Coexistence of Topological Edge State and Superconductivity in

Apr 18, 2017 - Ultrathin freestanding bismuth film is theoretically predicted to be one kind of two-dimensional topological insulators. Experimentally...
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Coexistence of Topological Edge State and Superconductivity in Bismuth Ultrathin Film Hao-Hua Sun,† Mei-Xiao Wang,† Fengfeng Zhu,† Guan-Yong Wang,† Hai-Yang Ma,† Zhu-An Xu,‡,§ Qing Liao,∥ Yunhao Lu,∥ Chun-Lei Gao,†,§ Yao-Yi Li,†,§ Canhua Liu,†,§ Dong Qian,†,§ Dandan Guan,*,†,§ and Jin-Feng Jia†,§ †

Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 100140, China ‡ Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang China § Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China ∥ Department of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China ABSTRACT: Ultrathin freestanding bismuth film is theoretically predicted to be one kind of two-dimensional topological insulators. Experimentally, the topological nature of bismuth strongly depends on the situations of the Bi films. Film thickness and interaction with the substrate often change the topological properties of Bi films. Using angle-resolved photoemission spectroscopy, scanning tunneling microscopy or spectroscopy and first-principle calculation, the properties of Bi(111) ultrathin film grown on the NbSe2 superconducting substrate have been studied. We find the band structures of the ultrathin film is quasi-freestanding, and one-dimensional edge state exists on Bi(111) film as thin as three bilayers. Superconductivity is also detected on different layers of the film and the pairing potential exhibits an exponential decay with the layer thicknesses. Thus, the topological edge state can coexist with superconductivity, which makes the system a promising platform for exploring Majorana Fermions. KEYWORDS: Ultrathin Bi(111), 2D topological insulator, proximity-induced superconductivity, topological edge state, coexistence suggested the band gap closed at Γ when the substrate Bi was thicker than 8 BLs, which makes the topological nature of the edge states on the topmost Bi BL ambiguous.15 Realizing 2D TIs in this single element material will be great advantageous for their applications. However, growing freestanding bismuth BL is difficult. Edge states of 1 BL Bi(111) were first experimentally observed on Bi(111) BL grown on Bi2Te316 and edge states of Bi(111) BLs on Bi2Te2Se and graphene were also reported.17,18 However, the topological properties of these edge states depend on the interactions between the Bi films and the substrates. Recently, edge states of Bi were observed on the topmost layer of bulk Bi crystal19 and on 96 BLs Bi on Si(111).20 The origin of these edge states is due to the weak interaction between the upper layer in the Bi BL structure and the underneath Bi BL. These results suggest a new direction in searching topologically nontrivial Bi films and motivate other experimental research in similar systems. Here we choose to study the electronic properties and edge states of epitaxial Bi(111) ultrathin films on a superconducting

T

wo dimensional (2D) topological insulators (TIs) are 2D materials that possess a pair of topological edge states connecting the bulk band gap.1,2 In real space, these chiral edge states are localized at the edge of the 2D TIs with spin-up electrons and spin-down electrons propagating in the opposite direction. Topological edge states in 2D TIs are protected by time reversal symmetry and are immune to nonmagnetic backscattering. The genuine transport properties of 2D TI have a promising future in the applications of spintronic devices. Moreover, combining a TI with superconductivity builds a platform for searching the Majorana Fermions.1−8 The first experimentally confirmed 2D TI is HgTe/CdTe semiconductor quantum well.9,10 Recently, another semiconductor quantum well InAs/GaSb was also discovered to be a 2D TI.11,12 However, fabrication of such quantum well is complex. This may hinder the application of those materials. Bismuth is a heavy element with strong spin orbit coupling (SOC) effect, and it is a common ingredient of 3D TIs such as Bi2Te3. The 2D single-bilayer bismuth was theoretically predicted to be a 2D TI.13 Later, freestanding Bi(111) films up to 8 bilayers (BLs) were also predicted to be 2D TIs.14 Above 8 BLs, Bi films changed into a topological trivial phase. Even for the topmost BL of Bi layer, theoretical calculation © 2017 American Chemical Society

