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arXiv:2109.04492 · Physical review. B./Physical review. B

Spin texture in doped Mott insulators with spin-orbit coupling

Shuai A. Chen, Zheng-Yu Weng, Jan Zaanen

Published Feb 22, 2022• 4 citations
arXivHTMLPDF

Abstract

A hole injected into a Mott insulator will gain an internal structure as recently identified by exact numerics, which is characterized by a nontrivial quantum number whose nature is of central importance in understanding the Mott physics. In this work, we show that a spin texture associated with such an internal degree of freedom can explicitly manifest after the spin degeneracy is lifted by a weak Rashba spin-orbit coupling (SOC). It is described by an emergent angular momentum ${J}_{z}=\ifmmode\pm\else\textpm\fi{}\frac{3}{2}$ as shown by both exact diagonalization and variational Monte Carlo calculations, which are in good agreement with each other at a finite size. In particular, as the internal structure such a spin texture is generally present in the hole composite even at high excited energies, such that a corresponding texture in momentum space, extending deep inside the Brillouin zone, can be directly probed by the spin-polarized angle-resolved photoemission spectroscopy (ARPES). This is in contrast to a Landau quasiparticle under the SOC, in which the spin texture induced by SOC will not be protected once the excited energy is larger than the weak SOC coupling strength, away from the Fermi energy. We point out that the spin texture due to the SOC should be monotonically enhanced with reducing spin-spin correlation length in the superconducting-pseudogap phase at finite doping. A brief discussion of a recent experiment of the spin-polarized ARPES will be made.

