Ferroelectricity in Covalently functionalized Two-dimensionalMaterials: Integration of High-mobility Semiconductors andNonvolatile MemoryMenghao Wu,*,† Shuai Dong,‡ Kailun Yao,† Junming Liu,*,§ and Xiao Cheng Zeng*,⊥,¶

†School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan430074, China‡Department of Physics, Southeast University, Nanjing 211189, China§Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China⊥Department of Chemistry, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States¶Collaborative Innovation Center of Chemistry for Energy Materials, University of Science and Technology of China, Hefei, Anhui230026, China

*S Supporting Information

ABSTRACT: Realization of ferroelectric semiconductors byconjoining ferroelectricity with semiconductors remains achallenging task because most present-day ferroelectricmaterials are unsuitable for such a combination due to theirwide bandgaps. Herein, we show first-principles evidencetoward the realization of a new class of two-dimensional (2D)ferroelectric semiconductors through covalent functionaliza-tion of many prevailing 2D materials. Members in this newclass of 2D ferroelectric semiconductors include covalentlyfunctionalized germanene, and stanene (Nat. Commun. 2014,5, 3389), as well as MoS2 monolayer (Nat. Chem. 2015, 7, 45),covalent functionalization of the surface of bulk semi-conductors such as silicon (111) (J. Phys. Chem. B 2006, 110 , 23898), and the substrates of oxides such as silica with self-assembly monolayers (Nano Lett. 2014, 14, 1354). The newly predicted 2D ferroelectric semiconductors possess high mobility,modest bandgaps, and distinct ferroelectricity that can be exploited for developing various heterostructural devices with desiredfunctionalities. For example, we propose applications of the 2D materials as 2D ferroelectric field-effect transistors with ultrahighon/off ratio, topological transistors with Dirac Fermions switchable between holes and electrons, ferroelectric junctions withultrahigh electro-resistance, and multiferroic junctions for controlling spin by electric fields. All these heterostructural devices takeadvantage of the combination of high-mobility semiconductors with fast writing and nondestructive reading capability ofnonvolatile memory, thereby holding great potential for the development of future multifunctional devices.

KEYWORDS: Ferroelectric semiconductors, multifunctional devices, covalent functionalization

Since early this century, dilute magnetic semiconductors(DMS) have received intensive interest along with the

arising of spintronics. When combined together, the semi-conducting part can be used for data operations (e.g., signalamplification with the requirement of maintaining a gatevoltage), while the ferromagnetic part can be used fornonvolatile magnetic storage of information. Therefore, theconventional semiconductor materials (Si, GaAs, ZnO, etc.)doped with magnetic ions possess both advantages whendirectly integrated in current semiconductor-based circuits.However, their practical applications are still hindered by theweak saturation magnetic moments and low Curie temper-ature,1 while doping stronger ferromagnetism may turnsemiconductors into metals.Over the past ten years or so, two-dimensional (2D) high-

mobility materials, such as graphene,2 silicene,3 germanene,4

stanene,5 transition-metal dichalcogenide (TMDC),6 andphosphorene,7,8 have also received considerable researchinterests. A reason behind such high interest is that theperformance of traditional transistors, when reduced tonanoscale, would be seriously influenced by the quantumeffect, whereas the 2D materials, because of their atomicthickness and high mobility, are promising candidates toreplace the current semiconductor materials in microelectronicsand to sustain the Moore’s Law for longer time. Nevertheless, itis even more challenging to achieve a 2D ferromagnetic (FM)semiconductor compared with DMS because doping magneticions into 2D materials like graphene or phosphorene will be

