Two-dimensional functional materials: from properties to potential applications

ABSTRACT Two-dimensional (2D) materials have been extensively investigated since the exfoliation of graphene. Due to the excellent and versatile properties, the promising applications in novel nanodevices have been proposed in the last few years. Here, we chose three stable 2D materials which have been experimentally synthesized and have potential to be used for next-generation nanodevices, namely semiconducting MoS2, Janus MoSSe, and magnetic CrI3, to review their electronic/magnetic properties, and reveal the relationship of the properties-applications in devices. The showcase review on property-application is expected to provide new research insights into the investigations of 2D materials. GRAPHICAL ABSTRACT


Introduction
Two-dimensional (2D) materials have boosted research interests of nanomaterials since the successful isolation of graphene in 2004 [1,2]. The new material consists of sp 2 hybridized carbon atoms, the long-range π-conjugation renders it exhibit extraordinary thermal,

Structure and electronic properties
Here we take monolayer MoS 2 as the typical example of TMDs. MoS 2 adapts trigonal prismatic (2 H) phase at room temperature, with ABA stacking order. As seen in Figure 2(a), Mo atom is coordinated by six S atoms and sandwiched by two layers of chalcogen atoms, it possesses inplane inversion asymmetry [28,49]. The bulk MoS 2 is a typical layered structure with intralayer strong S-Mo-S bond, and the interlayers are connected by Van der Waals interaction. Bulk MoS 2 has an indirect bandgap with valence-band maximum (VBM) located at Г point, conduction-band minimum (CBM) located between K and Г [28,50,51]. When it is thinned down to monolayer, it turns out to be a direct-bandgap semiconductor with both CBM and VBM at the two inequivalent high-symmetry points K and -K because of the broken inversion symmetry, which makes the valleytronics applications possible [48,52]. The bandgap for bulk MoS 2 is calculated to be 0.88 eV, but increases to 1.71 eV for monolayer [53,54], as shown in Figure 2(b). In addition, because of the contribution of d orbitals in Mo atoms, MoS 2 shows a strong spin-orbit coupling (SOC), which will lead to a spin splitting at K and -K valley. The spin splitting at VBM is up to 0.15 eV, but much smaller at CBM. In addition, because of the time-reversal symmetry, the spin splitting of bands at K and -K is opposite as shown in Figure 2(c). The strong coupling of spin and valley degrees of freedom renders MoS 2 a novel material to integrate the valleytronics and spintronics.

The application of monolayer MoS 2 in electronics device
Different from zero-bandgap graphene, monolayer MoS 2 exhibits sizable bandgap, which makes it promising for application in FET and optical devices. Monolayers MoS 2 has a bandgap of about 1.8 eV, but the carrier mobility is only among 0.5-3 cm 2 V −1 s −1 as measured from experiments, thus unsuitable for device application [15,55,56]. Luckily, the recent investigations indicated that the carrier mobility of MoS 2 can be improved to 200 cm 2 V −1 s −1 at room temperature by using atomic layer deposition (ALD) with HfO 2 as gate dielectric, and Si/SiO 2 as the substrate. The schematic diagram is shown in Figure 3(a). The direct bandgap together with excellent carrier mobility make monolayer MoS 2 a potential candidate for inter-band tunnel FETs. The gating characteristics show that the MoS 2 device is an FET with n-type channels. This transistor shows a current on/off ratio up to 1 × 10 8 and carrier mobility up to 217 cm 2 V −1 s −1 (the mobility is calculated as μ ¼ dI ds =dV bg � � � ½L= WC i V ds ð Þ�, where L represents the channel length, W is the channel width, C i is the capacitance between the channel and the back gate per unit area). As shown in Figure 3(b), an ohmic I ds À V ds behavior could be achieved in this device. The drain-source current as the function of drain-source bias shown in Figure 3(c) indicates an excellent current control in this device. This is the first realization of monolayer MoS 2 as a transistor.
Constructing vertical heterostructure is an alternative way of TMD-based device. For example, it was demonstrated that the heterostructure of monolayer MoS 2 and graphene can be built to realize an FET for information storage [57]. The device is constructed by graphene layers, and HfO 2 as tunneling oxide layer, MoS 2 serve as the floating gate as shown in Figure 3(d). The schematic view of the memory device and fabrication process is also shown in Figure 3(e). The charge stored on the floating gate is calculated to be 2.8 × 10 13 cm −2 (n ¼ ðΔV � C FGÀ CG Þ=q, where ΔV represents the difference in the threshold voltage for read and erase states, the C FGÀ CG represents the capacitance between the floating gate and the control gate), the value is much larger than the value of graphene, which indicates a larger memory window for multilevel data storage. The stability of Erase and Program states is also investigated as shown in Figure 3(f). The erase state current is in the range of 10 −8 -10 −7 A, the corresponding program state would be stabilized in the range of 10 −12 -10 −10 A, the maximal program/erase current ratio is up to 10 4 . In vertical stacked double-layer MoS 2 , memristors can be realized with an extremely low switching voltages, the resistance of grain boundaries in single-layer MoS 2 devices makes the switching ratios up to 10 3 and realizes effective gate tuning [58,59].

