Squeezed metallic droplet with tunable Kubo gap and charge injection in transition metal dichalcogenides

Jiaren Yuana,b,c, Yuanping Chena, Yuee Xiea, Xiaoyu Zhangb, Dewei Raob, Yandong Guod, Xiaohong Yana,b,1, Yuan Ping Fengc,e,1, and Yongqing Caif,1

aCollege of Science, University, 212013 , ; bSchool of Material Science and Engineering, Jiangsu University, 212013 Zhenjiang, China; cDepartment of Physics, of , 117551 Singapore; dCollege of Electronic Science and Engineering, University of Posts and Telecommunications, 210046 Nanjing, China; eCentre for Advanced Two-Dimensional Materials, National University of Singapore, 117551 Singapore; and fJoint Key Laboratory of the Ministry of Education, Institute of Applied Physics and Materials Engineering, University of Macau, Taipa, Macau, China

Edited by Donald G. Truhlar, University of Minnesota, Minneapolis, MN, and approved February 18, 2020 (received for review November 14, 2019) Shrinking the size of a bulk metal into nanoscale leads to the phases which trigger significant interests in catalysis and nano- discreteness of electronic energy levels, the so-called Kubo gap δ. electronics (13–16). Many of these TMDs, stabilizing in a hex- Renormalization of the electronic properties with a tunable and agonal (1H) phase, show a semiconducting characteristic with a size-dependent δ renders fascinating photon emission and electron strong spin–orbit coupling and excitonic effects, which are suitable tunneling. In contrast with usual three-dimensional (3D) metal clus- for diverse applications in field effect transistor (17), magnetic δ ters, here we demonstrate that Kubo gap canbeachievedwitha tunnel junction (18), valleytronics (19), and optoelectronic devices two-dimensional (2D) metallic transition metal dichalcogenide (i.e., (20). Unlike the 1H phase, the metallic octahedral 1T and its ′ 1T -phase MoTe2) nanocluster embedded in a semiconducting poly- distorted octahedral 1T′ phase exhibit a large magnetoresistance morph (i.e., 1H-phase MoTe ). Such a 1T′/1H MoTe nanodomain 2 2 (21), intriguing quantum spin Hall effect (22), and high catalytic resembles a 3D metallic droplet squeezed in a 2D space which activities (23, 24). Among the various TMDs, MoTe2 is particularly shows a strong polarization catastrophe while simultaneously main- ∼ taining its bond integrity, which is absent in traditional δ-gapped 3D interesting due to the smallest free energy difference [ 40 meV per clusters. The weak screening of the host 2D MoTe leads to photon unit cell (25, 26)] between the semiconducting 1H phase and me- 2 ′ emission of such pseudometallic systems and a ballistic injection of tallic 1T phase (27). Recent theoretical work revealed a laser-

carriers in the 1T′/1H/1T′ homojunctions which may find applica- induced mechanism of vacancy ordering and growth of 1T′ seed CHEMISTRY tions in sensors and 2D reconfigurable devices. in the transition (28). By taking advantage of this phase tunability, here we demonstrate that through creating the 1T′/1H MoTe2 two-dimensional materials | Kubo gap | transition metal dichalcogenides coplanar heterophase structure, conducting carriers confined in 1T′ MoTe2 nanodomain show a Kubo gap opening. Different from the uantum confinement and surface effect strongly alter the traditional three-dimensional (3D) metallic nanoparticles which Qelectronic and chemical properties of nanoparticles ranging have undesirable surface dangling bonds, the conducting carriers in from atom to several nanometers (1). The electronic structure of the two-dimensional (2D) nanodomain which mimics a metallic a nanoparticle strikingly depends on the size. As the size of a droplet are squeezed into atomically thin 2D triangular space with metallic nanoparticle is reduced, its extending electronic wave- function becomes quantum-confined and electronic levels evolve Significance into shell-like behaviors, that is, discretization of energy levels (2). The average spacing of the successive levels, known as the We propose an approach to realize Kubo gap in 2D nanodomains, δ E N E N Kubo gap , scales with f/ , where f and are the Fermi which mimics three-dimensional (3D) metallic droplets squeezed energy of the bulk metal and the nuclearity of the particle, re- into atomically thin 2D space. We demonstrate 1H/1T′ phase spectively (3). For an Ag nanoparticle of 3 nm in diameter (N ∼ transition of the MoTe nanodomain driven by strain and excess 3 2 10 atoms) δ is 5 to 10 meV (4), while for an Na nanoparticle of carriers, and a strong anisotropy for a ballistic injection of carriers. 2.4 nm δ would be ∼26 meV (3). Striking phenomena occur when Breaking away from traditional trend of focusing almost exclu- δ is greater or comparable to thermal energy kBT (at room sively on 3D metal clusters for producing Kubo gap, our work temperature, kBT = 25 meV), which renders its nonmetallicity reveals the possibility of Kubo gap production in 2D systems like (5). The occurrence of the Kubo gap in metallic nanoparticles MoTe2. By overcoming the intrinsic limitations of the former, this also accounts for other fascinating properties such as signifi- approach can bring about potential technical possibilities, as well cantly lower melting points (6), nonmagnetic–magnetic transi- as new scientific activities related to the Kubo-gapped systems, tions (7), and changes in spectral features (8). However, the such as efficient quantum emitters and catalysis, and reconfig- moderate δ−gapped metallic particles tend to suffer from mul- urable devices. tiple structural variations, that is, isomerization of Ag and Au nanoparticles of different charging states (9, 10). The multiva- Author contributions: X.Y., Y.P.F., and Y. Cai designed research; J.Y. performed research; J.Y., Y. Chen, Y.X., X.Z., D.R., and Y.G. analyzed data; and J.Y., Y.P.F., and Y. Cai wrote lence of these nanoclusters leads to varying structures (11), un- the paper. stable magnetic ordering, and spin excitation (12), which severely The authors declare no competing interest. hinders their applications. Because of the dramatic structural discontinuity at the particle-vacuum/liquid interface of these This article is a PNAS Direct Submission. metallic nanoparticles it is hard to reach true monodispersity due Published under the PNAS license. to structural agglomerations and reconstruction. Data deposition: All files which were used to produce the data presented in this paper (atomic models of the transition metal dichalcogenides, input files, figures, etc.) have Here we demonstrate a scheme for the realization of a Kubo been deposited in the GitHub database at https://github.com/yuanjiaren/PNASdata. gap in a lattice-continual metallic nanophase embedded in a 1To whom correspondence may be addressed. Email: [email protected], [email protected]. semiconducting host using transition metal dichalcogenides sg, or [email protected]. (TMDs) MX2 (M: Mo or W and X: S, Se, or Te). These TMDs This article contains supporting information online at https://www.pnas.org/lookup/suppl/ have a strong lattice, spin, and orbital coupling and a wealth of doi:10.1073/pnas.1920036117/-/DCSupplemental. polymorphs with semiconducting (1H), metallic (1T and 1T′)