Received: October 14, 2016Published: October 14, 2016

Letter

pubs.acs.org/NanoLett

© 2016 American Chemical Society 7309 DOI: 10.1021/acs.nanolett.6b04309Nano Lett. 2016, 16, 7309−7315

much more difficult than replacing Ga in GaAs or Zn in ZnOby 3D magnetic ions like Cr or Mn. Meanwhile, the saturationmagnetization, along with the magnetic anisotropy energy,would be much lower than 3D magnetism in 3D DMS. On theother hand, most ferromagnets are not semiconductors butmetals.It is known that ferroelectric (FE) materials can be used as

nonvolatile random access memory (RAM) as well. Destructiveelectrical reading is usually involved in FE RAM, while highwriting energy is required in FM RAM. Therefore, multiferroicmaterials combining fast electrical writing with magneticreading are highly desirable.9 Contrary to ferromagnets thatare mostly metallic, FE materials must be nonmetallic and donot conflict with semiconductivity. If semiconducting FEmaterials can be made with a moderate bandgap, they wouldentail both functions of nonvolatile memory and manipulationof signals. Unlike 3D DMS that can be produced by directlycombining semiconductors and ferromagnetism, ferroelectricsemiconductors by combining semiconductors and ferroelec-

tricity are scarce10 because most ferroelectric materials (e.g.,perovskites and polyvinylidene fluoride materials) are large-gapinsulators rather than semiconductors. Although bulk semi-conductor-based ferroelectric cannot be achieved by directlydoping like doping 3D ions in DMS, surface functionalizationcan make nonferroelectric 2D materials ferroelectric (hereafter,we use FF2D to denote ferroelectric functionalized 2Dmaterials). In our previous work, hydroxylized graphene,denoted as graphanol, was predicted as the first 2D van derWaals FE material with high polarizations.11 Subsequentcalculations show that the Curie temperature of the graphanolcan be higher than 700 K.12 Note that the FE Curietemperature of 2D materials can be retained much higherthan the room temperature as long as the barrier for switchingis within a suitable range.10 In this work, we propose a novelapproach to achieve 2D FE materials that can dodge variousissues illustrated above. This approach can only apply to low-dimensional structures where most atoms are exposed. Thisapproach is also practically feasible in view of many successes in

Figure 1. Side and top views of (a) methyl-terminated germanene/stanene and (b) Sn(P, As, Sb)−CH2OCH3, where the blue arrow denotes thatthe polarization is switchable. Side and top views of (c) germanene/stanene functionalized by −CH2F, −CHO, and −COOH, respectively. Side viewof MoS2 monolayer functionalized by (d) −COOH and (e) −CONH2, respectively. The reports of fabrications for panels a, b, d, and e are in refs 15,14, 18, and 17.

Nano Letters Letter

DOI: 10.1021/acs.nanolett.6b04309Nano Lett. 2016, 16, 7309−7315

7310

synthesizing covalently functionalized 2D materials in recentyears. For example, it has been reported that silicene,germanene, and stanene can be functionalized by hydroxyl,13,14

methyl,15 or ligands like −CH2OCH3; boron nitride can bepartially hydroxylized;16 and MoS2 and phosphorene can befunctionalized by amides,17 carboxyl,18 or aryl diazonium.19

These functionalized 2D materials are all semiconductors withmodest bandgaps. For the group-IV elements of Si, Ge, and Sn,the sp3 state is more favorable compared to the sp2 state. Thus,2D silicene, germanene, and stanene are more easily function-alized than graphene. Moreover, silicene, germanene, andstanene have larger lattice constants than graphene so thatlonger ligands could be chosen for the functionalization. Forgraphene, the hydroxyl group appears to be only choice sincelonger ligands would lead to stronger repulsion among adjacentfunctional groups.In this Letter, we show that many surface functionalized 2D

materials are ferroelectric, and with proper substitution, the FEpolarization can be tuned. In addition, similar functionalizationof the surface of conventional semiconductors like Si and III−Vcompound can also give rise to ferroelectricity. Thefunctionalization is through self-assembled monolayers(SAMs). Given the recent experimental evidence that a MoS2monolayer on silica functionalized with various SAMs (−OH,−SH, −CH3, −CF3, −NH2, etc.) can exhibit distinct electronicand optical properties,20 we predict that substrates like silicaterminated with those SAMs can exhibit ferroelectricity and canbe used to modify physical properties of supported 2Dmaterials. With the ferroelectric 2D materials, various deviceswith distinct functions are readily designed.Computational Methods. Our density functional theory

