aa r X i v : . [ c ond - m a t . m e s - h a ll ] D ec Perfect charge compensation in WTe for the extraordinary magnetoresistance: Frombulk to monolayer H. Y. Lv, W. J. Lu, ∗ D. F. Shao, Y. Liu, S. G. Tan, and Y. P. Sun
1, 2, 3, † Key Laboratory of Materials Physics, Institute of Solid State Physics,Chinese Academy of Sciences, Hefei 230031, People’s Republic of China High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, People’s Republic of China Collaborative Innovation Center of Advanced Microstructures,Nanjing University, Nanjing, 210093, People’s Republic of China
The electronic structure of WTe bulk and layers are investigated by using the first principlescalculations. The perfect electron-hole ( n - p ) charge compensation and high carrier mobilities arefound in WTe bulk, which may result in the large and non-saturating magnetoresistance (MR)observed very recently in the experiment [Ali et al ., Nature , 205 (2014)]. The monolayerand bilayer of WTe preserve the semimetallic property, with the equal hole and electron carrierconcentrations. Moreover, the very high carrier mobilities are also found in WTe monolayer,indicating that the WTe monolayer would have the same extraordinary MR effect as the bulk,which could have promising applications in nanostructured magnetic devices. PACS numbers:
In the past few decades, transition metal dichalco-genides (TMDs) with the formula MX (M=transitionmetal of group 4-10; X=S, Se, or Te) have received alot of attention due to their diverse properties. Rang-ing from insulating to metallic, some of them exhibit be-haviors of superconductivity and charge density wave. Most of the MX systems crystallize in a layered struc-ture, with the building blocks X-M-X sandwiches stackedalong the c -axis. Within the sandwich layer, the atomsare covalently bonded, while the interactions among thelayers are much weaker, mainly of the van der Waals type.The recent advances in the experimental techniques havemade it possible to exfoliate two-dimensional (2D) ul-trathin layers from the MX bulk. The 2D MX ma-terials can largely preserve the versatile properties, butsome distinctive characteristics can be introduced due tothe quantum confinement effect. For example, the tran-sition of indirect-direct band gap takes place in MoS when the bulk structure is exfoliated into a monolayer, which opens up new potential applications in the fields ofphototransistors, photocatalyst, electroluminescence, etc.Very recently, extremely large magnetoresistance (MR)without saturation even at very high fields was observedin WTe . MR evaluates the change in electrical resis-tance by the application of a magnetic field. Large MReffect can have promising applications such as magneticfield sensors and magnetic information storage. Themain origin of the extraordinary MR effect in WTe is as-cribed to the perfect n - p charge compensation in this ma-terial, based on the investigations by the angle-resolvedphotoelectron spectroscopy (ARPES). When applied innanoelectronics, it is desirable to obtain nanostructuredsystems which have the performance as good as or evenbetter than their bulk counterparts. Almost at the sametime, huge negative MR effect was reported in the ultra-thin layers of TiTe − x I x due to the frustrated magneticstructures induced by the anionic doping. The excel-
FIG. 1: Crystal structure of WTe bulk viewed along (a) the a axis (parallel to the W-W zigzag chains) and (b) the c axis(perpendicular to the stacked layers); (c) the correspondingfirst Brillouin zone. The red and yellow balls represent Wand Te atoms, respectively. Te(i) and Te(o) stand for theatoms shrunk inside and moved outside the sandwich layer,respectively. lent MR effect of WTe bulk inspires us to explore howthe WTe layer will perform, which is very critical in theapplications of nanoelectronics.In this work, the electronic properties of WTe layersas well as the bulk structure are investigated based onthe first-principles calculations. Our results show thatboth the monolayer and bilayer of WTe maintain thesame semimetal properties as the bulk, with equal holeand electron carrier concentrations, suggesting that thenon-saturating MR effect may also exist in the WTe lay-ers. Moreover, the high carrier mobilities found in WTe monolayer indicate that the MR effect in the monolayerwould be comparable to that in the bulk system.Our calculations were performed via a projector aug-mented wave (PAW) pseudopotential approach withinthe density functional theory (DFT) as implemented inthe ABINIT code. The generalized gradient approxi-mation (GGA) with the Perdew-Burke-Ernzerhof (PBE)functional were used for exchange-correlation energy.For bulk and bilayer, the van der Waals interactions weretreated by the vdW-DF1 functional. Spin-orbit cou-pling was included in the calculations of the electronicproperties. The plane-wave cutoff energy was set to be600 eV in all the calculations. In the self-consistent calcu-lations, the Brillouin zones were sampled with an 8 × × k mesh. All the structures were