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We study the transport properties of silicene in a perpendicular magnetic field by evaluating the Hall and longitudinal conductivities and resistivities when the acoustic phonon correction to the Landau level (LL) energy is taken into account. The acoustic phonons are considered by three modes: the transverse (TA), longitudinal, and out-of-plane ones. Under the influence of the acoustic phonon correction, the quantum Hall effect plateaus occur at higher values of the magnetic field, where the TA phonon displays the strongest effect. The combined effects of the strong spin-orbit coupling in silicene, the external electric field, and the Zeeman field on the transport parameters are investigated. These combined effects lift the spin and valley degeneracy of the LLs, leading to the additional plateaus in the Hall conductivity with the sequence being found as ${\ensuremath{\sigma}}_{yx}=(4{e}^{2}/h)(n/4+1/2)$. The temperature has a significant effect on the width of the Hall conductivity plateaus. We also appraise the longitudinal conductivity ${\ensuremath{\sigma}}_{xx}$ and the Hall, ${\ensuremath{\rho}}_{xy}$, and longitudinal, ${\ensuremath{\rho}}_{xx}$, resistivities and show the difference between the present results and those for graphene as well as for silicene without the Zeeman field effect. The combined effects of the electric and Zeeman fields lead to the quadrupled peaks of ${\ensuremath{\rho}}_{xx}$ and the sequence of $(h/{e}^{2})/(n+2)$ in the height of the plateaus in ${\ensuremath{\rho}}_{xy}$.

Graphene-based van der Waals heterostructures have received tremendous interest from both fundamental and experimental studies because they can enhance the properties and expand the possibility of applications of both graphene and two-dimensional materials. Motivated by the successful synthesis of the graphene/$\mathrm{Bi}{\mathrm{I}}_{3}$ heterostructure [Chang et al., Adv. Funct. Mater. 28, 1800179 (2018)]., here, we systematically investigate the electronic structure and interfacial characteristics of this material using first-principles simulations. We find that the structure of the graphene/$\mathrm{Bi}{\mathrm{I}}_{3}$ heterostructure is mainly characterized by weak van der Waals interactions, which keeps the heterostructure feasible. In the ground state, the graphene/$\mathrm{Bi}{\mathrm{I}}_{3}$ heterostructure forms the $n$-type Schottky contact with a barrier of 0.53 eV. The barriers of the Schottky contact can be adjusted by various factors, including interlayer coupling and electric gating. Both the interlayer coupling and electric gating lead to the transformation from the $n$-type Schottky contact to the $p$-type one or to the $n$-type Ohmic contact. These findings demonstrate that graphene/$\mathrm{Bi}{\mathrm{I}}_{3}$ can be considered a promising building block for high-performance photoresponsive optoelectronic devices.

The breaking of the vertical symmetry in Janus monochalcogenides gave rise to many properties that were not present in the original monochalcogenide monolayers. However, recent papers have often focused only on Janus monochalcogenides containing S, Se, and Te elements despite that O is also one of the group VI chalcogen elements. In this paper, we systematically investigate the electronic, transport, optical, and thermoelectric properties of Janus monolayers ${\mathrm{In}}_{2}X\mathrm{O}$ ($X=\mathrm{S},\mathrm{Se},\mathrm{Te}$) using first-principles calculations. Based on phonon spectrum analysis and ab initio molecular dynamics simulations at room temperature, ${\mathrm{In}}_{2}X\mathrm{O}$ monolayers were reported to be stable. Our calculations reveal that, while ${\mathrm{In}}_{2}\mathrm{SO}$ is an indirect semiconductor, ${\mathrm{In}}_{2}\mathrm{SeO}$ exhibits a direct semiconducting characteristic, and biaxial strain can lead to the semiconductor-metal phase transition in ${\mathrm{In}}_{2}\mathrm{SeO}$. Monolayer ${\mathrm{In}}_{2}\mathrm{TeO}$ is metal at equilibrium, and its metallic characteristics are prevented under biaxial strains. Calculations for transport properties show that the carrier mobilities of ${\mathrm{In}}_{2}\mathrm{SO}$ and ${\mathrm{In}}_{2}\mathrm{SeO}$ monolayers are highly anisotropic, and electron mobility of ${\mathrm{In}}_{2}\mathrm{SO}$ exceeds $3\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}/\mathrm{Vs}$. In this paper, the optical and thermoelectric properties of ${\mathrm{In}}_{2}\mathrm{SO}$ and ${\mathrm{In}}_{2}\mathrm{SeO}$ monolayers are also investigated and discussed in detail. Finally, the electronic properties of all four possible stacking configurations of the Janus bilayers are briefly calculated. Our findings not only contribute to a more general view of the physical properties of the Janus group III monochalcogenides but also recommend them as potential nanomaterials for applications in optoelectronic and thermal devices.

