Stripe order enhanced superconductivity in the Hubbard model

Unidirectional (“stripe”) charge density wave order has now been established as a ubiquitous feature in the phase diagram of the cuprate high-temperature superconductors, where it generally competes with superconductivity. Nonetheless, on theoretical grounds it has been conjectured that stripe order (or other forms of “optimal” inhomogeneity) may play an essential positive role in the mechanism of high-temperature superconductivity. Here, we report density matrix renormalization group studies of the Hubbard model on long four- and six-leg cylinders, where the hopping matrix elements transverse to the long direction are periodically modulated—mimicking the effect of putative period 2 stripe order. We find that even modest amplitude modulations can enhance the long-distance superconducting correlations by many orders of magnitude and drive the system into a phase with a substantial spin gap and superconducting quasi–long-range order with a Luttinger exponent, Ksc∼1.

Topological Doping and Superconductivity in Cuprates: An Experimental Perspective

Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phases. The topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with their environment. In the case of cuprates, where the charge stripes have the character of a hole-doped two-leg spin ladder, with corresponding pairing correlations, anti-phase Josephson coupling across the spin stripes can lead to a pair-density-wave order in which the broken translation symmetry of the superconducting wave function is accommodated by pairs with finite momentum. This scenario is now experimentally verified by recently reported measurements on La2−xBaxCuO4 with x=1/8. While pair-density-wave order is not common as a cuprate ground state, it provides a basis for understanding the uniform d-wave order that is more typical in superconducting cuprates.

Metallic and insulating stripes and their relation with superconductivity in the doped Hubbard model

The dualism between superconductivity and charge/spin modulations (the so-called stripes) dominates the phase diagram of many strongly-correlated systems. A prominent example is given by the Hubbard model, where these phases compete and possibly coexist in a wide regime of electron dopings for both weak and strong couplings. Here, we investigate this antagonism within a variational approach that is based upon Jastrow-Slater wave functions, including backflow correlations, which can be treated within a quantum Monte Carlo procedure. We focus on clusters having a ladder geometry with MM legs (with MM ranging from 22 to 1010) and a relatively large number of rungs, thus allowing us a detailed analysis in terms of the stripe length. We find that stripe order with periodicity \lambda=8λ=8 in the charge and 2\lambda=162λ=16 in the spin can be stabilized at doping \delta=1/8δ=1/8. Here, there are no sizable superconducting correlations and the ground state has an insulating character. A similar situation, with \lambda=6λ=6, appears at \delta=1/6δ=1/6. Instead, for smaller values of dopings, stripes can be still stabilized, but they are weakly metallic at \delta=1/12δ=1/12 and metallic with strong superconducting correlations at \delta=1/10δ=1/10, as well as for intermediate (incommensurate) dopings. Remarkably, we observe that spin modulation plays a major role in stripe formation, since it is crucial to obtain a stable striped state upon optimization. The relevance of our calculations for previous density-matrix renormalization group results and for the two-dimensional case is also discussed.