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Register a new userStripe order enhanced superconductivity in the Hubbard model
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Unidirectional (stripe) charge-density-wave order has now been established as a ubiquitous feature in the phase diagram of the cuprate high temperature (HT) superconductors, where it generally competes with superconductivity (SC). None-the-less, on theoretical grounds it has been conjectured that stripe order (or other forms of optimal inhomogeneities) may play an essential positive role in the mechanism of HTSC. Here we report density matrix renormalization group studies of the Hubbard model on long 4 and 6 leg cylinders where the hopping matrix elements transverse to the long direction are periodically modulated - mimicing the effect of putative period-2 stripe order. We find even modest amplitude modulations can enhance the long-distance SC correlations by many orders of magnitude, and drive the system into a phase with a substantial spin gap and SC quasi-long-range-order with a Luttinger exponent, $K_{sc} sim 1$.
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A microscopic understanding of the strongly correlated physics of the cuprates must account for the translational and rotational symmetry breaking that is present across all cuprate families, commonly in the form of stripes. Here we investigate emergence of stripes in the Hubbard model, a minimal model believed to be relevant to the cuprate superconductors, using determinant quantum Monte Carlo (DQMC) simulations at finite temperatures and density matrix renormalization group (DMRG) ground state calculations. By varying temperature, doping, and model parameters, we characterize the extent of stripes throughout the phase diagram of the Hubbard model. Our results show that including the often neglected next-nearest-neighbor hopping leads to the absence of spin incommensurability upon electron-doping and nearly half-filled stripes upon hole-doping. The similarities of these findings to experimental results on both electron and hole-doped cuprate families support a unified description across a large portion of the cuprate phase diagram.
Competing inhomogeneous orders are a central feature of correlated electron materials including the high-temperature superconductors. The two- dimensional Hubbard model serves as the canonical microscopic physical model for such systems. Multiple orders have been proposed in the underdoped part of the phase diagram, which corresponds to a regime of maximum numerical difficulty. By combining the latest numerical methods in exhaustive simulations, we uncover the ordering in the underdoped ground state. We find a stripe order that has a highly compressible wavelength on an energy scale of a few Kelvin, with wavelength fluctuations coupled to pairing order. The favored filled stripe order is different from that seen in real materials. Our results demonstrate the power of modern numerical methods to solve microscopic models even in challenging settings.
We study the interplay of nematic and superconducting order in the two-dimensional Hubbard model and show that they can coexist, especially when superconductivity is not the energetically dominant phase. Due to a breaking of the $C_4$ symmetry, the coexisting phase inherently contains admixture of the $s$-wave pairing components. As a result, the superconducting gap exhibits very non-standard features including changed nodal directions. Our results also show that in the optimally doped regime the superconducting phase is typically unstable towards developing nematicity (breaking of the $C_4$ symmetry). This has implications for the cuprate high-$T_c$ superconductors, for which in this regime the so-called intertwined orders have recently been observed. Namely, the coexisting phase may be viewed as a precursor to such more involved patterns of symmetry breaking.
We study the competition between stripe states with different periods and a uniform $d$-wave superconducting state in the extended 2D Hubbard model at 1/8 hole doping using infinite projected entangled-pair states (iPEPS). With increasing strength of negative next-nearest neighbor hopping $t$, the preferred period of the stripe decreases. For the values of $t$ predicted for cuprate high-T$_c$ superconductors, we find stripes with a period 4 in the charge order, in agreement with experiments. Superconductivity in the period 4 stripe is suppressed at $1/8$ doping. Only at larger doping, $0.18 lesssim delta < 0.25$, the period 4 stripe exhibits coexisting $d$-wave superconducting order. The uniform $d$-wave state is only favored for sufficiently large positive $t$.
We investigate melting of stripe phases in the overdoped regime x>0.3 of the two-dimensional t-t-U Hubbard model, using a spin rotation invariant form of the slave boson representation. We show that the spin and charge order disappear simultaneously, and discuss a mechanism stabilizing bond-centered and site-centered stripe structures.
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