www.pnas.org/cgi/doi/10.1073/pnas.1920036117 PNAS Latest Articles | 1of8 Downloaded by guest on September 25, 2021 well-passivated edge atoms. It is potentially useful for robust cre- phase diagram in the («, q) space is plotted through comparing ation/injection of quantum dots with a weak screening. the energies E (e, q) of the 1H and 1T′ phases, which are eval- uated by density functional theory (DFT) calculation, for each of Results the six group-VI TMDs. Reversible Phase Transition Induced by Charge Doping and Strain. Interestingly, all of the strain-doping curves corresponding to Group VI TMDs with the chemical formula MX2 (M: Mo or W the phase transition are monotonically U-shaped, indicating a and X: S, Se, or Te) have a variety of polymorph structures, such synergistic effect of the strain and carrier doping. The critical as the honeycomb 1H, 1T, and monoclinic 1T′ phases (Fig. 1 A– value of charge doping (strain) for driving the phase transition C) with space group of P6m2, P3m1, and P21/m, respectively. decreases when a uniaxial strain (charge doping) is applied si- The optimized lattice constants and the energetics relative to the multaneously. For instance, 0.13 q0 of electron doping or −0.2 q0 1H phase are given in SI Appendix, Table S1. The electronic of hole doping is required for the realization of the 1H–1T′ ′ structure and stability of 1H, 1T, and 1T MoTe2 are discussed in transition in MoTe2 without strain. With 3% strain, for both SI Appendix , Fig. S1. Governed by the crystal field-induced polarities only ∼0.05 q0 is required to activate the transition. Our splitting of the d-orbitals of the M cation, a facile transforma- findings explain the observed long-range phase transition of ′ tion from semiconducting 1H to metallic 1T/1T occurs, driven MoTe2 due to the charge transfer with a density of 0.11 q0 when 2 + – by increasing electron density of the M orbitals from d to the contacted with the 2D electride [Ca2N] ·e substrate (29). +x d2 via lithium exfoliation or doping. Since such a transition Concerning the pure strain effect without charge doping, our involves a strong orbital–lattice–charge coupling with breaking calculations reveal that only ∼4% strain is required to induce the octahedral symmetry of the 1H phase, below we mainly focus on 1H–1T′ phase transition of the MoTe2, which is consistent with the transition between the high symmetric 1H and the low the result of previous experiments (30). According to the ex- symmetric 1T′ phase. The estimation of the 1H–1T′ transition periment (30), a moderate tensile 0.2% strain can trigger the can serve as an upper limit for the metastable 1T phase in those transition at room temperature. This discrepancy between the 1H–1T and 1T–1T′ processes under external stress fields and experiment and our estimation may be due to the chemical ad- chemical doping. sorbates during transfer process which induce the doping of the As shown in Fig. 1D, we explore coupled effects of the strain sample, thus reducing the critical strain. Another reason could and doping on the thermodynamics of the phase transition of be due to the biaxial strain being applied during the measure- TMDs. In our work, to be consistent with the varied phases, an ment, while uniaxial strain is used in our study. orthorhombic cell of MX2 phases is used. Uniaxial strain « is For X = S and Se series, without charge doping, the critical applied along the armchair direction and the lattice constant strain for realizing the phase change is extremely high, ranging along the zigzag direction is relaxed for each strain. The doping around 17 to 22%, which exceeds their strength limits. Charge charge density q is calculated by adding/depleting electrons in doping reduces the critical strain, but it (>8%) is still beyond what the orthorhombic cell (dashed rectangles in Fig. 1 A–C) and can be reached in real experiments. Strong epitaxial strain up to measured in the unit of q0, calculated as one electron injected 3.4% was obtained through fabricating coherent WS2/WSe2 into the equilibrium orthorhombic cell containing two chemical superlattices while retaining the 1H phase (31). Nevertheless, our 15 −2 formulas (for MoTe2, q0 is ∼0.92 × 10 ecm ). A positive work shows that charge doping, especially electron doping, is an (negative) value of q represents electron (hole) doping. The effective means of reducing the relative energies of the 1H and 1T′

Fig. 1. Phase diagram of isolated MX2 (M: Mo or W and X: S, Se, or Te) under strain and excess charges. The polytypic structures of MX2:(A) 1H, (B) 1T, and (C) 1T′. Blue spheres are M or W atoms, and orange spheres are X atoms. (D) The phase diagrams of six VI-group TMDS as a function of both charge doping and uniaxial strain along the long rectangular lattice. The star points represent the phase transition at room temperature with the vibrational free energy

correction under quasi-harmonic approximation. Experimental values for MoTe2 (29, 30), WS2 (31), and WTe2 (32) are plotted for comparison.

