Tunable Electronic Structures of GeSe Nanosheets and Nanoribbons

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Tunable Electronic Structures of GeSe Nanosheet and Nanoribbon Zhi-Qiang Fan, Xiang-Wei Jiang, Zhongming Wei, Jun-Wei Luo, and Shu-Shen Li J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b04607 • Publication Date (Web): 19 Jun 2017 Downloaded from http://pubs.acs.org on June 24, 2017

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The Journal of Physical Chemistry

Tunable Electronic Structures of GeSe Nanosheet and Nanoribbon Zhi-Qiang Fan,†,‡ Xiang-Wei Jiang,†, §,* Zhongming Wei,† Jun-Wei Luo,†, §,* Shu-Shen Li†,§ †

State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese

Academy of Sciences, Beijing 100083, People’s Republic of China ‡

School of Physics and Electronic Science, Changsha University of Science and Technology,

Changsha 410114, People’s Republic of China §

Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science

and Technology of China, Hefei, Anhui 230026, China

ABSTRACT: Germanium selenide (GeSe) is an isoelectronic analogue of phosphorene, which has been studied widely in recent experiments. In this paper, we have investigated tunable electronic structures and transport properties of the 2D and quasi-1D GeSe by using a self-consistent ab initio approach. The calculated band structures show the stretching and compression on zigzag direction and the stretching on armchair direction all can enlarge the band gap of 2D GeSe nanosheet. However, the compression on armchair direction will reduce the band gap of 2D GeSe nanosheet. In addition, the appropriate compressions on both directions all can change 2D GeSe nanosheet from indirect band gap to direct band gap. When the 2D GeSe nanosheet is cut into quasi-1D nanoribbon, the band structures can be modulated by the ribbon width and the passivation. The unpassivated zigzag GeSe nanoribbons are metals regardless of the ribbon width. The H-passivated zigzag GeSe nanoribbons are semiconductors with direct band gaps and the band gaps decrease with increasing ribbon width. The unpassivated armchair GeSe nanoribbons are semiconductors with direct band gaps and H-passivated armchair GeSe nanoribbons are semiconductors with indirect band gaps. Their band gaps all decrease with increasing ribbon width. In addition, we find the in-plane contact structure of unpassivated zigzag GeSe nanoribbon and H-passivated zigzag GeSe nanoribbon can lead to the formation of a Schottky barrier, which results in rectifying current-voltage characteristics.

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INTRODUCTION Two-dimensional (2D) materials with monolayer thickness, such as graphene,1,2 silicene,3,4 phosphorene,5,6 and transition-metal dichalcogenides (TMD)7-9 have attracted great interest recently because of their novel properties that differ from their bulk counterparts. The electronic and optoelectronic devices based on 2D materials will minimize their sizes dramatically and is maybe a possible way to solve the miniaturization problem of traditional silicon based device. So far, various interesting electronic transport properties such as switch,10-12 rectifier,13-15 negative differential resistance,16-18 and field-effect transistors19,20 have been found in these 2D devices. In addition, a lot of molecules switching between the nanoribbons of these 2D materials also can be made as the functional electronic, spintronics, and optoelectronic devices.21-24 Besides further exploring the novel properties of the existing 2D materials, the search for new 2D

materials has recently been expanded to include the neighbors of group V elements, namely, IV-VI binary analogous sheets such as GeS, SnS, GeSe, SnSe and SiTe.25-30 Among them, Ge-based chalcogenides, such as GeSe, have been extensively studied owing to their unique optical and electronic properties, as well as their high stability, abundance, environmental friendliness, and low toxicity. Each layer of GeSe can be viewed as consisting of six-membered rings in chair conformation. Theoretical studies show 2D GeSe nanosheet is dynamically stable at the freestanding state, which share similar semiconducting behaviors to phosphorene.31-33 The experimental results demonstrated GeSe is a IV-VI p-type semiconductor with a narrow indirect band gap in the range of 1.0-1.2 eV.34-36 So far, the photo-switching behavior based on GeSe nanosheets, have been reported, which revealed a comparable photo-responsivity with other TMDs.35-38 Its intrinsic physical properties and future utilization in functional devices are still a lack of systematic knowledge. So, in this paper, we have performed comprehensive first-principles investigations of tunable electronic structures of GeSe nanosheet and transport properties of GeSe nanoribbon. The results show the band structures of GeSe nanosheet can be modulated effectively by external strain. When its nanosheet is cut into nanoribbon, the band structures are sensitive to the ribbon width and the passivation.

