Theoretical Design of Robust Ferromagnetism and Bipolar

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A Theoretical Design of Robust Ferromagnetism and Bipolar Semiconductivity in Graphene-Based Nanoroads Lixue Liu, Shudun Liu, Zhenyu Zhang, and Wenguang Zhu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b07036 • Publication Date (Web): 12 Oct 2017 Downloaded from http://pubs.acs.org on October 23, 2017

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The Journal of Physical Chemistry

A Theoretical Design of Robust Ferromagnetism and Bipolar Semiconductivity in Graphene-Based Nanoroads Lixue Liu†, Shudun Liu//, Zhenyu Zhang†,‡ , and Wenguang Zhu＊, †, ‡,§ †

International Center for Quantum Design of Functional Materials (ICQD), Hefei National Laboratory

for Physical Sciences at the Microscale (HFNL), University of Science and Technology of China, Hefei, Anhui 230026, China // ‡

Department of Physics and Astronomy, University of Louisville, Louisville, Kentucky 40292, USA

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

Technology of China, Hefei, Anhui 230026, China §

Key Laboratory of Strongly-Coupled Quantum Matter Physics, Chinese Academy of Sciences, School of Physical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China

＊

E-mail [email protected]

ABSTRACT The search for graphene-based materials for spintronics applications has intensified in recent years, and numerous designs have been proposed based on various modifications to pristine graphene. Despite the tremendous progresses made in the past, to find a design that can be realized in practice remains as a challenging task. Encouraged by recent experimental breakthroughs, here we propose a feasible scheme to realize graphene-based spin field-effect transistors. This new material consists a half-hydrogenated graphene nanoroad embedded in a fully-hydrogenated graphene sheet. Using first-principles density functional theory calculations, we demonstrate that such a design can convert non-magnetic pristine graphene into a bipolar ferromagnetic semiconductor. More importantly, as a result of areal magnetization enabled by half-hydrogenation, the overall magnetism of such a nanoroad is very robust against a variation of either its width or orientation. We also propose a simple design of an all-electric controlled device based on the new material for generation and regulation of a fully spin-polarized electric current.

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1. INTRODUCTION The key to successful development of spintronic devices is that the spin degrees of freedom of electrons can be utilized in a controllable and convenient fashion. To this end, the search of new materials, in particular, two-dimensional materials with magnetic properties, that provide us such a capability has intensified in recent years.1,2 Among various two-dimensional materials, graphene has been identified as an ideal candidate for spintronics due to its long mean free path for spin transport as a result of its intrinsically weak spin-orbit coupling.3–6 In addition, graphene has many other superior properties for spintronics such as high carrier mobility and high thermal conductivity.7–11 However, pristine graphene is by itself intrinsically nonmagnetic, so certain modifications have to be made before it can be applied for spintronics. In the last decade, through either chemical or structural modifications, many attempts have been made to search for graphene-based materials that are magnetic with spin-polarized electronic states.3,12–17One notable example of such modifications is the construction of the socalled graphene nanoribbons.18–27 In a seminal work by Son et al.,18 it was found that graphene nanoribbons with zigzag edges can be made half-metallic through an application of a transverse external electric field across the nanoribbons. The ground state of a zigzag graphene nanoribbon itself is actually antiferromagnetic with opposite spin polarization at different edges, and the spins along each edge are ferromagnetically coupled. This antiferromagnetic ground state is consistent with a well-known theorem for spins of a bipartite lattice.28 Such a zigzag graphene nanoribbon becomes a half metal as a result of a relative shift of the localized and spin-polarized energy bands of the two edges, when a transverse electric field is applied.18 Although the halfmetallicity of such a graphene nanoribbon makes its application for spintronics possible in theory, the strict requirement for the nanoribbon with exact zigzag edges poses a daunting task in practice,29 as a theoretical study shows that the spin-polarized edge states could be easily suppressed by even a modest amount of impurities, structural defects at the edges.30,31 Since the work by Son et al.,18 magnetic properties of many other nanosized graphene systems32 (nanoroads,33 nanoholes,34 nanoislands,35 nanoflakes,36,37 etc.) have been studied theoretically. However, the overall magnetism of all these systems still critically depends on their edge states, which once again make it vulnerable to modest edge defects or chemical contamination, and so far none of these proposals has been successfully realized experimentally.


