11 Original Research Article Spin thermoelectric effects of new-style one-dimensional carbon-based nanomaterials Yushen Liu1*, Jinfu Feng1, Xuefeng Wang2 1 School of Physics and Electronic Engineering, Changshu Institute of Technology, Changshu 215500, China. E-mail: ysliu@cslg.edu.cn 2 College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, China ABSTRACT Based on first-principles methods, the authors of this paper investigate spin thermoelectric effects of one-dimen- sional spin-based devices consisting of zigzag-edged graphene nanoribbons (ZGNRs), carbon chains and graphene nanoflake. It is found that the spin-down transmission function is suppressed to zero, while the spin-up transmission function is about 0.25. Therefore, an ideal half-metallic property is achieved. In addition, the phonon thermal conduc- tance is obviously smaller than the electronic thermal conductance. Meantime, the spin Seebeck effects are obviously enhanced at the low-temperature regime (about 80 K), resulting in the fact that spin thermoelectric figure of merit can reach about 40. Moreover, the spin thermoelectric figure of merit is always larger than the corresponding charge thermo- electric figure of merit. Therefore, the study shows that they can be used to prepare the ideal thermospin devices. Keywords: Graphene Nanoribbons; Carbon Chains; Graphene Nanoflake; Spin Seebeck Coefficients; Thermoelectric Figure of Merit Characterization and Application of Nanomaterials (2021) Volume 4 Issue 1 doi:10.24294/can.v4i1.1323 ARTICLE INFO Received: 15 November 2020 Accepted: 8 January 2021 Available online: 14 January 2021 COPYRIGHT Copyright © 2021 Yushen Liu, et al. EnPress Publisher LLC. This work is licensed under the Creative Commons Attribution- NonCommercial 4.0 International License (CC BY-NC 4.0). https://creativecommons.org/licenses/by- nc/4.0/ 1. Introduction Carbon is one of the elements widely distributed in nature. As a tetravalent non-metallic element, it can form covalent bonds with met- als and non-metals and combine into a variety of carbon-based nano- materials. Graphene, as a two-dimensional allotrope of carbon, has been widely studied because of its unique electrical properties. Review- ing its development history, it is found that it has attracted early atten- tion in theory, but the extensive research on its properties began with Geim and Novoselov, who obtained nearly perfect monolayer and free state graphene by simple mechanical method for the first time[1]. From the atomic level, graphene is composed of sp2 hybrid carbon atoms. It is also an aromatic compound with a large π electron conjugate system. The special energy band structure leads to a semiconductor with zero energy gap. Unlike traditional semiconductor materials, graphene fol- lows Dirac equation rather than Schrodinger equation. The migration rate of carriers in the conjugate system is very high, even close to the speed of light, making graphene one of the materials with the lowest resistivity at present. Although graphene has very unique electrical properties, it cannot be directly used in logic devices due to the energy band structure of zero energy gap. In order to open the energy gap, a common method is 12 to shear two-dimensional graphene into one-dimen- sional nano band structure and introduce quantum confined domain effect and boundary effect. When the width is less than 10 nm, graphene nanoribbons will open the energy gap. The preparation methods of graphene nanoribbons can be divided into two kinds: one is the top-down synthesis method. For example, carbon nanotubes can be cut by physical or chemical methods using carbon nanotubes as basic raw materials. The other is the bottom-up synthesis method, that is, the nanoribbon structure is synthe- sized from small molecular raw materials. According to the boundary structure characteristics of the rib- bons, graphene nanoribbons can be divided into two types: armchair and zigzag. Armchair nanoribbons (AGNRS) show non-magnetic semiconductor be- havior, and the band gap decreases with the gradual increase of width[2]. Zigzag nanoribbons (ZGNRs) have spin-polarized boundary states due to the pres- ence of non-bonding electrons in boundary carbon atoms. Theoretical study shows that the ground state of zigzag nanoribbons (ZGNRs) is that the boundary spin has antiferromagnetic order, that is, the direc- tions of different boundary spins are opposite, but on the same side, the boundary spins show ferromag- netic arrangement. With a suitable applied magnet- ic field, we can realize the ferromagnetic order of different boundary spins[3]. Regardless of whether different boundary carbon atoms show ferromagnetic order or antiferromagnetic order, the density of states at the Fermi plane is spin degenerate, which limits their application in spintronics. However, using a transverse electric field, we can make ZGNRs realize semi-metallic property[4]. Here, the semi-metallic property refers to the fact that the Fermi surface shows an insulating state for one spin band structure and a metallic state for the other. In addition, the magnetic property and transport property of ZGNRs are also affected by chemical element doping or de- fect[5–7]. Interestingly, some studies show that a single spin negative differential resistance is found in the boundary doped ZGNRs[5]. In addition to voltage driving electrons or holes in materials to move at a certain direction, tem- perature difference can also drive electrons. More electrons or holes are often accumulated at the high and low temperature ends, so the voltage caused by temperature difference will appear in this material. This phenomenon is called Seebeck effect. Recently, with the progress of spin detection technology, K. Uchida, et al. firstly observed spin voltage caused by temperature difference in metal magnets, which is called spin Seebeck effect[8]. This pioneering exper- iment inspired people to theoretically study spin-re- lated thermoelectric effects in various systems[9–21]. Recently, we have obtained high spin polarizability and large single spin Seebeck effect at the Fermi plane by doping ferromagnetic ZGNRs with bound- ary non-magnetic elements[16]. At present, a stable carbon atom chain (CAC) can be synthesized from graphene by electron irradiation technology using high-resolution transmission electron microscope[22]. Shen, et al. found that the channel transport property