Electronic structure of ${\mathrm{V}}_2\mathrm{AlC}$

We report an experimental and theoretical study of the electronic band structure and Fermi surfaces (FSs) of ${\mathrm{V}}_2\mathrm{AlC}$ single crystals using angle-resolved photoemission spectroscopy and density functional theory (DFT) calculations. We provide evidence of the existence of equivalent, complex hole FSs with a nearly tubular form along the $c$ axis, and of an intricate electron FS exhibiting tubes parallel to $c$ connected to one another by smaller tubes with axes parallel to the $ab$ plane. The electron FS thus exhibits a small delocalization along the $c$ axis. The local orbital character of each observed band is experimentally and theoretically assessed. DFT calculations show an excellent agreement with experiment. We also report the observation of an unstable surface state.

Figure 1

(a) ${\mathrm{V}}_2\mathrm{AlC}$ FS calculated with wien2k, plotted in the first BZ (left figure) and in a cell centered on A (right figure). Only one electron band and one hole band are crossing $E_F$, and (b) shows the two bands separately. The overall morphology of the FS is rather complex, band 40 exhibiting 3D features with tubes perpendicular to the $c$ axis (directed over AH) and tubes parallel to the $c$ axis connected altogether.

Figure 2

${\mathrm{V}}_2\mathrm{AlC}$ band structure as calculated by the wien2k software. $E_F$ is chosen as the origin of energy. Colors refer to the orbital character of each band.

Figure 3

${\mathrm{V}}_2\mathrm{AlC}$ FS cut over Γ (a) and A (b) planes, respectively, both issued from DFT calculations. Yellow lines stand for band 39. Gray lines in (c) stand for band 40, and red lines stand for the degenerate bands 39 and 40 in the A plane. (c) The projection of the full ${\mathrm{V}}_2\mathrm{AlC}$ FS with a $d_{z^2}$ orbital character onto the horizontal plane. Areas with $d_{xz}+d_{yz}$ character near the BZ boundaries are also represented.

Figure 4

FS images of ${\mathrm{V}}_2\mathrm{AlC}$ obtained by ARPES with S-pol configuration and $h\nu =100\mathrm{eV}$ photons. The image in (a) is the raw Fermi surface data for a high angular range in order to display several BZs. Image in (b) shows the FS in wave-vector units over a single BZ, along with a cut of the DFT FS across the Γ plane (dotted lines; the yellow one stands for band 39 and the white one for band 40) and across the A plane (full white lines).

Figure 5

AΓML (a, b) and AΓKH (c, d) ARPES photoemission maps and FS cuts from wien2k. Purple lines stand for band 39 and green lines for band 40. An acceptable matching between DFT and ARPES is found for ΓM, while photon-energy-dependent ARPES data over ΓK (c) fails to reproduce features from DFT, therefore corroborating the three-dimensional character of the ${\mathrm{V}}_2\mathrm{AlC}$ electronic structure along this direction.

Figure 6

(a) Indicates which $k_{\perp }$ value is probed at a given $k_{//}$ value, for various values of photon energy $h\nu$. 100 eV corresponds to a $k_{\perp }$ wave-vector component lying between A and Γ planes. (b) ${\mathrm{V}}_2\mathrm{AlC}$ band structure along ΓA. The good matching between ARPES data and calculations shows that bulk electronic states are observed. $V_0$ was extracted from the half period of the band.

Figure 7

Band structure from ARPES over ΓK (a) and ΓK (b). Black lines are the output of DFT calculations. Experimental and theoretical Fermi velocities and effective masses are compared at the α and γ points.

Figure 8

(a) ARPES FS mapping measured during 30 min with a low angular resolution and immediately after crystal cleavage. (b) FS mapping measured about 7 h after cleavage and during about 2 h on the same sample as in (a). (c) Band structure along the direction given by the blue dotted line in (a), and (d) band structure measured along the direction given by the blue dotted line in (b). A surface state not predicted by bulk DFT is clearly visible in (a) and (c). In (a) and (b), a small energy shift of 10 meV below $E_F$ was chosen in order to enhance the signal due to the surface state, when present.

Figure 9

(a) Location of six Dirac points appearing roughly at 0.25ΓM, evidenced on the DFT FS by increasing the energy by 10 meV above $E_F$. [For the sake of clarity, just the Dirac points have been kept in (a).] This shift reveals nearly punctual and anisotropic electron pockets which are located in the FS loop shown in the inset of (a). Those features are due to the presence of “double” Dirac points also visible by plotting, e.g., the band structure along ΓM, as achieved in (b).