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It is thus clear that to build a robust magnetic graphene-based material for spintronics, it is highly desirable to find a way to reduce the dependence of its magnetism on the edge states. According to Lieb’s theorem for the ground state of the Hubbard model in bipartite lattices,28 the total spin of the system equals to one half of the difference between the numbers of sites in the two sublattices. By all accounts, Lieb’s theorem appears to be applicable to graphene, whose honeycomb structure consists of two triangular interpenetrating sublattices, and as a result, whose overall magnetism can only arise from an imbalance of the numbers of carbon atoms at the two sublattices, which inevitably leads to a strong dependence of the overall magnetism of a pristine graphene system on its edges. It is evident that to build a robust magnetic system using a graphene-based material, one needs to modify the graphene as a whole substantially. Halfhydrogenated graphene is such an example15, in which only the carbon atoms in one of the graphene sublattices are hydrogenated from one side of the graphene layer. This strict requirement again makes the sample fabrication extremely challenging, if the fabrication starts from a pure graphene layer then followed by a self-organized hydrogenation process. Therefore, there has been no successful realization of half-hydrogenated graphene reported. In this work, we propose a new graphene-based material that is made of fullyhydrogenated graphene with a narrow stripe of hydrogen atoms on one side of the graphene removed, as shown in Figure 1. The essential part of our system is a road-like region, free of hydrogen on its top surface and hydrogenated underneath, referred hereafter to as “halfhydrogenated graphene nanoroad” (HHGNR). There are reasons to believe that such a system could be easier to be realized in practice, in light of two recent experimental breakthroughs: in one case, fully-hydrogenated graphene38 was successfully fabricated, with hydrogen atoms on the two different graphene sublattices sitting on the two different sides of graphene;39-47 in another case, a nanoroad-like structure was carved out of a graphene oxide through catalytic scanning probe lithography.48 We will demonstrate through first-principles density function theory calculations that HHGNR is a bipolar ferromagnetic semiconductor, whose magnetism is very robust: independent of its width and orientation, owing to an areal effect. We will also present a design of an all-electric controlled approach to examine the predicted bipolar ferromagnetic semiconducting nature of HHGNR.


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2. COMPUTATIONAL METHODS Our spin-polarized density functional theory (DFT) calculations were performed using the Vienna ab initio simulation package (VASP)49 with projector-augmented-wave potentials

50,51

and the Perdew-Burke-Ernzerhof version of generalized gradient approximation for exchangecorrelation functional.52 The default plane-wave cut-off energy of 400 eV was used consistently in all calculations. The system was modeled by a graphene sheet containing a stripe of halfhydrogenated region and a stripe of fully-hydrogenated region within a supercell, as illustrated in Figure 1b. The width of the fully-hydrogenated region was set to be more than 12 Å to avoid the spurious interactions between the half-hydrogenated region and its in-plane images due to the periodic condition, and likewise a vacuum space of over 15 Å was added to separate the graphene sheet with its images in the out-of-plane direction. The Monkhorst-Pack scheme was used for Brillouin zone sampling.53 The structures including the supercell volumes were fully relaxed without any symmetry constraints until the force on each atom was smaller than 0.01 eV/Å. 3. RESULTS AND DISCUSSION 3.1. The spin-polarized nature with width- and orientation- independence in the HHGNRs. We first investigated the electronic structures of zigzag-edged HHGNRs and their dependence on the widths of the HHGNRs. Figure 2a-f exhibits the calculated band structures for different widths ranging from 1 to 6 units as defined in Figure 1d. It can be seen clearly that in each case the energy bands near the Fermi level are fully spin-polarized with a persistent gap separating the conduction band of one spin and the valence band of the opposite spin, making the whole system a bipolar ferromagnetic semiconductor whose magnetic moment equals to the number of the dangling bonds of the unhydrogenated carbon atoms times µB, the Bohr magneton. For zigzag-edged HHGNRs, the number of the dangling bonds per unit cell equals to the width number N. With the increase of the width from N=1 to 6, the band gap narrows from 1.46 eV to 0.78 eV, and the rate of change reduces dramatically beyond N larger than 3, as shown in Figure 2g. As the width further increases, the system should approach the case of an infinite halfhydrogenated graphene, which is also a bipolar ferromagnetic semiconductor with a band gap of 0.46 eV according to the previously DFT calculations.15 But we note that there remains a substantial difference between the gap of an infinite sheet and that of our widest HHGNR. It is