(DFT) computations and scanning tunneling microscope(STM) simulation are performed with the generalized gradientapproximation (GGA) in the Perdew−Burke−Ernzerhof(PBE)21 form implemented in the Vienna Ab initio SimulationPackage (VASP 5.3)22,23 code. The projected augmented wave(PAW)24 method with a plane-wave basis set was used. Theenergy cutoff and convergence for the force were set to be 400eV and 0.01 eV/Å, respectively. A vacuum space of 15 Å wasadopted to minimize the artificial interaction between 2Dmaterial layer and its images. The PBE-D2 functional ofGrimme25 was utilized to account for the dispersive forces. TheBerry-phase method26 was employed to evaluate crystallinepolarization. Transmission spectra were computed by using thenonequilibrium Green’s function (NEGF) and Landauer-Buttiker formula,27 implemented in the QuantumWise ATKcode,28 with which the 30 × 1 × 100 k-point mesh wasemployed in the Brillouin zone. For the ab initio Born-Oppenheim molecular dynamics simulation (BOMD) (seebelow), we adopted the PBE-D2 functional and the samevacuum spacing. The simulation was performed in the constanttemperature and volume ensemble with the temperaturecontrolled at 350 K.Functionalized 2D Materials and Surfaces of Bulk

Materials. We first investigate covalent functionalizedgermanene and stanene. Importantly, methyl-terminatedgermanene and stanene (Figure 1a) have been fabricated by

Goldberger and co-workers recently, which are air stable andfree-standing with moderate bandgaps and have high mobilitycomparable to phosphorene.14,15,29 Goldberger and co-workersalso reported successful synthesis of a 2D analogue Sn(P, As,Sb)−CH2OCH3. We speculate that this ligand with a dipolemoment may induce ferroelectricity as long as it is switchableupon an external electric field, as shown in Figure 1, panel b. Byusing nudged elastic band (NEB) method, we estimated theaverage rotation barrier (or the barrier of switching) to beabout 0.09 eV per ligand (Figure S1a), which is much higherthan the ferroelectric switching barrier reported previously for3D ferroelectric BaTiO3

30 and 2D ferroelectric SnSe.10 Thisrotational barrier, defined as Ek, is the collective rotationalbarrier (supposing all spins/dipoles rotating spontaneouslytoward one direction in ferromagnetic/ferroelectric materials).Note that in the Ek computation, the nearest-neighborinteractions that play the key role in Curie temperatureestimation are not taken into consideration. Therefore, Ekcannot be used to determine the Curie temperature. However,Ek can be used to determine whether a ferroic material is “hard”or “soft”. For a material with a higher Ek, a higher externalmagnetic/electric field is required for the polarization switch-ing. Note also that thermal activation can increase structuraldisorder in the system and make spins/dipoles rotation morerandomly, but it cannot make all (infinite number of) spins/dipoles switch uniformly toward one direction. Whatdetermines the Curie temperature should be Ej, defined asthe switching barrier for one spin/dipole, while all othersurrounding spins/dipoles are fixed. In the ground state, thedipole moments of ligands are along the zigzag direction of thehoneycomb lattice. Here, the Ej value will be very high becausethe dipole of adjacent ligands cannot be opposite (to avoidcollision) since −CH2OCH3 is a long stick-like ligand anchoredat one side. As such, all the ligands are aligned toward the samedirection, thereby making the intrinsic ferroelectricity ultra-robust. The computed 2D switchable polarization is 0.31 ×10−10C/m for SnSb-CH2OCH3, which is around 4.5 μC/cm

2 in3D unit when the thickness of monolayer is taken as 7 Å. Thispolarization may be further enhanced by substitution of ligandswith larger dipole moments.For methyl-terminated germanene or stanene, substitution of

a hydrogen atom in each methyl group by a halogen atomwould make the system ferroelectric. All ligands can be alsosubstituted by other ligands such as −CHO or −COOH. Asshown in Figure 1, panel c, for germanene or staneneterminated by −CH2F or −COOH, the polarization is alignedalong the zigzag direction, while for those terminated by−COH, the ligands form zigzag hydrogen-bonded chains justlike hydroxyls in graphanol, and the polarization is along thearmchair direction. For all three liganded monolayers, theirpolarizations can be switched upon rotation of ligands. With−COOH, the ferroelectricity can be also switched by protontransfer along the hydrogen-bonded chains. By taking function-alized germanene as an example, the computed polarizations(see Table 1) are much higher than those of SnSb-CH2OCH3,while their bandgaps seem suitable for nanoelectronicapplications. Various system configurations including antiferro-