METHOD The geometric optimization and electron transport properties were calculated by using the 2


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first-principle software package Atomistix ToolKit (ATK), which is based on density-functional theory (DFT) in combination with the non-equilibrium Green’s function (NEGF).39-41 The exchange and correlations were described by the Perdew-Burke-Ernzerhof (PBE) functional under the generalized gradient approximation (GGA). The real space grid techniques are used with the energy cut off of 150 Ry as a required cut off energy in numerical integration and the solution of Poisson equation using fast Fourier transform (FFT). A Monkhorst-Pack k-point grid of 1×45×45 and 1×1×45 were employed in the electronic calculations of 2D nanosheets and 1D nanoribbons, respectively. The geometries are optimized until all residual force on each atom is smaller than 0.05 eV Å-1. When a bias voltage is applied to the device, the current I (Vb ) can be calculated by the Landauer formula: I (Vb ) =

2e T ( E ,Vb )[ f L ( E ,Vb ) − f R ( E ,Vb )]dE .42 Here, h ∫

Vb is the bias voltage, T ( E ,Vb ) is the transmission coefficient, f L ( E , Vb ) and f R ( E , Vb ) are the Fermi-Dirac distribution functions of the left and right electrodes.

RESULTS AND DISCUSSION

Figure 1 The geometry of 2D GeSe nanosheet (a) and the corresponding band structure (b). (c) Total DOS of GeSe and projected DOS of Se and Ge respectively. Projected DOS of s, p orbitals of Se (d) and Ge (e).

Fig. 1(a) depicts the geometrical structure 2D GeSe nanosheet which is similar to phosphorene. The lattice constants a along the zigzag direction and b along the armchair direction are 3.88 Å and 4.45 Å. The band structure of 2D GeSe nanosheet in Fig. 1(b) indicates the 2D GeSe nanosheet is a semiconductor with an indirect band gap of 1.04 eV which is in line with the previous experimental results34-36 and the theoretical results obtained by using other methods.43,44 Projected DOS in Fig. 1(c) shows valence states are originated from Ge and Se equally, while the conduction states are primarily composed of the Ge. If the DOS is further projected on the 3



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separate orbital of atom, one can find the contributions on valence states mainly originate from the p orbitals of Se and Ge. The s orbital of Ge has a few contributions on valence states, but the contribution from s orbital of Se nearly equals to zero. The conduction states are almost originated from the p orbitals of Ge, the contribution from its s orbital also equals to zero.

Figure 2 Band gaps (a) and band structures (b) of 2D GeSe nanosheet under different strains. Fermi energy is set to zero in the energy scale. Here, “−” represents compression and “+” represents stretching.

Because the geometrical structure of 2D IV-VI semiconductor is similar to phosphorene, its electronic structure will be also sensitive to the in-plane strain like phosphorene.45-47 Strain can be understood as an elastic field applied to materials, which can be used to tune the physical properties of materials. Under different strain, the geometrical structure of crystal changes due to the interaction between the elastic field and crystalline field, which induces different distributions of electron density in the material and then electronic properties. Most recently, the band gap of 2D GeS nanosheet had been found can be modulated under external strain.48 So, the effect of the in-plane strain on the band structure of 2D GeSe nanosheet is deserved to study thoroughly. In general, the biaxial uniform strain are considered to modulate the band structures of the materials. Although the 2D GeSe nanosheet is similar to phosphorene, there still exist some differences. Unlike the phosphorene, 2D GeSe is consist of two chemical elements Ge and Se leading to the different in-plane elastic stiffness along the armchair or zigzag direction. If the biaxial uniform strain is added, the geometrical structures of 2D GeSe will be changed hugely, even forming the defects. So, this paper, we just consider the uniaxial strain separately. Fig. 2(a) shows the evolutions of band gaps of 2D GeSe nanosheet with the applied in-plane strain along the zigzag direction and armchair direction. Like phosphorene and GeS, the band gaps of 2D GeSe

