Fermionic spinon theory of the hourglass spin excitation spectrum of the cuprates

TL;DR

The paper tackles the problem of reproducing the characteristic hourglass spin excitation spectrum in hole-doped cuprates within a microscopic framework that ties spin fluctuations to fractionalized excitations. It adopts the Ancilla Layer Model with a $\pi$-flux spin liquid in the bottom layer, yielding four spinon pockets of area $p/8$ and Dirac nodes, and introduces a period-4 CDW order via a Higgs field $B$ that confines spinons at low energies. Using mean-field ALM plus RPA, the authors obtain a triplon branch below the spinon continuum that forms an hourglass around $(\pi,\pi)$ after averaging over CDW domains, with high-energy weight arising from the spinon continuum. The results provide a microscopic link between FL* pseudogap physics and experimental spin fluctuations observed in neutron scattering and RIXS, and they generate concrete predictions such as magnetic-field–induced splitting of the hourglass branches.

Abstract

We present a theory for the spin fluctuation spectrum of the hole-doped cuprates in a ground state with period 4 unidirectional charge density wave (`stripe') order. Motivated by recent experimental evidence for a fractionalized Fermi liquid (FL*) description of the intermediate temperature pseudogap metal, we employ a theory of fermionic spinons which are confined with the onset of stripe order at low temperatures. The theory produces the `hourglass' spectrum near stripe-ordering wavevector observed by neutron scattering. Additional scattering from spinon continua and bound states appears at higher energies and elsewhere in the Brillouin zone, and could be observed by neutron or X-ray scattering.

Figures (11)

• Figure 1: Bare $\pi$-flux spin structure factor $-\Im \chi^0(\omega,q)$ on a logarithmic scale along high-symmetry directions in the Brillouin zone. The regions of strong intensity correspond to a spinon continuum, having a Dirac-like shape near $(\pi,\pi)$.
• Figure 2: Bare $\pi$-flux spin structure factor $-\Im \chi^0(\omega,q)$ on a logarithmic scale in the presence of CDW order, averaged over the $x$ and $y$-directions. As a result of CDW order, the gap opens throughout the Brillouin zone, moving the spinon continuum to higher energies.
• Figure 3: RPA $\pi$-flux spin structure factor $-\Im \chi^{RPA}(\omega,q)$ on a logarithmic scale in the presence of CDW order, averaged over the $x$ and $y$-directions. RPA corrections to the susceptibility introduce a triplon line-shape of high intensity, having an hourglass-like form near $(\pi,\pi)$.
• Figure 4: RPA $\pi$-flux spin structure factor on a logarithmic scale in the presence of CDW order along the $x$-direction (a) and along the $y$ direction (b). The minimum of the triplon branch is centered at $(\pi,\pi)$ when the CDW order is set along the $x$-direction, and it is shifted from $(\pi,\pi)$ when the order is along the $y$-direction, producing a famous hourglass-like spectrum after averaging over both directions.
• Figure 5: RPA spin structure factor on a logarithmic scale in the presence of CDW order averaged over the $x$ and $y$-directions, when all three ancilla layers hybridize and contribute to the overall susceptibility. The presence of hole pockets and gapless excitations in the first two layers result in the finite spectral weight inside the CDW gap and broadens the triplon branch.