2of8 | www.pnas.org/cgi/doi/10.1073/pnas.1920036117 Yuan et al. Downloaded by guest on September 25, 2021 phases. On the other hand, tensile deformation of the lattice re- be obtained. According to our thermodynamics screening of the duces hybridization of the electronic states and shallows the gap various TMDs shown above, the MoTe2 shows the best facile d =d between the z2 x2−y2,xy splitting associated with a weakened li- transition under finite strain and moderate doping, and thus gand field effect of the chalcogens. This is the underlying root of we will only focus on activation analysis of MoTe2 below. Two reduction in energy difference among the phases. different pathways (1H–1T–1T′ and 1H–1T′), depending on Surprisingly, unlike the aforementioned S- and Se-based whether the intermediate 1T phase is included, are identified. By dichalcogenides, WTe2 shows an opposite phase hierarchy, with using the climbing-image nudged elastic band (CI-NEB) method, the 1T′ phase being more stable than the 1H phase under zero the energy barriers are evaluated (SI Appendix, Fig. S3). The strain and without doping. This is in good agreement with the re- energy barrier of the displacive phase transition of 1H–1T–1T′ cent experiment (32) revealing an extremely large magnetoresis- occurs by the migration of Te atoms while the Mo atoms remain tance under strain. Our calculation shows that WTe2 can be fixed, and the barrier is 1.09 eV per chemical formula. In con- transformed from 1T′ to 1H by a compression strain of about −6%. trast, the 1H–1T′ pathway involves sliding of Te and Mo atoms However, in real circumstances, compression tends to induce simultaneously and the barrier is 0.87 eV per chemical formula. structural rippling. In addition, according to our prediction, un- Therefore, the 1H–1T′ transition is more likely to take place via intentional charge doping due to defects and adsorbates stabilizes the cooperative process which involves displacements of both the 1T′ phase and increases the cost of phase transition. Therefore, cationic and anionic atoms. This process can be affected by strain SI Appendix WTe2 tends to be stable and suffers less from phase variations and charge doping ( , Fig. S4). Further calculations compared with its TMD cousins. This should be the underlying reveal that a tensile uniaxial strain continuously reduces the reason for the WTe2 being as phase stabilizers for mixing with barrier, down to 0.63 eV at 10% strain. Concerning the charge other 1H materials (33). doping, the energy barrier reduces quickly for both electron and D The curves shown in Fig. 1 are derived based on total en- hole doping, reaching 0.52 eV for −0.5 q0 hole doping and 0.60 ergies from DFT calculation at 0 K, which does not include the eV for 0.5 q0 electron doping. It is expected that the coupling of contribution of vibrational free energy. For MoTe2 the energy strain and charge doping would lead to an even lower value. difference between the 1H and 1T′ phases (about 42 meV) is comparable with kBT which is of the order of 10 meV at finite Energetics and Kubo Gap of Embedded Metallic Quantum Dot. The temperature (T). For a more accurate prediction of the transi- deformation of the 1H/1T′ lattice in the strain/doping induced tion at finite T and to obtain a complete picture of the strain– phase transition discussed above is driven by the excess carriers charge–temperature relationship, we calculate the thermody- occupying the d-orbital of the cations. The highly localized na- namic potential U («, q, T), defined as U («, q, T) = E («, q) + F ture of the d-orbitals suggests a realization of locally controlled CHEMISTRY («, q, T), where F («, q, T) is the vibrational free energy cor- atomic displacement in TMDs through doping via local gating rection under quasi-harmonic approximation (34). The phase together with a proper strain engineering (i.e., via nanoindentation; A d2 diagrams of MoTe2 as a function of both charge doping and see schematics in Fig. 2 ). While phase engineering of -type temperature (SI Appendix, Fig. S2) and the phase transition TMDs has been previously demonstrated (14, 26, 35, 36), re- point reevaluated using this potential at 300 K indicates that the alization of nano-patterning of these semiconducting 1H– me- phase transition condition is relaxed by the Helmholtz free en- tallic 1T′ phase in a single sheet is still challenging owing to the ergy correction in both cases of strain and charge doping, as inherent complex boundaries (37). Here we show that formation of shown in Fig. 1D. The improvement with free energy correction confined nano 1T′ MX2 phase, resembling normal 3D nanocluster/ has no change in the shape of the phase diagram but slightly dots but squeezed in 2D, creates a sizable and tunable Kubo gap. softens the critical strains for the 1H–1T′ transition. Owing to the small energy difference between the 1H and 1T′ phase Thus far we report the thermodynamics of the 1H–1T′ energy of MoTe2 which benefits formation of stable heterostructures, we offset of TMDs. For an appropriate prediction of the effect of focus on MoTe2 in the following discussion. doping on the kinetics process of the transition, realistic de- The triangular-shaped metallic 1T′ phase domain of MoTe2 is scriptors like thermal activation barrier for the transition should modeled since the 60° intersected boundaries dominate in the

Fig. 2. Formation and scaling behavior of Kubo gap δ in 1H/1T′ MoTe2 nanodomain. The schematic of local phase transition induced by charge doping and strain (A), structure of triangular 1T′ domain in 1H phase with ZZ-Mo boundary (B), the formation energies of triangular 1T′ domain with different sizes (C), the size-dependent δ gap (D) derived with computing the HOMO–LUMO gap of a 1T′ domain with the boundary length of l = nb defined in B. The charge distribution of HOMO (E) and LUMO (F)ofa1T′ domain.