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important to point out that there is a significant structural bending in the HHGNR region, as shown in Figure 1c. Such a bending is caused by asymmetrical hydrogenation occurs for all HHGNRs, as reported previously,54,55 and the degree of bending increases with the width of the HHGNR, which may explain the difference between the gaps. Overall, one can conclude that the bipolar ferromagnetic nature of a zigzag-edged HHGNR is very robust against variation of its width. To evaluate the dependence of the transport performance of the HHGNR on the width, we estimate the carrier effective masses at the top of valence bands (VBM) and the bottom of conduction bands (CBM) of the zigzag-edged HHGNRs with different widths, following the డమ ா

standard definition of the effective mass as ݉∗ = ℏଶ ( మ )ିଵ . The results, as summarized in డ௞ Table 1, indicate a clear trend that the carrier effective masses at both VBM and CBM monotonically decreases as the width of the HHGNR increases. A critical question is how the magnetism of a HHGNR depends on its orientation. We studied HHGNRs of five different representative orientations of similar width. Figure 3 shows their initial configurations and the corresponding energy bands. It is clear that in all cases the energy bands near the Fermi level remain fully spin-polarized and the gap is practically independent of the orientation and all five HHGNRs are bipolar ferromagnetic semiconductors. The total magnetic moment of an HHGNR again equals to the total number of the unhydrogenated carbon atoms times µB, the same as the above-discussed zigzag edged cases. This orientational independence of the magnetism of HHGNRs further increases their robustness, and marks a critically important improvement over that of previously proposed graphene nanoribbons whose magnetic properties are critically determined by the orientation. The results of the calculated carrier effective masses for differently orientated HHGNRs, as summarized in Table 2, do not exhibit a clear trend, but there exists an optimal orientation that gives rise to the smallest effective mass. Together with the width dependence results, these analyses provide a guideline to optimize the electronic transport performance by reducing the carrier effective mass via either increasing the width or choosing the optimal orientation of the HHGNR. To understand the robustness of the magnetism of the HHGNRs, we need to go back and exam the effects of hydrogenation on graphene. While graphene itself is a gapless non-magnetic


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semiconductor, fully-hydrogenated graphene is a non-magnetic semiconductor with a large gap as a result of saturation and localization of all the dangling bonds of carbon atoms.38 Halfhydrogenated graphene, on the other hand, is a ferromagnetic semiconductor with a small band gap.15 Recall that in case of half-hydrogenated graphene, all the carbon atoms exclusively on one of the two sublattices are hydrogenated, leaving those on the other sublattice completely unhydrogenated. There is a localized and unpaired electron at each of an unhydrogenated carbon atom, resulting in a local magnetic moment at that site.17 Since all the unhydrogenated sites belong to the same sublattice, those local magnetic moments are ferromagnetically coupled, which makes half-hydrogenated graphene a ferromagnetic semiconductor. As an example, Figure 2h and 2i illustrate the charge density of fully spin-polarized conduction bands and valence bands of a zigzag-edged HHGNR with a width of N=5, respectively, which clearly indicate that the spin-polarized states of the HHGNR are mainly attributed to all the unhydrogenated carbon atoms in the HHGNR region and the edges between the half- and the fully-hydrogenated regions do not create any new electronic edges states. It is noteworthy to point out that since halfhydrogenation breaks the symmetry of the two sublattices of graphene, the limitations on the overall magnetism of graphene imposed by Lieb’s theorem28 no longer apply, and this is the key to the existence of the robust ferromagnetism in HHGNRs. In a word, the contribution to ferromagnetism of a HHGNR comes from the whole area (area effect), in sharp contrast to that of other proposed designs of graphene-based magnetic materials in which the magnetic moments are localized at the edges (edge effect), which gives a critically important advantage to HHGNRs for spintronics applications. 3.2. The stability of HHGNRs. We also studied the stability of the HHGNRs and found that the HHGNRs, once realized, are quite stable. The stability of a hydrogenated graphene has been studied recently, and there has been a debate about the difficulty of forming a halfhydrogenated graphene sheet in the first place.15,56 The system we proposed here, however, is based on a fully-hydrogenated sheet, which has already been fabricated experimentally.39-47 So our focus here is on the stability of an HHGNR once it is carved out of a fully-hydrogenated graphene sheet. We examined energy barriers for various desorption and diffusion processes. For desorption, we found desorption of two hydrogens, both located at the edge of an HHGNR to be the easiest, with a barrier of ~2.8 eV. Barriers for other desorption processes are all substantially higher. For diffusion, we found the diffusion barrier for a hydrogen atom at the edge to a


