Site-specific symmetry sensitivity of angle-resolved photoemission spectroscopy in layered palladium diselenide

Two-dimensional (2D) materials with puckered layer morphology are promising candidates for next-generation opto-electronics devices owing to their anisotropic response to external perturbations and wide band gap tunability with the number of layers. Among them, PdSe2 is an emerging 2D transition-metal dichalcogenide with band gap ranging from 1.3 eV in the monolayer to a predicted semimetallic behavior in the bulk. Here we use angle-resolved photoemission spectroscopy to explore the electronic band structure of PdSe2 with energy and momentum resolution. Our measurements reveal the semiconducting nature of the bulk. Furthermore, constant binding-energy maps of reciprocal space display a remarkable site-specific sensitivity to the atomic arrangement and its symmetry. Supported by density functional theory calculations, we ascribe this effect to the inherent orbital character of the electronic band structure. These results not only provide a deeper understanding of the electronic configuration of PdSe2, but also establish additional capabilities of photoemission spectroscopy.

Transition metal dichalcogenides (TMDs) host highly attractive properties for fundamental studies of novel physical phenomena and for applications ranging from opto-electronics to sensing at the nanoscale [1,2]. Among all TMDs, those based on noble metals (Pd, Pt) have received less attention because of their high cost, until the recent discovery of a layercontrollable metal-to-semiconductor transition [3][4][5][6], which motivated their investigation in the last few years. Similar to the extensively investigated black phosphorus [7][8][9][10], with a band gap varying from 0.3 eV in the bulk to 1.5 eV in the monolayer [11], PdSe 2 is characterized by an in-plane puckered structure resulting in an anisotropic response to external stimuli, such as light [12], electric field [13] and strain [14,15]. In addition, a linear dependence of the band gap with the number of layers has been observed [3,16]: the monolayer is predicted to have an indirect gap of 1.3 eV [17] which monotonically decreases to 0 eV as the thickness exceeds 40 − 50 layers, suggesting semimetallic behavior. However, unlike black phosphorous and the majority of TMDs which share hexagonal crystal structures, the low-symmetry pentagonal atomic arrangement of PdSe 2 gives rise to exotic thermoelectric, mechanical and optical properties [18][19][20].
Here, we investigate the electronic structure of PdSe 2 for the first time by angle-resolved photoemission spectroscopy (ARPES). We clarify the semiconducting nature of the bulk by direct measurements of the electronic bands in reciprocal space. Furthermore, we reveal a previously unexplored sensitivity of photoemission to the site-specific crystal symmetry. In particular, constant binding-energy cuts of the surface-projected Brillouin zone (BZ) disclose the dominant chemical/orbital character of the metal atoms on the top-most valence band, while the effect of the chalcogen species becomes relevant at binding energies exceeding 1 eV. This finding is corroborated by plane wave density functional theory (DFT) calculations employing Perdew-Burke-Ernzerhof (PBE) functional.
The crystallographic morphology of PdSe 2 is sketched in Fig.1. Its stable configuration is orthorhombic with Pbca space group (#61) and experimental lattice parameters a = 0.575 nm, b = 0.587 nm and c = 0.77 nm [21], see Fig.1a. Layers are normal to the caxis. The top view (panel b) shows the characteristic pentagonal atomic arrangement of the monolayer, while the side view (panel c) reveals its puckered structure. Each PdSe 2 layer is formed by three atomic planes: Pd atoms in the middle are covalently bound to four Se atoms located on the top and bottom sub-layers. In contrast with other TMDs where the metal atom has +4 oxidation state, PdSe 2 adopts the +2 oxidation [22]. This is achieved    . This result is in agreement with recent optical measurements [23,24], but diverges from calculations that predict semimetallic behaviour [3,17,25,26]. While it is known that DFT generally underestimates band gaps in semiconductors [27,28], the fact that VB and CB are well separated in reciprocal space preserves their individual electronic features, regardless of the computed value of the band gap. In particular, the occupied states (experimentally observed by ARPES) are reproduced by DFT with remarkable accuracy.
More insight on the electronic structure of PdSe 2 is achieved by inspecting the ARPES isoenergetic maps. Fig.3a shows the photoemission spectral weight measured on the reciprocal We will unfold this concept referring to Fig.3d-f. Panel d recalls the orthorhombic unit cell of PdSe 2 and the corresponding BZ. It is known that ARPES measurements of solids probe the so-called surface-projected BZ (SBZ) based on energy and momentum conservation [29].
