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2017 2D Mater. 4 015015

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2DMater. 4 (2017) 015015 doi:10.1088/2053-1583/4/1/015015

PAPER

Conetronics in 2Dmetal-organic frameworks: double/half Diraccones and quantum anomalous Hall effect

MenghaoWu1,2, ZhijunWang1, Junwei Liu3,Wenbin Li2, Huahua Fu1, Lei Sun4, Xin Liu1,MinghuPan1,HongmingWeng5,MirceaDincă4, Liang Fu3 and Ju Li2

1 School of Physics andWuhanNationalHighMagnetic Field Center,HuazhongUniversity of Science andTechnology,Wuhan,Hubei430074, People’s Republic of China

2 Department ofNuclear Science andEngineering andDepartment ofMaterials Science and Engineering,Massachusetts Institute ofTechnology, Cambridge,MA02139,USA

3 Department of Physics,Massachusetts Institute of Technology, Cambridge,MA02139,USA4 Department of Chemistry,Massachusetts Institute of Technology, Cambridge,MA 02139,USA5 BeijingNational Laboratory forCondensedMatter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190,

People’s Republic of China

E-mail: wmh1987@hust.edu.cn and liju@mit.edu

Keywords: first-principles calculations, 2D metal-organic frameworks, quantum anomalous Hall effect, cone selecting/filtering, double/half Dirac cones

Supplementarymaterial for this article is available online

AbstractBandstructure withDirac cones gives rise tomasslessDirac fermions with rich physics, and herewepredict rich cone properties inM3C12S12 andM3C12O12, whereM=Zn, Cd,Hg, Be, orMg based onrecently synthesizedNi3C12S12—class 2Dmetal-organic frameworks (MOFs). ForM3C12S12, theirband structures exhibit doubleDirac cones with different Fermi velocities that are n (electron) and p(hole) type, respectively, which are switchable by few-percent strain. The crossing of two cones aresymmetry-protected to be non-hybridizing, leading to two independent channels at the same k-pointakin to spin-channels in spintronics, rendering ‘conetronics’ device possible. ForM3C12O12, togetherwith conjugatedmetal-tricatecholate polymersM3(HHTP)2, the spin-polarized slowDirac conecenter is pinned precisely at the Fermi level,making the systems conducting in only one spin/conechannel. Quantum anomalousHall effect can arise inMOFswith non-negligible spin–orbit couplinglike Cu3C12O12. Compounds ofM3C12S12 andM3C12O12with differentM, can be used to build spin/cone-selecting heterostructure devices tunable by strain or electrostatic gating, suggesting theirpotential applications in spintroincs/conetronics.

Introduction

It is well known that graphene possesses a bandstructure with Dirac cones touching at the Fermi levelat each K point in the Brillouin zone, giving rise tomassless Dirac fermionswith rich physics [1]. Over thelast few years, linear band dispersion and the asso-ciated Dirac physics have been explored in othermaterials [2], such as graphyne [3, 4] and the surface of3D topological insulators [5]. Similar phenomena havealso been investigated in artificial graphene, such asmetal surfaces with hexagonal assemblies of COmolecules [6], or ultra-cold atoms trapped in honey-comb optical lattices [7–9]. For 2D or quasi-2Dcrystals with three-fold symmetry, generally, K and K′

points of Brillouin zone are symmetry related, leadingto two-fold degenerate bands generally with a Dirac-like dispersion at K and K′ [2]. Recently, somedesigned 2D conjugated polymer [10] with three-foldsymmetry have been predicted to have graphene-likeelectronic structures. Some structures with spin-split-ting were shown to exhibit quantum anomalousHall effect (QAHE) [11–13]when spin–orbit coupling(SOC) is taken into account. Actually, Ni3C12S12, aconjugated 2D nanosheet comprising of planarnickel bis(dithiolene) complexes that has beensuccessfully synthesized by Kambe et al [14, 15],also has three-fold symmetry and has shown highelectrical conductivity (up to 160 S cm−1 at 300 K)and controllable oxidation states (reduced using

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7,7,8,8- tetracyanoquinodimethane sodium (NaTCNQ)and oxidized using tris(4-bromophenyl)aminiumhexachloroantimonate) [10], analogous to 2D gra-phene/graphene oxide. Band structure calculationshows that native undoped Ni3C12S12 single-sheet is asemiconductor, while a topological insulator (TI) stateis predicted within a bandgap ofDirac band opened upby SOC at around 0.5 eV above the undoped Fermilevel [16].

