Robust spin and charge excitations throughout high-$T_c$-cuprate phase diagram from incipient Mottness

Abstract

The generic phase diagram of lightly hole-doped high-$T_c$-cuprates hosts antiferromagnetic insulating phase with well-defined spin-wave excitations. Contrary to the weak-coupling prediction, these modes persist up to the overdoped metallic regime as intense and dispersive paramagnons. Here we report on our study of the low-energy magnetic and charge excitations within the extended Hubbard model at strong-coupling, using a modified $1/N$ expansion method with a variational state serving as the saddle point solution. Despite clear separation of magnetic and Hubbard-$U$ energy scales, we find that incipient Mottness affects qualitatively dispersions and widths of magnetic modes throughout entire phase diagram. The obtained magnetic and charge dynamical structure factors agree semi-quantitatively with recent resonant $X$-ray and neutron scattering data for $\mathrm{L}{\mathrm{a}}_{2-x}\mathrm{S}{\mathrm{r}}_x\mathrm{Cu}{\mathrm{O}}_4$ and $(\mathrm{Bi},\mathrm{Pb}{)}_2(\mathrm{Sr},\mathrm{La}{)}_2\mathrm{Cu}{\mathrm{O}}_{6+\delta }$ at all available doping levels. The weak-coupling random-phase-approximation fails already for underdoped samples, pointing to the non-trivial intertwining of distinct energy scales in cuprate superconductors. The existence of a discrete charge mode which splits off the electron-hole continuum is also predicted.

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• Superconductivity in high-$T_c$ and related strongly correlated systems from variational perspective: Beyond mean field theory
• A unified theory of spin and charge excitations in high-$T_c$ cuprates: Quantitative comparison with experiment and interpretation
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• Superconductivity in the three-band model of cuprates: nodal direction characteristics and influence of intersite interactions
• Ising and XY paramagnons in two-dimensional 2H-NbSe${}_2$
• Universal collective modes from strong electronic correlations: Modified $1/{\mathcal{N}}_f$ theory with application to high-$T_c$ cuprates
• Coexistence of $s$- and $d$-wave gaps due to pair-hopping and exchange interactions
• Collective spin and charge excitations in the $t$-$J$-$U$ model of high-$T_c$ cuprates
• Collective mode excitations and simulated $L$-edge resonant-inelastic x-ray scattering spectra in antiferromagnetic Ca${}_2$RuO${}_4$
• Electron-hole asymmetry of quantum collective excitations in high-$T_c$ copper oxides