Doping-controlled phase transitions in single-layer ${\mathrm{MoS}}_2$

The electronic properties of single-layer ${\mathrm{MoS}}_2$ make it an ideal two-dimensional (2D) material for application in electronic devices. Experiments show that ${\mathrm{MoS}}_2$ can undergo structural phase transitions. Applications of single-layer ${\mathrm{MoS}}_2$ will require firm laboratory control over the phase formation. Here we compare the stability and electronic structure of the three experimentally observed single-layer ${\mathrm{MoS}}_2$ phases, $2H,1T$, and $1T^{\prime }$, and an in-plane metal/semiconductor heterostructure. We reveal by density-functional theory calculations that charge doping can induce the phase transition of single-layer ${\mathrm{MoS}}_2$ from the $2H$ to the $1T$ structure. Further, the $1T$ structure undergoes a second phase transition due to the occurrence of a charge-density wave (CDW). By comparing the energies of several possible resulting CDW structures, we find that the $1T^{\prime }$ orthorhombic structure is the most stable one, consistent with experimental observations and previous theoretical studies. We show that the underlying CDW transition mechanism is not due to Fermi surface nesting, but nonetheless, can be controlled by charge doping. In addition, the stability landscape is highly sensitive to charge doping, which can be used as a practical phase selector. We also provide a prescription for obtaining the $1T^{\prime }$ structure via growth or deposition of ${\mathrm{MoS}}_2$ on a Hf substrate, which transfers electrons uniformly and with minimal structural distortion. Finally, we show that lateral heterostructures formed by the $2H$ and $1T^{\prime }$ structures exhibit a low interfacial energy of 0.17 eV/Å, a small Schottky barrier of 0.3 eV for holes, and a large barrier of 1.6 eV for electrons.

Figure 1

Atomic structures of the (a) $2H$, (b) $1T$, (c) $1T^{\prime }$, (d) $2a\times 2a$, and (e) $\sqrt{3}a\times \sqrt{3}a$ phases of single-layer ${\mathrm{MoS}}_2$. The unit cells are enclosed by dashed lines. Molybdenum and sulfur atoms are represented by blue and red spheres, respectively.

Figure 2

Energy landscape along the path between the $1T$ and the $2H$ structure as a function of reaction coordinate and charge doping.

Figure 3

Phonon spectra of (a) $2H{\mathrm{MoS}}_2$, (b) $n$-type, and (c) $p$-type doped $1T{\mathrm{MoS}}_2$. The phonon spectrum of intrinsic $1T{\mathrm{MoS}}_2$ is shown in both panels (b) and (c) for comparison.

Figure 4

Electronic structure of $1T$ single-layer ${\mathrm{MoS}}_2$: (a) band structure and (b) Fermi surface, (c) and (d) real part, and (e) and (f) imaginary part of the electronic susceptibility, for intrinsic and $p$-type doped $1T{\mathrm{MoS}}_2$, respectively.

Figure 5

Electronic band structures of the various polymorphs of single-layer ${\mathrm{MoS}}_2$ exhibiting the (a) $2H$, (c) $1T^{\prime }$, (e) $2a\times 2a$, and (g) $\sqrt{3}a\times \sqrt{3}a$ structures. The corresponding band structures with SOC are shown in panels (b), (d), (f), and (g). The valence band maximum is set to zero.

Figure 6

Formation energy relative to the 3D bulk phase of ${\mathrm{MoS}}_2$ for the three single-layer polymorphs of ${\mathrm{MoS}}_2$ when free standing and adsorbed on a Hf(0001) substrate. Adsorption on Hf(0001) leads to electron doping and stabilizes the $1T^{\prime }$ polymorph.

Figure 7

Top and side view of the $2H$/$1T^{\prime }$ heterostructure after geometry optimizations. The dashed lines illustrate rectangular unit cells of the $2H$ and $1T^{\prime }$ structures.

Figure 8

Local electronic density of states of one unit of $2H$ single-layer ${\mathrm{MoS}}_2$ which is far away from the interface of the $2H$/$1T^{\prime }$ heterostructure.