Optical properties and application
The optical properties are usually determined by direct transitions of electrons between VBM and CBM. However, TMDs have large exciton binding energies (0.5-1 V) [60][61][62][63][64][65]. The high-order excitonic like trion binding energy of monolayer MoS 2 is almost an order of magnitude larger than that in other quasi-2D systems [66,67]. The primary reason is the heavy particle band masses because of the Mo d-manifolds [28,50,68]. The absorption spectrum of monolayer MoS 2 , schematic diagram of exciton, and higher order excitonic complexes are shown in Figure 2(d). The strong excitonic effects could give a strong transfer of oscillator strengths and a large exciton radiative rate, which is essential in optoelectronics applications [69,70]. For example, vertical heterostructure of monolayer MoS 2 and nitrogenated porous 2D material C 2 N have been proposed to be a potential photovoltaic material by first principle calculation [71]. Experimentally, the photovoltaic performance of MoS 2 has been proven in the device of vertically stacked indium tin oxide (ITO) electrode/MoS 2 /metal electrode [72]. TMDs have also been widely utilized in photodetection and excitonic LEDs due to its light absorption over a wide range of wavelengths [73][74][75][76][77][78].

Electronic properties of Janus TMDs
For traditional TMD, the out-of-plane mirror symmetry is reserved since the two chalcogen atom layers are identical. When one chalcogen atom layer is replaced by a different species of chalcogen atom, the mirror symmetry will be broken, leading to the Janus TMDs with C 3 v symmetry as shown in Figure 4(a). Due to the electronegativity difference for different species of chalcogen atoms, a vertical dipole moment will be induced [79]. The bonding characteristics and charge density distribution will thus be affected. Result shows that there exists a covalent character of the metal-chalcogen atom bonding, and charge distributions are different for different species of chalcogen atom [80]. Early in 2013, the stabilities of these structures have been checked from Phonon dispersion calculations, it shows that MoSSe, WSSe, WSeTe, and WSTe monolayers are stable, while MoSeTe and MoSTe monolayers are unstable due to the imaginary frequencies in the phonon dispersion [81]. Indeed, Janus MoSSe monolayer recently has been synthesized in the experiment by selenization method or modified CVD methods [32,33].
As a result of the symmetry breaking, the electronic band structure is significantly affected. From the band structure in Figure 4(b), MoSSe is a semiconductor and the band gap is 1.56 eV with both CBM and VBM located at the Κ points [82]. The conduction band minimum (CBM) is composed of out-of-plane Mo-d 2 z states, the valence band edge mainly arises from in-plane Mo-d x 2 À y 2 and d xy orbitals. When SOC is considered, a large valley-spin -splitting (169 meV) can be induced at the valence band, however the spin splitting at conduction band is trivial (14 meV). The time-reversal symmetry leads to the reversed spin order at K and -K, and the couple of spin and valley. Rashba effect is observed around Γ point, caused by the mirror symmetry breaking in Janus TMDs [83,84]. The Rashba spin splitting in Janus TMDs can be demonstrated from the explicit spin vortex in Figure 4(c). The Rashba parameter α R is 77 meV.Å for MoSSe, and 514 meV.Å for WSeTe [85]. In addition, the Rashba splitting could be enhanced by external electric field or compressive strain as shown in Figure 4(d).