In panel d the SBZ is represented by the orange-shaded area. A closer inspection of the unit cell reveals that Pd atoms arrange on a face-centered orthorhombic (fco) lattice, as evident in panel f: if chalcogen atoms were absent, the corresponding first BZ would be the one sketched on the right-hand side [30] (notice the similarity with the BZ of the standard face-centered cubic lattice) [31]. Panel e compares the SBZs of the orthorhombic (panel d) and the fco (panel f) cells with identical lattice parameters. It can easily be verified that the following relations hold among wavevectors:ΓX = π/a,ΓȲ = π/b,ΓC = 2π/a,ΓD = 2π/b.
Returning to the photoemission map of Fig.3c, the blue dashed lines identify the SBZ of the fco unit cell and each elliptical shape is centered at theΓ point of the face-centered lattice. Since Pd atoms arrange on an fco lattice, our ARPES analysis suggests that the top-most VB originates predominantly from Pd orbitals with little contribution from Se. In order to support this hypothesis, we have computed the orbital-projected k-DOS and wave functions at selected points of the band structure. Fig.4a reports the difference between it is dominated by Se 4p orbitals [32], while at Γ (label 4) it is combination of Pd 4d states.
These results support our hypothesis that the same single orbital of Pd (i.e. 4d z 2 ) shapes the top-most VB. Recalling that Pd atoms form an fco lattice, this symmetry is retained also in reciprocal space, as revealed by our ARPES data (see Fig.3c). A simple tight binding approach leads to the same conclusion and is reported in the Methods section. At larger binding energies both Pd and Se orbitals contribute to the band structure, exhibiting the standard orthorhombic symmetry of Fig.3a.
In conclusion, we have measured the electronic band structure of bulk PdSe 2 by angleresolved photoemission spectroscopy. Within the experimental accuracy, our data confirm its semiconducting nature with a minimum band gap of 50 meV (i.e. the instrumental resolution) since no evidence of conduction band across the Fermi level has been observed, while all electronic dispersive features below E F are well-reproduced by our DFT calculations. Furthermore, we have demonstrated a remarkable sensitivity of the ARPES technique to site-specific symmetries of the electronic structure. This finding can be pivotal in tuning the electronic properties of PdSe 2 -based heterostructures [33], analogous to the observed dependence of the gap on the band character of MoS 2 /graphene [34,35]. Moreover, we envisage that the chemical selectivity of ARPES allows a fine-tuning of the electronic properties. For example, chemical substitution of metal atoms [36] will give rise to specific changes in the VB related both to doping and to modifications in the surface symmetry, to which ARPES will be sensitive. We believe this implementation is not limited to PdSe 2 , but it applies to a much wider class of compounds with complex crystal structures and can help clarify the subtle interactions related to correlated electronic phases, such as metal-insulator transitions, charge density waves and superconductivity [37,38].

Competing interests
The authors declare no competing interests. DFT. The electronic band structure of PdSe 2 was computed with the Quantum Espresso package [41]. Exchange-correlation was considered using the Perdew-Burke-Ernzerhof functional revised for solids (PBEsol). Van der Waals interaction among PdSe 2 layers was included using the semiempirical Grimme's DFT-D2 correction [42]. Atoms were allowed to relax until the residual forces were below 0.0026 eV/Å. Cutoff energy of 60 Ry and 8 × 8 × 6 k-point mesh were used. The iso-surface rendering in Fig.4b was performed with the VESTA software [43].
Absence of CB evidence in ARPES data. Each map employs a logarithmic intensity scale ranging from 5% to 100% of the respective maximum. Even well above E F we have detected no sign of electron pockets originating from the CB, as DFT calculation would predict. Although we are not able to determine the value of the band gap with static ARPES, our data uphold the semiconducting nature of bulk PdSe 2 .