Table 1. Computed Polarizations and Bandgaps of Various Functionalized Monolayers

SnSb-CH2OCH3 Ge-CH2F Ge-CHO Ge-COOH Si−OH MoS2−COOH MoS2−CONH2 MoS2 + Silica−OH

polarization (10−10C/m) 0.31 1.17 0.81 0.68 0.76 0.55 0.50 0.37bandgap (eV) 1.1 1.0 1.66 1.36 0.51 0.20 0.11 1.80

Nano Letters Letter

DOI: 10.1021/acs.nanolett.6b04309Nano Lett. 2016, 16, 7309−7315

7311

electric configurations are examined to confirm that theferroelectric states shown in Figure 1 are indeed the groundstate (see Figure S1). We also performed ab initio BOMDsimulation with the temperature controlled at 350 K to confirmthat the ferroelectricity can still be retained above the ambienttemperature (Figure S2). Meanwhile, we also simulated theSTM images for comparison with future STM experiments(Figure S2). Moreover, we computed the strain energyfollowing previous studies.31,32 It turns out that the strainenergy is negative for −CH2OCH3, −CH3F, −CHO, and−COOH functionalization. When the coverage of ligandsdecreases from 100% to 50% (half passivated by ligands andanother half by hydrogen), the (negative) strain energybecomes less negative, with an energy change of 0.056, 0.075,0.067, and 0.042 eV per ligand, respectively. This isunderstandable as ligands are separated by more hydrogen atthe lower coverage, while hydrogen bonds are interrupted. Thecombined situation may not be favorable in energy change.It is worthy of mentioning that the partially hydroxylized

coun t e rpa r t s , l i k e S i 6H3 (OH) 3 ( s i l o x ene) andGe1−xSnxH1−x(OH)x, have also been synthesized.14 Here, thehydroxylized part also possesses ferroelectricity like graphanol.For example, the polarization of a fully hydroxylized silicene(silicanol) is actually greater than that of SnSb-CH2OCH3.Moreover, TMDCs like MoS2 were also functionalized withdifferent functional groups such as amide17 and carboxyl18 inexperiments. In particular, the 1T phase of MoS2 was shown tobecome a stable semiconductor when functionalized,17,33 andthe associated polar groups may induce ferroelectricity as well.As shown in Figure 1, panels d and e, the ligands (−COOH,−CONH2) are aligned in one direction, which should beswitchable upon an external electric field. The computedpolarizations (Table 1) are comparable to the functionalizedgermanene.The (111) surface configuration of cubic Si, Ge, and Sn is

similar to that of silicene, germanene, and stanene, and thus,similar functionalization may also induce ferroelectricity onthese surfaces. Silicon (111) surface, for example, can becomeferroelectric when functionalized by SAM of ligands like −SH(Figure 2a). The ligands can also serve as n or p dopants: −OHis an electron withdrawing group, while ligands like −CHO,−COOH, and −CONH2 are electron-donating groups.Similarly, binary semiconductors like III−V or II−VIcompounds can become ferroelectric when functionalizedwith ferroelectric SAMs (see Figure 2b). Compared to recentprogress on functionalization of 2D materials, functionalizationof surfaces of conventional bulk semiconductors is expected tobe much more practical at present, especially noting that thecovalent functionalization of silicon surfaces has already beenreported for decades.31,32,34 It may be also possible that withcurrent techniques the surface functionalization of particularregion of a wafer can make that local region ferroelectric;thereby, the latter region can be directly integrated with currentsilicon-based circuits. SAMs can be also used to functionalize2D insulating materials. A previous experiment20 demonstratedthat MoS2 monolayer on silica functionalized with variousSAMs (terminated by −OH, −SH, −CH3, −CF3, −NH2, etc.)can exhibit distinct electronic and optical properties. Here, wesuggest that the MoS2 monolayer on silica functionalized withSAMs can be ferroelectric also, for example, with −OHfunctionalization (Figure 2c). The surface-hydroxylized silicaexhibits polarization (Table 1), which thereby results in ahorizontal electric field along the MoS2 monolayer. When used

in photovoltaics, the electric field can facilitate the departure ofelectrons and holes so that the lifetime of excitons and thephotovoltaics efficiency may be enhanced.