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neighboring unhydrogenated site is found to be ~2.0 eV. The barriers for these processes are so high that they are very unlikely to occur at room temperature. We believe that the stability of an HHGNR is aided by its surrounding fully-hydrogenated regions which also help to maintain the overall flatness of the sheet. Furthermore, the significant bending of an HHGNR allows it to evolve into a lower energy state, and leads naturally to a more stable structure. Thus we believe that an HHGNR carved out of a fully-hydrogenated graphene sheet can be stable at room temperature. 3.3. Spintronic devices based on the HHGNRs. As a bipolar ferromagnetic semiconductor, an HHGNR can potentially be used, for example, to generate a fully spinpolarized electric current with all-electric controllability. Since the top of the valence bands and the bottom of the conduction bands in a bipolar ferromagnetic semiconductor are oppositely spin-polarized, a fully spin-polarized electric current can be naturally generated through tuning the Fermi level into either the valence bands or the conduction bands with a gate voltage.57 We designed, as a proof of principle, a simple HHGNR-based device that may function as a spin field-effect transistor. As sketched in Figure 4a, the device consists a source and a drain electrode at the two ends of the HHGNR with two top gates placed side by side along the HHGNR, and the gates can be independently controlled to regulate spins of the electric current. When both gates lift or lower the Fermi level, a current with a single spin component can pass through the device, as illustrated in Figure 4b and c; if one gate lifts the Fermi level, while the other gate lowers it, no current can pass through the device (Figure 4d). As a result, a spin current can be manipulated electrically. This simple device may serve multiple purposes, such as generating a spin-polarized current and acting as a logic gate. It also can be conveniently used to experimentally verify the bipolar ferromagnetic semiconducting nature of an HHGNR. 4. DISCUSSION Finally, we would like to discuss some potential challenges in practical fabrication of HHGNR-based spintronic devices such as the one discussed above. Firstly, to carve out an HHGNR from a fully-hydrogenated graphene sheet, it needs to be done on a single domain to ensure its bipolar magnetism. In case of multiple domains, the size of such a domain needs to be large enough for construction of all the necessary parts (gates and electrodes) of a device. Fortunately, because of the robustness of the magnetism of an HHGNR, there is a considerable


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tolerance on the precision of the carving itself: the variation of either the width or the orientation along the length of an HHGNR will not change its bipolar ferromagnetic semiconducting nature. Secondly, it is important that an application of gates does not lead to saturation of the dangling bonds, at least not completely, as the magnetism mainly arises from those bonds. This can be achieved, for example, either by first covering the HHGNR with a layer of Boron Nitride (BN) or similar materials to protect the dangling bonds, or by applying the gates on the backside of the HHGNR. 5. CONCLUSIONS In this work, we have proposed HHGNR as an experimentally more feasible strategy to achieve graphene-based magnetic material for spintronics. We have demonstrated that, based on firstprinciples density functional theory calculations, the electronic band structures of an HHGNR are fully spin-polarized, and its bipolar ferromagnetic semiconducting nature is very robust against a variation of either its width or orientation as a result of areal magnetization, in sharp contrast to most of previously proposed designs of graphene-based magnetic materials which rely on the edge effect and are vulnerable to chemical contamination or structural defects. We have also proposed a design of an HHGNR-based device to examine the predicted bipolar ferromagnetic semiconducting nature through an all-electric controlled approach. ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant Nos. 11374273 and 11034006) and the Fundamental Research Funds for the Central Universities (Grant Nos. WK2090050027, WK2060190027, WK2340000063). Computational support was provided by National Supercomputing Center in Tianjin and NERSC of US Department of Energy.


