Emergence of a Coherent In-Gap State in the ${\mathrm{SmB}}_6$ Kondo Insulator Revealed by Scanning Tunneling Spectroscopy

We use scanning tunneling microscopy to investigate the (001) surface of a cleaved ${\mathrm{SmB}}_6$ Kondo insulator. Variable temperature $dI/dV$ spectroscopy up to 60 K reveals a gaplike density of state suppression around the Fermi level, which is due to the hybridization between the itinerant Sm $5d$ band and localized Sm $4f$ band. At temperatures below 40 K, a sharp coherence peak emerges within the hybridization gap near the lower gap edge. We propose that the in-gap resonance state is due to a collective excitation in magnetic origin with the presence of spin-orbital coupling and mixed valence fluctuations. These results shed new light on the electronic structure evolution and transport anomaly in ${\mathrm{SmB}}_6$.

Figure 1

(a) Schematic crystal structure of ${\mathrm{SmB}}_6$ where two possible cleaving planes parallel to the (001) surface are shown in purple and blue. (b) Photograph of the cleaved (001) surface of a ${\mathrm{SmB}}_6$ crystal. (c) The $R$ vs $T$ curve of ${\mathrm{SmB}}_6$ shows the insulating behavior at high $T$ and the saturation at $T<5\mathrm{K}$ (inset). (d) Inverse magnetic susceptibility as a function of $T$ shows the deviation from the high $T$ Curie-Weiss behavior at $\sim 120\mathrm{K}$.

Figure 2

(a)–(d) STM images on the cleaved (001) surface of ${\mathrm{SmB}}_6$. Four types of surface structures are observed, including atomically resolved A1 (a) and A2 phases (b), donutlike D1 (c) and D2 (d) phases. The weak $\sqrt{2}\times \sqrt{2}$ pattern in the A1 phase is indicated by the dashed circles in (a). The insets are the corresponding FTs. (e)–(h) Schematic top view of the four cleaved surfaces. The black circles in (g) and (h) mark the positions of the donuts. (i)–(l) $dI/dV$ spectra taken at $T=5\mathrm{K}$ on the representative locations marked by solid circles with corresponding colors in (a)–(d). Vertical offset is used for clarity.

Figure 3

(a) High-resolution image of the majority D2 phase. The STS measurements at different temperatures are all done on donuts in this phase. (b) High energy $dI/dV$ spectra taken on the donuts in the D2 phase at four selected temperatures. (c) Low energy spectra (black open circles) taken at varied temperatures from 5 to 60 K, revealing the emergence of the resonance peak below 40 K, and the simulations of the $dI/dV$ spectra (red lines). For curves above 40 K, the hybridization gap is simulated only by the co-tunneling model. For curves below 40 K, the data are simulated by the co-tunneling model and a Guassian term for the resonance peak.

Figure 4

(a) Theoretical simulation of the $dI/dV$ spectra. For $T=60\mathrm{K}$ only the cotunneling model is used to simulate the hybridization gap. For $T=5\mathrm{K}$, the simulated gap feature (red curve) is subtracted from the raw data, and the remaining resonance peak is fitted by a Gaussian term (blue curve). (b) The weight and FWHM of the Gaussian peak as a function of $T$, showing the disappearance of the coherence peak above 40 K. (c) $T$-dependent gap amplitude and quasiparticle scattering rate ${\gamma }_f$ of $f$ electrons extracted from the cotunneling simulation [Fig. 3].