Heterostructure Devices. It is known that polar disconti-nuity at the interface can induce polarization charges andelectric fields that drive metal−insulator transition.35 Here webuild a heterojunction by functionalizing a single 2D material ora semiconductor surface by two different ligands (e.g., Si (111)by −SH and Cl) so that one region is ferroelectric and theother nonferroelectric, and within the associated boundary freecharge accumulates along the 1D interface. The density of freecarrier λF will balance the polarization charge density λP:

λ λ= − = −P P n( )F F NF P

Here PF and PNF are the polarization of ferroelectric andnonferroelectric regions, respectively, and n is a unit vectorpointing from the ferroelectric region to nonferroelectricregion, normal to the interface. By switching the direction ofpolarization, the free carriers at the interface can be switchedbetween electrons and holes, as shown in Figure 3, panel a. Tosimulate the metal−insulator transition upon polar disconti-nuity, we consider a graphene sheet functionalized by arrays of−OH and −F nanostripes, where the hydroxylized regions areferroelectric and the polarization of zigzag O−H···O−H chainis aligned in the armchair direction of graphene lattice,11 whichgenerates a difference in potential between two sides, as shownin Figure 3, panel b. When the polarization is aligned in thedirection of 60 degrees away from −X, the system issemiconducting with a bandgap ∼0.15 eV. When it is directlyalong −X, the system is metallic along the −Y direction with a1D Dirac cone located at the Fermi level. In this case, the 1Dfree electron gas and hole gas are formed, respectively, atdifferent sides of hydroxylized nanostripes. In contrast, the

Figure 2. (a) Silicon (111) passivated by −SH and (b) cubic boronnitride (111) passivated by −OH. (c) MoS2 monolayer on a silicasubstrate passivated by hydroxyl (fabrication was reported in ref 20).

Nano Letters Letter

DOI: 10.1021/acs.nanolett.6b04309Nano Lett. 2016, 16, 7309−7315

7312

hydroxylized graphene and fluorinated graphene are insulatingwith bandgaps larger than 2.7 eV. Thus, the interface offunctionalized ferroelectric and nonferroelectric regions can beused as ferroelectric field-effect transistor with ultrahigh on/offratio (on/off states are respectively metallic/semiconducting).If the nonferroelectric regions are pristine graphene nanostripe,where the two ferromagnetic zigzag edges of the graphenenanostripe are antiferromagnetically coupled in the groundstate, the difference of potential between two spin-polarizededges may push the edge states toward the Fermi level in onespin-channel, which makes the system half-metallic. As shown

in Figure 3, panel c, the system is metallic in the spin-upchannel but insulating in the spin-down channel when thepolarization of hydroxylized nanostripes is aligned to the left,but vice versa when it is switched toward the right. Therefore, itis feasible to use electric field to control spin, which wouldrender the combined electrical writing and magnetic readingpossible in data storage.Ferroelectric tunnel junction (FTJ)36 is an alternative way for

nondestructive reading, where switching the polarization of asandwiched ferroelectric layer between two different metals canproduce a change in tunneling resistance, known as tunneling

Figure 3. Top-view and side-view for (a) silicon (111) passivated by −SH and −Cl; (b) graphene nanostripes functionalized by −OH and −F; (c)partially hydroxylized graphene nanostripes, where spin density distributions are marked by yellow (spin-up) and blue (spin down), and in the bandstructures, red and black lines denote different spin channels. The directions of polarization (marked by arrows) in ferroelectric regions point fromthe center of negative ions (like S, F, O) to the center of positive ions (like H), the same as those of the overall dipole of the ligands,.

Figure 4. Ferroelectric junction of germanene passivated by −CH2F and −CH3. The directions of polarization in ferroelectric regions are marked byarrows.