The application of monolayer Janus TMDs in device
Compared with traditional TMDs, the out-of-plane electronic polarization resulted from the break of mirror symmetry in Janus TMDs will bring distinctive applications in nanodevice design and other fields. A device of monolayer MoSSe sandwiched between two graphene electrodes is shown in Figure 5(a) [34]. A pn-junction is presented due to the intrinsic dipoles in MoSSe. Graphene is chosen as the metallic leads to screen the cross-plane-field. Furthermore, graphene is turned out to be strongly doped on the top and bottom layers, and an energy shift of 0.4 eV appears between the graphene layers as shown in the band structure in Figure 5(c). The current injected between the top and bottom graphene layers can be calculated.
A high transmission appears for a bias above the gap of MoSSe, and a small transmission between two graphene layers is also found at the Fermi level. To examine the photogenerated current, a device composed of three layers of MoSSe is constructed, seen in Figure 5(b). A voltage is applied to the gate to offset the built-in electrical field of MoSSe. A direct tunneling current between graphene layers is found from the I À V curve in Figure 5(d). As shown in Figure 5(e), the cross-plane-channel leads to a peak at −0.67 eV when zero gate voltage is applied. In addition, there is a van Hove-like transmission peak which is result from the less dispersed bands. The asymmetric structure in Janus MoSSe provides a way to tune the dispersion of the band by applying gate voltage.
The presence of polarization induced by the symmetry breaking also makes monolayer MoSSe an ideal 2D photocatalyst for water splitting [86]. The superiority of MoSSe as efficient photocatalyst is that the built-in electric field induced by the intrinsic dipoles could separate the photo-generated electrons and holes to a different surface, which in turn reduce the possibility of carrier recombination and spatially separate the generated H 2 from O 2 . Moreover, it shows that the optical absorption could be tuned by applying strain as shown in Figure 6(a). Similarly, Janus TMDs are also promising candidates for HER catalyst [87]. As indicated by the current density and HER volcano curve in Figure 6(b), the Janus asymmetry leads to the enhanced catalytic activity because of the in-gap states and a shift in the Fermi level. HER activity of WSSe monolayers can be further improved with the S/Se-vacancies, the can reach −15 meV. Gas adsorption behavior can be even enhanced or weakened by the polarization of Janus MoSSe depending on the S or Se terminated surface [86]. On the other hand, it is found that the significant valley polarization can be achieved in Cr/V-doped MoSSe, the schematic diagram is shown in Fig.6(c) [82]. The magnetic doping could lift the spin degeneracy, and the energy difference is up to 0.059 eV as shown in Figure 6(d), which is large enough for observing the valley Hall effect. This provides a promising aspect for applications of Janus TMDs in valleytronics.