Received: January 26, 2017 Revised: April 12, 2017 Published: April 18, 2017 3035

DOI: 10.1021/acs.nanolett.7b00365 Nano Lett. 2017, 17, 3035−3039

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Nano Letters substrate 2H-NbSe2 by using angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy or spectroscopy (STM/STS), and density functional theory (DFT) calculation. First of all, it is possible to find the topological edge state on Bi(111) ultrathin film based on theoretical predictions and former experiments. Second, superconductivity induced by superconducting substrate may be detected on such an ultrathin film and makes the system a new platform to search Majorana Fermions. Bi has a rhombohedra crystal structure as indicated by blue solid line or a hexagonal structure indicated by green dashed line in Figure 1a.21 Each atom and its three covalently bonded

Figure 2. Band structure of NbSe2 and 3 BLs Bi(111) on NbSe2. (a) Fermi surface of NbSe2. (b) Fermi surface of 3 BLs Bi(111)/NbSe2. The blue solid hexagon is the first Brillouin zone of Bi(111). (c) Band structure of 3 BLs Bi(111))/NbSe2 along the Γ̅ K̅ high symmetry direction. (d) Band structure of 3 BLs Bi(111))/NbSe2 along the Γ̅ M̅ high symmetry direction. The DFT calculated bands of freestanding 3 BLs Bi(111) are plotted as blue dashed line in (c,d). (a) was taken at photon energy of 70 eV, and the others were taken at photon energy of 21.2 eV.

growing 3 BLs Bi(111), the Fermi surface of the sample exhibits two structures as shown in Figure 2b. One is the hole pocket centered at Γ̅ point, which belongs to the Fermi surface of the NbSe2 substrate.34 Another Fermi surface inside the hole pocket of NbSe2 belongs to Bi(111), which consists of six hole pockets in the Γ̅ M̅ direction and an electron pocket centered at Γ̅ point.21 The coexistence of two band structures is due to the ultrathin thickness of the Bi(111) on the substrate. Three BLs Bi(111) films together with 2 BLs Bi(110) have a thickness of 2.66 nm. At such length, the phonon can penetrate through the ultrathin film and interact with the substrate. We note that Bi has a very long mean free path13 so that the electron from the photoemission of the substrate can get through the ultrathin film. The blue hexagon in Figure 2b marks the Brillouin zone of Bi(111) ultrathin film. The hole pocket of NbSe2 shows a hexagonal shape and is at the same direction with its Brillouin zone hexagon (not shown in the figure). The directions of the two Brillouin zones show that the lattice of Bi(111) film is rotated for 30° according to the NbSe2 lattice underneath. To help understand the experimental results, DFT calculations for freestanding 3 BLs Bi(111) were performed. The calculation results (blue dashed line) are plotted on the experimental data along Γ̅ K̅ and Γ̅ M̅ directions, as shown in Figure 2c,d, respectively. The high symmetry directions are according to the Brillouin zone of Bi(111). Along the Γ̅ K̅ direction the experimental bands fit well with the bands of calculated freestanding Bi (Figure 2c). There are some discrepancies along Γ̅ M̅ direction in the large momentum regime, especially close to M̅ point (Figure 2d). Near the M̅ point, bands originated from the hybridization of pz and py are not consistent with experimental observation. Owing to the unsaturated nature of pz orbital, adsorbates (such as hydrogen) can bind on Bi, shifting these two bands away from Fermi Level. The existence of adsorbates in the experiments that is not included in the calculation may lead to the disappearance of the two bands. However, it does not affect the band features around Γ̅ point.