Nano Letters Letter

DOI: 10.1021/acs.nanolett.6b04309Nano Lett. 2016, 16, 7309−7315

7313

electroresistance (TER). Previous studies on TER were focusedon metal oxide bulk systems. Here, we demonstrate a high TERfrom the design of a 2D ferroelectric/nonferroelectric junctionbased functionalized 2D materials or semiconductor surfaces.For example, as shown in Figure 4, our first design is a p-doped(0.001e/atom) junction of germanene passivated by −CH3 andgermanene passivated by −CH2F, where the latter region isferroelectric. With the switching of polarization in the regionpassivated by −CH2F from right to left, more holes areaccumulated at the boundary, and the transmission would begreatly enhanced from 1.4 × 10−4 to 0.042, as shown in theclear transmission spectrum in Figure 4, upon differentpolarization directions. In this case, the TER is over 300,much larger than current TER measured in experiments.Other Device Designs. Previous studies have predicted that

germanene, stanene, and their functionalized counterpart are2D topological insulators (TIs),37,38 while half-passivated Ge−Ior Sn−I exhibit quantum anomalous Hall effect.39 Amongthem, the hydroxylized stanene is also ferroelectric. Theferroelectric TIs with switchable polar surfaces and spin-momentum locked Dirac cones can render electric-field controlof topological surface states and the surface spin currentpossible. Figure 5, panel a displays an in-plane heterostructureof TI and ferroelectric functionalized region (Ge−I and Ge-CH2F, for example). At the interface, the Dirac Fermions at theedge of TI can switch between holes and electrons upon thepolarization switching of Ge-CH2F. A topological transistor canbe composed of two ferroelectric domains of functionalizedgermanene or stanene, and the on/off state is switchable anddepends on the parallel/antiparallel configurations of ferro-electric domains, where the edge in antiparallel configuration isactually a 1D PN junction. It is known that PN junctiontypically has a low resistance state with narrower depletionregion upon a forward bias and a high resistance state withwider depletion region upon a reverse bias. The effect offerroelectric polarization can be equivalent to an external field.Therefore, the ferroelectric PN junction, like a silicon PNjunction with hydroxylized surface or a MoS2 PN junction on ahydroxylized silica substrate (Figure 5b), can switch betweenhigh/low resistance states upon the switching of polarization.Since the diffusion length can be up to micrometers, ourdesigns are still qualitative.Conclusion. On the basis of the first-principles calculations,

we show the rise of ferroelectricity40,41 in a series of covalent

functionalized silicene, germanene, stanene, and MoS2monolayer as well as the surface of bulk semiconductors likesilicon (111) or substrates like silica functionalized with SAMs.Most of these systems have already been synthesized in thelaboratory. These FF2Ds mostly possess both high mobilityand moderate bandgaps for nanoelectronic applicationstogether with ferroelectricity for nonvolatile memory. On thebasis of these ferroelectric 2D materials, we design a number ofheterostructure devices with various useful functions: 2Dferroelectric FTEs with ultrahigh on/off ratio, topologicaltransistors with Dirac Fermions switchable between holes andelectrons, ferroelectric junctions with ultrahigh electro-resist-ance, and multiferroic junctions controlling spin by electricfields. These systems can combine high-mobility semiconduc-tors for nanoelectronics and fast writing and nondestructivereading for nonvolatile memory, holding great promise asmultifunctional devices.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.nano-lett.6b04309.

Configurations of SnSb-CH2OCH3, and germanenefunctionalized by −CH2F, −CHO, and −COOH;simulated STM images upon Vbias = 1.5 V and snapshotsof equilibrium structures at 350 K at the end of BOMDsimulation (PDF)

■ AUTHOR INFORMATIONCorresponding Authors*E-mail: wmh1987@hust.edu.cn.*E-mail: liujm@nju.edu.cn.*E-mail: xzeng1@unl.edu.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSM.W., K.Y., and J.L. are supported by the National NaturalScience Foundation of China (Nos. 21573084, 11274130, and51431006). X.C.Z. is supported by the U.S. National ScienceFoundation through the Nebraska Materials Research Scienceand Engineering Center (MRSEC) (Grant No. DMR-

Figure 5. (a) In-plane heterostructure of germanene passivated by −CH2F and −I. (b) Ferroelectric PN junction based on hydroxylized Si (111)surface and MoS2 on hydroxylized silica surface.