DOI
10.1103/physrevb.105.075136

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A hole injected into a Mott insulator will gain an internal structure as recently identified by exact numerics, which is characterized by a nontrivial quantum number whose nature is of central importance in understanding the Mott physics. In this work, we show that a spin texture associated with such an internal degree of freedom can explicitly manifest after the spin degeneracy is lifted by a weak Rashba spin-orbit coupling (SOC). It is described by an emergent angular momentum Jz=\ifmmode±\else\textpm\fi32{J}_{z}=\ifmmode\pm\else\textpm\fi{}\frac{3}{2}Jz​=\ifmmode±\else\textpm\fi23​ as shown by both exact diagonalization and variational Monte Carlo calculations, which are in good agreement with each other at a finite size. In particular, as the internal structure such a spin texture is generally present in the hole composite even at high excited energies, such that a corresponding texture in momentum space, extending deep inside the Brillouin zone, can be directly probed by the spin-polarized angle-resolved photoemission spectroscopy (ARPES). This is in contrast to a Landau quasiparticle under the SOC, in which the spin texture induced by SOC will not be protected once the excited energy is larger than the weak SOC coupling strength, away from the Fermi energy. We point out that the spin texture due to the SOC should be monotonically enhanced with reducing spin-spin correlation length in the superconducting-pseudogap phase at finite doping. A brief discussion of a recent experiment of the spin-polarized ARPES will be made.
The internal structure of doped holes in the Mott insulator may provide important insight into the physics of doped cuprates. Its observability via a single-particle probe by scanning tunneling spectroscopy (STS) and angle-resolved photoemission spectroscopy (ARPES) is explored in this paper. Specifically, we study the single-particle spectral function based on a two-hole variational ground-state wave function [J.-Y. Zhao et al., Phys. Rev. X 12, 011062 (2022)] in the $t\text{\ensuremath{-}}J$ model. The latter as a strongly correlated state possesses a dichotomy of ddd-wave Cooper pairing and sss-wave ``twisted'' hole pairing. This pairing structure will give rise to two branches of local spectral function at finite energies. The low-lying one corresponds to a nodal-like quasiparticle excitation and the higher branch is associated with the pair breaking of ``twisted'' quasiparticles, with the threshold energy resembling a pseudogap, which is consistent with the recent STS observation. It can be further extended into energy spectra in momentum space measurable by ARPES, where the low-energy dispersion is also shown to agree well with the quantum Monte Carlo numerical result for a single hole. It implies that the dominant pairing force arises from the twisted holes showing up in the high-energy branch. The effect of the next-nearest-neighbor hopping integral ${t}^{\ensuremath{'}}$ is also examined, which shows an interesting distinction between ${t}^{\ensuremath{'}}/t>0$ and ${t}^{\ensuremath{'}}/t\ensuremath{\le}0$ with a dramatic shift of the low-lying excitation from the nodal region to the antinodal region, but with the high-energy branch remaining insensitive to ${t}^{\ensuremath{'}}$. Finally, a possible ``orthogonality catastrophe'' effect, namely, a ``dark matter'' component in the strongly correlated wave function that cannot be directly detected by the single-electron spectroscopy, is briefly discussed.
Recent angle-resolved photoemission spectroscopy (ARPES) for a newly discovered doped one-dimensional (1D) Mott insulator ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ proposed the presence of attractive charge interactions between neighboring sites if a 1D Hubbard model is employed to describe the material. On the other hand, long-range repulsive charge interactions were proposed to be crucial for understanding the optical excitations of undoped 1D Mott insulators. Motivated by these contrasting proposals, we perform density-matrix renormalization group calculations of the single-particle spectral function as well as dynamical spin and charge structure factors for two kinds of extended 1D Hubbard models. The spectral function for the long-range repulsive model less agrees with the ARPES data as compared with that for the attractive one. The dynamical spin and charge structure factors also exhibit contrasting behaviors between the two models: The attractive model shows less momentum dependence of the integrated weight in the dynamical spin structure factor and more accumulation of the weight on the upper edge of particle-hole-type excitation in the dynamical charge structure factor. These features give a good criterion of an appropriate model for doped 1D Mott insulators, which can be judged by resonant-inelastic x-ray scattering experiments.
A central issue of Mott physics, with symmetries being fully retained in the spin background, concerns the charge excitation. In a two-leg spin ladder with a spin gap, an injected hole can exhibit either a Bloch wave or a density wave by tuning the ladder anisotropy through a ``quantum critical point'' (QCP). The nature of such a QCP has been a subject of recent studies by density matrix renormalization group. In this paper, we reexamine the ground state of the one doped hole, and show that a two-component structure is present in the density wave regime, in contrast to the single component in the Bloch-wave regime. In the former, the density wave itself is still contributed by a standing-wave-like component characterized by a quasiparticle spectral weight ZZZ in a finite-size system. But there is an additional charge incoherent component emerging, which intrinsically breaks the translational symmetry associated with the density wave. The partial momentum is carried away by neutral spin excitations. Such an incoherent part does not manifest in the single-particle spectral function, directly probed by the angle-resolved photoemission spectroscopy measurement, however, it is demonstrated in the momentum distribution function. Landau's one-to-one correspondence hypothesis for a Fermi liquid breaks down here. The microscopic origin of this density wave state as an intrinsic manifestation of the doped Mott physics will be also discussed.
We study a ground-state ansatz for the single-hole-doped $t\text{\ensuremath{-}}J$ model in two dimensions via a variational Monte Carlo method. Such a single-hole wave function possesses finite angular momenta generated by hidden spin currents, which give rise to a novel ground-state degeneracy in agreement with recent exact diagonalization (ED) and density matrix renormalization group (DMRG) results. We further show that the wave function can be decomposed into a quasiparticle component and an incoherent momentum distribution in excellent agreement with the DMRG results up to an $8\ifmmode\times\else\texttimes\fi{}8$ lattice. Such a two-component structure indicates the breakdown of Landau's one-to-one correspondence principle, and in particular, the quasiparticle spectral weight vanishes by a power law in the large sample size limit. By contrast, turning off the phase string induced by the hole hopping in the so-called $\ensuremath{\sigma}\ifmmode\cdot\else\textperiodcentered\fi{}t\text{\ensuremath{-}}J$ model, a conventional Bloch-wave wave function with a finite quasiparticle spectral weight can be recovered, also in agreement with the ED and DMRG results. The present study shows that a singular effect already takes place in the single-hole-doped Mott insulator, by which the bare hole is turned into a non-Landau quasiparticle with translational-symmetry breaking. Generalizations to pairing and finite doping are briefly discussed.
Motivated by recent experimental development, we investigate spin–orbit coupled repulsive Fermi atoms in a one-dimensional optical lattice. Using the density-matrix renormalization group method, we calculate the momentum distribution function, gap, and spin-correlation function to reveal rich ground-state properties. We find that spin–orbit coupling (SOC) can generate unconventional momentum distribution, which depends crucially on the filling. We call the corresponding phase with zero gap the SOC-induced metallic phase. We also show that SOC can drive the system from the antiferromagnetic to ferromagnetic Mott insulators with spin rotating. As a result, a second-order quantum phase transition between the spin-rotating ferromagnetic Mott insulator and the SOC-induced metallic phase is predicted at the strong SOC. Here spin rotating means the spin orientations of the nearest-neighbor sites are not parallel or antiparallel, i.e., they have an intersection angle Finally, we show that the momentum k peak , at which the peak of the spin-structure factor appears, can also be affected dramatically by SOC. The analytical expression of this momentum with respect to the SOC strength is also derived, which suggests that the predicted spin-rotating ferromagnetic ( k peak < π /2 ) and antiferromagnetic ( π /2 < k peak < π ) correlations can be detected experimentally by measuring the SOC-dependent spin-structure factor via time-of-flight imaging.
We show here that many of the normal state properties of the cuprates can result from the new charge 2e2e2e bosonic field which we have recently [Phys. Rev. Lett. 99, 046404 (2007); Phys. Rev. B 77, 014512 (2007)] shown to exist in the exact low-energy theory of a doped Mott insulator. In particular, the (1) midinfrared band including the nonvanishing of the restricted fff-sum rule in the Mott insulator, (2) T2{T}^{2}T2 contribution to the thermal conductivity, (3) pseudogap, (4) bifurcation of the electron spectrum below the chemical potential, as recently seen in angle-resolved photoemission, (5) insulating behavior away from half-filling, (6) high- and low-energy kinks in the electron dispersion, and (7) TTT-linear resistivity all derive from the charge 2e2e2e bosonic field. We also calculate the inverse dielectric function and show that it possesses a sharp quasiparticle peak and a broad particle-hole continuum. The sharp peak is mediated by a new charge eee composite excitation formed from the binding of a charge 2e2e2e boson and a hole and represents a distinctly new prediction of this theory. It is this feature that is responsible for the dynamical part of the spectral weight transferred across the Mott gap. We propose that electron-energy loss spectroscopy at finite momentum and frequency can be used to probe the existence of such a sharp feature.