Local electronic nematicity in the two-dimensional one-band Hubbard model

Abstract

Nematicity is a well-known property of liquid crystals and has been recently discussed in the context of strongly interacting electrons. An electronic nematic phase has been seen in many experiments in certain strongly correlated materials, in particular, in the pseudogap phase generic to many hole-doped cuprate superconductors. Recent measurements in high Tc superconductors have shown that even if the lattice is perfectly rotationally symmetric, the ground state can still have strongly nematic local properties. Our study of the two-dimensional one-band Hubbard model provides strong support for the recent experimental results on local rotational C4 symmetry breaking. The variational cluster approach is used here to show the possibility of an electronic nematic state and the proximity of the underlying symmetry-breaking ground state within the Hubbard model. We identify this nematic phase in the overdoped region and show that the local nematicity decreases with increasing electron filling. Our results also indicate that strong Coulomb interaction may drive the nematic phase into a phase similar to the stripe structure. The calculated spin (magnetic) correlation function in momentum space shows the effects resulting from real-space nematicity.

Spontaneous nematicity triggered by impurities in a Hubbard model for the cuprates

“…This is to be contrasted with the results of Ref. [21], obtained in the variational cluster approximation (VCA), where spontaneous nematicity is found in the SC phase in a pure system and extends very far from half-filling. We could likewise define a nematic order parameter based on site (not bond) charges, for instance by considering the densities n x and n y on the two nearest neighbors of the impurity site at the lower-left corner of Fig.…”

Orbital nematic order and interplay with magnetism in the two-orbital Hubbard model

“…Using this approach, the authors found that anisotropy can develop in the overdoped region. 79 However, the multi-orbital nature of the iron pnictides was not taken into account in these studies.…”

“…Both groups found that for a sufficiently large interaction U , a small orthorhombic distortion can lead to a large nematic response in the low-energy electron scattering rate. Another way to study the spontaneous development of nematicity in the one-band Hubbard model is by introducing an anisotropic hopping inside the cluster alone Ĥcl = δt r ( ĉ † r ĉr+x − ĉ † r ĉr+y )+h.c., and then optimize the strength of δt variationally in VCA [79]. Using this approach, the authors found that anisotropy can develop in the overdoped region [79].…”

“…Another way to study the spontaneous development of nematicity in the one-band Hubbard model is by introducing an anisotropic hopping inside the cluster alone Ĥcl = δt r ( ĉ † r ĉr+x − ĉ † r ĉr+y )+h.c., and then optimize the strength of δt variationally in VCA [79]. Using this approach, the authors found that anisotropy can develop in the overdoped region [79]. However, the multi-orbital nature of the iron pnictides was not taken into account in these studies.…”

Unconventional non-Fermi liquid state caused by nematic criticality in cuprates

“…Halboth and Metzner [35] studied a two-dimensional Hubbard model using functional renormalization group (RG) method, and revealed Pomeranchuk instability and nematic order. More recently, the square lattice Hubbard model is studied by variational cluster approximation [45,46] and found to display a local nematic phase under certain circumstances, which might be applied to understand the intra-unit-cell electronic nematicity observed in the scanning tunneling spectroscopy (STS) measurements by Lawler et al [13].…”