Yuan et al. PNAS Latest Articles | 3of8 Downloaded by guest on September 25, 2021 1H/1T/1T′ MX2 sheet (38). In contrast to traditional metallic the far-infrared region (39). The monotonic decrease of the gap clusters which can show symmetries (i.e., fivefold symmetric δ with the domain size is in agreement with the convergence of operations) different from their bulk counterparts, here the 1H/1T′ electronic structure to that of monolayer 1T′ MoTe2, similar to domains have less symmetry possibilities owing to the limited the size-dependent electronic properties found in traditional 3D twinning operations from respective hosts. Considering the metallic nanoparticles (40). Apparently, the gap δ would disap- structural similarity of MoS and MoTe and the scanning trans- pear when the domain size is big enough. The partial charge 2 2 E mission electron microscopy images of 1H/1T′ domains in MoS2 densities of the HOMO and the LUMO are shown in Fig. 2 (38), we propose and build three different models for the 1H/1T′ and F, respectively, for l = 2.1 nm. The charge distribution is boundaries which are named, according to the edge of the 1T′ different for the HOMO and the LUMO. The HOMO charge is phase, as the Te-terminated (ZZ-Te) and the Mo-terminated distributed in the entire 1T′ domain, while the LUMO charge (ZZ-Mo) interfaces along the zigzag direction and the armchair is primarily located at the vertices of the 1T′ domain. Such (AC) interface which is aligned along the armchair direction. To characteristics of the 2D quantum dots may found in applications compare the stability of each interface, the interface energy of such as nanoemitters. phase boundary (Kb) is calculated which is a quantity insensitive to Quantum Transmission and States Alignment of Homojunction. To the length of the boundary. We show below that the Kb can be derived through varying the size of the 1T′ phase. The relaxed understand the effect of phase boundaries on the electronic transport properties, nonequilibrium Green’s function (NEGF) structure of 1T′ domain with ZZ-Mo boundary is shown in Fig. simulations were performed to investigate the quantum ballistic 2B. l = nb is the boundary length of the triangular 1T′ domain tunneling of carriers across the 1H/1T′ boundary of MoTe .We where n is the integer number (n = 3 to 7) and b is the lattice 2 construct asymmetric junctions which include three parts: the parameter of 1T′ along zigzag direction. The formation energy can semiinfinite left (1T′ phase) electrode, the central scattering be expressed as the following formula: (1H/1T′ interface) region, and the right (1H phase) electrode (Fig. 3A). The three types of 1H/1T′ boundaries discussed above nðn + 1Þ nðn + 1Þ Eform = Et − ET′ − 90 − EH + nuTe, [1] are investigated. The calculated spatially resolved local densities 2 2 of states (LDOS) around the interfaces are shown in Fig. 3B. Surprisingly no in-gap defective states are found in the band gap E E ′ E where t is the total energy of the compound system. T and H of the 1H phase at the interface, which can be ascribed to the ′ are the energies of the 1H and 1T per chemical unit, respec- overall structural integrity of the 1H/1T′ interface. Nevertheless, u tively. Te is the chemical potential of tellurium. It is noted that the semiconductor–metal heterostructure allows a charge spill- n the number of Te atom lost in the ZZ-Mo domain is equal to . over from the metallic phase to the semiconducting phase. This For a triangular domain structure, the formation energy accounts for the band bending where the energy bands of the ðE Þ ′ E form consists of two parts: the 1H/1T boundary energy ( b) carriers (electrons/holes) in the semiconductor are dependent on E ′ E and the corner energy ( c). For a large-sized 1T phase, c is a the position of carriers, originated from the electric field asso- E constant while b is linearly proportional to the size of the ciated with the accumulated charges. The spatially dependent boundary ðKblÞ, where Kb is the energy per unit length of the band energies of electrons in the proximity of the 1H/1T′ in- boundary. Thereby, the formation energy is fitted as terface can affect the transporting characteristics (i.e., rectifying or ohmic). Similar effect on the Schottky barrier at such a E = E + E = K ðu Þl + E ðu Þ [2] form 3 b 3 c 3 b Te 3 c Te . semiconductor–metal interface is well-reported (41, 42). Indeed, as shown in the LDOS in Fig. 3B, there is a substantial upward It is noted that the three boundaries of the triangular domain are band bending (0.75 eV) in the 1H phase in the ZZ-Mo type different, and therefore Kb could be different for different 1H/1T′ MoTe2 interface while less significant bending is boundaries. Here, we consider the three edges (corners) as a found for the other types of interface, which indicates that the whole. Since all edges expand or shrink in proportion, their dif- ZZ-Mo type 1H/1T′ boundary favors charge transfer from the 1T′ K ferences are irrelevant and b can be considered as the average to 1H phase. Our work shows that the band bending, the Schottky boundary energy per unit length. For a given chemical potential barrier height, and the charge flow in such a 1H/1T′ in-plane u K 2 Te, b can be obtained by fitting Eq. to the formation energy heterostructure are very sensitive to the interfacial atomic ′ vs. size data of the triangle 1T domain. The calculated formation structures. ′ C energies for various sizes of the 1T domain are shown in Fig. 2 , For the energetically favored lattice registry with 1H/1T′ phase u with Te taken from bulk Te. From the fitting, we obtained boundaries, new atomic bonding and large atomic displacements K = K b 1.50 eV/nm for the ZZ-Mo boundary. b for the ZZ-Te occur at the boundaries due to the breaking of the periodicity of SI Appendix and AC boundaries are obtained similarly ( , Fig. the host phases. The patterns of atomic displacement at the S5) and the values are 2.37 and 2.82 eV/nm, respectively. Since phase boundaries, relative to their equilibrium positions in re- the formation energy of the ZZ-Mo boundary is much lower than spect 1H or 1T′ phases, are depicted in Fig. 3C. Large dis- those of the other two boundaries, the ZZ-Mo boundary should placements are found in the proximity of the interface, with the ′ prevail for 1T MoTe2 embedded in 1H MoTe2. strain field in the ZZ-Mo type 1H/1T′ boundary attenuating Interestingly, the triangular nanometer-sized fragment of the much faster than that in the other two cases. There is no local ′ 1T domain embedded in the 1H phase behaves as a quantum geometric curvature at the interface, which is consistent with the dot, as indicative of the bound states and size-dependent discrete fact that the displacements are largely in-plane. The local strain electronic levels (Fig. 2 D–F) predicted by our DFT calculations field at the phase boundaries induces a redistribution of charge which are shown below. Due to quantum confinement effect, a density and affects the band alignments across the interface. metal-to-semiconductor transition in the 1T′ domain takes place The transmission spectra of the asymmetric two-probe model as the size of the 1T′ fragment is reduced. The highest occupied are mapped in Fig. 3D at the equilibrium state (zero voltage). molecular orbital (HOMO)–lowest unoccupied molecular or- One can see that there exists a transmission gap in all cases as- bital (LUMO) gap evaluated at the DFT–generalized gradient sociated with the semiconducting 1H phase as the electrode. The approximation (GGA) level is shown in Fig. 2D and it increases transmission gap of the ZZ-Te– and AC-type interfaces is close gradually from 31 meV to 240 meV when the domain size is to 1.1 eV which is equal to the band gap of the 1H phase, while reduced from l = 2.5 nm to l = 1 nm. A HOMO–LUMO gap in the ZZ-Mo case has a slightly larger transmission gap (about 1.3 the range of millielectron volts corresponds to a Kubo gap δ in eV). The band bending for the ZZ-Mo boundary may account for

