Electronic structures of WS2 armchair nanoribbons doped with transition metals

Armchair WS2 nanoribbons are semiconductors with band gaps close to 0.5 eV. If some of the W atoms in the ribbon are replaced by transition metals, the impurity states can tremendously affect the overall electronic structure of the doped ribbon. By using first-principles calculations based on density functional theory, we investigated substitutional doping of Ti, V, Cr, Mn, Fe, and Co at various positions on WS2 ribbons of different widths. We found that Fe-doped ribbons can have two-channel conduction in the middle segment of the ribbon and at the edges, carrying opposite spins separately. Many Co-doped ribbons are transformed into spin filters that exhibit 100% spin-polarized conduction. These results will be useful for spintronics and nanoelectronic circuit design.

Doping at the center of 15-WS 2 . We next discuss the configuration in which the substitutional doping occurs in the central position of the 15-WS 2 ribbon and a W atom is replaced by a Ti atom at a concentration of 1/15 (6.67%). Figure 2 plots the exact position of the substitution and calculated electronic structure. Compared with the pristine 15-WS 2 , the most striking features are three (with two almost degenerate) energy bands crossing the Fermi level E F , rendering the centrally doped Ti-15-WS 2 structure a conductor. The band with the highest energy of the three is almost exclusively composed of the d orbitals from the Ti impurity and its nearest neighbors of W atoms, which are marked collectively by green spheres in Fig. 2b with sizes proportional to their contributions, and also curves of local density of states (LDOS) in partial waves in Fig. 2c,d. The other two bands are likewise derived heavily from the d orbitals of the Ti, but a conspicuous presence of edge W atoms (as indicated by brown spheres in Fig. 2b and the corresponding LDOS in Fig. 2e) also emerges, largely below E F . We therefore established that conduction of the centrally doped Ti-15-WS 2 ribbon at a concentration of 6.67% is overwhelmingly carried out by the Ti and its neighboring W atoms, whereas the basic architecture of the pure WS 2 ribbon energy bands consisting of edge W and S atoms remains largely intact. The wave function of Ti does not have an appreciable overlapping with those of W atoms at both edges. Analysis of the d orbitals by partial waves further identifies the three major constituents in d xy , d x2−y2 , and d z2 .
Many of the descriptions of the centrally doped Ti-15-WS 2 can also be applied to V-15-WS 2 . The dopant V, however, has one more electron in its d shells, or one hole less as compared with Ti. Implied in the rigid band estimate is that fewer bands would cross E F as a result. This is exactly what the density functional calculation shows in Fig. 3a, in which only two bands cross E F and most of their electronic states are below E F . The reduction in the available states also proceeds through the impurity and its surrounding W atoms, where the wave functions have the same d components just as those in the Ti case.
Having exactly the same electrons in the d shell as W, Cr as a dopant is not expected to alter the electrical property of the pure WS 2 ribbon. The bands contributed by Cr either stay well below E F or are pushed high above E F , with little mixing between the orbitals of Cr and W atoms at the edges (Fig. 3b). Centrally doped Cr-15-WS 2 remains a semiconductor.
Ti, V, and Cr-doped WS 2 ribbons are essentially non-magnetic, but doping with Mn, Fe, and Co, classified as N-type, renders the ribbon magnetic. Using spin-polarized calculation, we are able to separate the energy bands corresponding to the majority spin ( Fig. 4a) from those of the minority spin (Fig. 4b), for the 15-WS 2 doped with a Mn in the center. Figure 4a clearly identifies two bands associated with the majority spin approaching E F from above and below separately. The former is contributed by edge W atoms and the latter mainly by the Mn and its neighboring W atoms. The two curves are flat when they are closest to the Fermi level and it is likely that these states will not contribute to conduction in an electronic transport setup. No bands of the minority spin come so close to E F in Fig. 4b. The imbalance of the distribution of spins produces a magnetic moment of 0.938 μ B per unit cell for the doped ribbon. To further clarify the band structure near E F , we also undertook calculations that incorporated the spin-orbit interaction. The result supports the idea of a semiconductor with an indirect band gap of approximately 60 meV (Fig. 4c).