fullyrelaxed until the force acting on each atom became lessthan 0 . × − eV / ˚A.The crystal structure of the WTe bulk viewed alongdifferent directions are demonstrated in Figs. 1(a) and(b), respectively, with the corresponding first Brillouinzone shown in Fig. 1(c). The space group of WTe bulk is P nm2 . Most of the sulfides and selenides are rhombohe-dral or hexagonal, and the metal atoms are trigonal pris-matic or octahedral coordinated by six chalcogen atoms.However, in WTe , the octahedron of tellurium atomsis slightly distorted and the metal atoms are displacedfrom their ideal octahedral sites, forming zigzag metal-metal chains along the a axis, which is demonstratedin Fig. 1(b). The structural difference has endowed thiskind of material with properties distinct from the otherMX system. After fully relaxation, the obtained crystalconstants are a =3.54 ˚A, b =6.34 ˚A and c =14.44 ˚A, whichagree well with the experimental results. The nearestdistance between W-W atoms along the zigzag chain is2.87 ˚A, only 0.14 ˚A larger than that in the pure metalcrystal of tungsten. Because of the distorted octahedralstructure, the Te atom layers become buckled (see Fig.1(a)), with Te(i) atoms shrunk a little inside the sand-wich layer and Te(o) atoms moved slightly outside.The electronic band structure and the density of states(DOS) of WTe bulk are shown in Figs. 2(a) and (b),respectively. A strong anisotropic band dispersion is ob-served in the band structure. The bands along the Γ- Z direction (perpendicular to the sandwich layers in realspace) are much flatter than those along the other direc-tions, reflecting the quasi-two-dimensional layered struc-ture of WTe bulk. The very small DOS at the Fermi en-ergy ( E F ) signals the semimetallic nature of WTe bulk.The corresponding W-5 d and Te-5 p partial DOS includedin Fig. 2(b) show that the DOS at the E F ( N ( E F )) isdominated by the W-5 d state, followed by the Te(i)-5 p state. The Te(o)-5 p state contributes little to the N ( E F ).The Fermi surface of WTe bulk is demonstrated in Fig.2(c), which exhibits highly anisotropic property. Notethat in the band structure, there exists a small overlapbetween the top of the valence band (hole pocket) andbottom of the conduction band (electron pocket) alongthe X -Γ direction in the vicinity of the Fermi level. Theenlarged overlap part of the band structure is shown inthe inset of Fig. 2(a). Hole and electron pockets withappropriately the same size are found, which agrees wellwith the ARPES results. In experiment, it was ana-lyzed that these two pockets may lead to the perfect car-rier compensation and therefore the large MR effect inWTe . However, the exact values of the hole ( p -type) FIG. 2: (a) Band structure, (b) total and partial density ofstates (DOS), and (c) Fermi surface (FS) of WTe bulk. and electron ( n -type) carrier concentrations are still lack-ing. To obtain these values, the band-decomposed DOSsare calculated. In particular, to calculate the p -type car-rier concentration, we calculate the DOS of the bands inblue color in Fig. 2(a) and then integrate the DOS from E F to the valence band maximum (VBM); to calculatethe n -type carrier concentration, the DOS of the bandsin red color is integrated from the E F to the conduc-tion band minimum (CBM). The carrier concentrations, p = 7 . × cm − and n = 7 . × cm − , are obtained,coinciding perfectly with each other.In the semiclassical two-band model, M R = σσ ′ ( σ/n + σ ′ /p ) ( B/e ) ( σ + σ ′ ) + σ σ ′ (1 /n − /p ) ( B/e ) , (1)where σ and σ ′ are the electrical conductivities of elec-trons and holes without external magnetic field, respec-tively. n and p are the electron and hole concentrations,respectively. When n = p , the MR increases as B with-out saturation. Using this two-band model, we can qual-itatively interpret the experimentally observed behaviorof MR as a function of external magnetic field in WTe .Next, we focus on the electronic properties of WTe ultrathin layers. The calculated electronic structures ofWTe monolayer and bilayer are plotted in Figs. 3(a)and (b), respectively. What is different from the case ofWTe bulk is that the VBM of WTe layers are locatedat the Γ point. From monolayer to bilayer, more va-lence (in blue color) and conduction (in red color) bandscross the Fermi energy, thus the overlap of valence andconduction bands becomes larger in bilayer, which can TABLE I: Effective mass m ∗ , elastic modulus C , deformation potential constant E , and room-temperature carrier mobility µ of WTe bulk and monolayer. direction carrier type m ∗ C E µ ( × )( m ) eV/˚A (eV/˚A ) eV cm V − s − bulk a -axis hole 0.19 0.94 − − a -axis hole 0.89 7.72 − − b -axis hole 0.54 9.12 0.58 21.25electron 0.28 9.12 − also be seen from the Fermi surface in Figs. 3(e) and(f). Combined with the calculated DOS (see Figs. 3(c)and (d)), we can see that the WTe monolayer and bi-layer remain semimetals. The semimetallic property isvery different from that reported in the WTe monolayerwith the artificial 2 H structure, which is a direct-band-gap semiconductor. The N ( E F ) for both the monolayerand bilayer are dominated by the W-5 d state, followedby the Te(i)-5 p state, which is the same as the caseof WTe bulk. Interestingly, for the semimetal mono-layer and bilayer, equal n - and p -type carrier concen-trations are also obtained. The calculated carrier con-centrations for monolayer and bilayer are, respectively, n = p = 1 . × cm − and n = p = 1 . × cm − .The perfect charge compensation indicates that the non-saturating MR as a function of the external magneticfield may also exist in the WTe monolayer and bilayer.From equation (1), we can see that when n = p , M R obeys