4of8 | www.pnas.org/cgi/doi/10.1073/pnas.1920036117 Yuan et al. Downloaded by guest on September 25, 2021 Fig. 3. Atomic adjustments and electronic renormalization at interfaces in 1H/1T′ MoTe2 homojunction. (A) Schematic atomic model for the different phase boundaries of 1H/1T′:ZZ-Mo, ZZ-Te, and AC. (B) Spatially resolved densities of states (DOS) in the proximity of the boundaries. The energy is relative to the

Fermi level (Ef) and the color bar denotes the amplitude of DOS. (C) The length and head of the arrows denote the magnitude and direction of the dis- placement of the corresponding atoms. (D) Transmission spectra of the asymmetric junction with 1H (1T′) phase as the right (left) electrode.

this larger transmission gap because no states are located between 1/3) point, the tunneling process in principle should be dominated CHEMISTRY 0.55 and 0.75 eV at the 1H MoTe2 side within 40 Å from the ZZ- by the evanescent states near the K point because of the lowest Mo interface. In this energy range, electrons from the 1T′ phase tunneling barrier. As seen from the complex band structure (Fig. (left electrode) must overcome a barrier to tunnel into the 1H 4B), evanescent states with the lowest decaying rate κ are all lo- phase (right electrode) and suffer from more scattering in this cated at K point and its symmetrically equivalent replicas, and the −1 process, resulting in a negligible tunneling probability. value at Ef is 0.19 Å . The angular dependence of κ at Ef is investigated by con- Anisotropic Tunneling of Homophase Junction. Homophase MoTe2 structing a series of rectangular supercells with one lattice di- ′ ′ tunnel junction in the form of 1T /1H/1T is highly appealing for rection along the transport direction which is at an angle θ from single-layered electronic devices. To identify the angular align- the ZZ direction of the 1H MoTe2 unit cell (SI Appendix, Fig. ment of the junction relative to the host phase, angular de- S6). The location of band maxima in the reciprocal space of each pendence of the transport efficiency is examined by aligning the ′ A supercell is determined by folding the K point of the unit cell two 1T leads along both AC and ZZ directions (Fig. 4 ). For into the Brillouin zone of the supercell (denoted as K′). As the AC-aligned junction, there are two asymmetric interfaces shown in Fig. 4C, the lowest κ along different directions at K′ are with the ZZ-Mo and ZZ-Te type boundaries in the left and right the same, while the κ at Γ appears to have a sixfold symmetry. parts of the central scattering region, respectively, while for the In fact, overall transport efficiency relies on a proper matching ZZ-aligned junction the interfaces are symmetric. To identify of evanescent states in the barrier with propagating Bloch states the efficiency of the quantum tunneling we have calculated the in the electrodes. Herein, transversal kx states-resolved trans- conductance as a function of the length of the 1H phase in the mission for the AC and ZZ junctions is depicted in Fig. 4D. The scattering region. As shown in Fig. 4A, the conductance (G) L major contribution to the conductance of the ZZ junction arises decreases exponentially with the length of the 1H phase in the k = ′ C central region for both junctions, which can be fitted by the from x 0, which coincides with the K point (refer to Fig. 4 ). following equation (43): In contrast, transmission of the AC junction is dominated by states at the point (kx = 0.15, 0) which is slightly away from K′ kx = ′ ½−2κðΦ, Ef ÞL ( 1/3, 0), despite the fact that smallest is always located at K G Ef = Gce , [3] point (Fig. 4C). We also calculated the transversal kx-resolved decaying rate (SI Appendix, Fig. S7). Interestingly, although we where Gc is the contact conductancep andffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiκ(Φ, Ef) is the tunneling found that the overall kx transmission profile is consistent with the decay coefficient which is given by 2meðΦ − Ef Þ=Z, with me the trend of the kx relationship (SI Appendix,Fig.S7), that is, a smaller electron mass and V the tunneling barrier. The Gc obtained from leads to a higher transmission, the location of the transmission the fitting of the AC junction (0.36 G0) is higher than that of the ZZ junction (0.003 G ), due to the larger lattice distortion and peak in the AC junction slightly deviates from the valley position of 0 k more scattering from the interfacial states in the latter. Interest- x curve. This can be traced back to the fact that the conductance is − ingly, the decay coefficient of the AC junction is 0.25 Å 1, which not solely dominated by the damping rate in the central 1H phase − is higher than 0.18 Å 1 of the ZZ junction. but is also related to the interfacial matching of the propagating As the transport efficiency of the junction is closely related to Bloch states in the 1T′ phase and the evanescent states in the 1H the intrinsic electronic property of the semiconducting phase in phase. Overall, our results demonstrate that such homophase the central region, we investigate the propagating and evanescent junctions could exhibit anisotropic transport characteristics owing states of the 1H phase by calculating its complex band structure. to the anisotropic κ and interfacial matching albeit host MoTe2 has Since the band extrema of 1H MoTe2 are located at the K (1/3, an isotropic structure.