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nanosheet are also sensitive to the in-plane strain. When the nanosheet is compressed or stretched along the zigzag direction, the band gaps all will be enlarged with the strain increasing. In addition, one can see the tunable effect of compression is more noticeable than that of stretching. The band gap changes to 1.27 eV at -10% compressed strain and 1.16 eV at +10% stretched strain. Fig. 2(b) presents the detailed band structures of 2D GeSe nanosheet at ±8% and ±10% strain along the zigzag direction. One can see the stretching just enlarge the indirect band gap between valence band maximum (VBM) and conduction band minimum (CBM). The relative position of VBM and CBM is not changed. The compressed strain also make the VBM and CBM shift away from each other leading to the increase of band gap, but the indirect band gap will be changed to direct band gap at −10%. When the strain is applied along the armchair direction, the band gaps nearly exhibit a linear response to the strain. The stretching will enlarge the band gap gradually, but the compression will enlarge the band gap at -2% compressed strain first then decrease the band gap gradually. It is because the CBM shifts up a little leaving the VBM unchanged at small compressed strain. When the compressed strain further increases, the CBM and the VBM shift close to each other leading to the decrease of the band gap. The band gap changes to 0.74 eV at -10% compressed strain and 1.42 eV at +10% stretched strain. Fig. 2(c) presents the detailed band structures of 2D GeSe nanosheet at ±8% and ±10% strain along the armchair direction. One can see the stretching also enlarge the indirect band gap between the VBM and the CBM. But, the compressed strain make the indirect band gap changes to direct band gap at −8%. The different changes of band gap along the armchair or zigzag direction is mainly because the particular geometrical structure of GeSe. GeSe is consist of two different chemical elements and the geometrical structures such as bond length, bond angle are different along the armchair or zigzag direction. More importantly, the strains along the armchair direction can change bond lengths between the co-planar and non-planar Ge atom and Se atom together. But, the strains along the zigzag direction mainly change bond lengths between the co-planar Ge atom and Se atom. So, we obtain the different changes of band gap along the armchair or zigzag direction in our work. The recent paper which studied tunable electronic properties of GeSe/phosphorene heterostructure also gets the same result. The changes of band structures of GeSe/phosphorene heterostructureare different along the armchair or zigzag direction.49

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Figure 3 Computed band structures of the unpassivated (a) and H-passivated (b) 8-zigzag and 12-zigzag GeSe nanoribbons. Right panels in (a) and (b) show the contours of Bloch state corresponding to the 1 and 2 bands. The isosurface value is 0.02. Fermi energy is set to zero in the energy scale.

When phosphorene is cut into nanoribbon, its band structures can be modulated by the ribbon width and the passivation obviously.50-53 Transport properties of phosphorene nanoribbons, especially zigzag phosphorene nanoribbons, were also explored by several groups.54-56 Therefore, we also study the electronic structures of GeSe nanoribbons with different width (Na and Nz) and passivation. We first calculated the magnetic of zigzag GeSe nanoribbon and found the H-passivated and unpassivated zigzag GeSe nanoribbon are all nonmagnetic. We also calculated the magnetic of armchair GeSe nanoribbon. The same result was obtained. Whatever H-passivated or unpassivated armchair GeSe nanoribbon is also nonmagnetic. Therefore, the spin-polarized band structures of the armchair and the zigzag GeSe nanoribbons are not considered in this paper. Fig. 3 illustrates band structures of the unpassivated (a) and H-passivated (b) 8-zigzag and 12-zigzag GeSe nanoribbons. Band structures of the unpassivated 8-zigzag and 12-zigzag GeSe nanoribbons all exhibit the metallic character. Two bands crossing the Fermi level, implying the existence of two one-dimensional metallic states. The contours of Bloch states corresponding to the 1 and 2 bands show these two metallic states localize on the edge of GeSe nanoribbon separately. In addition, the width of the nanoribbon has no effect on its band structure around the Fermi energy. Band structure of the H-passivated 8-zigzag GeSe nanoribbon exhibits semiconductor character with a direct band gap. The contours of Bloch states show VBM and CBM states are same to that of the unpassivated 8-zigzag GeSe nanoribbon localizing on the edge of GeSe nanoribbon separately. When the width Nz increases, VBM and CBM all shift to Fermi energy level leading to the reduction of the band gap. For 12-zigzag GeSe nanoribbon, CBM overlaps with Fermi energy level and its band structure exhibits the metallic character. In other

