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Keywords:

  • density functional theory;
  • electronic properties;
  • graphene;
  • half-metallic nature;
  • quantum dots

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. Computational Details
  5. 2. Results and Discussion
  6. 3. Conclusions
  7. Acknowledgements
  8. Supporting Information

A comprehensive first-principles theoretical study of the electronic properties and half-metallic nature of zigzag edge-oxidized graphene quantum dots (GQDs) is carried out by using density functional theory (DFT) with the screened exchange hybrid functional of Heyd, Scuseria and Ernzerhof (HSE06). The oxidation schemes include -OH, -COOH and -COO groups. We identify oxidized GQDs whose opposite spins are localized at the two zigzag edges in an antiferromagnetic-type configuration, showing a spin-polarized ground state. Oxidized GQDs are more stable than the corresponding fully hydrogenated GQDs. The partially hydroxylated and carboxylated GQDs with the same size exhibit half-metallic state under almost the same electric-field intensity whereas fully oxidized GQDs behave as spin-selective semiconductors. The electric-field intensity inducing the half metal increases with the length of the partially oxidized GQDs, ranging from M=4 to 7.


1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. Computational Details
  5. 2. Results and Discussion
  6. 3. Conclusions
  7. Acknowledgements
  8. Supporting Information

Since graphene was discovered in 2004,1 materials of the graphene family, which include two-dimensional (2D) graphene, one-dimensional (1D) graphene nanoribbons (GNRs), and zero-dimensional (0D) graphene quantum dots (GQDs), have caught much attention of scientists, from both experimental and theoretical points of view, because of their particular properties,2, 3 A zero-dimensional rectangular GQD is formed with four egdes and four seam regions at the corners when the length and width of graphene is reduced to a finite size. Recently, the successful fabrication of GQDs was reported.4 Quantum dots with electrons confined in three dimensions represent tantalizing objects for researchers.

Graphene is a zero-bandgap material; however, cutting the graphene sheet into small pieces (GNRs or GQDs), making defects or introducing chemical modification in graphene can induce a bandgap. Graphene oxide has been intensively studied recently owing to its fundamental properties and potential applications. The oxidation of graphene serves as an example for chemical modification of graphene, which is of great interest to tune the electronic, mechanical, and optoelectronic properties of graphene.5 GNRs have been reported as a promising material for applications of spintronic devices that is related to the half-metallic behavior of GNRs. Half metal, which has a metallic nature for electrons in one spin channel and an insulating or semiconducting nature in the other spin channel, can provide completely spin-resolved electric current. The half-metallic nature is related to the edge states of GNRs. The most studied edges, zigzag and armchair, have drastically different electronic properties.6 Zigzag GNRs (ZGNRs) with particular localized electronic states at each edge are semiconductors with nonzero energy gaps due to the existence of ferromagnetically ordered edge states at each zigzag edge, with an antiferromagnetic (AFM) arrangement of spins between two zigzag edges. The interaction between spins on opposite edges increases with decreasing width, so the total energy of a ZGNR with AFM arrangement across opposite edges is always lower than that of a ferromagnetic (FM) arrangement. However, armchair GNRs (AGNRs) are nonmagnetic. Zigzag edges can sustain edge surface states and resonances that are absent in the armchair case. Many researches have shown that the application of an external electric field across the ZGNRs results in lifting the spin degeneracy by widening the band gap for one spin channel while reducing the gap for the other spin channel.7 Energy-level shifts of opposite signs for the spatially separated spin-ordered edge states are induced by the applied electric fields, as a result, when the electric field is increased up to a certain point, ZGNRs turn into half metals, which makes them ideal materials for spin-dependent devices and spin injection.3f, 7c, 8 Structural and edge modification along edges is inclined to have a great influence on the properties of ZGNRs over AGNRs.9 It has been reported that edge oxidization could enhance the half-metallicity of ZGNRs by lowering the critical electric field needed to induce the half-metallic state.8c