Yuan et al. PNAS Latest Articles | 5of8 Downloaded by guest on September 25, 2021 2 Fig. 4. Orientation effect of electronic injection and damping across 1H/1T′ MoTe2 homojunction. (A) Conductance G (in units of G0 = 2e =h)of1T′/1H/1T′ junctions at Ef as a function of length L of the central 1H MoTe2 phasealongACandZZdirections.(B) Complex band structure of 1H MoTe2 along ZZ direction at the Γ point. The real (Right)andimaginary(Left) parts represent propagating and evanescent states, respectively. (C) Polar plot of the lowest value of κ at Ef for both Γ and K′ along different directions. Note zero degree corresponds to ZZ direction. (D) Transversal kx resolved transmission of the junctions along the AC and ZZ direction.

Discussion the well-known underestimation of band gap in GGA calculations, The interplay between charge, spin, and orbital results in ex- the exact measured value of the gap could be even larger. Previous tremely rich crystal phases (i.e., 1H, 1T, and 1T′) and quantum studies showed that this ultimate confinement leads to a strong excitations such as charge density waves and spin density waves exciton binding energy in TMDs (48). Notably, a similar quantum in TMD materials, which enable versatile applications in opto- confinement effect was well measured in a nanometer-sized electronics and valleytronics (44–46). Existence of ubiquitous graphene quantum dot with level spacing up to 0.5 eV, dem- inhomogeneous electron-hole puddles within a single sheet of onstrating the possibility of molecular-scale electronics (49). the TMDs triggers the coexistence of multiple phases in a single Here the opening of a finite gap in the nanosized metallic sheet, and thereafter the formation of various interfaces allowing phase, that is, 1T′ MoTe , may lead to a size-dependent plas- molecular patterning (47). While the transition can be triggered 2 monic oscillation of carriers which can serve as efficient photon by application of a strain (30), our work shows that the atomi- emitters. Patterned 1T′/1H phase with metallic–semiconducting cally thin lattice is highly sensitive to the density of excess car- periodicity may create metamaterials with novel plasmon– riers, that is, the 1T′–1H phase transition temperature of MoTe2 decreases linearly with both electron and hole doping and drops polariton interactions and allow unique spin manipulation owing to its largely coherent interfaces. to 300 K with a small hole doping about 0.08 q0 and electron doping about 0.04 q , equivalent to 0.08 hole and 0.04 electron 0 Conclusions doped per unit cell, respectively. Note our predicted transition Ultrathin TMDs have rich electronic properties with tunable temperature of undoped MoTe2 is 1,200 K (SI Appendix, Fig. S2), slightly higher than the experimental value of 1,100 K (30). lattice and spin configurations. Our work reveals another scien- The analysis of crystal orbital Hamilton population (SI Appendix, tific possibility of TMDs: Kubo gap formation that is normally Fig. S8) reveals that the electron occupations of nonbonding realized in 3D nanosystems. By overcoming the intrinsic limita- states (electron count) play an important role for the stability tions of the latter, this approach can bring about potential property of the 1H phase. Furthermore, the strain and charge technical possibilities and new scientific activities related to the doping destabilize the 1H phase (SI Appendix, Fig. S9) and Kubo-gapped systems such as efficient photon emitters and ca- promote the phase transition. talysis and reconfigurable devices. The 2D nanodomains of TMDs We predict that quantum confinement and injection of carriers with appreciable Kubo gap mimic 3D metallic droplets squeezed ′ in 1T MoTe2 lead to the formation of Kubo gap, which was only into atomically thin 2D space with well-passivated edge atoms of observed in 3D metallic nanoclusters such as nano gold clusters TMDs. This is a useful demonstration of the Kubo gap via proper previously. The finite Kubo gap in nanosized 1T′ phase of MoTe , 2 confinement of delocalizing carriers in ultrathin dimensions. In a metallic droplet squeezed in atomically thin 2D sheet, implies a ′ strong quantum confinement effect. This is reflected by the ap- addition, we examine the 1H/1T phase transition of the MoTe2 preciable HOMO–LUMO gap of 31 meV predicted for the 1T′ nanodomain driven by strain and excess carriers and reveal a ′ phase of MoTe2 of size l = 2.5 nm embedded in 1H MoTe2,which strong anisotropy for a ballistic injection of carriers in the 1T /1H/ reaches 240 meV when the size of the quantum dot is reduced to 1T′ homojunctions. Such findings shed light on the importance l = 1 nm. Notably this gap of 2.5-nm-sized triangular 1T′ MoTe2 is of orientations of nanodomains or interfaces for nanoelectronic comparable to that of a 0.2-nm gold nanoparticle (4). Owing to devices.