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(41) Li, L.; Qin, R.; Li, H.; Yu, L.; Liu, Q.; Luo, G.; Gao, Z.; Lu, J. Functionalized Graphene for High-Performance Two-Dimensional Spintronics Devices. ACS Nano 2011, 5, 2601–2610. (42) Eng, A. Y. S.; Poh, H. L.; Šaněk, F.; Maryško, M.; Matějková, S.; Sofer, Z.; Pumera, M. Searching for Magnetism in Hydrogenated Graphene: Using Highly Hydrogenated Graphene Prepared via Birch Reduction of Graphite Oxides. ACS Nano 2013, 7, 5930–5939. (43) Smith, D.; Howie, R. T.; Crowe, I. F.; Simionescu, C. L.; Muryn, C.; Vishnyakov, V.; Novoselov, K. S.; Kim, Y.-J.; Halsall, M. P.; Gregoryanz, E.; et al. Hydrogenation of Graphene by Reaction at High Pressure and High Temperature. ACS Nano 2015, 9, 8279–8283. (44) Abdelkader, A. M.; Patten, H. V.; Li, Z.; Chen, Y.; Kinloch, I. A. Electrochemical Exfoliation of Graphite in Quaternary Ammonium-Based Deep Eutectic Solvents: A Route for the Mass Production of Graphane. Nanoscale 2015, 7, 11386–11392. (45) Lin, C.; Feng, Y.; Xiao, Y.; Dürr, M.; Huang, X.; Xu, X.; Zhao, R.; Wang, E.; Li, X.-Z.; Hu, Z. Direct Observation of Ordered Configurations of Hydrogen Adatoms on Graphene. Nano Lett. 2015, 15, 903–908. (46) Yang, Y.; Li, Y.; Huang, Z.; Huang, X. (C1.04H)n: A Nearly Perfect Pure Graphane. Carbon 2016, 107, 154–161. (47) Schäfer, R. A.; Dasler, D.; Mundloch, U.; Hauke, F.; Hirsch, A. Basic Insights into Tunable Graphene Hydrogenation. J. Am. Chem. Soc. 2016, 138, 1647–1652. (48) Zhang, K.; Fu, Q.; Pan, N.; Yu, X.; Liu, J.; Luo, Y.; Wang, X.; Yang, J.; Hou, J. G. Direct Writing of Electronic Devices on Graphene Oxide by Catalytic Scanning Probe Lithography. Nat. Commun. 2012, 3, 1194. (49) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169–11186. (50) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953–17979. (51) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758–1775. (52) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. (53) Monkhorst, H. J.; Pack, J. D. Special Points for Brillonin-Zone Integrations. Phys. Rev. B 1976, 13, 5188–5192. (54) Yu, D.; Liu, F. Synthesis of Carbon Nanotubes by Rolling up Patterned Graphene


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Nanoribbons Using Selective Atomic Adsorption. Nano Lett. 2007, 7, 3046–3050. (55) Li, M.; Wang, L.; Yu, N.; Sun, X.; Hou, T.; Li, Y. Structural Stability and Band Gap Tunability of Single-Side Hydrogenated Graphene from First-Principles Calculations. J. Mater. Chem. C 2015, 3, 3645–3649. (56) Šljivančanin, Ž.; Balog, R.; Hornekær, L. Magnetism in Graphene Induced by Hydrogen Adsorbates. Chem. Phys. Lett. 2012, 541, 70–74. (57) Li, X.; Wu, X.; Li, Z.; Yang, J.; Hou, J. G. Bipolar Magnetic Semiconductors: A New Class of Spintronics Materials. Nanoscale 2012, 4, 5680–5685.