Herein, we report a series of 2Dmetal-organic fra-mework (MOF) semimetals in their native, undopedstate with intriguing electronic and magnetic proper-ties. Some of these proposed materials possess twoindependent Dirac cones of different Fermi velocity ateach K point that are N (electron) and P (hole) type,respectively, and the relative energy alignment of fastand slow Dirac cones can be tuned via few-percenttensile strain so as to switch between N and P designa-tion; for some others there is only one spin-polarizedDirac cone (half Dirac cone) crossing the Fermi level ateach K point, making the systems ferromagnetic andconducting in only one spin channel and one conechannel. The latter are predicted to exhibit the QAHEwhen SOC is taken into account. Finally, we show that‘conetronics’ devices can be designed for manipulat-ing carriers in different cones. Previous experimentalreports have already shown that in Ni3C12S12, Niatoms may be replaced by other transition metalatoms while S atoms can be replaced by O or –NHgroups [17–19], and some of themwere also predictedto exhibit TI state around 0.5 eV away from Fermilevel [20, 21]. Here we mainly focus onM3C12S12 andM3C12O12 where M=Zn, Cd, Hg, Be, Mg. Thesemetals strongly favor the 2+ formal oxidation state,and thus are expected to donate two s electrons tonearby four S (or O) atoms. They contribute no d elec-trons to the density of states near Fermi level andrequire no external chemical doping. We note thatalthough square planar complexes of these metals areuncommon, their closed-shell electronic configura-tions do not favor any particular crystal field geometry,their coordination geometry being influenced eitherby steric effects or other global stabilization effects,such as strain or Coulombic interactions.

Methods

First-principles calculations are performed within theframework of spin-unrestricted density-functional-theory calculations implemented in the Viennaab initio Simulation Package [22]. The projectoraugmented wave potentials [23] for the core and thegeneralized gradient approximation in the Perdew-Burke-Ernzerhof [24] form for the exchange-correla-tion functional are used. The Monkhorst-Pack k-meshes are set to 5×5×1 in the Brillouin zone andthe nearest distance between two adjacent layers is setto 12 Å. All atoms are relaxed in each optimization

cycle until atomic forces on each atom are smaller than0.01 eV Å−1 and the energy variations between subse-quent iterations fall below 10−6 eV. We also examinethermodynamic stability of M3C12S12 and M3C12O12

(take M=Cd for example) at 700 K using the Born–Oppenheimer molecular dynamics simulation [25],and the snapshots in figure S6 suggest that bothsystemswill be stable.