6of8 | www.pnas.org/cgi/doi/10.1073/pnas.1920036117 Yuan et al. Downloaded by guest on September 25, 2021 Materials and Methods for the grid integration. Pseudoatomic orbitals basis sets s3p2d1 and s2p2d1 are utilized for Mo and Te atoms, respectively. Here abbreviations like Electronic Structure Calculations. The ground-state electronic structure cal- 3 2 1 culations are performed by using the Vienna Ab initio Simulation Package s p d mean that three, two, and one primitive basis orbitals are employed ζ (VASP) (50) within the framework of DFT. We use projected augmented for s-, p-, and d-orbitals, respectively (52). Double- -polarized basis is adop- wave together with cutoff energy of 400 eV. The GGA in the Perdew–Burke– ted in transport calculations. In the metallic tunneling junction with the ′– – ′ Ernzerhof form is chosen as exchange correlation functional. In addition, the 1T 1H 1T configuration, the energy (E) and the transversal momentum (k//) σ Brillouin zone is sampled by an 11 × 21 × 1 k-point grid. The convergence resolved ballistic transmission (T) at equilibrium of spin component is cal- − criterion of total energy is set to be 10 6 eV. All of the structures are fully culated by the formula  à relaxed until the forces on atoms are smaller than 0.01 eV/Å. The kinetics r a Tσ E, k== = Tr Γ E, k== G E, k== Γ E, k== G E, k== , [5] analysis of the activation barrier of the 1H/1T′ structural phase trans- L σ R σ formation is conducted by the CI-NEB calculation. where ΓL/R is the self-energy item which takes the coupling of the central scattering region and the left (L)/right (R) electrode into consideration, and Phononic and Thermodynamics Calculation. To evaluate the stability of r=a Gσ · ðE, k==Þ is the retarded/advanced Green’s function matrix of the system. structures under different doped and strained conditions, phonon dispersion Along the transporting direction, the zero-bias quantum conductance G is is calculated by using the displacement method. The second-order force computed as constants are obtained with calculating the energies of displaced configu- × × × × rations based on a 3 3 1 supercell together with a 6 6 1 k-point grid. e2 X Based on the obtained Hessian matrics, quasi-harmonic vibrational free- G = Tσ E, k== . [6] h k==,σ energy correction is added to the total energy evaluated by the DFT and

the Helmholtz free energy is calculated as In this work, the G along AC and ZZ directions of MoTe2 is evaluated by integrating the electron transmission at the E for over k states along the X X   f // 1  transverse direction, respectively. FðTÞ = ћωqj + kBT ln 1 − exp −ћωqj , [4] qj2 qj kBT Data Availability. All files which were used to produce the data presented in where ω , T, and k are the frequencies, the reduced Planck constant, qj B this paper (atomic models of the TMDs, input files, figures, etc.) have been temperature and Boltzmann constant, respectively. q and j denote the deposited at https://github.com/yuanjiaren/PNASdata. momentum and mode index of the phonon. ACKNOWLEDGMENTS. We acknowledge the support from the computational Quantum Ballistic Transport Analysis by NEGF. The transport calculations in the resources provided by the Centre for Advanced 2D Materials at the National ballistic region are performed by using Atomistix Tool Kit which is based on University of Singapore. This work is supported by the University of Macau DFT combined with the NEGF method (51). The OPENMX norm-conserving (SRG2019-00179-IAPME) and the National Natural Science Foundation of China pseudopotentials with GGA are adopted with 100 Hartree density mesh cutoff (NSFC91750112). CHEMISTRY

1. P. Jena, A. W. Castleman, Jr, Clusters: A bridge across the disciplines of physics and 23. M. A. Lukowski et al., Enhanced hydrogen evolution catalysis from chemically exfo-

chemistry. Proc. Natl. Acad. Sci. U.S.A. 103, 10560–10569 (2006). liated metallic MoS2 nanosheets. J. Am. Chem. Soc. 135, 10274–10277 (2013). 2. R. Kubo, Electronic properties of metallic fine particles. I. J. Phys. Soc. Jpn. 17, 975–986 24. G. Gao et al., Charge mediated semiconducting-to-metallic phase transition in mo- (1962). lybdenum disulfide monolayer and hydrogen evolution reaction in new 1T′ phase. J. 3. B. von Issendorff, O. Cheshnovsky, Metal to insulator transitions in clusters. Annu. Phys. Chem. C 119, 13124–13128 (2015).

Rev. Phys. Chem. 56, 549–580 (2005). 25. D. H. Keum et al., Bandgap opening in few-layered monoclinic MoTe2. Nat. Phys. 11, 4. C. N. Ramachandra Rao, U. G. Kulkarni, P. J. Thomas, P. P. Edwards, Metal nano- 482–486 (2015). particles and their assemblies. Chem. Soc. Rev. 29,27–35 (2000). 26. K. A. N. Duerloo, Y. Li, E. J. Reed, Structural phase transitions in two-dimensional Mo-

5. T. Higaki et al., Sharp transition from nonmetallic Au246 to metallic Au279 with nascent and W-dichalcogenide monolayers. Nat. Commun. 5, 4214 (2014). surface plasmon resonance. J. Am. Chem. Soc. 140, 5691–5695 (2018). 27. S. Cho et al., DEVICE TECHNOLOGY. Phase patterning for ohmic homojunction con-

6. F. Baletto, R. Ferrando, Structural properties of nanoclusters: Energetic, thermody- tact in MoTe2. Science 349, 625–628 (2015). namic, and kinetic effects. Rev. Mod. Phys. 77, 371–423 (2005). 28. C. Si et al., Photoinduced vacancy ordering and phase transition in MoTe2. Nano Lett. 7. M. Moseler, H. Häkkinen, R. N. Barnett, U. Landman, Structure and magnetism of 19, 3612–3617 (2019).

neutral and anionic palladium clusters. Phys. Rev. Lett. 86, 2545–2548 (2001). 29. S. Kim et al., Long-range lattice engineering of MoTe2 by 2D electride. Nano Lett. 17, 8. K. K. Nanda, On the paradoxical relation between the melting temperature and 3363–3368 (2017).

forbidden energy gap of nanoparticles. J. Chem. Phys. 133, 054502 (2010). 30. S. Song et al., Room temperature semiconductor–metal transition of MoTe2 thin films

9. C. Liu et al., Chiral Ag23 nanocluster with open shell electronic structure and helical engineered by strain. Nano Lett. 16, 188–193 (2016). face-centered cubic framework. Nat. Commun. 9, 744 (2018). 31. S. Xie et al., Coherent, atomically thin transition-metal dichalcogenide superlattices 10. B. Weng, K. Q. Lu, Z. Tang, H. M. Chen, Y. J. Xu, Stabilizing ultrasmall Au clusters for with engineered strain. Science 359, 1131–1136 (2018). enhanced photoredox catalysis. Nat. Commun. 9, 1543 (2018). 32. N. H. Jo, L.-L. Wang, P. P. Orth, S. L. Bud’ko, P. C. Canfield, Magnetoelastoresistance in

11. M. Gao, A. Lyalin, M. Takagi, S. Maeda, T. Taketsugu, Reactivity of gold clusters in the WTe2: Exploring electronic structure and extremely large magnetoresistance under regime of structural fluxionality. J. Phys. Chem. C 119, 11120–11130 (2015). strain. Proc. Natl. Acad. Sci. U.S.A. 116, 25524–25529 (2019).

