Topological Properties and the Dynamical Crossover from Mixed-Valence to Kondo-Lattice Behavior in the Golden Phase of SmS

We have investigated temperature-dependent behaviors of electronic structure and resistivity in a mixed-valent golden phase of SmS, based on the dynamical mean-field-theory band-structure calculations. Upon cooling, the coherent Sm $4f$ bands are formed to produce the hybridization-induced pseudogap near the Fermi level, and accordingly the topology of the Fermi surface is changed to exhibit a Lifshitz-like transition. The surface states emerging in the bulk gap region are found to be not topologically protected states but just typical Rashba spin-polarized states, indicating that SmS is not a topological Kondo semimetal. From the analysis of anomalous resistivity behavior in SmS, we have identified universal energy scales, which characterize the Kondo–mixed-valent semimetallic systems.

Figure 1

Isostructural phase transition in SmS. (a) Bulk and surface Brillouin zones (BZs) of fcc SmS. (b) The pressure dependence of the lattice constant and the Sm valence state of SmS (data taken from Ref. [22]).

Figure 2

Electronic structure of $g$-SmS ($a=5.6\AA$). (a) The DMFT band structure at $T=13\mathrm{K}$. (b) Surface band structure obtained by the model slab calculation based on the DFT band structure. The surface states in the inset manifest a typical Rashba splitting with a tiny gap, and so they are not topologically protected states. (c) $T$-dependent band structures in the DMFT scheme. Upon cooling, the coherent Sm $4f$ band emerges near $E_F$, and the hybridization gap appears below $T=26\mathrm{K}$. (d) $T$-dependent FS evolution in the DMFT scheme, which is compared with the DFT FS with 10 times enhanced SOC scheme of the Sm $4f$ electron (top left) [39]. Upon cooling, $X$-centered $d$-band pockets are reduced, while $f$-band pockets emerge at $\mathrm{\Gamma }$.

Figure 3

$T$-dependent behaviors in $g$-SmS ($a=5.6\AA$). (a) $T$-dependent DOS variation in the DMFT scheme. Upon cooling, the $J=5/2$ DOS behaves like a Kondo resonance with the pseudogaplike dip feature near $E_F$. The $J=7/2$ DOS peak near $-0.17\mathrm{eV}$ is also shown. (b) The number of occupied $f$ electrons ($n_f$) as a function of the logarithmic $T$ scale. Upon cooling, $n_f$ increases monotonically from a trivalent state to the mixed-valent state. The effective valence transition (VT) occurs at $T\simeq 80\mathrm{K}$, as indicated by the peak in $-d(n_f)/d(\log T)$. (c) Resistivity vs $T$ obtained by the DMFT scheme. The experimental data are taken from Ref. [37], which are shifted by 9.3 K toward higher $T$. Upon cooling, SmS undergoes several crossover transitions from valence fluctuation liquid (VFL), Kondo liquid (KL), pseudogap (PG), to Landau Fermi liquid (LFL).