Orbital character of the band structure (Fig.4a). Pd 4d and Se 4p electrons determine the valence and conduction states of PdSe 2 . It is instructive to "visualize" the specific orbital character and in particular the Pd-Se duality along high symmetry lines of the BZ. Here, we employ a simple colour-coded approach: the k-resolved density of states projected on Pd 4d and Se 4p are shown in Fig.6a and Fig.6b, respectively. Taking the difference between the data of these two graphs we obtain Fig.4a, where blue and red colours encode positive (Pd) and negative (Se) values. As an example, the Pd and Se k-DOS (the latter is represented on the negative abscissa) and their difference at the Γ point are shown in Fig.6c. Notice, in particular, that the Pd-projected k-DOS at the Fermi level (i.e. the VB top) is approximately 3 times larger than Se, as claimed in the main manuscript.
Tight binding approach and matrix element effect. In a regular MX 6 octahedral complex (O h symmetry) the five outer d orbitals of the transition metal M arrange into the high-energy, double-degenerate e g and the low-energy, triple-degenerate t 2g states [44], as sketched in Fig.7a. A closer look at the crystal structure of PdSe 2 , shown in Fig.7b, reveals that each Pd is surrounded by four Se atoms belonging to the same monolayer and two apical atoms (in yellow colour) belonging to the nearest upper and lower layers. The six chalcogen atoms form an octahedron elongated along the c-axis (D 4h symmetry). This distortion lifts the degeneracy of the e g states, resulting in the d z 2 orbital being energetically more favorable than the d x 2 −y 2 [44][45][46]. As we already pointed out, in PdSe 2 the oxidation state of Pd is +2 and its electronic configuration is therefore 4d 8 : six of these electrons fill the t 2g states completely, while the remaining two occupy the d z 2 orbital, leaving d x 2 −y 2 empty. d z 2 is therefore the highest occupied molecular orbital (HOMO) forging the top of the VB, while d x 2 −y 2 represents the lowest unoccupied molecular orbital (LOMO) contributing the bottom of the CB, in agreement with our own calculations (Fig.4b) and other recent work [47].
We can now elucidate the symmetry features of the top-VB observed by photoemission using a simple 2D tight binding approach that involves only the HOMO. Metal atoms of a PdSe 2 monolayer arrange on a rectangular lattice as shown in Fig.8. For simplicity we will In the fco case, a tight binding approach is straightforward. Let |R A be the Wannier wave function at the specific lattice site R (i.e. the d z 2 orbital). The ovelap integral is γ = R A |U|0 A (U is the periodic lattice potential), where R runs over the 4 nearest neighbors (+a/2, +a/2), (+a/2, −a/2), (−a/2, +a/2), (−a/2, −a/2) and the eigenvalue of the hamiltionian H is E(k) = E A + γ n.n. e ikR = E A + 4γ cos(k x a/2) cos(k y a/2), Fig.8c shows the resulting VB dispersion along the x-axis (k y = 0).
If the orthorhombic cell is used, two Wannier wave functions |R A and |R B form the basis of the tight binding hamiltonian: It can easily be verified that the hopping term between sites A and B is h = 4γ cos(k x a/2) cos(k y a/2) like in the previous fco case. Since sites A and B are equivalent, it also follows that E A = E B . Thus, the two eigenvalues are E ± (k) = E A ± |4γ cos(k x a/2) cos(k y a/2)|. Fig.8d depicts E ± (k) along the x-axis (k y = 0). The corresponding eigenstates are (± h |h| , 1) and the generic wave function at the lattice site R reads [48]: |R ± = ± h |h| e ikR A |R + R A + e ikR B |R + R B . In the free electron final state approximation (here, the final state |k f is a plane wave with wavevector k f ), the photoemission matrix element M is expressed as the Fourier component of the tight binding orbital |0 ± [48], i.e.
which, using the momentum conservation (k = k f ), leads to the following photoemission intensity: that simplifies to I ± ∝ 2 | k f |0 A | 2 1 ± h |h| since |0 A = |0 B . At this point we notice that h |h| = sgn[cos(k x a/2) cos(k y a/2)]. Thus, I ± ∝ (1± sgn[cos(k x a/2) cos(k y a/2)]. Referring to Fig.8d, it is easily verified that the previous equation completely suppresses the photoemission intensity of one eigenvalue E ± (k) depending on the values of k x and k y . Fig.8e-f show the results: as expected, the fco band structure of Fig.8c and the experimental data of Fig.3c are recovered since the use of two equivalent sites is redundant and the appropriate unit cell is the fco.