Following the investigations of quasi-one-dimensional GNRs, much research has been reported on the electronic and magnetic properties of GQDs.6c,h, 10 GQDs present a spin-polarized ground state. The special property is related to edge states and chemical modification along zigzag edges. Rudberg et al.7a presented that 8-ZGNRs with finite length never show half-metallicity under the application of electric field by using B3LYP functional with nonlocal exchange interaction being considered, however, Kan et al.7c revisited the problem of the ZGNR electronic structure under electric field, they predicted that the half-metallicity in ZGNR can be achieved when an external electric field is applied across the ribbon at B3LYP level of theory. Kan et al. illustrated the difference is because that 8-ZGNR is limited to a finite length in Rudberg’s study, while in Kan’s study, the ZGNR with infinite length is investigated. Kan et al. believed that the finite size effect induces this difference. Recently, Hod et al.10c reported that half-metallic state of finite-sized GNR (GQD) can also appear under the influence of the electric field across the zigzag edges, which is different from the result reported by Rudberg et al., the different results of the half-metallicity for GNRs with finite width and length could be explained from the method used in the calculation. Hod et al. adopted a more accurate method, the screened exchange hybrid density functional due to Heyd, Scuseria, and Ernzerhof (HSE06),11 which has been tested in many materials and has been proved to accurately reproduce experimental bandgaps.12

In addition, Shemella et al.10b studied the energy gaps in zero-dimensional GQDs and reported finite size effects on the electronic structure of GQDs by using density functional theory (DFT). The results suggest that besides quantum confinement arising due to the width, finite-size effects emerge along the length of the GQDs and intensely modify the electronic states, particularly for those with zigzag-terminated edges whose length is confined. Quantum-confinement effects are present in a wide range of systems, in the quantum dots, the boundary conditions are quite complex due to the shape of the surface, atomic surface reconstructions and chemical passivations. Zheng et al.6c researched edge modification in GQDs by first-principles and showed that chemical modification of zigzag edges can significantly alter the electronic and magnetic properties of GQDs because a large proportion of the spin density is localized on the zigzag edges.

Graphene oxide contains a range of reactive oxygen-containing functional groups, such as hydroxyl, carboxyl, ketone, ether, and so on. The properties of graphene oxide depend on their structure and the number and position of the oxygen-containing groups.13 However, the stability of different spin configurations for various sized zero-dimensional (0D) GQDs with oxygen-containing groups are not clear, the effect of oxygen-containing groups on the AFM ground state stability and energy gap between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are also unknown, and even the field effect on the half-metallicity of edge-oxidized GQDs has not been discussed so far. An interesting question is whether the spin-polarized ground state and half-metallicity could be preserved in finite-sized zigzag edge-oxidized GQDs. It is our purpose in this paper to present a comprehensive and systematic analysis of electronic properties of zigzag edge-oxidized rectangular GQDs with different size. To clarify how the oxygen-containing groups and their density influence the electronic properties, we adopt first-principles to conduct our research. We discuss the stability and electronic properties of different types of GQDs with oxygen-containing groups. In addition, we apply an electric field to examine its influence on the half-metallic nature of the zigzag edge-oxidized GQDs. We elucidate the effect of edge oxidation on the stability and half-metallicity of finite-sized GQDs in detail.

Computational Details

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. Computational Details
  5. 2. Results and Discussion
  6. 3. Conclusions
  7. Acknowledgements
  8. Supporting Information

In this work, we studied a series of rectangular GQDs with oxygen-containing groups and we notated the dots with N×M convention, where N and M represents the number of rows and columns across the GQD width and length, respectively (see Figure 1). We considered a large set of GQDs with different width and length, different types and numbers of oxygen-containing groups on the zigzag edges. In the present work, we labeled the oxidized GQD to be N×M-xyz-2Z-Oxygen-containing groups GQD, xyz means the position of the oxygen-containing groups on the zigzag edge, 2Z means the substituted groups on both zigzag edges. In addition, oxygen-containing groups mean the type of groups substituted on the edge, including -OH, -COOH, and -COO. Different oxidized 8×6 GQDs are shown in Figures 1 b–i. The GQDs with oxygen-containing groups we considered constitute three subsets corresponding to three ribbon widths: 4×M, 6×M, and 8×M, where M=3, 4, …, and 7. All the calculations on the geometry optimizations and electronic properties of GQDs with oxygen-containing groups were performed based on first-principles DFT using the Gaussian 09 program package.14 We conducted spin-polarized ground-state calculations using the screened exchange hybrid functional HSE06,11 which has been tested on many materials and has been verified to accurately reproduce the experimental band gaps12 and the optical excitation energies in semiconducting and metallic single-walled carbon nanotubes (SWCNTs).15 In addition, the inclusion of short-range exact exchange in the HSE06 functional makes it suitable to deal with electronic localization effects16 that are known to be important in these types of materials.17 Furthermore, it is supported by the good agreement between predicted band gaps18 of narrow nanoribbons and measured values.19 It is important to relax the geometry of the finite-sized GQDs with oxygen-containing groups for each spin polarization to obtain a reliable ordering of different magnetization states. Therefore, all the geometry optimizations and electronic properties of the GQDs with oxygen-containing groups were implemented using the HSE06 and polarized 6-31G** Gaussian basis set.20 However, it was difficult to obtain an AFM state for some of the GQDs with oxygen-containing groups using the general method, so we adopted the fragment molecular orbital method to get the spin-polarized ground state, the calculation details are available in the Supporting Information (SI).

