Fermi surface and band structure of ${\mathrm{Ti}}_2\mathrm{SnC}$ as observed by angle-resolved photoemission spectroscopy

We present an experimental study of the electronic states of the nanolamellar compound ${\mathrm{Ti}}_2\mathrm{SnC}$ by means of angle-resolved photoemission spectroscopy (ARPES). Experiments were performed on macroscopic single crystals, and the observed Fermi surface and band structure were systematically compared with the output of density functional theory calculations. The fine details of the Fermi surface predicted by theory are duly evidenced by the ARPES measurements. The multiply connected Fermi surface (FS) is formed by a combination of quasi-two-dimensional corrugated tubes and quasi-one-dimensional thin plates, centered on high-symmetry axes and points, respectively. The quasi-one-dimensional FS region displays a clear Dirac-like dispersion. An evanescent surface state is observed in addition to the bulk bands.

Figure 1

(a) ${\mathrm{Ti}}_2\mathrm{SnC}$ unit cell. (b) Fermi surfaces of ${\mathrm{Ti}}_2\mathrm{SnC}$ plotted over the first BZ, for the four-hole bands (b39-42) and the two-electron bands crossing $E_F$ (b43-44). (c) Sketch of the first Brillouin zone of ${\mathrm{Ti}}_2\mathrm{SnC}$, with indicated directions. (d) ${\mathrm{Ti}}_2\mathrm{SnC}$ band structure projected onto Ti $d$ orbitals, dominant at the Fermi level, and Sn $p_x+p_y$ orbitals.

Figure 2

(a) Extended ARPES Fermi surface mapping centered in Γ. The six directions indicated, respectively, correspond to the $k_x$ axes for the BS in Figs. 5 (no. 1), 6 (no. 3), 7 and 7 (nos. 2 and 4), and 9 and 9 (nos. 5 and 6). For this intensity scale, the maximum of the ARPES signal is 471 and the minimum is 14. The ${\mathrm{Ti}}_2\mathrm{SnC}$ FS computed by DFT is given within both the first BZ (b) and an alternative BZ centered in $L$ (c), with the FS velocity moduli $v_F$ represented as a color plot on the top of the surfaces.

Figure 3

Part (a) indicates which $k_{\perp }$ value is probed at a given $k_{//}$ for several $h$ν's. $h\nu =97.5$ and 22.5 eV correspond to $k_{\perp }$ lying around Γ planes. (b) Interplane ARPES Fermi surface mapping of ${\mathrm{Ti}}_2\mathrm{SnC}$. ARPES trace lines nos. 7 and 8 in (c)–(e) are shown in (a) and (b). (c)–(e) Band structures along the cut no. 7 [(c) $k_x=0.65{\AA }^{-1}$], no. 8 [(d) $k_x=0.9{\AA }^{-1}$], and no. 9 [(e) $k_x=1.35{\AA }^{-1}\sim \mathrm{KH}$], respectively.

Figure 4

Raw ARPES spectra of ${\mathrm{Ti}}_2\mathrm{SnC}$ shown as energy distribution curves (EDCs) (a),(b) and momentum distribution curves (MDCs) (c), (d) along Γ$M$Γ (a), (c) (no. 1 in Fig. 3) and Γ$\mathit{KM}$ (no. 4 in Fig. 3), respectively.

Figure 5

ARPES BS mapping of a ${\mathrm{Ti}}_2\mathrm{SnC}$ single crystal oriented over Γ$M$Γ (respectively ALA, and corresponding to no. 1 as above), together with the corresponding bulk bands computed by DFT, in full burgundy lines for Γ$M$Γ in the Γ plane and dotted gray lines for bands in the $A$ planes, along ALA. An additional band is featured, whose trace disappears after a few hours and which is not reproduced by bulk DFT calculation (see the dotted red line, used as a guide for the eyes). It shows a minimum at Γ for $E\approx -2.2\mathrm{eV}$. As in all other figures, the color scale is linear.

Figure 6

(a) $k_z$ projected bulk DFT bands over KMK (HLH) for $k_z$ ranging from 0 (black color) to $\pi /c$ (green). (b) ARPES band mapping along no. 3, which corresponds to KMK (HLH) and extends close to Γ($A$). The color labels of the DFT bands lying either within the Γ or $A$ plane correspond to Fig. 5.

Figure 7

(a) $k_z$ projected DFT BS along $K$Γ$K$. ARPES spectra along directions no. 2 (b) and no. 4 (c) of Fig. 2. Both spectra account for a band structure along Γ$K$ ($\mathit{AH}$), and they are plotted with corresponding theoretical bands from DFT calculations (in full burgundy for Γ$K$ and dotted gray for $\mathit{AH}$). Part (b) is recorded for relatively large ${\theta }_y$ angles, in a range of 25°–30°, while (c) was recorded at a smaller ${\theta }_y$ value, close to 0°. In (c), the same evanescent dispersions as in Fig. 5 are located near Γ.

Figure 8

(a) Electron FS of band 45, which consists of triangular plates centered at the $H$ point and defined in a very narrow window around $H$. These plates are connected by tubes whose axes are located between Γ and $K$. (b) Zoom over the $k_z$-broadened band structure of ${\mathrm{Ti}}_2\mathrm{SnC}$ near the $K$ point. The dispersion of band 45 is nearly flat around $H$ and for energies close to $E_F$. (c) ${\mathrm{Ti}}_2\mathrm{SnC}$ GGA and GGA+SOC band structures along Γ$\mathit{KH}$. Two linear band crossings are observed at δ and ζ points. Both are gapped when SOC is taken into account, with a gap of roughly 73 meV at δ and 29 meV at ζ.

Figure 9

(a) ARPES mapping of ${\mathrm{Ti}}_2\mathrm{SnC}$ Fermi surface (in arbitrary angular units) near δ, close to the center of the two-dimensional tubes joining the triangulate plate of Fig. 8. Corresponding DFT Fermi surface cuts are given in (b), where the full and dotted lines stand for the Fermi lines in the AHL and the Γ$\mathit{KM}$ planes, respectively. (c) ARPES spectra and DFT bands along no. 5 and (d) along no. 6. Both BSs cross two δ points. Thick darker gray lines stand for the corresponding BS over the Γ plane, and dotted lighter gray lines stand for the $A$ plane.