Figure 1. Crystal structure of bulk Bi and epitaxial Bi(111) on NbSe2. (a) Rhombohedra structure (blue solid line) and hexagonal structure (green dashed line) of Bi. (b) Crystal structure of Bi(111) surface. Top layer atoms (red spheres) and bottom layer atoms (blue spheres) form a buckled honeycomb structure. (c) STM image of Bi(111) on NbSe2. Inset: Atomic resolution image taken from the surface in (c). (d) Line profile taken from the dashed (blue) line in (c). The STM image was taken with tunneling current I = 0.1 nA and STM bias V = 1.0 V. Atomic resolution image was taken with I = 0.2 nA and V = 100 mV.

equidistant nearest neighbors, which are coplanar in rhombohedra [111] direction, form a BL structure. The interBL bonding is much weaker than the bonding within the BL. Such that bulk Bi crystal has a (111) cleave plane and epitaxial Bi(111) thin films grow in BL mode. Epitaxial Bi thin film was grown on several substrates and exhibited a Bi(110) to Bi(111) transition growth behavior.22−32 Similarly, Bi forms 2 BLs Bi(110) first on NbSe2 and then Bi(111) BL films grown above. Figure 1c shows an STM image of Bi on NbSe2 after the transition thickness. Truncated triangle islands are formed on the substrate. In the inset of Figure 1c, an atomic resolution image taken on one of those islands shows a hexagonal-shaped lattice. In Figure 1d, a line profile taken along the blue dashed line in Figure 1c shows four Bi layer steps with height of 3.94 Å. Both the atomic resolution image and the step height of the layer agree with the Bi(111) surface crystal structure in Figure 1b. The electronic structures of Bi(111)/NbSe2 were studied by ARPES. Figure 2a shows the Fermi surface mapping of the bare NbSe2 substrate before Bi deposition. There are two sets of hole pockets centered at Γ̅ point and also at K̅ point.33 After 3036

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Nano Letters The band near M̅ point observed in experiment belongs to the hole pocket feature of NbSe2. The good agreement between the experimental results and the DFT calculations of freestanding Bi indicates that Bi(111) ultrathin films have no strong interaction with NbSe2 substrate or Bi(110) film in between. As mentioned before, Bi(111) BL thin films below 8 BLs have been predicted to be 2D TIs,14 but interactions between Bi and its substrate usually change the bands’ topology. Here the Bi(111) ultrathin films grown on NbSe2 are quasi-freestanding; thus there is great possibility to find the topological edge states on this system and STS measurements employed to study them. Figure 3a shows the topography of 3 BLs Bi(111) on the substrate. The hexagonal shape island with 3.94 Å step height