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Figure 1. a) Atomic structures of: a) an N × M GQD, where M and N are the number of columns and rows of atoms used to label the N x M dot, b) 8×6-16-2Z-OH GQD, c) 8×6-25-2Z-OH GQD, d) 8×6-135-2Z-OH GQD, e) 8×6-123456-2Z-OH GQD, f) 8×6-16-2Z-COOH GQD, g) 8×6-25-2Z-COOH GQD, h) 8×6-135-2Z-COOH GQD, and i) 8×6-123456-2Z-COO GQD.

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2. Results and Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. Computational Details
  5. 2. Results and Discussion
  6. 3. Conclusions
  7. Acknowledgements
  8. Supporting Information

2.1. Total Energy of Different Spin Configurations and Effect of Oxygen-Containing Groups on the AFM Stability and Energy Gap of GQDs

For the GQDs with oxygen-containing groups, we compare three different spin states including spin-polarized singlet state (ferromagnetically ordered spins at each edge but with anti-parallel spin orientations between the edges), spin-polarized triplet state (with parallel spin orientations at both edges), and closed-shell state, whose total energies are EAFM, EFM, and ENOM, respectively.

Table 1 demonstrates the energy differences between the AFM, FM, and nonmagnetic (NOM) states of GQDs with oxygen-containing groups. It shows that EAFM is the lowest energy among the three spin states, the energy difference between the AFM state and FM state is larger than 25 meV (we indicate kBT=25 meV with kB being Boltzmann’s constant at room temperature T=298 K) for most of the GQDs studied, which means that the AFM state is detectable at room temperature.17a The AFM state of 8×4 GQDs can be detected below room temperature (160 K). 8×5-12345-2Z-OH GQD presents an AFM state somewhat below room temperature. For the smaller 4×3 systems, the NOM state below room temperature is very close in energy to the AFM state. The depicted oxidized structures exhibit a spin-polarized ground state where the spin magnetizations on the opposite edges of GQDs are aligned anti-parallel. The isosurface spin densities of the AFM ground state of different oxygen-containing-group-decorated 8×6 GQDs are exhibited in Figure 2. The GQDs display an AFM ground state regardless of the type of oxygen-containing groups. The spin density for GQDs terminated by oxygen-containing groups mainly distributes on the edge atoms, as H termination, the oxygen-containing groups including -OH, -COOH and -COO compensate the dangling sp2 equation image orbital at each carbon edge site and have little contribution to the equation image orbitals of the edge states.