12. I. M. Billas, A. Châtelain, W. A. de Heer, Magnetism from the atom to the bulk in iron, 33. D. Rhodes et al., Engineering the structural and electronic phases of MoTe2 through cobalt, and nickel clusters. Science 265, 1682–1684 (1994). W substitution. Nano Lett. 17, 1616–1622 (2017).

13. Y. Yoo et al., In-Plane 1H-1T′ MoTe2 homojunctions synthesized by flux-controlled 34. N. Mounet, N. Marzari, First-principles determination of the structural, vibrational phase engineering. Adv. Mater. 29, 1605461 (2017). and thermodynamic properties of diamond, graphite, and derivatives. Phys. Rev. B 71,

14. Y. Wang et al., Structural phase transition in monolayer MoTe2 driven by electrostatic 205214 (2005). doping. Nature 550, 487–491 (2017). 35. W. Li, J. Li, Ferroelasticity and domain physics in two-dimensional transition metal

15. X. Zhang et al., Low contact barrier in 1H/1T′ MoTe2 in-plane heterostructure syn- dichalcogenide monolayers. Nat. Commun. 7, 10843 (2016). thesized by chemical vapor deposition. ACS Appl. Mater. Interfaces 11, 12777–12785 36. R. C. Cooper et al., Nonlinear elastic behavior of two-dimensional molybdenum di- (2019). sulfide. Phys. Rev. B 87, 035423 (2013).

16. H. Yang, S. W. Kim, M. Chhowalla, Y. H. Lee, Structural and quantum-state phase 37. G. Eda et al., Coherent atomic and electronic heterostructures of single-layer MoS2. transitions in van der Waals layered materials. Nat. Phys. 13, 931 (2017). ACS Nano 6, 7311–7317 (2012).

17. B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, A. Kis, Single-layer MoS2 38. Y. C. Lin, D. O. Dumcenco, Y. S. Huang, K. Suenaga, Atomic mechanism of the

transistors. Nat. Nanotechnol. 6, 147–150 (2011). semiconducting-to-metallic phase transition in single-layered MoS2. Nat. Nano-

18. W. Wang et al., Spin-valve effect in NiFe/MoS2/NiFe junctions. Nano Lett. 15, 5261– technol. 9, 391–396 (2014). 5267 (2015). 39. S. K. Ghosh, Kubo gap as a factor governing the emergence of new physicochemical

19. H. Zeng, J. Dai, W. Yao, D. Xiao, X. Cui, Valley polarization in MoS2 monolayers by characteristics of the small metallic particulates. Assam Univ. J. Sci. Technol. 7, 114– optical pumping. Nat. Nanotechnol. 7, 490–493 (2012). 121 (2011). 20. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, M. S. Strano, Electronics and 40. O. D. Häberlen et al., From clusters to bulk: A relativistic density functional in-

optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nano- vestigation on a series of gold clusters Aun,n= 6,..., 147. J. Chem. Phys. 106, 5189– technol. 7, 699–712 (2012). 5201 (1997).

21. M. N. Ali et al., Large, non-saturating magnetoresistance in WTe2. Nature 514, 205– 41. J. Bardeen, Surface states and rectification at a metal semi-conductor contact. Phys. 208 (2014). Rev. 71, 717 (1947). 22. X. Qian, J. Liu, L. Fu, J. Li, Solid state theory. Quantum spin Hall effect in two- 42. W. Mönch, Role of virtual gap states and defects in metal-semiconductor contacts. dimensional transition metal dichalcogenides. Science 346, 1344–1347 (2014). Phys. Rev. Lett. 58, 1260–1263 (1987).

Yuan et al. PNAS Latest Articles | 7of8 Downloaded by guest on September 25, 2021 43. P. Mavropoulos, N. Papanikolaou, P. H. Dederichs, Complex band structure and tun- 48. G. Eda et al., Photoluminescence from chemically exfoliated MoS2. Nano Lett. 11, neling through ferromagnet /Insulator /Ferromagnet junctions. Phys. Rev. Lett. 85, 5111–5116 (2011). 1088–1091 (2000). 49. L. A. Ponomarenko et al., Chaotic Dirac billiard in graphene quantum dots. Science 44. Y. I. Joe et al., Emergence of charge density wave domain walls above the super- 320, 356–358 (2008).

conducting dome in 1T-TiSe2. Nat. Phys. 10, 421–425 (2014). 50. G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals

45. Y. Katagiri et al., Gate-tunable atomically thin lateral MoS2 Schottky junction pat- and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6,15–50 terned by electron beam. Nano Lett. 16, 3788–3794 (2016). (1996).

46. X. Yin et al., Tunable inverted gap in monolayer quasi-metallic MoS2 induced by 51. J. M. Soler et al., The SIESTA method for ab initio order-N materials simulation. J. strong charge-lattice coupling. Nat. Commun. 8, 486 (2017). Condens. Matter Phys. 14, 2745 (2002). 47. X. Lin et al., Intrinsically patterned two-dimensional materials for selective adsorption 52. T. Ozaki, H. Kino, Numerical atomic basis orbitals from H to Kr. Phys. Rev. B 69, of molecules and nanoclusters. Nat. Mater. 16, 717–721 (2017). 195113 (2004).

8of8 | www.pnas.org/cgi/doi/10.1073/pnas.1920036117 Yuan et al. Downloaded by guest on September 25, 2021