Nano Letters Letter

DOI: 10.1021/acs.nanolett.6b04309Nano Lett. 2016, 16, 7309−7315

7314

1420645), a Qian-ren B (One-thousand Talents Plan B)summer research fund from USTC, and by a State Key R&DFund of China (2016YFA0200600 and 2016YFA0200604) toUSTC. We also thank Shanghai Supercomputing Center forproviding computational resources.

■ REFERENCES(1) Dietl, T. Nat. Mater. 2010, 9 (12), 965−974.(2) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang,Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Science 2004, 306(5696), 666−669.(3) Aufray, B.; Kara, A.; Vizzini, S.; Oughaddou, H.; Leandri, C.;Ealet, B.; Le Lay, G. Appl. Phys. Lett. 2010, 96 (18), 183102.(4) Bampoulis, P.; Zhang, L.; Safaei, A.; van Gastel, R.; Poelsema, B.;Zandvliet, H J W. J. Phys.: Condens. Matter 2014, 26 (44), 442001.(5) Zhu, F.-f.; Chen, W.-j.; Xu, Y.; Gao, C.-l.; Guan, D.-d.; Liu, C.-h.;Qian, D.; Zhang, S.-C.; Jia, J.-f. Nat. Mater. 2015, 14, 1020.(6) Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, V.; Kis, A.Nat. Nanotechnol. 2011, 6 (3), 147−150.(7) Liu, H.; Neal, A. T.; Zhu, Z.; Luo, Z.; Xu, X.; Tomanek, D.; Ye, P.D. ACS Nano 2014, 8 (4), 4033−4041.(8) Li, L.; Yu, Y.; Ye, G. J.; Ge, Q.; Ou, X.; Wu, H.; Feng, D.; Chen,X. H.; Zhang, Y. Nat. Nanotechnol. 2014, 9 (5), 372−377.(9) (a) Wang, K. F.; Liu, J. M.; Ren, Z. F. Adv. Phys. 2009, 58 (4),321−448. (b) Wang, K. F.; Liu, J. M.; Cheong, S. W.; Ren, Z. F. Adv.Phys. 2015, 64, 519−626.(10) (a) Wu, M.; Zeng, X. C. Nano Lett. 2016, 16 (5), 3236−3241.(b) Fei, R.; Kang, W.; Yang, L. Phys. Rev. Lett. 2016, 117 (9), 097601.(11) Wu, M.; Burton, J. D.; Tsymbal, E. Y.; Zeng, X. C.; Jena, P. Phys.Rev. B: Condens. Matter Mater. Phys. 2013, 87 (8), 081406.(12) Kan, E.; Wu, F.; Deng, K.; Tang, W. Appl. Phys. Lett. 2013, 103(19), 193103−193103−4.(13) Dettlaff-Weglikowska, U.; Honle, W.; Molassioti-Dohms, A.;Finkbeiner, S.; Weber, J. Phys. Rev. B: Condens. Matter Mater. Phys.1997, 56 (20), 13132−13140.(14) (a) Jiang, S.; Arguilla, M. Q.; Cultrara, N. D.; Goldberger, J. E.Acc. Chem. Res. 2015, 48 (1), 144−151. http://meetings.aps.org/link/BAPS.2016.MAR.X14.9.(15) Jiang, S.; Butler, S.; Bianco, E.; Restrepo, O. D.; Windl, W.;Goldberger, J. E. Nat. Commun. 2014, 5, 3389.(16) Sainsbury, T.; Satti, A.; May, P.; Wang, Z.; McGovern, I.;Gun’ko, Y. K.; Coleman, J. J. Am. Chem. Soc. 2012, 134 (45), 18758−18771.(17) Voiry, D.; Goswami, A.; Kappera, R.; de Carvalho Castro e Silva,C.; Kaplan, D.; Fujita, T.; Chen, M.; Asefa, T.; Chhowalla, M. Nat.Chem. 2014, 7 (1), 45−9.(18) Zhou, L.; He, B.; Yang, Y.; He, Y. RSC Adv. 2014, 4 (61),32570−32578.(19) Ryder, C. R.; Wood, J. D.; Wells, S. A.; Yang, Y.; Jariwala, D.;Marks, T. J.; Schatz, G. C.; Hersam, M. C. Nat. Chem. 2016, 8, 597.(20) Najmaei, S.; Zou, X.; Er, D.; Li, J.; Jin, Z.; Gao, W.; Zhang, Q.;Park, S.; Ge, L.; Lei, S.; Kono, J.; Shenoy, V. B.; Yakobson, B. I.;George, A.; Ajayan, P. M.; Lou, J. Nano Lett. 2014, 14 (3), 1354−1361.(21) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77(18), 3865−3868.(22) Kresse, G.; Furthmuller, J. Phys. Rev. B: Condens. Matter Mater.Phys. 1996, 54 (16), 11169−11186.(23) Kresse, G.; Furthmuller, J. Comput. Mater. Sci. 1996, 6 (1), 15−50.(24) Blochl, P. E. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50(24), 17953−17979.(25) Grimme, S. J. Comput. Chem. 2006, 27 (15), 1787−1799.(26) King-Smith, R. D.; Vanderbilt, D. Phys. Rev. B: Condens. MatterMater. Phys. 1993, 47 (3), 1651−1654.(27) Buttiker, M.; Imry, Y.; Landauer, R.; Pinhas, S. Phys. Rev. B:Condens. Matter Mater. Phys. 1985, 31 (10), 6207−6215.(28) Brandbyge, M.; Mozos, J.-L.; Ordejon, P.; Taylor, J.; Stokbro, K.Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 65 (16), 165401.