belong to the lower layer atoms of the BL. The former kind of edge is defined as type-A edge and the latter one is defined as type-B edge, which follows the definition in the previous work.19,20 In Figure 3b normalized dI/dV spectra taken at those three positions manifest different features: At position A, the spectrum (solid (blue) curve) shows a strong peak at STM bias +183 mV. At position B and C (dashed (red) curve for B and dot dashed (black) curve for C), dI/dV maximum do not appear at such position, while broad peaks centered at +240 mV are shown. The +183 mV peak is also detected on the other edge adjacent to position B, which was indicated by a dashed (blue) line in Figure 3a. STS spectra taken along this line are shown in Figure 3c. The existence of the +183 mV peak is consistent along the edge. We also measured the spatial distribution of the +183 mV state, STS spectra (Figure 3d) were taken on 16 equal-distance points on a 13 nm line across the edge, starting from upper Bi(111) BL to the lower Bi(111) BL, indicated by a black arrow in Figure 3a. At first the spectrum shows similar features with that on island terrace: a peak shows up at +240 mV and a dip is near +100 mV. While moving closer to the edge, at point 9, the +183 mV dI/dV peak appears abruptly. Such peak lasts for three spectra points 9, 10, and 11 and then disappears from point 12 to the last point 16. Point 11 is right on the edge and the three points with +183 mV dI/dV peak along the line give a spatial distribution of 1.73 nm. Similar spatial distribution was found on the edge state of Bi(111) on Bi2Te3 system.16 The consistent characteristic energy peak at +183 mV and a narrow spatial distribution on the edge are the signatures of a 1D edge state on the hexagonal Bi(111) BL edge. It is worth noting that in the STS spectra taken on all three typical positions shown in Figure 3b, a dip exists at energy around 100 mV. This fact suggests that no significant doping effect exists in the sample that would cause the spectrum peak at 240 mV on the terrace shifting to 183 mV on the type-A edge and disappearing on the type-B edge, since the energy of the dip at the three positions remains the same. We also note that the continuous behavior of the previous spectra peaks shifting in spectra 1 to 6 is clearly different with the consistent peak at 183 mV near the edge in spectra 9 to 11, which is an obvious signature of an edge state. This difference can distinguish localized edge states from quantum-confinement caused standing waves. Standing waves usually have their energy moving with their real space position, while the real edge states’ energy position is localized at the edge and irrelevant to the real space position. In Figure 3d, the black dashed line indicates the energy position of the edge states that does not change in three spectra while the gray dashed line indicates moving energy peaks that may be caused by standing wave. This 1D edge state is extremely similar to the previously reported 1D topological edge state identified on one kind of the zigzag edges of Bi(111) on Bi bulk crystal and on Si(111).19,20 Both of them show a +183 mV energy peak and a dependence on edge structures. This result is straightforward since the existence of the 1D edge state is due to the weak interaction between the out most atoms on the edge and the underlying Bi layer, which is “lifted” from the underlying Bi layer due to the buckled honeycomb structure. This weak interaction nature makes the above edge be indifferent to the underlying layer to be epitaxial thin films or a bulk crystal. Thus, the 1D topological edge state of Bi(111) BL can exist at layer thickness as thin as three BLs. After confirming the existence of edge states on the ultrathin film, it is interesting to see the effects of the superconducting

Figure 3. dI/dV spectra on Bi(111) BLs. (a) STM image of Bi(111) on NbSe2. The topmost hexagonal shape island corresponds to one Bi(111) BL. (b) Three dI/dV spectra taken at three positions on the island labeled by A, B, and C in (a). The spectrum (solid (blue) line) taken at edge A shows a +183 mV peak while such peak is missing in the spectra from edge B and the terrace. (c) Sixteen dI/dV spectra taken along the edge indicated by the dashed (blue) line in (a). The dashed (black) line indicates the consistency of the peak. (d) Sixteen dI/dV spectra were taken along the arrow in (a), starting (number 1) from the topmost Bi(111) BL, crossing the edge and ending (number 16) at the lower Bi(111) BL. The spectra on the terrace, 1 to 8 and 12 to 16, show similar features as spectrum taken at position C in (b). Spectra 9 to 11 were taken near the edge and show a +183 mV peak as in position A, indicated by a dashed (black) line. The peak on the terrace shows an energy shift, indicated by a dash curve (gray). Spectra in (c,d) are shifted vertically for a clearer view. The STM image (a) was taken at bias 1.0 V and tunneling current 0.1 nA. The STS spectra in (c,d) were taken at tunneling current 0.2 nA.

corresponds to 1 BL Bi(111). The underlying two layers are also Bi(111) BLs. Three spectra were taken on the island at three typical positions labeled with A, B and C in Figure 3a: position A is on one step edge of the island, position B is on the adjacent step edge and position C is on the island terrace. The two adjacent edges of Bi(111) bulked honeycomb BL have different atomic structures, considering the underlying Bi(111) layer. Both of them have zigzag structures while one kind of the edges has its out most atoms belong to the upper layer atoms of the BL and the other kind of the edges has its out most atoms 3037

