Point and complex defects in monolayer $\mathrm{Pd}{\mathrm{Se}}_2$: Evolution of electronic structure and emergence of magnetism

Layered transition-metal dichalcogenides (TMDs) constitute an emerging class of materials that provide researchers a platform to realize fundamental studies and to design promising optoelectronic devices. While defects are an almost unavoidable part of TMDs, they bring additional interesting properties absent in defect-free layers. Moreover, the controlled introduction of defects in TMDs makes it possible to tailor the electromagnetic properties of the materials. Here we report defect-induced properties of single-layer $\mathrm{Pd}{\mathrm{Se}}_2$ and demonstrate the emergence of magnetism at the nanoscale. Our first-principle calculations indicate that Se vacancies create in-gap defect states, which can be responsible for trapping of carriers. The complex square $V_{\mathrm{Pd}+4\mathrm{Se}}$ vacancy induces spin-polarized states with a total local magnetic moment of $2{\mu }_{\mathrm{B}}$ per defect, making it possible to introduce magnetization into $\mathrm{Pd}{\mathrm{Se}}_2$ and therefore expand the family of two-dimensional (2D) magnets. The defect formation energies are much lower compared to many other TMD materials that can explain the presence of a large number of Se defects after mechanical exfoliation of $\mathrm{Pd}{\mathrm{Se}}_2$ layers, while the central location of the Pd atoms preserves them from exfoliation-induced defect formation. The negatively charged vacancies are prone to form and in many cases demonstrate spin-polarized states. The small diffusion barrier of ${\mathrm{V}}_{\mathrm{Se}}$ in 2D $\mathrm{Pd}{\mathrm{Se}}_2$ leads to an easy room-temperature migration, while ${\mathrm{V}}_{\mathrm{Pd}}$ demonstrates a high diffusion barrier preventing its spontaneous migration. As a guide for experimentalists, we simulate and characterize scanning tunneling microscope images in valence and conduction states and estimate the electron-beam energy for a controllable production of various defect patterns. These intriguing findings make $\mathrm{Pd}{\mathrm{Se}}_2$ an ideal platform to study defect-induced phenomena.

Figure 1

(a) Top and side views of the optimized 2D $\mathrm{Pd}{\mathrm{Se}}_2$ supercell and its unit-cell vectors marked by black arrows. Se and Pd atoms are in yellow-green and gray, respectively. (b) Spatial distribution of electron density in valence (left panel, isosurface level $0.0002\mathrm{e}/{\AA }^3$) and conduction (right panel, isosurface level $0.005\mathrm{e}/{\AA }^3$) bands.

Figure 2

The relaxed atomic structures of defect SL $\mathrm{Pd}{\mathrm{Se}}_2$ and the respective simulated STM images: (a) ${\mathrm{V}}_{\mathrm{Se}}$, (b) $V_{\mathrm{Pd}+\mathrm{Se}}$, (с) ${\mathrm{V}}_{\mathrm{Pd}}$, (d) $V_{\mathrm{Se}+\mathrm{Se}}$, and (e) $V_{\mathrm{Pd}+4\mathrm{Se}}$. “Top” and “bottom” correspond to the different views with respect to the layer of vacancy location. VBM and CBM STM are simulated at (a) $V_s=-0.5\mathrm{eV}$ and ${\mathrm{V}}_{\mathrm{s}}=1.8\mathrm{eV}$, (b) ${\mathrm{V}}_{\mathrm{s}}=-0.5\mathrm{eV}$ and ${\mathrm{V}}_{\mathrm{s}}=1.8\mathrm{eV}$, (c) ${\mathrm{V}}_{\mathrm{s}}=-0.5\mathrm{eV}$ and ${\mathrm{V}}_{\mathrm{s}}=1.9\mathrm{eV}$, (d) ${\mathrm{V}}_{\mathrm{s}}=-0.8\mathrm{eV}$ and ${\mathrm{V}}_{\mathrm{s}}=1.8\mathrm{eV}$, and (e) ${\mathrm{V}}_{\mathrm{s}}=-0.5\mathrm{eV}$ and ${\mathrm{V}}_{\mathrm{s}}=1.6\mathrm{eV}$ with respect to the Fermi level.

Figure 3

Formation energies of neutral vacancies in SL $\mathrm{Pd}{\mathrm{Se}}_2$ as a function of the Se chemical potential. The left- and right-hand limits correspond to Pd-rich and Se-rich conditions, respectively.

Figure 4

TDOS defected 2D $\mathrm{Pd}{\mathrm{Se}}_2$: (a) ${\mathrm{V}}_{\mathrm{Pd}}$, (b) ${\mathrm{V}}_{\mathrm{Se}}$, (с) ${\mathrm{V}}_{\mathrm{Pd}+\mathrm{Se}}$, (d) $V_{\mathrm{Se}+\mathrm{Se},}$ and (e) $V_{\mathrm{Pd}+4\mathrm{Se}}$ in blue lines with respect to the defect-free $\mathrm{Pd}{\mathrm{Se}}_2$ monolayer (gray filling). The Fermi level is set to 0 eV. (f) Spatial distribution of spin density $\left(0.001\mathrm{e}/{\AA }^3\right)$ in the monolayer contained $V_{\mathrm{Pd}+4\mathrm{Se}}$ vacancy.

Figure 5

Formation energies of charged vacancies in SL $\mathrm{Pd}{\mathrm{Se}}_2$ as a function of Fermi level position under Pd-rich (left pictures) and Se-rich (right pictures) conditions.

Figure 6

Total density of states of energetically favorable charged vacancies in 2D $\mathrm{Pd}{\mathrm{Se}}_2$: ${\mathrm{V}}_{\mathrm{Se}}, {\mathrm{V}}_{\mathrm{Pd}}$, and $V_{\mathrm{Pd}+4\mathrm{Se}}$ from top to bottom. −1 and −2 charge states are shown in red and blue lines, respectively.

Figure 7

Vacancy diffusion: (a) Initial (1) and final (2) states of different vacancy diffusion in single-layer $\mathrm{Pd}{\mathrm{Se}}_2$. (b) AIMD of ${\mathrm{V}}_{\mathrm{Se}}$ stability at 350 K. (c) Calculated energy barriers for the respective vacancy diffusion in (a).

Figure 8

Schematic representation of knock-on mechanism where arrows represent electron-beam and sputtering atom directions (left panel). Calculated electron-beam energy (keV) for respective vacancy (right panel).