Table 1. HSE/6-31G** AFM ground state bandgaps Eg [eV] and energy differences [eV] between the spin-unpolarized singlet state (ENOM), spin-polarized triplet state (EFM), and spin-polarized singlet state (EAFM) of the studied GQDs with oxygen-containing groups.
GQDEgEFMEAFMENOMEAFMGQDEgEFMEAFMENOMEAFM
4×31.5000.4890.0038×4-1234-2Z-COO1.1130.0120.550
4×3-2-2Z-OH1.3880.4090.0078×51.4010.0460.771
4×3-2-2Z-COOH1.4300.4490.0058×5-24-2Z-OH1.1840.0460.696
4×3-123-2Z-OH1.2540.4140.0028×5-24-2Z-COOH1.2250.0450.722
4×41.5090.1460.2738×5-135-2Z-OH1.1980.0380.684
4×4-13-2Z-OH1.3630.1270.2558×5-135-2Z-COOH1.2300.0430.694
4×4-13-2Z-COOH1.3630.1290.2658×5-12345-2Z-OH0.9300.0220.569
4×4-1234-2Z-OH1.1960.0910.2578×61.0610.2040.930
4×4-1234-2Z-COO1.1780.0840.2818×6-16-2Z-OH1.0250.1920.880
6×31.3180.1240.2018×6-16-2Z-COOH0.9880.1940.853
6×3-2-2Z-OH1.2380.1050.2068×6-25-2Z-OH1.0100.2080.866
6×3-2-2Z-COOH1.2590.1160.1978×6-25-2Z-COOH1.0230.2010.877
6×3-123-2Z-OH1.1310.1050.1738×6-135-2Z-OH1.0000.1940.831
8×31.2450.0350.4038×6-135-2Z-COOH0.9810.1960.858
8×3-2-2Z-OH1.1800.0300.3968×6-123456-2Z-OH0.6770.1080.611
8×3-2-2Z-COOH1.1900.0330.3878×6-123456-2Z-COO0.7790.1630.681
8×3-123-2Z-OH1.0740.0300.3508×71.1110.5081.211
8×41.4080.0160.6848×7-147-2Z-OH1.0280.2011.097
8×4-13-2Z-OH1.2810.0140.6298×7-246-2Z-OH1.0200.1811.207
8×4-13-2Z-COOH1.2690.0140.6278×7-1357-2Z-OH1.0350.4781.082
8×4-1234-2Z-OH1.1490.0090.6628×7-1234567-2Z-OH0.6580.3280.913
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Figure 2. Isosurface spin densities of the AFM ground state of different oxygen-containing-group-substituted GQDs as obtained using the HSE06 functional and the 6-31G** basis set. Black: equation image spin; gray: equation image spin. The isovalue is 0.002 e Å−3.

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Just as the report10c from a qualitative analysis of the spin density maps, we find that the edge atoms can be divided into three subgroups as follows: atoms that distinctly belong to the zigzag edge, atoms that distinctly belong to the armchair edge, and those belonging to the seam region between the two types of edges, which are presented in Figure 2 a. As a rule, in rectangular GQDs, the carbon atoms distinctly belonging to the zigzag edge are spin-polarized. Comparatively, the seam-region edge atoms have a lower spin polarization, while those carbon atoms on the purely armchair edge are considerably less polarized. Oxidation schemes have little effect on the spin density map of GQDs, see Figures 2 b–h.

Our calculations show that 4×3 is the smallest size of oxidized GQDs to exhibit an AFM ground state, which is somewhat different from the results reported by Jiang et al.10a but similar to those obtained by Hod et al.10c for fully hydrogenated GQDs. Jiang et al. reported that 4×4 is the smallest size of GQD to exhibit an AFM ground state. We attribute these differences to the methods used. Jiang et al. adopted B3LYP, whereas in the present work, we choose HSE06, which is the same method that Hod et al. used. HSE06 has been successfully used in materials and has been shown to accurately reproduce experimental values.12 The inclusion of short-range exact exchange in the HSE06 functional makes it suitable to treat electronic localization effects that are very important in this type of materials.16, 17

It is interesting to find that the energetic ordering of the three spin states is EAFM<EFM<ENOM for GQDs larger than 4×3, which is consistent with the energetic ordering of infinite long ZGNRs. The stability ordering of the AFM, FM, and NOM states could be illustrated from the energy of the HOMO (EHOMO). The lower the value of EHOMO, the more stable the system is; for example, for 6×3 GQD, EHOMO is −4.244, −3.979, and −3.931 eV for the AFM, FM, and NOM states, respectively, which is in accordance with EAFM<EFM<ENOM. However, the energetic ordering of the three spin states is EAFM<ENOM<EFM for 4×3 GQDs. This is because 4×3 is the smallest size of GQDs to exhibit an AFM state. 4×3 GQDs present different properties compared to larger GQDs. Figure 3 displays the HOMO of different spin configurations for 4×3 and 6×3 GQDs. The energetic ordering of the three spin states of edge-oxidized GQDs is the same as that of GQDs with hydrogen-terminated edges.

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Figure 3. HOMOS of GQDs in the AFM, FM, and NOM states. The total energy (E) and EHOMO of GQDs in different spin states are also presented: a) 4×3 GQD, b) 6×3 GQD.

