Rotational Phonons Drive Low-Energy Kinks in Cuprate Superconductors

Abstract

Angle-resolved photoemission spectroscopy (ARPES) reveals ubiquitous quasiparticle ``kinks'' near $\sim$70 meV and $\sim$40 meV across cuprate superconductors, often accompanied by peak--dip--hump (PDH) structures. These features point to strong coupling between electrons and low-energy bosonic excitations, but the microscopic origin has remained elusive due to the limitations of conventional density-functional theory (DFT) and the high cost of beyond-DFT methods. Here, we systematically study the electron--phonon coupling (EPC) in hole-doped infinite-layer CaCuO$_2$ using the Strongly Constrained and Appropriately Normed (SCAN) density functional, explicitly including magnetic effects. We find a substantial EPC strength $λ$ of $\sim$0.5 in the magnetic phase, producing kinks and PDH structures in the 40-80~meV window in excellent agreement with experiments. The dominant contribution arises from rotational oxygen phonons, while breathing modes contribute little. Our results establish strong EPC in cuprates, highlight the key role of rotational phonons, and provide a framework for understanding spectral anomalies in cuprates and beyond.

Figures (2)

• Figure 1: Calculated phonon dispersion and EPC of $G$-AFM phase of CaCuO$_2$ with 25% hole doping. (a) Left panel: calculated folded phonon dispersion along high-symmetry lines in the first BZ; marker color-intensity indicates the value of the EPC strength, $\lambda_{\textbf{q}\nu}$, for the doped phase; Middle panel: site-projected phonon density of states (PhDOS). Right panel: calculated Eliashberg spectral functions, $\alpha^2F(\omega)$ (solid red lines), and the cumulative EPC strength, $\lambda$ (dashed blue lines). A $k$-mesh of $60 \times 60 \times 60$ and a $q$-mesh of $30 \times 30 \times 30$ were used for full BZ sampling. (b) Phonon dispersion color-coded by the $z$-component of the circular polarization for vibrations of four representative oxygen sites in the same sense. Red, blue, and gray denote right-handed $s^{\alpha}_{\mathbf{q},\sigma}>0$, left-handed ($s^{\alpha}_{\mathbf{q},\sigma}<0$), and non-polarized ($s^{\alpha}_{\mathbf{q},\sigma}=0$) phonon modes. (c) Schematic of the NM and AFM BZs in the $k_z = 0$ plane, with high-symmetry points marked. (d) Closeup of the area marked by the black-dashed rectangle in (b) to highlight the rotational phonon modes. (e)-(h) Side view of selected phonon modes marked at (b), with green arrows representing the direction of atomic vibrations. Brown, light green, and red balls represent Cu, Ca, and O atoms, respectively.
• Figure 2: Comparison of the expermental and calculated spectral functions (a)-(c) Measured ARPES spectra at $T=20K$ for Bi2201 with a similar hole doping level of approximately 20%, extracted from Ref. Hongtao_PNAS. Red arrows indicate high-energy humps and dips, while blue arrows indicate low-energy ones. (d) Calculated spectral function along the $\Gamma$–$N$ direction. (e) shows the second derivative of the spectral function with respect to energy, showing the absolute magnitude of the negative values, while (c) presents the corresponding positive components. Red arrows indicate high-energy humps and peaks. (g)-(i) same as (d)-(f), but only considering the rotational phonon contributions. Note that peaks in the second derivative correspond to dips in the phonon spectrum, and vice versa.