Proceeding next to Fe doping, which has one more electron available per unit cell, the electronic structure is very different from the previous examples. The 15-WS 2 with a centrally doped Fe is now a conductor with two  www.nature.com/scientificreports/ bands crossing E F . Each band is associated with the conductance of one quantum unit e 2 /h in a ballistic regime for a perfect periodic system, where e is the electron charge and h is Planck constant. The band with the majority spin (Fig. 5a) is comprised of the orbitals mainly from Fe and its surrounding W, indicating available states in the central region of the ribbon. The band of the minority spin ( Fig. 5b) is strongly associated with W atoms at both edges. Mixing of wave functions between Fe and the edges generally occurs at energies greater than E F . Thus, even though charge transport can occur both in the interior and edges of the ribbon, the associated spins are separately carried by electrons in the two channels, with the former bearing the majority spin and the latter the minority spin. The entire unit cell of the ribbon exhibits a magnetic moment of 1.128 μ B . A further calculation taking into account the spin-orbit interaction also confirms this two-channel transport scenario (Fig. 5c). Figure 5d shows the distribution of spin density, where the majority spin occupying the central region of the ribbon is clearly separated from the minority spin confined at the edges.  www.nature.com/scientificreports/ Continuing the study of TM-doped 15-WS 2 nanoribbons, we now substitute a Co for the W atom at the central position of the unit cell. The calculated band structure is surprising in terms of its physical significance. There are now two bands crossing E F , both exclusively associated with the majority spin (Fig. 6a), but there are none doing so for the minority spin (Fig. 6b). The ribbon is therefore transformed into a spin filter, allowing only passage of electrons that have the majority spin.
From partial wave analysis of the LDOS (Fig. 7), it is easy to establish that the two bands of the majority spin crossing E F are formed by d orbitals of Co and the W atoms nearby, and negligibly hybridize with edge atoms in the context of conduction.
Dopants closer to one side of 15-WS 2 . If the doped impurity atom is placed closer to one side of the nanoribbon, its wave function is expected to overlap more with those of the edge atoms on that side, and the resulting hybridization can significantly affect the electronic structure. In Fig. 8a, six sites away from the center of the 15-WS 2 nanoribbon and numbered from 1-6 are marks for substitutional doping of the TM atoms. A larger number corresponds to a dopant that is closer to the left edge. Figure 8b plots the binding energies E B for each dopant at the six sites and the central position (marked by 0). E B is defined as the difference between the total energy of the doped structure E total (ribbon − W + dopant) and the sum of the total energies of the structure with a W vacancy E total (ribbon − W) and the free dopant E total (dopant), or E B = E total (ribbon − W + dopant) − [E total (ribbon − W) + E total (dopant)]. It is clear that Ti is most tightly bound to the 15-WS 2 nanoribbon, and each of the TM atoms is more likely to stay close to the center of the ribbon than the edges.
We also calculated average formation energy E form for each of the configurations in Fig. 8b. E form was derived by calculating the difference between E total (ribbon − W + dopant) and the sum of total energies of its constituents in isolation and then dividing the difference by the total number of atoms in the system. The results are plotted in Fig. 8c.
Continuing with Co-15-WS 2 , the structure remains a 100% spin polarizer with Co occupying position 1, 2, or 3. Figure 9a demonstrates that only energy bands associated with the majority spin cross E F for the first three doping sites. If Co is placed in positions even closer to the left edge, the larger overlapping of wave functions between Co and W at the left edge significantly changes the energy bands. At positions 4 and 6, band gaps are opened and the ribbon becomes a semiconductor. Although a single band does cross E F for the dopant at position 5, the band carries both spins and is not a spin filter. As expected, the bands responsible for conduction of the doped structure with the dopant Co at position 1, 2, 3, or 5 consist of d orbitals of Co ( Fig. 9 b), LDOS], and its W neighbors. Part I of Supplementary Information provides a detailed illustration of the evolution of the LDOS for Co at various positions and W atoms at both edges.