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Nano Letters substrate on the ultrathin film, because proximity effect is likely to be strong at such thin thickness. The superconductivity of Bi(111) BLs was studied by cooling down the system to 400 mK. In Figure 4a, dI/dV spectra clearly

worth noting that a BCS-type function can only capture the proximity superconducting gap spectrum inside the coherence peaks, as shown in the inset of Figure 4b. The coherence peak of the proximity superconducting gap is sharper compared with the fitted BCS-type spectrum, which is more broadened outside the gap. This can be explained by a bound state effect between a superconducting phase and a nonsuperconducting phase.36 As discussed above, the superconducting gap on Bi(111) thin film are induced from NbSe2 substrate via proximity effect. The decay length of the gap strongly depended on the vertical coherence length of NbSe2, Bi(111) BLs and Bi(110) layers in between. Compared with previously reported Bi2Se3/NbSe2 and Bi2Te3/NbSe2 heterostructures, superconducting gap in Bi decay faster with increasing layer thickness than in Bi2Se3 and Bi2Te3, indicating a shorter coherent length in Bi(111) thin film.5,6 It is worth noting that the 1D edge state on Bi(111) BL exists at a very thin layer thickness so that superconductivity from the substrate does not vanish. Whereas for 3 BLs Bi(111) where the 1D edge state is confirmed, the proximity effect still exits, and the superconducting gap is 0.6 meV. In summary, we have grown Bi(111) ultrathin films on superconducting (SC) substrate NbSe2 for the first time. Also, Bi(111) BLs can exist on the substrate stably after 2 BLs of Bi(110). This Bi(111)/SC system has two advantages. One is that the interaction between the ultrathin film and the substrate is weak, because the band structure of 3 BLs Bi(111) film shows quasi-freestanding feature. Also, the 1D edge state also remains the same with that found on the bulk Bi(111) crystal. These indicate the Bi(111) ultrathin film is still topologically nontrivial. Another is that on such ultrathin film, superconducting proximity effect from the substrate is still strong enough to be detected. Therefore, Bi(111)/NbSe2 heterostructure is a good platform to study the topological properties of Bi(111) and even to search Majorana Fermions with proximity induced superconductivity. The ARPES experiment was carried out in a molecular beam epitaxy (MBE)-STM-ARPES joint system. The STM/STS experiment was carried out in a MBE-STM joint system. Samples were grown in the MBE chamber and then measured via different approaches in situ. The 2H-NbSe2 substrate was prepared by chemical vapor transport (CVT) method. After degassing at 500 K for more than 4 h, substrate was cleaved at room temperature in the MBE chamber with base pressure better than 2 × 10−10 Torr. High purity Bi (99.999%) was then deposited on the substrate using a standard Knudsen cell at substrate temperature 350 K. The ARPES measurements were performed at 90 K using He−Iα light (21.2 eV) in the lab, and some data were taken at the SGM-3 beamline of the synchrotron radiation source ASTRID. The energy resolution is better than 15 meV and angular resolution is better than 1% of the Brillouin zone. Measurements for topography and large energy scale STS were performed at 4.2 K. STS measurements of superconductivity were measured at 400 mK, using liquid 3 He refrigerant. Electrochemical etched W tips were used for STM and STS measurements. STS spectra were obtained via lock-in technique with modulation frequency at 991 Hz and amplitude at 10 mV. A bias divider was used in the measurement of superconductivity STS. First-principle calculations were performed using the DFT from Vienna ab initio simulation package with a plane wave basis.37 Local density approximation was used for the exchange and correlation functional,38 and van der Waals corrections to the density functional in the Grimme implementation39 were also included.

Figure 4. dI/dV spectra on different thickness of Bi(111) ultrathin films with/without magnetic field. (a) dI/dV spectra from Bi(111) 1 BL to Bi(111) 7 BLs. Superconducting gaps with strong coherence peaks are shown for all layers. (b) BCS fitted gap sizes of the spectra from the 7 layers. The decay of the gap sizes together with gap size of NbSe2, 1.1 meV, was fitted exponentially against sample thickness (dashed curve). Inset: BCS fitting for the 7 BLs spectrum. (c,d) The magnetic field dependence of the superconducting spectra on 1 BL and 4BLs Bi(111) respectively. Spectra in (a,c,d) are shifted vertically for a clearer view. The STS spectra were taken at tunneling current 0.2 nA.