M R = σσ ′ ( B/e ) /n = µ e µ h B , where µ e and µ h are the carrier mobilities of electrons and holes, re-spectively. Therefore, in order to obtain a large MR ata specific magnetic field, high carrier mobility will bedesirable. The carrier mobility can be calculated usingthe deformation potential (DP) model based on the ef-fective mass approximation. The mobilities for thebulk ( µ Dβ ) and two-dimensional system ( µ Dβ ) along acertain direction β are respectively expressed as µ Dβ = 2 √ πe ~ C Dβ k B T ) / ( m ∗ ) / E (2)and µ Dβ = 2 e ~ C Dβ k B T | m ∗ | E . (3)Here C is the elastic modulus and can be defined as C Dβ = [ ∂ E/∂δ ] /V and C Dβ = [ ∂ E/∂δ ] /S for 3 D and 2 D systems, respectively, where E , δ , V , and S are, respectively, the total energy, the applied strainalong β direction, the volume, and the area of the in-vestigated system. T is the temperature and m ∗ is theeffective mass. The DP constant E is obtained by E = dE edge /dδ , where δ is the applied strain by a stepof 0.5% and E edge is the energy of the band edges (VBM FIG. 3: Band structure of WTe (a) monolayer and (b) bi-layer; total and partial density of states (DOS) of WTe (c)monolayer and (d) bilayer; Fermi surface (FS) of WTe (e)monolayer and (f) bilayer. for the holes and CBM for the electrons). Here we onlycompare the values of WTe monolayer with those of thebulk. The calculated m ∗ , C , E , and room-temperature µ are summarized in Table I. For WTe bulk, becausethe large MR was measured along the a axis, we onlycalculate the mobilities along this direction. The calcu-lated effective masses of the hole and electron are 0.19 m and 0.15 m ( m is the mass of an electron), respec-tively. The very small effective masses result in the ex-tremely high carrier mobilities in WTe bulk, 1 . × and 4 . × cm V − s − for p - and n -type carriers, re-spectively. The very large µ h and µ e as well as the perfect n - p charge compensation as discussed above may be re-sponsible for the measured large and non-saturating MRin WTe bulk. For WTe monolayer, the effective mass m ∗ of hole along the a axis is 0.89 m , larger than thatalong the b axis (0.54 m ), due to the relatively flatterband along the Γ- X direction. Besides, DP constants E along the a axis are much larger than those along the b axis. Consequently, the mobilities along the b axis aremuch larger than those along the a axis. The electronictransport of WTe monolayer exhibits strong anisotropicproperty. On the other hand, for the direction of b axis,the mobilities of both the hole and electron as well astheir product ( µ h µ e ) are comparable to the bulk results.Thus, our results indicate that not only the WTe bulkbut also the monolayer may exhibit the extraordinaryMR effect.In summary, we have investigated the electronic prop-erties of WTe bulk and layers. The perfect charge com-pensation as well as the large carrier mobilities are foundin WTe bulk, which is ascribed to be the source ofthe large and non-saturating MR observed experimen-tally. Moreover, WTe monolayer and bilayer preservethe semimetallic property and both of them are found to have equal hole and electron carrier concentrations. Ourresults indicate that the same extraordinary MR effect asin WTe bulk may also exist in WTe monolayer, whichwill have promising applications in nanostructured mag-netic devices. Further experimental investigations aredeserved to confirm our computational results.This work was supported by the National Key BasicResearch under Contract No. 2011CBA00111, the Na-tional Natural Science Foundation of China under Con-tract Nos. 11274311 and 11404340, the Joint Funds of theNational Natural Science Foundation of China and theChinese Academy of Sciences’ Large-scale Scientific Facil-ity (Grant No. U1232139), the Anhui Provincial NaturalScience Foundation under Contract No. 1408085MA11,and the China Postdoctoral Science Foundation (GrantNo. 2014M550352). The calculation was partially per-formed at the Center for Computational Science, CA-SHIPS. ∗ Corresponding author: [email protected] † Corresponding author: [email protected] B. Sipos, A. F. Kusmartseva, A. Akrap, H. Berger, L.Forr´o, and E. Tutiˇs, Nature Mater. , 960 (2008). J. A. Wilson, F. J. di Salvo and S. Mahajan, Adv. Phys. , 117 (1975). J. N. Coleman, et al., Science , 568 (2011). R. J. Smith, P. J. King, M. 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