Strongly anisotropic high-temperature Fermi surface of the Kondo semimetal CeNiSn revealed by angle-resolved photoemission spectroscopy

The semimetallic behavior of the so-called “failed Kondo insulator” CeNiSn has been ascribed to a nodal line in the Kondo hybridization derived from a particular symmetry of the Ce $4f$ orbitals ground state. Here we investigate the geometry of the CeNiSn conduction band by combined angle-resolved photoemission spectroscopy (ARPES) in the high-temperature regime and Open core generalized gradient approximation plus spin-orbit coupling calculations, in order to determine how the nodal hybridization takes place. We identify the Fermi sheet involved in the semimetallic regime from its locus and its shape, respectively, in agreement with the expected nodal line and with quantum oscillations. We further extrapolate and discuss the low-temperature Fermi surface in terms of the expected nodal hybridization with a localized $f$-level. The obtained hypothetical low-temperature Fermi surface is compatible with the description from quantum oscillations, and with both the highly anisotropic magnetoresistance and the isotropic Nernst effect. This work offers an overview of the conduction band of CeNiSn before hybridization, and it paves the way to a definitive understanding of its low-temperature state. In addition, this work serves as a basis for more challenging low-temperature ARPES measurements.

Figure 1

Kondo hybridization of a holelike conduction band with a localized $f$-level. The Fermi surface at high temperature (without hybridization) and at low temperature is drawn at the bottom of each graph. Different scenarios give rise to different ground states: (a) Heavy Fermi liquid. (b) Insulator. (c) Semimetal.

Figure 2

(a) Representation of the crystal structure of CeNiSn. (b) Picture of an actual single crystal of CeNiSn, with cleaved pieces. Insets are displays of the crystal orientation made by Rigaku's R-AXIS RAPID II. (c) Representation of a cleave (101) plane from the $〈010〉$ axis. (d) CeNiSn Brillouin zone, with the $〈101〉$ axis upward.

Figure 3

(a) Ce $4d\to 4f$ resonant PES: On- and off-resonance spectra integrated around the normal emission at $T=12$ K. (b) Total and partial density of states from GGA+SOC and Open core GGA+SOC calculations. See Sec. 2 for details about the calculations. (c) Photon energy dependence showing the Fano shape of the Ce $4d\to 4f$ resonance. (d) Close-up of the Ce $4f_{5/2}$ level divided by the Fermi-Dirac distribution at $T=12$ and 60 K, to highlight its binding energy.

Figure 4

(a) Brillouin-zone scheme. Photon energy dependence maps the red plane, while angular mapping of panels (d) and (e) is in the blue plane. (b) Photon energy dependence with the $〈010〉$ direction along the analyzer slit. Inner potential is determined to be about $V_0\approx 15$ eV. The red arc represents the position reached with $h\nu =78$ eV. Colored lines are Open core GGA+SOC calculations. (c) Geometry of the measurements of this figure. (d) Angular mapping at the Fermi level with a constant photon energy of $h\nu =78$ eV. Linear horizontal and vertical data have been summed up. Colored lines are Open core GGA+SOC calculations at $E_{\mathrm{F}}^{\mathrm{ARPES}}$. (e) Same 0.05 eV below the Fermi level. (f) Binding energy vs momentum cuts along the red line of panel (d), with linear horizontal polarization. (g) Same with linear vertical polarization. (h) Three-dimensional Fermi surface from Open core GGA+SOC calculations at $E_{\mathrm{F}}^{\mathrm{ARPES}}$.

Figure 5

(a) Cut along the $Y\text{−}\mathrm{\Gamma }\text{−}Y$ line $\left(〈010〉\right)$ measured at 12 K and $h\nu =78$ eV. The $\mathrm{\Pi }$-shape band can be observed. The blue curve is an EDC at $\mathrm{\Gamma }$. (b) Open core GGA+SOC calculation along the $Y\text{−}\mathrm{\Gamma }\text{−}X$ line. (c) Brillouin-zone scheme. Here, photon energy dependence maps the green plane. (d) Geometry of the measurements of this figure. (e) Photon energy dependence measured with the analyzer slit aligned along the $〈101〉$ direction, i.e., mapping of the $\mathrm{\Gamma }XUZ$ plane. The open rectangles indicate the ranges over which spectra of panels (g) and (h) have been integrated. (f) Binding energy vs momentum cut along the $U\text{−}X\text{−}U$ line. (g) Same along the $\mathrm{\Gamma }\text{−}X\text{−}\mathrm{\Gamma }$ line. (h) EDC at the $X$ point (black open circles), integrated around the $X$ point, divided by the effective Fermi-Dirac step in red. The bold blue curve is a fit of this EDC with two peaks, displayed with blue thin curves below. The blue area depicts the same fit, without the Fermi-Dirac cut.

Figure 6

(a) Same as Fig. 5. The open rectangles indicate the ranges over which spectra of panels (b) and (c) have been integrated. Diamond markers are Fermi momentum extracted from ARPES, $k_{\mathrm{F}}^{\mathrm{ARPES}}$. (b),(c). Binding energy vs momentum cuts along lines parallel to the $\mathrm{\Gamma }\text{−}X\text{−}\mathrm{\Gamma }$ line, as can be seen in panel (a). (d) Fermi momenta from ARPES are symmetrized around the $X$ point. Bold colored lines are Open core GGA+SOC calculations at $E_{\mathrm{F}}^{\mathrm{GGA}}$, while thin colored lines are the same calculation at $E_{\mathrm{F}}^{\mathrm{ARPES}}$. (e) 3D Fermi surface from Open core GGA+SOC calculations at $E_{\mathrm{F}}^{\mathrm{ARPES}}$. The black broken lines indicate the plane cut by panel (d).

Figure 7

(a) Angle-dependent area cross section of the calculated and measured ${\beta }_2$ Fermi sheet. The equivalent oscillation frequency is displayed on the right axis of the graph in units of T. The SdH data extracted from Ref. [19] are reproduced by the full pink circle markers. (b) Representation of the calculated and measured ${\beta }_2$ Fermi sheet in the $\mathrm{\Gamma }XUZ$ and XSRU planes. The black curve is a power fit of $k_{\mathrm{F}}^{\mathrm{ARPES}}$. The blue area is a sketch of the hypothetical low-temperature Fermi sheet after the expected nodal hybridization is turn on, with the nodal line being the $\mathrm{\Gamma }\text{−}X$ line, here in orange. (c) Simplified sketch of how the nodal hybridization may take place with a concave quasi-2D Fermi sheet. We see how the low-temperature Fermi sheet is light along the nodal line but very heavy in the other direction.