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words, the band structures of H-passivated zigzag GeSe nanoribbon are sensitive to their width dramatically.

Figure 4 Computed band structures of the unpassivated (a) and H-passivated (b) 8-armchair and 12-armchair GeSe nanoribbons. Right panels in (a) and (b) show the contours of Bloch state corresponding to the 1 and 2 bands. The isosurface value is 0.02. Fermi energy is set to zero in the energy scale.

Contrary to the zigzag GeSe nanoribbon, band structures in Fig. 4 indicate all the armchair GeSe nanoribbons are semiconductors. Band structures of the unpassivated 8-armchair and 12-armchair GeSe nanoribbons all exhibit the semiconductor character with the direct band gap. The contours of Bloch state show CBM state (1) mainly localizes on one edge of GeSe nanoribbon, but VBM state (2) delocalizes on the whole GeSe nanoribbon. When the width Na increases, VBM and CBM of 12-armchair GeSe nanoribbon all shift to Fermi energy level slightly leading to a tiny reduction of the band gap. Band structures of the H-passivated 8-armchair and 12-armchair GeSe nanoribbons still exhibit semiconductor character with the indirect band gaps. The contours of Bloch state show CBM state (1) delocalizes on the whole GeSe nanoribbon including the passivated H atoms, but VBM state (2) localizes on the central region of the GeSe nanoribbon. Moreover, one can see the increase of the width also can reduce the band gap of H-passivated armchair GeSe nanoribbon, but not obvious.

Figure 5 Variations of the band gap of unpassivated armchair, H-passivated armchair and H-passivated zigzag 7



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GeSe nanoribbons versus their width N.

To further explore the effects of the width on the band gap of GeSe nanoribbons, variations of the bandgap of unpassivated armchair, H-passivated armchair and H-passivated zigzag GeSe nanoribbons versus their width N are shown in Fig. 5. It can be seen that the band gaps of all configurations decrease with increasing width of nanoribbons. The band gaps of unpassivated armchair GeSe nanoribbon are not sensitive to its width, only ranging from 0.69 eV (Na=4) to 0.51 eV (Na=26). However, the band gap of H-passivated armchair GeSe nanoribbon decreases rapidly from 1.68 eV to 1.07 eV when the width Na changes from 4 to 12. Then it also decreases slowly when the width Na further increases and just drops to 0.97 eV at Na=26. The band gap of H-passivated zigzag GeSe nanoribbon also decreases rapidly from 1.21 eV to 0.09 eV when the width Nz changes from 4 to 10. When the width Nz increases to 12, the H-passivated zigzag GeSe nanoribbon varies from a semiconductor to a metal. Even the width Nz increases to 26, it always maintains the metallic character. The tunable band gaps with different widths lead the GeSe nanoribbon, especially the H-passivated zigzag GeSe nanoribbon, have more potential in electronic, spintronics, and optoelectronic devices.