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In addition, different types and numbers of oxygen-containing groups change the total energy and energy gap between HOMO and LUMO. Oxidation lowers the total energy and energy gap of the GQDs. Table 1 gives the energy gaps of different GQDs. The calculations show that in the absence of an electric field, the energy gaps of carboxylated and hydroxylated GQDs are both lower than that of fully hydrogenated GQDs; for example, the energy gaps of 8×6, 8×6-135-2Z-OH, and 8×6-135-2Z-COOH GQD are 1.061, 1.000, and 0.981 eV, respectively. This is because the higher electron density of the oxygen-containing groups lifts the energy of occupied orbitals, and thus, the energy gaps of the GQDs are reduced.8a When we turn to study the concentration effects of hydroxyl groups, we find that the most stable structure corresponds to the fully hydroxylated GQDs, which is attributed to the hydrogen bonds between the nearest groups on the edge. The larger the number of the hydroxyl groups on the zigzag edges, the lower the total energy is. These conclusions are consistent with the results reported for edge-modified GNRs.8c

2.2. Effect of an Electric Field on the Electronic Properties of Finite-Sized GQDs with Oxygen-Containing Groups

Following the analysis above, oxidation schemes present an AFM ground state, and therefore, we expect edge-oxidized GQDs to behave as half metals under the influence of an electric field. To verify this assumption, in this part, we report the effect of applying an external electric field across the zigzag edge-oxidized GQDs, the electric-field direction is along the y axis, see Figure 1 a.

First, we discuss the effect of the electric field on the electronic properties of GQDs with different oxygen-containing groups at the zigzag edges. We mainly investigate 8×6 GQDs with different oxygen-containing groups including -OH, -COOH, and -COO. In Figure 4, we plot the spin-resolved band gap as a function of the field intensity for GQDs with oxygen-containing groups. When the electric field is applied, the spin-up energy gap (equation image spin gap) increases and the spin-down gap (equation image spin gap) decreases as the intensity of the electric field increases. The band-gap splitting increases with the field intensity up to a point where the system turns into a half-metallic state. From Figures 4 c and d, we see that 8×6-135-2Z-OH and 8×6-135-2Z-COOH GQDs exhibit a half-metallic state under a similar field intensity at about 0.35 V Angstrom−1 whereas fully oxidated GQDs 8×6-123456-2Z-OH and 8×6-123456-2Z-COO show a spin-selective semiconducting state under the electric field. This difference could be explained by the spin density of the oxidized GQDs under the application of an electric field, which can be seen in Figure 5. For a small field intensity, the spin-density configuration differs only slightly from the zero-field case. However, as the field increases, the spin density is drastically reduced. It can be seen from Figures 4 c and d that the equation image spin gap stops decreasing at a field of around 0.20 and 0.25 V Angstrom−1 for 8×6-123456-2Z-OH and 8×6-123456-2Z-COO GQDs. The discontinuity in the gaps of the two GQDs at around 0.25 V Angstrom−1 is clearly explained by the change to a qualitatively different electronic state, where the spin density is annihilated at part of each zigzag edge, as shown in the 0.25 and 0.35 V Angstrom−1 spin density maps. The spin density of the 8×6-123456-2Z-COO and 8×6-123456-2Z-OH GQDs at around 0.25 and 0.35 V Angstrom−1 is quite different from the case for partially hydroxylated 8×6-135-2Z-OH GQD and fully hydrogenated 8×6 GQD, which explains why the fully oxidized GQDs do not exhibit half-metallicity under an electric field. This discussion is just like that of the report by Rudberg et al.7a

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Figure 4. Spin-polarized HOMO–LUMO gap dependence on the intensity of an external in-plane electric field for GQDs with oxygen-containing groups, as calculated by the HSE06 functional. Fixed geometries of the relaxed structures in the absence of the external field at this level of theory were used.

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Figure 5. Spin-density map of the AFM ground state of 8×6 GQDs, terminated by different groups under cross zigzag edge electric fields of different intensities, namely, 0.00, 0.15, 0.25, and 0.35 V Angstrom−1, as labeled below the figures: a) 8×6 GQD, b) 8×6-135-2Z-OH GQD, c) 8×6-123456-2Z-OH GQD, and d) 8×6-123456-2Z-COO GQD. Black: equation image spin; gray: equation image spin. The isovalue is 0.002 e Å−3.