Structure and electronic properties
Bulk CrI 3 presents rhombohedral BiI 3 structure with a monoclinic lattice and possesses R � 3 symmetry when the temperature is below 210 K. At room temperature, the space group symmetry becomes C2/m [89,90]. The low-temperature configuration could be viewed as ABC stacked structure, each layer shifts by [2/3, 1/3] along in-plane axis relative to nearest layer, while the high-temperature phase refers to a lateral shift of [1/3, 0] and [2/3, 0] for two layers, respectively, relative to the other layer [91]. In monolayer CrI 3 , the chromium ions are sandwiched by two halide planes, and a unit cell contains two chromium atoms and six halide atoms as shown in Figure 7(a).
Magnetism in CrI 3 roots in the partially filled d orbitals in Cr ions. The crystal field splits the five d-orbitals (d xy ; d xz ; d yz ; d x 2 À y 2 ; d 3z 2 À r 2 ) of Cr atom to triply degenerate t 2g orbitals and doubly degenerate e g orbitals [92]. The three t 2g electrons yield S = 3/2, which is consistent with the experimental measured atomic magnetic moment of 3μ B per chromium atom [93]. The monolayer CrI 3 exhibits ferromagnetic order with the Curie Figure 7. (a) Top and side view of crystal structure for monolayer, low-temperature and hightemperature bilayers CrI 3 , respectively. (b) Band structure of monolayer CrI 3 with magnetic moment along the out-of-plane axis and in-plane axis, respectively. (c) From left to right, differential charge density of low-temperature phase (red arrows refer to the interacting I atoms), spin density of interlayer I atoms for low-temperature phase (red and green isosurface indicate spin-up and spindown charge densities), differential charge density of high-temperature phase for bilayer CrI 3 (red arrows refer to the interacting I atoms), spin density of the interlayer I atoms for high-temperature phase (red and green isosurface indicate spin-up and spin-down charge densities). (d) The interlayer exchange energy for low-temperature phase and high-temperature phase from bilayer to bulk CrI 3 . ((a): Reprinted with permission from Reference [91]. Copyright 2018 American Chemical Society; (b): Reference [98]. Copyright 2018 American Chemical Society; (c) and (d): Reference [99]. Copyright 2019 American Physical Society). temperature of 45 K, due to the ferromagnetic superexchange interaction [94,95]. CrI 3 displays the magnetic anisotropy due to the large magnetic anisotropy energy (804 μeV/ Cr, MAE: the energy difference between magnetization in the in-plane and out-of-plane directions). The easy axis for spontaneous magnetization is the out-of-plane spin orientation [93,96].
The electronic properties of single-layer CrI 3 show strong sensibility to the magnetic ordering, the exchange-correlation functional, and SOC [97]. The nonmagnetic (NM) phase exhibits a zero band gap because of the half-filled t 2g orbitals by 3d 3 electrons in Cr 3+ . Both the FM and AFM phases are semiconductors with a finite band gap, which results from the Mott-Hubbard mechanism. The band structure of FM phase is shown in Figure 7(b). When spin polarization is along the c axis, CrI 3 has a direct band gap of 1.64 eV from Heyd-Scuseria-Ernzerhof (HSE) hybrid functional [98]. The energy splitting is 174.50 meV at VBM, but only 64.42 meV at CBM. When the magnetic moment is rotated to in-plane axis, CrI 3 becomes an indirect semiconductor with the CBM shifted from Γ to a point between M and K, and the energy splitting vanishes at both CBM and VBM.
Although bulk and monolayer CrI 3 are both FM, bilayer CrI 3 is an AFM due to the close correlation between stacking orders and the magnetic ground state of bilayer CrI 3 [91,99]. The interlayer exchange of bilayer CrI 3 is responsible for the intrinsic mechanism of AFM coupling [99]. From spin-dependent differential charge density (DCD) in Figure 7(c), electrons gathered at I-I pairs. The orbit for interlayer I-I pairs could be regarded as p x=y (the orbit of intralayer superexchange labeled as p x and p y ). The shared electrons and a nearly linear configuration of two p x=y orbits indicate a direct FM coupling for the interlayer I atoms. The intralayer Cr-I-Cr superexchange is relatively strong and the interlayer Cr-I . . . I-Cr direct exchange is in the weak-interaction limit. Thus, it is easy to tune the interlayer magnetism. In the case of high-temperature phase, the interlayer electron sharing is through a tri-I cluster, which leads to the Cr-I . . . I-Cr interaction, a 135° configuration with a minor p z spin density. This direct p x=y -p z interaction produces an AFM coupling. This explains why the bilayer CrI 3 exhibits AFM. The slight shifts of one layer would lead to the change of the interlayer hybridization, which will in turn change the interlayer magnetic coupling. In addition, for the high-temperature phase, the trilayer, quadlayer, and bulk CrI 3 are also in AFM state as shown in Figure 7(d).