Results

DoubleDirac cones ofM3C12S12Figures 1(a)–(e) display the band structures ofM3C12S12, where M=Zn, Cd, Hg, Be, Mg. They allexhibit two Dirac cones near the Fermi level at each Kpoint, with different cone-tip energies that are sepa-rated by the Fermi-level and with different Fermivelocity. ForM=Zn, Cd, Hg, at each K point, the fastDirac cone is found above the Fermi level (P-type)where the Dirac fermion carriers are excess holes,while the slow Dirac cone is below the Fermi level (N-type)where the Dirac fermion carriers are electrons, atthe native undoped state. In contrast, forM=Be,Mg,the fast Dirac cone is P-type while the slow one isN-type. For the fast Dirac cones, Hg3C12S12 has thehighest Fermi velocity vF (approximately half of that ofgraphene) which is almost three times larger than thatofMg3C12S12 (supplementary table S1), and four timeslarger than vF′ of the slow Dirac cone. The bandstructures in figure 1 exhibit closed band crossing linesby intersections of two bands, namely, node-line rings,right at the Fermi level, making those systems perfect2D node-line semimetals, as shown on the right panelwhere those rings are marked by purple: forM=Zn,Cd, Be, there is a node-line ring locate around each Kpoint due to the intersections of fast and slow Diraccones, and in the displayed band structures we can findan intersection point of the fast and slow Dirac conealong the path Γ–K and K–M respectively. For theband structures ofM=Hg, Mg, a closed ring aroundthe C6 rotation axis at Fermi level is formed by theband crossings, exhibiting linear dispersions along Γ–K and Γ–M. For all those systems, no gap opened atthe crossing of two cones, indicating no hybridization,so the slow and fast Dirac cones can be regarded as twoindependent channels just like spin-up and spin-downin spintronics, whichwill be discussed for constructing‘conetronics’ devices in the last section. We have alsochecked the energy of buckled states which may existin such 2DMOFs [26], and found that forM=Mg, itsbuckled state is quite close to the planar state in energy:upon a biaxial strain of −1.3%, the buckled state willbe the ground state with a magnetic moment of 2μB

per supercell. The spin-splitting makes the systemmetallic only in the slow Dirac cone and in only onespin channel; upon a biaxial tensile strain of 1.3%, thesystem is planar but also becomes ferromagnetic. Theband structures of these buckled systems are displayed

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2DMater. 4 (2017) 015015 MWu et al

in supplementaryfigure S1. IfM is substituted by otheralkali earth metal such as Ca, Sr, Ba, the buckled statesare the ground states where S atoms will be more than0.4 Å away from the MOF plane, which may indicateinstability as their planar tetracoordinate (square-planar) structures are not favorable in energy. Here weonly focus on M=Zn, Cd, Hg, Be, Mg where theoptimized structures may reveal that their square-planar coordination are favorable in 2D periodicstructures.

Since the orbitals of fast and slowDirac cones referto different resonance structures that favor differentbond length patterns, it is possible to use strain to con-trol the radius of rings formed by the crossings of fastand slow Dirac cones. For M=Zn and Cd, the fastand slow Dirac cones are both close to the Fermi level,giving rise the possibility to tune the relative energyalignment between fast and slow Dirac cones. TakeM=Zn as an example, as shown in figure 1(e), we

defineΔE=E(slow) – E(fast) as the energy differencebetween the slow Dirac cone and fast Dirac cone tips.Upon a biaxial strain, the fast cone will shift downwhile the slow cone will move upwards. As the strainreaches around 1.9%, where ΔE=0, two Diracpoints coalesce exactly at the Fermi level, forming aDirac point with two different Fermi velocities: withlarger strain, the fast cone will switch to N-type whilethe slow one will become P-type. We note that 1.9%tensile strain should be achievable experimentally inmost 2Dmonolayermaterials without fracture [27].

We have investigated the origin of zero hybridiza-tion between the fast and slowDirac cones. As a proto-type, in figure 2(a) we plot the highest occupiedelectron state (HOES), second and third highest occu-pied electron state (SHOES and THOES) atΓ point forCd3C12S12 in comparison with graphene (figure 2(b)).Surprisingly, we find that the fast Dirac cone (THOES)has contribution only from the px and py orbitals of

Figure 1. (a)–(e)Band structures ofM3C12S12 forM=Zn, Cd,Hg, Be, andMg, and their node-line rings in Brillouin zone. (f)Dependence of energy difference between the slowDirac cone and fast Dirac cone on biaxial strain for Zn3C12S12. The gray, yellow,green and red spheres denote carbon, sulfur,magnesium and copper atoms respectively.

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2DMater. 4 (2017) 015015 MWu et al

sulfur, which is scarcely distributed on C or Cd atoms.This electronic state is also delocalized with high sym-metry resembling the π electron of graphene(THOES). Here in the big red circle, the two config-urations are equivalent and should have equal energylevel. The THOES is highly delocalized between adja-cent S atoms, where electron delocalization movesTHOES away from Cd atoms, which may indicate theresonance between two configurations in the redcircle.