reveal the superconducting gaps on Bi(111) from 1 BL to 7 BLs. Distance between the coherent peaks which corresponds to the gap size gradually narrows with increasing layer thickness. Zero bias conductances are none-zero for all the spectra. The dI/dV spectra are fitted with a BCS s-wave superconducting spectrum function including a broadening factor35 dI ∝ dV

+∞

∫−∞

⎡ |E − i Γ| Re⎢ ⎢⎣ (E − i Γ)2 − Δ2

⎛ (E + eV ) ⎤⎜ exp⎡⎣ kT ⎤⎦ ⎥⎜ ⎥⎦⎜ ⎜ kBT 1 + exp⎡⎣ (E + eV ) ⎤⎦ kT ⎝

{

⎞ ⎟ ⎟dE 2 ⎟ ⎟ ⎠

}

(1)

Fitted superconducting gap sizes of different BLs are plotted in Figure 4b together with the gap size of NbSe2 substrate. The distance between NbSe2 and 1 BL Bi(111) is an indication of Bi(110) in between. On 1 BL Bi(111), the superconducting size is slightly below 0.80 meV and decays to 0.46 meV on 7 BLs. Gap decay with layer thickness from NbSe2 to Bi(111) can be roughly fitted with an exponential curve. Magnetic field dependence of the superconducting gaps is shown in Figure 4c,d for 1 BL and 4 BLs Bi(111) respectively. With magnetic field increasing, superconducting gaps become shallower and eventually vanish at 1.4 T for 1 BL and 0.6 T for 4 BLs. It is 3038