Applications of magnetic CrI 3
As a 2D magnetic material, the spintronic device can be proposed based on the magnetic properties of CrI 3 . A gated bilayer CrI 3 device is fabricated to realize a metamagnetic transition by electrostatic gate controlling [47]. The device is illustrated in Figure 8(a), consisted of a bilayer CrI 3 flake and a graphite contact. The magnetization could be probed by magneto-optical Kerr effect (MOKE) microscopy. From Figure 8(b), the light color indicates low MOKE signal, which refers to the AFM state, the dark colors represent the two FM states. The metamagnetic transition lies on the back-gate voltage V bg . As revealed by the reflectance magneto-circular dichroism (RMCD) microscopy, the applied gate voltage would induce interlayer bias and electrostatic doping. The critical field between FM and AFM (Figure 8c) could be affected by doping level while the doping could control orbital occupation, exchange interactions as well as the magnetic coupling [100][101][102][103]. This work designed a new device based on bilayer CrI 3 to explore magnetoelectric effects and their potential applications in gate-tunable spintronics.
Magnetic CrI 3 can be also used for the information storage. For example, the FET composed of graphene and CrI 3 flakes is designed, as illustrated in Figure 8(d) [104]. The photocurrent increases quickly when the photon energy exceeds 1.2 eV, seen Figure 8(e), referring to the bandgap of CrI 3 . The magnetoresistance is probed at different temperatures with external magnetic field in the direction of out-of-plane. Large jumps are probed with a magnitude variation reaches 10,000% as B in the range of 2 T. The large magnetoresistance results from the transform of magnetic state for the CrI 3 . From Figure 8(f), three states can be observed as a result of the resistance jumps. The boundaries of the states are unchanged whether by varying B with T unchanged or by changing T with B unchanged. This finding proves that the magnetoresistance is resulted from the different magnetic states of CrI 3 .

Conclusion and prospective
In this review, we chose three stable 2D materials which have been experimentally synthesized, semiconducting MoS 2 , Janus MoSSe with out-of-plane polarization, and magnetic CrI 3 to reveal the unique electronic/magnetic properties, and clarify the relationship between properties and applications. The semiconducting properties and high carrier mobility make monolayer MoS 2 show an excellent performance in interband tunnel FETs. The heterostructure of monolayer MoS 2 and graphene can be used as a FET for information storage. Janus MoSSe has an out-of-plane dipole moment due to the different electronegativity for different chalcogen atoms. The device based on MoSSe can fully utilize the merit of out-of-plane polarization, like stacked graphene and MoSSe device with a cross-plane transport channel, photocatalysis for water splitting, HER catalyst, and applications in valleytronics. Monolayer CrI 3 is in FM state with out-ofplane spin orientation as the easy axis. In contrast, the bilayer CrI 3 exhibits AFM resulting from direct-exchange interactions, the interlayer magnetic coupling could be tuned by changing the stacking orders. Bilayer CrI 3 device can be realized with a metamagnetic transition by electrostatic gate controlling, and present a large tunneling magnetoresistance.
Due to the quick development in the research area, large number of new 2D materials have been found. The novel structural, mechanical, electronic, and magnetic properties in these materials lay the foundations for the application in electronic devices and energy storage/conversion, like photo-and electro-catalysis, solar cell, topological insulator, and so on. However, there are still many challenges to develop the devices based on the new materials and properties, such as the demand for stability, multifunctionality, and low-energy cost. As a powerful tool, currently, most of theoretical researches focused on fundamental properties or 2D materials predictions but barely devoted the investigations to the performance of devices or design of nanodevices. Even so, the comprehensive studies of electronic or magnetic properties for these low-dimensional materials still provide some useful guidelines for device design. It is insightful to clarify the relationship between properties and applications. The potential applications based on the unique mechanical, electronic, and magnetic of nanomaterials should be proposed. For instance, borophene is hydrogenated to realize simultaneous ferroelastic and auxetic properties, which can be used for lowdimensional mechanical devices. Bismuth layer is functionalized with CH 2 OH to achieve ferroelectric and topologically insulating orders for quantum computations. Ferroelectric AgBiP 2 Se 6 monolayer can be used for photocatalysis in water splitting, and realize effective regulations of photocatalytic properties by ferroelectricparaelectric phase transition [105][106][107]. 2D nanomotors device can be designed by utilizing the stiffness differences of the substrate, due to the nanodurotaxis of 2D materials [108].

Funding
This work was supported by the ARC Discovery Project [DP190101607].