The slow cone (HOES) is made up primarily fromthe pz orbitals of S andC, similar to SHOES (σ band) ofgraphene. Judging from the symmetry of electronstates for the fast and slow Dirac cones, either at theGamma point or at the crossing point of cones alongΓ–K (supplementary figure S2), their Dirac crossingsare symmetry-protected in the absence of SOC.According to the symmetry of SHOES (flat bands),their crossing with both fast and slow Dirac cones canalso be symmetry-protected, which can be observed inthe band structure. Therefore those flat bands, slowcones, fast cones are completely independent channelsand will not mix with each other. The wavefunction ofslow cones (HOES) corresponds to the configurationwhere C=C double bonds are formed favoring a

smaller bond length compared with C–C bonds. Thisexplains why upon biaxial tensile strain the slow coneswill rise in energy relative to fast cones infigure 1.

It is intriguing that all the bands near the Fermilevel contain no contribution from the metal orbitals,but from C or S atoms only, so SOC near the Fermienergy induced by these light elements is negligiblysmall. Indeed, even for the heaviest M=Hg, thebandgap induced by SOC is within 2.9 meV. It is espe-cially intriguing that the orbital of the fast Dirac conefinds contribution only from the S atoms, where everyfour S atoms (as marked in red rectangle) share two selectron donated from Cd, and the delocalized orbitalbetween two nearest S atoms indicates the formationof multicenter electron-deficient covalent bonds. Thenon-hybridization between the fast and slow cones isdue to the symmetry of the 2D atomic sheets and theorthogonality between the px–py and pz orbitalmanifolds.

It is evident from the literature that when Zn2+,Cd2+, and Hg2+ are coordinated by two 1,2-benzene-dithiolates molecules [28], the resulting coordinationcomplexes tend to adopt tetrahedral geometry. Thetetrahedral coordination environment maximizes thedistance between coordination ligands, thus

Figure 2.Analysis of electron states of (a)Cd3C12S12 comparedwith (b) graphene.

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2DMater. 4 (2017) 015015 MWu et al

minimizing the electro-repulsive interaction betweenthem. However, the square planar coordinationenvironment of Zn2+, Cd2+, and Hg2+ may also bepossible if other stabilization energy compensates theelectro-repulsion energy. For example, in the case ofCd3C12S12, the S–S bonding interaction in a [CdS4]unit and the in-plane conjugation throughout the 2Dsheet (figure 2(a) THOES) both stabilize the squareplanar coordination environment of Cd2+. As a result,the Cd3C12S12 sheet is likely to be planar, especiallyunder tensile strain. A similar stabilization effect couldalso lead to planar ground states of the other 2DMOFsproposed here.

Magnetic halfDirac cones andQAHE inM3C12O12

and other 2DMOFsReplacing sulfur by oxygen is chemically feasible andwas investigated here computationally as well.Remarkably, we find thatM3C12O12 exhibit dissimilarband structures compared with M3C12S12. As shownin figures 3(a)–(d),M3C12O12 (M=Zn, Cd, Hg, Mg)all become spontaneously spin-polarizedwith amagn-etic moment of 2μB per supercell, which is evenlydistributed on C and O atoms but scarcely onM. Thatis, they are ferromagnetic monolayers in their nativeundoped condition. We check their magnetism bydoubling the size of the supercell, and for all of them,ferromagnetic state is more favorable in energy thanantiferromagnetic state and the magnetic moment isstill 2μB per format unit.

