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Despite decades of intensive experimental and theoretical efforts, thephysics of cuprate high-temperature superconductors in general, and, inparticular, their normal state, is still under debate. Here, we report ourinvestigation of low-energy charge excitations in the normal state. We findthat the peculiarities of the electronic band structure at low energies have aprofound impact on the nature of the intraband collective modes. It gives riseto a new kind of mode with huge intensity and non-Lorentzian spectral functionin addition to well-known collective excitations like conventional plasmons andspin fluctuation. We predict two such modes with maximal spectral weight in thenodal and antinodal directions. Additionally, we found a long-livingquasi-one-dimensional plasmon becoming an intense soft mode over an extendedmomentum range along the antinodal direction. These modes might explain some ofthe resonant inelastic X-ray scattering spectroscopy data.

Unusual Low-Energy Collective Charge Excitations in High-$T_c$ Cuprate Superconductors