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Second, it is essential to investigate how the concentration (number) of oxygen-containing groups influences the electronic properties of GQDs under the electric field. In this section, we explore a series of GQDs with different numbers of oxygen-containing groups to elucidate the concentration effect. For 8×6 GQDs with hydroxyl groups, we compare three different concentrations, as shown in Figure 4 c. The results reveal that partially hydroxylated 8×6 GQDs with different concentrations of hydroxyl groups adopt a half-metallic state under almost the same electric-field intensities whereas 8×6-123456-2Z-OH GQDs behave as a spin-selective semiconductor with different energy gaps for both spin-up and spin-down electrons. Carboxyl groups show a similar behavior to hydroxyl groups. These results for 8×6 GQDs with hydroxyl and carboxyl groups are different from the conclusions for edge-oxidized 8-ZGNRs reported by Hod et al.,8c who found that when the zigzag edges of the ribbon are fully hydroxylated and carboxylated, the field intensity needed to switch the system to half-metallic is lower than that of partially hydroxylated GNRs. GNRs have a finite width but a periodic repeated unit of length, whereas in the case of GQDs with oxygen-containing groups, both the width and length are confined to a small size with boundary conditions. Thus, differences may result from the effects of the finite size of GQDs with oxygen-containing groups, where the electrons are confined to a small region of space. The electronic properties of GQDs with oxygen-containing groups are affected by the quantum confinement of the system. Additional confinement of the π electrons has a considerable influence on the electronic properties of the quantum dots.21 As a result, the spin density of 8×6-123456-2Z-OH and 8×6-123456-2Z-COO GQD is annihilated at part of each zigzag edge under the influence of the electric field and thus induces the disappearance of half-metallicity.

We have also studied a large set of GQDs with different lengths, including 8×M (M=4, 5, and 7) structures with different concentrations of hydroxyl or carboxyl groups at the zigzag edges. We found that 8×M (M=5 and 7) GQDs with oxygen-containing groups exhibit similar properties to 8×6 GQDs with oxygen-containing groups (see Figure 4). However, 8×4-1234-2Z-OH and 8×4-1234-2z-COO GQDs, whose zigzag edges are fully hydroxylated or carboxylated, present a half-metallic nature under almost the same field intensity as the partially hydroxylated, carboxylated, and fully hydrogenated 8×4 GQDs. This exceptional property may be due to the small size effect, as discussed by Shemella,10b who showed that a finite size effect emerges along the length of the ribbons. The different properties of fully oxidized GQDs and GNRs could also be explained by quantum-confinement and finite-size effects in GQDs.

From the discussion above, we summarize that for different oxygen-containing substituted GQDs, partially oxidized dots of the same size present a half-metallic state under almost the same electric-field intensity, whereas fully hydroxylated and carboxylated GQDs exhibit a spin-selective semiconducting state, except for fully oxidized 8×4 GQDs, which present a half-metallic state.

Moreover, we compare partially oxidized GQDs of different lengths with M=4, 5, 6, and 7, and the intensity of the electric field inducing the half metal increases with the length, from 0.20 to 0.40 V Angstrom−1, see Figure 4.

3. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. Computational Details
  5. 2. Results and Discussion
  6. 3. Conclusions
  7. Acknowledgements
  8. Supporting Information

In this work, we study the electronic and spintronic properties of a series of GQDs terminated by different oxidation groups by using first-principles calculations. We find that finite-sized GQDs with oxygen-containing groups possess a spin-polarized ground state. Oxidation of GQDs lowers the total energy and the HOMO–LUMO gap. The energetic ordering for the three spin states of GQDs is consistent with the ordering of the EHOMO of each spin state.

Moreover, we discuss the impact of the electric field on the electronic properties of different types of GQDs. Partially hydroxylated and carboxylated GQDs of the same size exhibit a half-metallic state under similar electric-field intensities. Fully oxidized GQDs, except for 8×4, present a spin-selective semiconducting state under an electric field. This is attributed to the different spin-density distributions, which are related to the joint action of size, quantum confinement, and oxygen-containing groups.

The field intensity needed to induce a half metallic state increases with the length of the partially oxidized GQDs, ranging from M=4 to 7. Quantum-confinement and finite-size effects are important in future nanospintronic and nonoelectronic applications. The specific interplay between size, quantum confinement, and oxygen-containing groups of edge oxidized GQDs under the application of an electric field needs to be further investigated.

Acknowledgements

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. Computational Details
  5. 2. Results and Discussion
  6. 3. Conclusions
  7. Acknowledgements
  8. Supporting Information

We greatly acknowledge the Natural Science Foundation of China (Grant 21075083) for supporting this work.

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. Computational Details
  5. 2. Results and Discussion
  6. 3. Conclusions
  7. Acknowledgements
  8. Supporting Information

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