According to the Stoner criterion ρ(EF)U�1,where U is the Hubbard correlation energy, sponta-neous spin-polarization (ferromagnetism) can beinduced by the high density of states at the Fermi levelρ(EF). In spin-restricted calculations, the flat bands arelocated right near the Fermi level in Cd3C12O12, forexample (supplementary figure S4(a)), leading to avery large ρ(EF) that can give rise to ferromagnetism.Similarmechanismmay also apply on the induced fer-romagnetism of Mg3C12S12 upon strain as mentionedabove, where the bands become more localized infigure S1.We can estimate theCurie temperatureTc byusing mean-field theory of Heisenberg model,

= DT ,kc

2

3 BwhereΔ is the energy cost to flip one spin in

ferromagnetic lattice. Here we can regard every C6O6

unit as a single spin, and for the case of Zn3C12O12,Δ=27 meV and Tc=209 K. Due to the spin-split-ting, the slow Dirac cones in one spin channel (halfDirac cones) place the Dirac points right at the Fermilevel, while the slow Dirac cones in the other spinchannel together with the fast Dirac cones are pushedaway from the Fermi level. As a result, those systemsare conducting in only one spin channel and one conechannel. Taking M=Cd as an example, the plot ofHOES and SHOES of Cd3C12O12 in figure S3 have aperfect match with HOES and SHOES of Cd3C12S12 infigure 2 corresponding to their slow Dirac cones,which are also distributed by O and C atoms, so SOCinduced bandgap is evenmore negligible (supplemen-tary table S1).

Figure 3. (a)–(d)Band structures ofM3C12O12 forM=Zn, Cd,Hg, andMg. Black and red lines represent spin-up and spin-downchannel, respectively.

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2DMater. 4 (2017) 015015 MWu et al

Half Dirac cones may still emerge upon substitu-tion ofMwith Cu, although the structure will becomebuckled just like Cu3(HITP)2 [26], which has beensynthesized recently [29]. As shown in figure 4(a),Cu3C12O12 exhibits similar half Dirac cones, with 1μBmagnetic moment per supercell. If SOC is taken intoaccount, due to the breaking of inversion symmetryinduced by buckling, a bandgap as large as 5.3 meV atK′ and 10.2 meV at K will open up in the band struc-ture of Cu3C12O12 and will give rise to 2DQAHE [30].Actually, all the systems with half Dirac cones in thispaper will exhibit QAHE if the SOC strength is notnegligible. To verify this, we calculate the Chern num-ber by a brief formula since they all have C3 rotationalsymmetry:

/ l l l= G ¢p p-

=

( ) ( ) ( )K Ke e ,C

i

n

i i ii 3

1

i

where λi is the C3 eigenvalues of the ith band and n isthe number of the valence bands. All the eigenvalues ofthe occupied states withmarked band index have beenobtained by first-principles calculations, as shown insupplementary figure S5. The Chern number turnsout to be −1 and 1 for Cu3C12O12 and Cd3C12O12,respectively, which signifies the existence of QAHEstate. To further enhance the chance of experimentalrealization of our predictions, we investigate moresimilar 2D MOFs that have been fabricated recently,for example those synthesized from 2, 3, 6, 7, 10, 11-hexahydroxytriphenylene (H12C18O6, HHTP) [17]and various metal ions, which assemble into 2Dporous extended frameworks, which may exhibitsimilar nontrivial properties. As shown in figure 4(c),Cd3(HHTP)2 exhibits a half Dirac cone at each K pointsimilar to M3C12O12 in figure 3. For Cu3(HHTP)2,

which has been synthesized in [15], although the Diracpoints do not coincide with the Fermi level, we findthat it is still conducting in only one cone channel andonly one spin channel.

