Stripe order enhanced superconductivity in the Hubbard model

Abstract

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.

Superconducting valence bond fluid in lightly doped 8-leg $t$-$J$ cylinders

“…(This is the same intuition as that of the short-range RVB picture [30]. This intuition is further supported by an earlier DMRG study of a striped Hubbard cylinder [31]), and a sign-problem free quantum Monte-Carlo simulation of lightly doped VBC on honeycomb lattice [32].…”

Strongly-overdoped La$_{2-x}$Sr$_x$CuO$_4$: Evidence for Josephson-coupled grains of strongly-correlated superconductor

“…The resulting "plum-pudding" model of overdoped cuprates has some overlap with the idea of phase separation [7][8][9][10]85], although our perspective is somewhat different. There is increasing experimental [30] and theoretical [86][87][88] evidence that charge stripe correlations, defined by antiferromagnetic spin stripe correlations, are relevant to pairing and superconductivity in cuprates. All doped holes effectively go into charge stripes at low doping, but the stripe density saturates at p ∼ 1/8, so that holes added beyond that point must go into more uniformly-doped regions [34].…”

Phonon-Mediated Long-Range Attractive Interaction in One-Dimensional Cuprates

“…Although numerical simulations using this model have reproduced some observations in cuprates, such as antiferromagnetism [8], spin and charge stripe phases [9][10][11][12], and strange metallic behavior [13][14][15], the most significant phase -high-T c d-wave superconductivity -remains an enigma. To date, numerical evidence for quasi-long-range-ordered superconductivity has been reported for specific systems and methods [16][17][18][19][20], but the exact solutions with cylinder geometry always reveal a coexistence of the charge order with comparable strength, and superconducting correlations progressively decay on shorter length scales as the numerical cluster size increases [21][22][23][24]. This contrasts sharply to the robust high-T c superconducting phases observed in a large family of cuprate compounds.…”