder is half filled for which the PDW phase appears even at weak coupling. The PDW phase is shown to be dual to a uniform superconducting (SC) phase with quasi long range order. By making use of bosonization and the renormalization group we determine the phase diagram of the spin-gapped regime and study the quantum phase transition. The phase boundary between PDW and the uniform SC ordered phases is found to be in the Ising universality class. We generalize the analysis to the case of other commensurate fillings of the bonding band, where we find higher order commensurate PDW states for which we determine the form of the effective bosonized field theory and discuss the phase diagram. We compare our results with recent findings in the Kondo-Heisenberg chain. We show that the formation of PDW order in the ladder embodies the notion of intertwined orders.
Spin dynamics in the pressure-induced two-leg ladder cuprate superconductor Sr$_{14-x}$Ca$_{x}$Cu$_{24}$O$_{41}$
基于动能驱动的超导机制，在两腿$t$梯内，研究了压力诱导两腿梯状铜氧化物超导体Sr $_{14-x}$ Ca $_{x}$ Cu $_{24}$ O $_{41}$的自旋动力学.结果表明，在压力诱导超导态中，欠压区出现无公度自旋关联，而最佳压力区和超压区出现公度自旋涨落.特别是，自旋-晶格弛豫时间主要由温度线性依赖项在低温下由低于超导转变温度下的峰开发，在定性上与Sr $_{14-x}$ Ca $_{x}$ Cu $_{24}$ O $_{41}$的实验观察。
We study the effect of inter-ladder ferromagnetic (FM) coupling in spin-1/2 two-leg ladders with antiferromagnetic (AFM) legs and rungs interactions using the stochastic series expansion quantum Monte Carlo. We have compared the results with the experimental measurement on Sr$_{14-x}$Ca$_{x}$Cu$_{24}$O$_{41}$ cuprate which is the candidate for spin-1/2 AFM two-leg ladders with FM inter-ladder interaction. A remarkable asymptotic behavior of susceptibility is observed at very low temperature. In the absence of the magnetic field, thermodynamic behavior of an individual spin-1/2 two-leg ladder i…
The electronic structure of BaFe$_2X_3$ ($X$ = S and Se) and CsFe$_2$Se$_3$ in which two-leg ladders are formed by the Fe sites are studied by means of x-ray absorption and resonant inelastic x-ray scattering spectroscopy. The x-ray absorption spectra at the Fe L edges for BaFe$_2X_3$ exhibit two components, indicating that itinerant and localized Fe 3$d$ sites coexist. Substantial x-ray linear dichroism (XLD) is observed in polarization dependent spectra, indicating the existence of orbital order or fluctuation in the Fe-ladder even above the Néel temperature $T_N$. Direct exchange interactio…
Nuclear Spin Relaxation in Hole Doped Two-Leg Ladders
本文测量了空穴掺杂的双柱梯形化合物Sr $_{14-x}$ Ca $_{x}$ Cu $_{24}$ O $_{41}$和未掺杂的母体材料La $_6$ Ca $_8$ Cu $_{24}$ O $_{41}$的核自旋-晶格弛豫速率（$1/T_{1}$）。在铜和两个不同的氧站点的$1/T_{1}$的比较显示，低频自旋波动的主要光谱权重位于附近的$q \sim (π, π)$的温度和掺杂范围的调查。在重掺杂$x$ =12样品中，两个氧位点的$1/T_1$的温度依赖性的显著差异揭示了两个腿之间的单线态相关性的降低，而不是随着温度的升高而沿着腿方向增长的反铁磁相关性。这种行为很可能是由束缚空穴对的解离引起的。
We study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (RPA+FLEX). Our calculations reveal that RPA+FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly-interacting electron-…
用随机级数展开量子蒙特卡罗方法研究了反铁磁自旋1/2海森堡阶梯中的随机键无序。我们发现，个别键杂质的影响有很大的不同，这取决于他们的位置腿和梯级。我们首先集中在如何分布的局部键能依赖于杂质浓度。然后我们研究了无规键掺杂对偶脚梯形相图的影响。我们观察到玻色玻璃相在两个制度（$h' < h \lesssim h_{c1}$和$h" < h <h_{c2}$）和玻色-爱因斯坦凝聚体之间。它们的存在进行了讨论的关系，当地的键能。
Two-leg spin-1/2 ladder systems consisting of a ferromagnetic leg and an antiferromagnetic leg are considered where the spins on the legs interact through antiferromagnetic rung couplings $J_1$. These ladders can have two geometrical arrangements either zigzag or normal ladder and these systems are frustrated irrespective of their geometry. This frustration gives rise to incommensurate spin density wave, dimer and spin fluid phases in the ground state. The magnetization in the systems decreases linearly with $J^2_1$, and the systems show an incommensurate phase for $0.0<J_1<1.0$. The spin-spin…
We examine the magnetic-field-induced criticality of phase boundary near saturation field $H_{\mathrm{c}}$ in the spin-1/2 ferromagnetic (FM)-leg ladder 3-Cl-4-F-V [=3-(3-chloro-4-fluorophenyl)-1,5-diphenylverdazyl], the predominant interactions of which arise from FM chains (strong-leg type). Critical temperatures were precisely determined through dc magnetization, specific heat, and magnetocaloric effect measurements. The criticality of 3-Cl-4-F-V is characterized by a linear phase boundary with respect to $H_{\mathrm{c}}-H$ near $H\,=\,H_{\mathrm{c}}$. This behavior is similar to that of an…
We consider the spin-1/2 two-leg ladders with ferromagnetic (FM) interactions along legs and rungs. Using the stochastic series expansion QMC method, we study the low-temperature magnetic behavior of the system. An isolated spin-1/2 FM two-leg ladder is in the gapped saturated FM phase at zero temperature. As soon as the spin-1/2 FM two-leg ladders are connected with antiferromagnetic (AFM) inter-ladder interaction, a first-order commensurate-incommensurate quantum phase transition occurs in the ground state magnetic phase diagram. In fact a jump in the magnetization curve is observed. We foun…
We study critical singularities in the d-wave-like superconducting phase of the hole-doped Hubbard model of repulsively interacting electrons, defined on a two-leg ladder, induced by a magnetic field applied parallel to the ladder plane. We argue that, provided the lowest energy spin excitations in doped ladders carry as well charge quantum numbers, the low temperature thermodynamic quantities, such as specific heat coefficient and magnetic susceptibility will show logarithmic singularities in quantum critical regime. This behavior is in drastic contrast with the magnetic field induced critica…