Figure 6 (a) Geometry Schematic illustration of the proposed Schottky contact structure based on unpassivated 4-zigzag GeSe nanoribbon (red dash line) and H-passivated 4-zigzag GeSe nanoribbon (blue dash line). M and N are the lengths of unpassivated and H-passivated 4-zigzag GeSe nanoribbons in the central region. (b) Transmission spectra of the Schottky contact structures with the different lengths of H-passivated 4-zigzag GeSe nanoribbons. Fermi energy is set to zero in the energy scale. 8


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The above results show the unpassivated 4-zigzag GeSe nanoribbon is a metal and the H-passivated 4-zigzag GeSe nanoribbon is a semiconductor with a direct band gap (1.21 eV). Therefore, we propose an in-plane metal-semiconductor junction in Fig. 6 and lead to the formation of a Schottky barrier between unpassivated and H-passivated 4-zigzag GeSe nanoribbons. The device is divided into three regions: left lead, right lead and central scattering region. The central scattering region contains four units (M=4) of unpassivated 4-zigzag GeSe nanoribbon and four units (N=4) of H-passivated 4-zigzag GeSe nanoribbon. For simplicity, we name this junction as M4N4. Here, we fix the length of unpassivated 4-zigzag GeSe nanoribbon. It is because the unpassivated zigzag GeSe nanoribbon is a metal and its electronic structure is seldom affected by the length. The similar study about this Schottky barrier diode had been done by using the phosphorene nanoribbon. The calculated results indicated the length of unpassivated zigzag phosphorene nanoribbon seldom affect the performance of the Schottky barrier diode.53 When the H-passivated 4-zigzag GeSe nanoribbon in the central scattering region extends to six units, eight units, ten units, twelve units and fourteen units, the junctions are named as M4N6, M4N8, M4N10, M4N12 and M4N14, respectively. Fig. 6(b) shows transmission spectra of the Schottky contact structures with the different lengths of H-passivated 4-zigzag GeSe nanoribbons. For M4N4, there is transmission forbidden region in the energy region [-0.6 eV, 0.6 eV] which just equals to the band gap of H-passivated 4-zigzag GeSe nanoribbon. The minimum transmission coefficient can be as low as 10-9. When the length of the H-passivated 4-zigzag GeSe nanoribbon increases, the transmission forbidden regions are still holding its previous energy position. But, the transmission coefficients in the forbidden region will further drop with N increasing. For M4N14, the minimum transmission coefficient can be as low as 10-16. That means the length of the H-passivated 4-zigzag GeSe nanoribbon plays an important role in the transport properties of this in-plane metal-semiconductor junction.

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Figure 7 Projected density of states of (a) left lead (unpassivated 4-zigzag GeSe nanoribbon) and (b) right lead (H-passivated 4-zigzag GeSe nanoribbon) for M4N4 and M4N14, respectively.

Analysis of projected density of states (PDOS) assists in understanding the drop of the transmission coefficients induced by extending the H-passivated 4-zigzag GeSe nanoribbon in central region. The calculated PDOS spectra of the left lead (unpassivated 4-zigzag GeSe nanoribbon) and right lead (H-passivated 4-zigzag GeSe nanoribbon) are presented in Fig. 7(a) and (b), respectively. From the figure (a), one can see the extending of the H-passivated ZPNR in the central scattering region hardly affect the PDOS of the left lead. PDOS spectra of the left lead of M4N4 nearly overlap with that of M4N14. In addition, there is a high PDOS peak around Fermi energy for M4N4 and M4N14. For M4N4, the minimum PDOS coefficient of right lead is below 10-3 at 0.1 eV due to it semiconductor character. Moreover, there is an obvious PDOS peak around Fermi energy. We believe this PDOS peak is induced by the high PDOS peak of left lead around Fermi energy. The means the length of H-passivated 4-zigzag GeSe nanoribbon in central is not wide enough to avoid the interaction of the left lead. For M4N14, the PDOS of right lead decrease obviously due to the extending the H-passivated 4-zigzag GeSe nanoribbon. The minimum PDOS coefficient of right lead is below 10-6 and the PDOS peak around Fermi energy in M4N4 disappears. In other words, the long H-passivated 4-zigzag GeSe nanoribbon in central can avoid the interaction of the left lead. 10


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Figure 8 (a) Current-voltage characteristics of M4N12 and M4N14 in the bias region from -0.4 V to 0.4 V. (b) Rectification ratios of M4N12 and M4N14 in the bias region from 0.05 V to 0.4 V.

