Spin loop-current textures in Hubbard models

Abstract

The recent experimental observations of loop current in Sr${}_2$IrO${}_4$, YBa${}_2$Cu${}_3$O${}_7$, and Sr${}_{14}$Cu${}_{24}$O${}_{41}$ have inspired a theoretical study that broadly redefines loop current as a manifestation of quantum liquid crystals. Using the density-matrix renormalization group method, we investigate the emergence of spin loop-current (sLC) textures in carrier-doped (i) excitonic insulators, (ii) orbital-selective Mott insulators, and (iii) two-dimensional Mott insulators, modeled by a two-orbital Hubbard model on a ladder lattice in (i) and (ii) and a single-orbital Hubbard model on a square lattice in (iii). Calculating the spatial distribution of spin current around a bond to which a pinning field is applied, we find conditions for longer-ranged sLC correlations. In system (i), when using the model parameters employed to describe the excitonic condensation, we find that a sLC texture appears near half filling, associated with an excitonic condensation in a spin channel. In system (ii), using typical sets of model parameters for BaFe${}_2$Se${}_3$, we find that a sLC texture appears at electron fillings where a block-type antiferromagnetism develops. In system (iii), introducing a next-nearest-neighbor hopping $t^{\prime }\sim -0.25$ (in units of the nearest-neighbor hopping) suggested for high-$T_{\text{c}}$ cuprates, we find that an axial-sLC texture emerges at hole-carrier density $\delta =0.125$, where the charge stripe simultaneously appears.

15 pages, 12 figures

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