Anomalous band renormalization due to a high-energy kink in ${\mathrm{K}}_{0.65}{\mathrm{RhO}}_2$ with colossal thermoelectric power factor

We identify highly correlated hole pocket on the Fermi surface of colossal thermoelectric material ${\mathrm{K}}_{0.65}{\mathrm{RhO}}_2$, studied using high-resolution angle-resolved photoemission spectroscopy (ARPES) and density-functional theory (DFT) calculations. Most importantly, two kinks at binding energies of 75 and 195 meV have been observed below the Fermi level. While the low-energy kink at 75 meV can be understood as a result of the electron-phonon interaction, the high-energy kink at 195 meV is a discovery of this system, leading to anomalous band renormalization, possibly originated from the bosonic excitations at higher frequencies. We further notice that the high-energy anomaly has important implications on the colossal thermoelectric power of ${\mathrm{K}}_{0.65}{\mathrm{RhO}}_2$.

Figure 1

ARPES measurements of ${\mathrm{K}}_{0.65}{\mathrm{RhO}}_2$. The data are measured using $p$-polarized light with a photon energy of 140 eV. (a) Fermi-surface map. (b) Constant energy map taken at a binding energy of 0.25 eV below $E_F$. (c) Energy distribution maps (EDMs) showing the band dispersions along the $\mathrm{\Gamma }\text{−}K$, $\mathrm{\Gamma }\text{−}M$, and $M\text{−}K$ high-symmetry directions.

Figure 2

(a) Energy distribution map taken along the $\mathrm{\Gamma }\text{−}M$ orientation as shown in the inset. (b) Band dispersion extracted by fitting the momentum distribution curves of the EDM shown in panel (a) using a Lorentzian function. Black dashed line in panel (b) is a linear fit to band dispersion at the higher binding energy within the window of ($-0.2$ eV, $-0.09$ eV). The arrows in panel (b) show the energy positions of the kinks. (c) Real part of the self-energy (${\mathrm{\Sigma }}^{\prime }$) extracted from the EDM shown in panel (a). In panel (c), the black line is linear fit to the data performed to extract the coupling constant $\lambda =2.7\pm 0.3$. (d) Imaginary part of the self-energy (${\mathrm{\Sigma }}^{″}$) extracted from the EDM shown in panel (a). In panel (d), the black curve represents fitting with combined functions of Fermi-liquid theory type and Eliashberg spectral functions (see text).

Figure 3

(b) In-plane momentum-dependant band dispersions extracted from the EDMs taken along the cuts by varying $\mathrm{\Phi }$ as shown in panel (a). (c) In-plane momentum dependant Fermi and group velocities extracted by fitting with linear function within the binding-energy windows as defined in panel (b). (d) In-plane momentum-dependent coupling constant $\lambda$ and carrier effective mass $m^{*}/m_e$. In panels (c) and (d) the data are fit with cosine functions.

Figure 4

(a) Out-of-plane Fermi-surface map taken in the $k_z\text{−}{k}_{\parallel }$ plane. (b) Representative $k_z$ ($h\nu$) dependent imaginary part of the self-energy ${\mathrm{\Sigma }}^{″}$. (c) Representative $k_z$-dependent band dispersions. (d) $k_z$-dependent strength of electron-electron correlation extracted by fitting with Fermi-liquid-type spectral function (see text). (e) $k_z$-dependent Fermi and group velocities extracted by fitting with linear function within the binding energy window as shown in panel (c). (f) $k_z$-dependent coupling constant and carrier effective mass. In panels (d) and (e) the data are fit with cosine functions.