Two-dimensional graphene-based van der Waals heterostructures have received considerable interest because of their intriguing characteristics compared with the constituent single-layer two-dimensional materials. Here, we investigate the interfacial characteristics, Schottky contact, and optical performance of $\mathrm{graphene}/{\mathrm{Ga}}_{2}\mathrm{SSe}$ van der Waals (vdW) heterostructure using first-principles calculations. The effects of stacking patterns, electric gating, and interlayer coupling on the interfacial properties of $\mathrm{graphene}/{\mathrm{Ga}}_{2}\mathrm{SSe}$ heterostructures are also examined. Our results demonstrate that the Dirac cone of graphene is well preserved at the $\mathrm{\ensuremath{\Gamma}}$ point in all stacking patterns due to the weak vdW interactions, which keep the heterostructures feasible such that they can be obtained in further experiments. Moreover, depending on the stacking patterns, a small band gap of about 13--17 meV opens in graphene and has a high carrier mobility, indicating that the $\mathrm{graphene}/{\mathrm{Ga}}_{2}\mathrm{SSe}$ heterostructures are potential candidates for future high-speed nanoelectronic applications. In the ground state, the $\mathrm{graphene}/{\mathrm{Ga}}_{2}\mathrm{SSe}$ heterostructures form an $n$-type Schottky contact. The transformation from an $n$-type to a $p$-type Schottky contact or to an Ohmic contact can be forced by electric gating or by varying the interlayer coupling. Our findings could provide physical guidance for designing controllable Schottky nanodevices with high electronic and optical performances.

Van der Waals heterostructures, created by putting graphene on other two-dimensional semiconducting materials, have become an effective strategy to enhance the physical properties and extend the possible applications of two-dimensional (2D) materials. Motivated by the successful synthesis of a graphene/${\mathrm{PbI}}_{2}$ heterostructure in a recent experiment [Nat. Commun. 11, 823 (2020)], here we use first-principles calculations to construct and investigate the electronic properties and interface characteristics of graphene/${\mathrm{PbI}}_{2}$ heterostructure. We find that the weak forces occurring at the interface keep heterostructures stable and maintain the intrinsic properties of the constituent graphene and ${\mathrm{PbI}}_{2}$ monolayers. At the equilibrium interlayer distance of 3.48 \AA{}, the graphene/${\mathrm{PbI}}_{2}$ heterostructure forms an $n$-type Schottky contact. More interestingly, the Schottky barrier height and contact types in the graphene/${\mathrm{PbI}}_{2}$ heterostructure can be adjusted by electric field and interlayer coupling. The graphene/${\mathrm{PbI}}_{2}$ heterostructure can transform from a $n$-type Schottky contact to a $p$-type one or to Ohmic contact by applying electric field or by adjusting interlayer distance. The controllable electronic properties and contact types in graphene/${\mathrm{PbI}}_{2}$ heterostructure make it a promising candidate for designing and improving the performance of high-efficiency Schottky nanodevices.

We study the optical absorption properties of silicene and germanene in the presence of the perpendicular magnetic and electric fields. Their low-energy Landau level (LL) spectra are controllable by an external electric field, where the spin- and valley-degeneracy of the LLs are strongly influenced by the electric and Zeeman fields. The electric field has removed spin-degeneracy at a given valley. Analytical expressions for the magneto-optical absorption coefficient (MOAC) are expressed in the presence of the interaction between carriers and random impurities and the intrinsic phonons including the spin and valley effects. The results evaluated for the topological insulator and valley-spin-polarized metal phases showed that when the electric field is included, the MOAC peaks are separated for opposite spin cases where the splitting in germanene is stronger than that in silicene. The peak's intensity caused by the carrier-photon-impurity scattering is the highest, the next is the carrier-photon scattering, while the carrier-photon-phonon scattering shows the lowest in both materials. Among the different phonon modes, the out-of-plane (ZA) mode in silicene dominates the others, being attributed to its buckled atomic structure, which does not exist in graphene. When the ZA mode is taken into account, the estimated resultant mobility from the full-width at half-maximum is significantly supported by the experimental result in silicene.