Design of heterostructures and cone selectingdevicesThe lattice constants of M3C12S12 are approximatelythe same forM=Cd, Hg, Mg (see table S1, variationsare all within 0.5%), and also for M=Zn, Ni, Be(around 2.0% difference, in which Ni3C12S12 issemiconductor with a Dirac cone 0.5 eV above theundoped Fermi level [16]). This good match in latticeconstants may give rise to the construction of a varietyof heterostructures with different Dirac fermions,motivated by ‘the interface is the device’ [31, 32]. Forexample, as shown in figure 5(a), a p–n Dirac fermionjunction can be constructed from Mg3C12S12 withn-type fast cone/p-type slow cone and Cd3C12S12 (orHg3C12S12) with p-type fast cone/n-type slow cone.Upon an electric forward bias to the left, the slow coneswill be pushed towards the same energy level for bothsides while the fast cones are pushed away, so thefavorable conducting channel will be the slow cones;upon an electric forward bias to the right, the fastcones will be pushed towards the same energy level forboth sides while the slow cones are pushed apart, sothe favorable conducting channel will be the fast cones.This device can be used to switch the conductingchannel between fast and slow cones, as illustrated inthe graph. ForM3C12O12material with slightly smallerlattice constant, Hg3C12O12 can match and join in theheterostructure composed by Zn3C12S12, Be3C12S12,or Ni3C12S12 (see table S1, variations are all within4%), which will bring in spintronic effect

Figure 4.Band structures of (a)Cu3C12O12, with andwithout SOC, (b)Cd3(HHTP)2 and (c)Cu3(HHTP)2.

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2DMater. 4 (2017) 015015 MWu et al

simultaneously. The half-metallic Zn3C12O12 can alsobe connected to nonmagnetic metal Ni3C12O12 (seefigure S4, 3% difference in lattice constant) for spin-injection. In fact, for any of these devices, the hetero-structures can be either in-plane or vertical, referringto previous design of all-metallic vertical transistorsbased on stacked Dirac materials, with Dirac cones indifferent positions of k-space due to bilayer twist or in-plane strains [33].

We note that the fast and slow cones represent twoindependent channels for Dirac fermions at the samek-point, resembling spin-channels in spintronics, butwith a new kind of pseudospin (px–py π-bonding ver-sus pz π-bonding) instead of true spin. Such ‘con-etronics’ device can be realized if we can designcomponents for selecting carriers of different cones.Our results have already shown thatM3C12S12 is con-ducting in both cone channels (and in both spin chan-nels)—see figure 1—but that M3C12O12 is metalliconly in the slow cone channel (and only for the spin-up channel)—see figure 3. The next desirable

component should be only conducting in the fast conechannel, and we find that Cd3C12S12 indeed meets thisrequirement upon a biaxial strain of 4.7%. This strainis still well within the realm of experimental feasibility:the spin-splitting in the band structure (see figure S4)pushes the slow cones away from the Fermi level leav-ing only the fast cones conducting. However, uponthis strain the lattice constant of Cd3C12S12 (16.29 Å)will be much larger than that ofM3C12O12. The bandstructure of Au3C12S12 calculated in [16] is conductingonly in the slow cone channel, and maintains thisproperty when stretched to the same lattice constant(see figure S4). These conetronic components aresummarized infigure 5(b).

An alternative way for conetronic manipulation iselectrostatic charge injection, as electrostatic gate dop-ing is highly feasible in 2D bulk monolayers but not soin 3D bulk materials due to Coulomb explosion. Asshown in figure 5(c), Hg3C12S12 will become metalliconly in the fast cone channel upon a electron injectionof −2e per supercell, while Mg3C12S12 will be

Figure 5. (a)Heterostructures composed of different 2DMOFs. (b)Cone selecting components. Band structures of (c)Hg3C12S12 and(d)Mg3C12S12 upon electron injection of−2e and−2.4e per supercell (containing 27atoms) respectively.

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2DMater. 4 (2017) 015015 MWu et al

conducting only in the slow cone channel upon anelectron injection of−2.4e per supercell. According toour calculations, electrostatic gate doping would allowone to manipulate the ferromagnetic properties ofM3C12O12 andM3(HHTP)2 monolayers, giving rise toelectrical control of magnetic properties, which is aform of the long-sought-after ‘multi-ferroic’ effect.For example, upon hole doping of +2e per supercell,Cd3C12O12 (27 atoms per supercell) and Cd3(HHTP)2(63 atoms per supercell) will all become completelynonmagnetic semiconductors. Here it is worth men-tioning that Dirac field-effect transistors with ultra-high on/off ratio can be obtained: for example, upon agate voltage, when the Fermi level of Mg3C12S12 israised by 0.3 eV, or the Fermi level of Cd3C12O12 andCd3(HHTP)2 declines by just 0.1 eV, they will switchfrom the relativistic high-mobility metallic state to thehigh-resistivity semiconducting state.