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(16) Yang, F.; Miao, L.; Wang, Z. F.; Yao, M.-Y.; Zhu, F.; Song, Y. R.; Wang, M.-X.; Xu, J.-P.; Fedorov, A. V.; Sun, Z.; Zhang, G. B.; Liu, C.; Liu, F.; Qian, D.; Gao, C. L.; Jia, J.-F. Phys. Rev. Lett. 2012, 109, 016801. (17) Kim, S. H.; Jin, K.-H.; Park, J.; Kim, J. S.; Jhi, S.-H.; Kim, T.-H.; Yeom, H. W. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 155436. (18) Lu, Y.; Xu, W.; Zeng, M.; Yao, G.; Shen, L.; Yang, M.; Luo, Z.; Pan, F.; Wu, K.; Das, T.; He, P.; Jiang, J.; Martin, J.; Feng, Y. P.; Lin, H.; Wang, X. S. Nano Lett. 2015, 15, 80−7. (19) Drozdov, I. K.; Alexandradinata, A.; Jeon, S.; Nadj-Perge, S.; Ji, H.; Cava, R. J.; Andrei Bernevig, B.; Yazdani, A. Nat. Phys. 2014, 10, 664−669. (20) Kawakami, N.; Lin, C.-L.; Kawai, M.; Arafune, R.; Takagi, N. Appl. Phys. Lett. 2015, 107, 031602. (21) Hofmann, P. Prog. Surf. Sci. 2006, 81, 191−245. (22) Yaginuma, S.; Nagao, T.; Sadowski, J. T.; Saito, M.; Nagaoka, K.; Fujikawa, Y.; Sakurai, T.; Nakayama, T. Surf. Sci. 2007, 601, 3593− 3600. (23) Scott, S. A.; Kral, M. V.; Brown, S. A. Surf. Sci. 2005, 587, 175− 184. (24) McCarthy, D. N.; Robertson, D.; Kowalczyk, P. J.; Brown, S. A. Surf. Sci. 2010, 604, 1273−1282. (25) Lükermann, D.; Banyoudeh, S.; Brand, C.; Sologub, S.; Pfnür, H.; Tegenkamp, C. Surf. Sci. 2014, 621, 82−87. (26) Kowalczyk, P. J.; Mahapatra, O.; McCarthy, D. N.; Kozlowski, W.; Klusek, Z.; Brown, S. A. Surf. Sci. 2011, 605, 659−667. (27) Kammler, M.; Horn-von Hoegen, M. Surf. Sci. 2005, 576, 56− 60. (28) Nagao, T.; Sadowski, J.; Saito, M.; Yaginuma, S.; Fujikawa, Y.; Kogure, T.; Ohno, T.; Hasegawa, Y.; Hasegawa, S.; Sakurai, T. Phys. Rev. Lett. 2004, 93, 105501. (29) Sharma, H. R.; Fournée, V.; Shimoda, M.; Ross, A. R.; Lograsso, T. A.; Gille, P.; Tsai, A. P. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 155416. (30) Scott, S. A.; Kral, M. V.; Brown, S. A. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 205424. (31) Nagao, T.; Doi, T.; Sekiguchi, T.; Hasegawa, S. Jpn. J. Appl. Phys. 2000, 39, 4567. (32) Chen, M.; Peng, J.-P.; Zhang, H.-M.; Wang, L.-L.; He, K.; Ma, X.-C.; Xue, Q.-K. Appl. Phys. Lett. 2012, 101, 081603. (33) Kiss, T.; Yokoya, T.; Chainani, A.; Shin, S.; Nohara, M.; Takagi, H. Phys. B 2002, 312-313, 666−667. (34) Yokoya, T.; Kiss, T.; Chainani, A.; Shin, S.; Nohara, M.; Takagi, H. Science 2001, 294, 2518. (35) Nishio, T.; Ono, M.; Eguchi, T.; Sakata, H.; Hasegawa, Y. Appl. Phys. Lett. 2006, 88, 113115. (36) Truscott, A. D.; Dynes, R. C.; Schneemeyer, L. F. Phys. Rev. Lett. 1999, 83, 1014−1017. (37) Kresse, G.; Hafner, J. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47, 558−561. (38) Solovyev, I. V.; Dederichs, P. H.; Anisimov, V. I. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 16861−16871. (39) Grimme, S. J. Comput. Chem. 2006, 27, 1787−1799. (40) Blöchl, P. E. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953−17979.

The core electrons were represented by the projectoraugmented wave potential.40 The kinetic energy cutoff is set above 400 eV on a 20 × 20 k-point mesh. The structure optimization process is performed with force convergence criteria at 0.01 eV/Å.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone: +86 21 5474 4616. ORCID

Yunhao Lu: 0000-0001-6825-7206 Dandan Guan: 0000-0002-3714-8813 Author Contributions

H.H.S. conducted the experiments with the help of M.X.W., F.F.Z., G.Y.W., and H.Y.M. Z.A.X. provided the NbSe2 crystals. Q.L. and Y.H.L carried out the calculations. C.L.G., Y.Y.L, C.H.L., D.Q., D.G., and J.F.J. analyzed the data. H.H.S., D.G., and J.F.J. wrote the manuscript. All the authors discussed the results. Funding

The work was supported by the Ministry of Science and Technology (MOST) of China (Grant 2013CB921902, 2016YFA0301003, 2016YFA0300403, 20130073120081), NSFC (Grant 11521404, 11504230, U1632102, 91421312, 11634009, 11574201, U1632272, 11574202, 16Z127060027, 61574123, 11464051) and Shanghai Committee of Science and Technology, China (Grant 14XD1401900, 15JC1402300). D.Q. acknowledges support from the Changjiang Scholars Program. Notes

The authors declare no competing financial interest.

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NOTE ADDED AFTER ASAP PUBLICATION This paper was published on the Web on April 20, 2017. Additional funding information was added, along with replacing the TOC/Abstract graphic, and the corrected version was reposted on April 24, 2017.

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DOI: 10.1021/acs.nanolett.7b00365 Nano Lett. 2017, 17, 3035−3039