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FIGURE CAPTIONS Figure 1. (a) Side view of a fully hydrogenated graphene sheet. (b) Side view of a HHGNR carved out of a fully hydrogenated graphene sheet. (c) Side view of a fully relaxed zigzag-edged HHGNR (N=5). Note there is a substantial bending in the HHGNR region. (d) Top view of a zigzag-edged HHGNR. The width of a zigzag-edged HHGNR is defined as illustrated in (d). Figure 2. (a)–(f) Spin-polarized band structures of zigzag-edged HHGNRs with the width N ranging from 1 to 6, respectively. The red and blue colors represent the bands of the two different spin components. (g) The width dependence of the band gap. Isosurfaces of the charge density of fully spin-polarized conduction bands (h) and valence bands (i) of a zigzag-edged HHGNR

with a width of N=5. Red, yellow, blue balls represent C atoms at A/B sublattice and H atoms, respectively. Figure 3. (a)–(e) Top views (top panels) and calculated band structures (bottom panels) of five HHGNRs in different orientations, respectively. The vertical dashed lines in the structures highlight the boundaries of the HHGNRs. The red and blue colors in the band structure plots represent the bands of the two different spin components. Figure 4. (a) Schematic illustration of a proposed device based on a HHGNR to verify its predicted bipolar ferromagnetic semiconductor nature. (b)–(d) Illustrations of three possible scenario of the density of states of the system tuned by the two top gates. The green dashed line in each panel indicates the position of the Fermi level of the system.


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Table 1. Calculated carrier effective masses (m*) of ziggag-edged HHGNRs (unit in the free electron mass m0) Width N

1

2

3

4

m* at VBM

2.30

1.73

1.22 1.11

0.97 1.08

m* at CBM

1.73

1.49

1.23 1.23

1.20 1.18

Table 1. Liu et al.


5

6


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Page 16 of 21

Table 2. Calculated carrier effective masses (m*) of differently orientated HHGNRs (unit in the free electron mass m0) Orientation

(1,1)

(1,2)

(1,3)

(2,3)

(1,4)

m* at VBM

2.16

3.09

2.05

2.51

3.28

m* at CBM

1.35

2.09

1.72

1.31

1.83

Table 2. Liu et al.


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(a)

(b)

(c)

(d)

N = 1

2 CA

3

4 CB

5 H

Figure 1. Liu et al.



Energy (eV)

(a)

N=1

(b)

N=2

(c)

N=3

(d)

N=4

(e)

33

3

3

3

3

22

2

2

2

2

11

1

1

1

1

00

0

0

0

0

-1−1

−1

−1

−1

−1

−2 -2

−2

−2

−2

−2

−3 -3

−3

0

−3

π 0

π 0

−3

π 0

−3

π 0

N=5

π

k(1/a) (f)

N=6

(g)

33

1.6

22

1.4

11

Band gap (eV)

Energy (eV)

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Page 18 of 21

00 -1−1

1.0 0.8 0.6

−2 -2

−3 -3

1.2

0

π

0.4

1

k(1/a)

2

3

4

5

6

Width number

(h) Fully spin-polarized valence bands

(i) Fully spin-polarized conduction bands



Page 19 of 21

(a) (1,1)

Energy (eV)

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(b) (1,2)

(c) (1,3)

(d) (2,3)

(e) (1,4)

33

3

3

3

3

22

2

2

2

2

11

1

1

1

1

00

0

0

0

0

−1 -1

−1

−1

−1

−1

−2 -2

−2

−2

−2

−2

−3 -3

0

π

−3

0

π

−3

0

π

−3

0

k(1/a)



π

−3

0

π


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Page 20 of 21

(a)

Top Gate A

Source

(b) Gate A

Gate B

Top Gate B

(c) Gate A

Gate B

Drain

(d) Gate A

Gate B

EF EF EF

Spin-up current

Spin-down current



No current

Page 21 of 21

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Table of Contents Graphic

EF

DOS


Theoretical Design of Robust Ferromagnetism and Bipolar

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