In Fe-15-WS 2 , the Fe atom at position 1 switches the structure from a conductor to a semiconductor (Fig. 10a,b). The shortest displacement from the central position is enough to break the symmetry and induces splitting of the energy bands. Combined with the mixing of wave functions between the off-centered dopant and the W atoms at the nearer edge, a zero-gap semiconductor is created. Two-channel conduction, however, is maintained for Fe at positions 2 or 3, where transport of electrons with the majority spin is still well inside the ribbon, whereas movement of electrons with the minority spin is now limited to the left edge only, which is now  Lower concentration of dopants. It is possible to reduce the interaction between the dopant and edge atoms by widening the width of the WS 2 nanoribbon. This is a method of reducing the dopant concentration. However, it should be cautioned that the calculation is still within the periodic framework and the system is highly ordered no matter how low the concentration is. We chose two widths designated as Na 20 and 25 for further study of the TM-doped system, with the dopant inevitably closer to one side of the ribbon in the former system and still occupying the central position in the latter. Ti and V-doped wider nanoribbons remain conductors through charge carriers of the dopants and their neighboring W atoms. Cr-doped ribbons are still semiconductors. Mn-doped ribbons are also semiconductors, all with small band gaps.
The most striking change occurs on Fe. As the width of the ribbon is widened, the energy bands contributed by the W atoms at the edges are raised and eventually above E F and out of conduction. This is mainly because of less hybridization between Fe and W atoms at the edges. Fe-25-WS 2 , for example, no longer provides twochannel conduction and effectively becomes a perfect spin polarizer by only passing electrons with the majority spin. Part II of Supplementary Information shows the evolution of spin density from Fe-15-WS 2 to Fe-25-WS 2 , www.nature.com/scientificreports/ and clearly indicates that the spin density at the edges of Fe-25-WS 2 vanishes. Partial wave analysis of its energy bands (Fig. 11) also assists in establishing this picture. Both Co-20-WS 2 and Co-25-WS 2 are also spin filters with larger ribbon widths. Two bands that are associated with the majority spin crossing E F are a feature common to both Co-doped ribbons (Fig. 12a,b), which suggests a reliable method of constructing a spin-polarized circuit through Co doping. One question arises whether a continuing Co chain (Fig. 13a, 15-WS 2 ) is also a spin filter. With two bands separately belonging to different spins  www.nature.com/scientificreports/ crossing E F (Fig. 13b), the structure-with 2× the Co concentration and thus strengthened interaction between the dopants-becomes an ordinary conductor. Another approach for evaluating the effect of doping at a lower concentration is to increase the distance between the dopants along the ribbon length. If the distance between the dopants is doubled in the 15-WS 2 ribbon, the concentration decreases to 3.33% and interaction between the dopants is expected to be considerably reduced. As it turns out, the lower concentration of dopants flattens their associated energy bands. Ti and V-doped structures are still conductors and the Cr-doped ribbon continues to have a band gap. Dopants of Mn, Fe, and Co behave quite differently, however, Mn-15-WS 2 at this low concentration becomes a conductor, whereas Fe and Co each opens a small band gap (Fig. 14).
In summary, we showed that the electronic structure of an armchair WS 2 nanoribbon can be tuned by substitutional doping of TM impurities. The dopant concentration, ribbon width, and dopant position all contribute to the doped nanoribbon's transformation between a semiconductor and metal. Among the dopants, Fe-15-WS 2 is capable of supporting two-channel conduction, and wider nanoribbons such as Fe-25-WS 2 are perfect spin filters. Co-15-WS 2 with the dopant closer to the center and corresponding wider versions also consistently support conduction of 100% spin polarization. These results will be useful for spintronics and designing nanoelectronic circuits in a broad range of applications.  www.nature.com/scientificreports/

Methods
In deriving the optimal configurations of nanoribbons and energy bands, we performed spin-polarized density functional calculations using the VASP code 32,33 . Projector augmented-wave pseudopotentials and the exchange-correlation functionals of Perdew, Burke and Ernzerhof 34 were chosen to execute the calculation. A 1 × 81 × 1 Monkhorst-Pack k-point mesh was used for sampling k points in the first Brillouin zone. We allocated a length of 20 Å in two perpendicular directions for vacuum space to eliminate artificial interaction between the supercells containing the ribbon. The cut-off energy for the expansion of the wave functions and potentials in the plane-wave basis was 400 eV.