We study the optical transport properties of the monolayer transition metal dichalcogenides (TMDCs) such as ${\mathrm{MoS}}_{2}$, ${\mathrm{WS}}_{2}$, ${\mathrm{MoSe}}_{2}$, and ${\mathrm{WSe}}_{2}$ in the presence of a magnetic field. The TMDCs band structures are obtained and discussed by using the effective massive Dirac model, in which the spin and valley Zeeman effects as well as an external electric field are included. The magneto-optical absorption coefficient (MOAC) is derived as a function of absorbed photon energy when the carriers are scattered by random impurities combined with the intrinsic acoustic and optical phonons in TMDCs and the surface optical (SO) phonons of substrates. Our result shows that the spin-splitting feature appeared in all four TMDC materials. The combination of strong spin-orbit coupling (SOC) and Zeeman fields has doubled the Landau levels but has not changed the energy gap of the TMDCs monolayer, which can be controlled by the electric field. Because of their strong SOC effect, the absorption spectrum in monolayer TMDCs is separated into two separate peaks caused by spin up and down. At the low temperature, the MOAC intensity via impurity scattering is the biggest followed by that of the SO phonons while the intrinsic acoustic and optical phonon scatterings display the smallest. For the monolayer TMDCs on substrates, ${\mathrm{SiO}}_{2}$ always shows its superiority in comparison with the others. Among the four TMDC materials, ${\mathrm{MoSe}}_{2}$ shows the biggest MOAC intensity, while ${\mathrm{WS}}_{2}$ has the biggest value of the absorbed photon energy. The full-width at half-maximum (FWHM) via impurity scattering achieves its highest value in ${\mathrm{WS}}_{2}$, while this occurs in ${\mathrm{MoSe}}_{2}$ and ${\mathrm{MoS}}_{2}$ via intrinsic acoustic and optical phonon scatterings, respectively. Our estimation of mobility from FWHM gives good agreement with the experimental results in ${\mathrm{WS}}_{2}$.

Vertical stacking of ultrathin two-dimensional materials via weak van der Waals (vdW) interactions is identified as an important technique for tuning the physical properties and designing viable products for nanoelectronics, spintronics, and renewable energy source applications. The geometry, electronic, and photocatalytic properties of vdW heterostructures of GeC and Janus transition metal dichalcogenides $M\mathrm{SSe}$ ($M$ = Mo, W) monolayers are investigated by performing first-principles calculations. Two different possible models of GeC-$M\mathrm{SSe}$ heterostructures are presented with an alternative order of chalcogen atoms at opposite surfaces in $M\mathrm{SSe}$. The most favorable stacking pattern of both models is dynamically and energetically feasible. A direct type-II band alignment is obtained in both models of understudy heterobilayer systems. The spin orbit coupling (SOC) effect causes considerable Rashba spin splitting in both $M\mathrm{SSe}$ monolayers. In particular, a greater Rashba spin polarization is demonstrated in model 1 (GeC-WSSe) than model 2 (GeC-MoSSe) caused by the alternative order of chalcogen atoms and larger SOC effect of heavier W than Mo atoms, which provides a platform for experimental and theoretical understanding of designing two-dimensional spintronic devices. More interestingly, the appropriate band alignments of model 1 with the standard water redox potentials enable its capability to dissociate water into ${\text{H}}^{+}/{\text{H}}_{2}$ and ${\text{O}}_{2}/{\text{H}}_{2}\text{O}$. In contrast to model 1, model 2 can only oxidize water into ${\text{O}}_{2}/{\text{H}}_{2}\text{O}$. The simulated design of GeC-$M\mathrm{SSe}$ is predicted for promising use in future electronic, spintronics, and photocatalytic water splitting.