(29) Jing, Y.; Zhang, X.; Wu, D.; Zhao, X.; Zhou, Z. J. Phys. Chem.Lett. 2015, 6 (21), 4252−4258.(30) Huang, H.-Y.; Wu, M.; Qiao, L.-J. Comput. Mater. Sci. 2014, 82,1−4.(31) Solares, S. D.; Michalak, D. J.; Goddard, W. A.; Lewis, N. S. J.Phys. Chem. B 2006, 110 (16), 8171−8175.(32) Yu, H.; Webb, L. J.; Solares, S. D.; Cao, P.; Goddard, W. A.;Heath, J. R.; Lewis, N. S. J. Phys. Chem. B 2006, 110 (47), 23898−23903.(33) Tang, Q.; Jiang, D.-e. Chem. Mater. 2015, 27 (10), 3743−3748.(34) Buriak, J. M. Chem. Rev. 2002, 102 (5), 1271−1308.(35) Gibertini, M.; Pizzi, G.; Marzari, N. Nat. Commun. 2014, 5,5157.(36) Tsymbal, E. Y.; Gruverman, A. Nat. Mater. 2013, 12 (7), 602−604.(37) Xu, Y.; Yan, B.; Zhang, H.-J.; Wang, J.; Xu, G.; Tang, P.; Duan,W.; Zhang, S.-C. Phys. Rev. Lett. 2013, 111 (13), 136804.(38) Si, C.; Liu, J.; Xu, Y.; Wu, J.; Gu, B.-L.; Duan, W. Phys. Rev. B:Condens. Matter Mater. Phys. 2014, 89 (11), 115429.(39) Wu, S.-C.; Shan, G.; Yan, B. Phys. Rev. Lett. 2014, 113 (25),256401.(40) Jain, P.; Stroppa, A.; Nabok, D.; Marino, A.; Rubano, A.; Paparo,D.; Matsubara, M.; Nakotte, H.; Fiebig, M.; Picozzi, S.; Choi, E. S.;Cheetham, A. K.; Draxl, C.; Dalal, N. S.; Zapf, V. S. NPJ Quant. Mat.2016, 1, 16012.(41) Ratcliff, W.; Lynn, J. W.; Kiryukhin, V.; Jain, P.; Fitzsimmons,M. R. NPJ Quant. Mat. 2016, 1, 16003.

■ NOTE ADDED AFTER ASAP PUBLICATIONThis paper was published on the Web on October 18, 2016.Additional text corrections were implemented, along with arevised Supporting Information file, and the paper was repostedon October 19, 2016.

Nano Letters Letter

DOI: 10.1021/acs.nanolett.6b04309Nano Lett. 2016, 16, 7309−7315

7315