Next, we calculate current-voltage (I-V) characteristics of M4N12 and M4N14 in Fig. 8(a). In the positive bias region, currents of M4N12 will increase rapidly after 0.1 V and reach to 0.011 nA at 0.4 V. However, the currents of M4N12 in negative bias region seem close to zero from 0.0 V to 0.4 V. Therefore, currents in positive bias region are much larger than that of the negative bias region and show a remarkable rectification behavior. For M4N14, the current values are a little smaller than that of M4N12 due to the decrease of the transmission coefficients in the forbidden region. The evolution of the I-V curve is same to that of M4N12 and also shows a remarkable rectification behavior. In order to show how good the rectification behavior in this Schottky contact structure, we calculated the rectification ratios (RR) of M4N12 and M4N14 in the bias region from 0.05 V to 0.4 V. Here, we define the rectification ratio as the ratio of the positive bias current to the negative bias one, RR (V) = I (+V)/I (-V). For M4N12, RR increases with the bias and reaches to the maximum value 4×102 at 0.25 V. Then RR decreases gradually, but still beyond 102 until 0.4 V. When the length of the H-passivated 4-zigzag GeSe nanoribbon increases, the transmission coefficient in the forbidden region will drops leading to the reduction of the current. Although the current of M4N14 is a little smaller than that of M4N12, the calculated RR is always higher than that of M4N12 in the whole bias region. The maximum value of RR also presents at 0.25 V and beyond 103.

CONCLUSIONS In summary, we have investigated tunable electronic structures and transport properties of

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the 2D and quasi-1D GeSe by using a self-consistent ab initio approach. The calculated band structures show the stretching and compression on zigzag direction and the stretching on armchair direction all can enlarge the band gap of 2D GeSe nanosheet. However, the compression on armchair direction will reduce the band gap of 2D GeSe nanosheet. In addition, the appropriate compressions on both directions all can change 2D GeSe nanosheet from indirect band gap to direct band gap. When the GeSe nanosheet is cut into quasi-1D nanoribbon, the band structures can be modulated by the ribbon width and the passivation. The unpassivated zigzag GeSe nanoribbons are metals regardless of the ribbon width. The band gap of H-passivated zigzag GeSe nanoribbon decreases rapidly from 1.21 eV to 0.09 eV when the width Nz changes from 4 to 10. When the width Nz increases to 12, the H-passivated zigzag GeSe nanoribbon varies from a semiconductor to a metal. The band gaps of unpassivated armchair GeSe nanoribbon are not sensitive to its width, only ranging from 0.69 eV (Na=4) to 0.51 eV (Na=26). However, the band gap of H-passivated armchair GeSe nanoribbon decreases rapidly from 1.68 eV to 1.07 eV when the width Na changes from 4 to 12. Then it also decreases slowly when the width Na further increases and just drops to 0.97 eV at Na=26. More importantly, we find the in-plane contact structure of unpassivated zigzag GeSe nanoribbon and H-passivated zigzag GeSe nanoribbon can lead to the formation of a Schottky barrier, which results in rectifying current-voltage characteristics. When the length of the H-passivated 4-zigzag GeSe nanoribbon increases, the transmission coefficients in the forbidden region drop gradually leading to the reduction of the currents. But, the calculated RR increases in the whole bias region. The maximum RR of M4N14 presents at 0.25 V and beyond 103.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (Xiang-Wei Jiang), [email protected] (Jun-Wei Luo). Notes The authors declare no competing financial interest.

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Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos. 11674039, 11574304, 61571415 and 61622406), the China Postdoctoral Science Foundation (Grant No. 2016M601099), the Hunan Provincial Natural Science Foundation of China (Grant No. 2015JJ2013), the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 15A004), and the Construct Program of the Key Discipline in Hunan Province, Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province. X. W. Jiang greatly acknowledges the support to this work by Chinese Academy of Sciences-Peking University Pioneer Cooperation Team (CAS-PKU Pioneer Cooperation Team) and the Youth Innovation Promotion Association CAS (grand No. 2016109).

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Tunable Electronic Structures of GeSe Nanosheets and Nanoribbons

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