Discussion

Dilute magnetic semiconductors have beenresearched, with the aim that magnetic devices can bedirectly integrated in the current semiconductor-based circuits. Now we have proposed 2D MOFs withdifferent properties: magnetic, nonmagnetic, semi-conducting, metallic, fast cone channel conductingonly, slow cone channel conducting only, both conechannels conducting, etc. They are 2D MOFs withdifferent M and may be directly integrated into amonolayer 2D MOF sheet, holding the promise tobuild multifunctional devices in the 2D MOF-basedcircuits.

In MOF based devices, fast Dirac fermions andslowDirac fermionsmay be distinguished by their dif-ference in carrier mobility, Landau energy levels, mag-neto-oscillation frequency, gate voltage-dependenteffective mass, Klein tunneling (with different ‘speedof light’), referring to reports by Kim’s group [34] andGeim’s group [35, 36], where comparing their mobi-lity should be the most convenient among them. Likethe magnetic and electric degrees of freedom inmulti-ferroics, we have already obtained spin and cone-pseu-dospin degrees of freedom in a number of 2D MOFs,that can be manipulated by strain, electric and magn-etic fields. Therefore, compared with spintronics andvalleytronics, conetronics may have some distinctadvantages. Besides high mobility and low power con-sumption by Dirac Fermion carriers, its manipulationusing electrical gate is more preferable compared withmagnetic field or optical pumping. Besides, higherdensity data storage requires smaller sizes or lower-dimensions, where the problem of super-paramagnetism or low Curie-temperature can alwaysarise in spintronics. Here the applications could be atroom temperature as the energy differences betweenthe cones are larger than 100 meV.

Conclusions

In summary, based on first-principles calculations, wehave proposed a concept of conetronics in M3C12S12and M3C12O12 where M=Zn, Cd, Hg, Be or Mgdonating only two s electrons with no contribution tobands near Fermi level. For M3C12S12, their bandstructures exhibit double Dirac cones with differentvelocity that are respectively n and p type, which aretunable for switching via strain. The fast and slowcones can represent two independent Fermion chan-nels since the Dirac crossing of two cones aresymmetry-protected, making the systems 2D node-line semimetals.While thoseM3C12S12 are conductingin both cone channels and both spin channels, forM3C12O12 the spin-polarized slow Dirac cones locateDirac cones precisely at the Fermi level, making thesystems conducting in only one spin channel and onecone channel. SomeMOFs with considerable SOC likeCu3C12O12 can even exhibit QAHE, while those basedon metal-hexahydroxytriphenylenes can exhibit simi-lar nontrivial properties. Finally, we design a variety ofheterostructure devices composed of differentM3C12S12 andM3C12O12 layers, giving rise to a varietyof spintronic conetronics devices. We anticipate thatelectrostatic gating would allow one to manipulate theferromagnetic properties of M3C12O12 andM3(HHTP)2 monolayers, giving rise to electrical con-trol ofmagnetic properties.

Acknowledgments

We acknowledge support by the Center for Excitonics,an Energy Frontier Research Center funded by the USDepartment of Energy, Office of Science and Office ofBasic Energy Sciences, under award number DE-SC0001088 (MIT).MWu andZWangwere supportedby the National Natural Science Foundation of China(No. 21573084 andNo. 11504117) and a start-up fundfrom Huazhong University of Science and Technol-ogy. H.H.F. is supported by the National NaturalScience Foundation of China (No. 11274128). Wethank Shanghai Supercomputer Center for makingsome of the computations possible.We are grateful forhelpful discussions with Pablo Jarillo-Herrero, MarcBaldo, Xi Dai, Zengwei Zhu, Yingshuang Fu, JingtaoLv and JinghuaGao.

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