Collective charge excitations in the kagome lattice driven by Holstein phonons and magnetic fields

Abstract

Abstract

The combined effects of Holstein electron–phonon coupling and an external magnetic field on the tunable charge-response resonances of the kagome lattice are investigated. Within the Holstein model supplemented by nearest- and next-nearest-neighbor hopping, a staggered sublattice potential, and Zeeman splitting, the single-particle Hamiltonian is diagonalized analytically to obtain the band dispersions and eigenvectors. The non-interacting Matsubara Green’s functions are constructed, and the frequency-dependent effective electron–electron interaction arising from virtual exchange of dispersionless Einstein phonons is incorporated into the random-phase approximation for the dynamical charge susceptibility. For the site-local Holstein kernel the defining RPA is the $$3\times 3$$ matrix equation in sublattice space; at the representative wave vector of the figures this matrix response coincides with the scalar total-density formula on the two principal resonances. The dynamical charge structure factor $$S_c({\textbf{q}},\omega )$$ and the static charge structure factor are subsequently obtained from the retarded susceptibility and the fluctuation–dissipation theorem, respectively. Numerical results at a representative wave vector in the Brillouin zone show that increasing the electron–phonon coupling strength redistributes spectral weight and shifts the high-energy charge resonance to higher frequencies, whereas the external magnetic field mainly suppresses the intensities of both charge resonances without appreciably shifting their positions. The next-nearest-neighbor hopping amplitude and the staggered gap allow selective tuning of the spectral weights of the low- and high-energy charge resonances. The static charge correlations exhibit non-monotonic dependencies on temperature and magnetic field, originating from the competition among thermal fluctuations, Zeeman splitting, and phonon-mediated attraction. These results demonstrate that Holstein phonons and an external magnetic field can be used in combination to control both the dynamical and static charge responses of the kagome lattice, including the tunable charge resonances.