of CACs does not depend on structural deformation, structural defects and hydrogen adsorption[23]. Car- bon-based nanostructures exhibit perfect spin filter- ing effect and giant magnetoresistance under near zero bias. Recently, Dong, et al. have studied the transport property of zigzag graphene nanoribbons connected with CACs[24]. It is found that the electron transport near the Fermi level can be changed by adjusting the position and the number of atoms in CACs. Fano resonance effect is an interference effect existing between the local state and the extended state. It was first found in the inelastic scattering of electrons in helium. In 2002, Kobayashi, et al. found that the adjustable Fano effect was observed in the Aharonov-Bohm ring embedded in quantum dots[25]. Two quantum dots can be coupled into an artificial molecule, and then the electrons will be shared by the two quantum dots. When the electron energy is close to Fano linear system, the Seebeck effect is significantly strengthened[26]. In this paper, the spin thermoelectric property of one-dimensional spin quantum devices composed of graphene nanoribbons, carbon chains and graphene nanosheets was studied. The first principle calcula- tion shows that the spin-down transfer function at the Fermi face is suppressed to almost zero, how- ever, the spin-up transfer function is close to 0.25. 13 Therefore, we got distinct semimetal property. In addition, the phonon partial thermal conductivity in the low-temperature region is significantly smaller than the corresponding electron partial conductance. However, in the low temperature region (near 80 K), the spin Seebeck coefficient is significantly strength- ened, resulting in the charge and spin thermoelectric quality factor close to 40. Moreover, in the whole temperature range (0 < T ≤ 400 K), the spin thermo- electric quality factor is always greater than the cor- responding charge thermoelectric quality factor, and becomes more obvious in the room temperature re- gion. Therefore, this one-dimensional carbon-based nanoribbon can be designed as an ideal spin thermo- electric device. 2. Model establishment In this paper, a one-dimensional nano double probe system as shown in Figure 1(a) was designed. The left electrode and the right electrode are com- posed of serrated graphene nanoribbons, and the boundary carbon atoms are saturated with hydrogen atoms. The central scattering region is connected by a graphene nano sheet to a zigzag graphene nanorib- bon through two carbon atom chains. The width of the graphene nanoribbon is represented by the num- ber of carbon atoms perpendicular to the transport direction. In this paper, the width is 6. Figure 1. Thermal spin quantum double probe model and corre- sponding spin density. All numerical calculations are completed based on the software package Atomistix Toolkit (ATK) of non-equilibrium Green’s function and density func- tional theory[27–28]. The system optimization adopts Newton optimization method; the exchange correla- tion function adopts generalized gradient approx- imation (GGA), and the basis vector adopts DZP (Double-Zeta-Polarized). The size of the reduced Brillouin zone is set to (1, 1, 100). In order to avoid the interaction between images, the vacuum layer is taken as 15 Å and the truncation energy is taken as 150 Ry. Using ATK software, the transmission coeffi- cient of spin resolvable electrons with energy of E is: (1) Here, ΓL/Rσ(E) is the linewidth function of the coupling between the central scattering region and the left/right electrode; σ is the spin index and E is the energy. is the delayed and advanced Green’s functions of the center scattering region. It can be determined by the equations and . I is the identity matrix. H is the Hamilto- nian of the central scattering region. The spin polarizability at the Fermi plane is de- fined as: (2) In order to study the spin thermoelectric effect, we give the expression of spin-dependent Seebeck coefficient in the linear region: (3) The thermal conductivity of the electronic part can be written as: Here, n = 0, 1, 2. fL(R) is the Fermi Dirac distribution func- tion. Spin Seebeck coefficient is expressed as Ss = (S↑–S↓)/2, and the corresponding charge Seebeck co- efficient is Sc = (S↑ + S↓)/2 [14]. Charge (spin) thermoelectric quality factors are obtained from the following equation: (4) Ge(S) is the corresponding charge and spin con- 14 ductance, which can be obtained by the following equation: (5) The phonon partial heat guide in formula (4) is available in the ATK2013 beta. 3. Results and discussion Figure 1(b) shows that ZGNR still has bound- ary spin state in the buffer region, and the ferromag- netic order is maintained at the three boundaries of graphene nanosheets, that is, the spins of boundary carbon atoms are arranged in parallel. In Figure 2(b), we draw the variation trend of spin resolvable transfer function with electron energy, and find a wide energy region near the Fermi plane (for ex- ample: –0.25 eV < E < 0.1 eV). The spin-up trans- fer function remains limited, while the spin-down transfer function is suppressed to zero. Therefore, this device shows obvious semi-metallic behavior, and the spin polarizability satisfies ζ = 1. In order to reveal the physical reason behind it, we draw the spatial distribution of spin dependent local density of states at the Fermi surface in Figures 2(c) and (d). Obviously, the spin-up local density of states is distributed in the whole central scattering region domain, including ZGNR, graphene nanosheets and carbon chains. However, the spin-down local density of states is only distributed in the ZGNR in the mid- dle scattering region, and does not appear on carbon chains and graphene nanosheets. This result further confirmed the semi-metallic property at the Fermi plane. We also found that the spin-up Fano type tun- neling spectrum appears in the –0.2 eV region below the Fermi plane, but the spin-down Fano type tunnel- ing spectrum appears at 0.1 eV on the Fermi plane. The corresponding trend of density of state with energy shows that these Fano type tunneling spectra come from the local state in the energy region (Fig- ure 2(a)). Fano resonance is formed when these lo- cal states and surrounding electronic states undergo quantum interference effect. Figure 2. The spin-dependent transport property. (a) and (b) rep- resent the variation trend of state density and transport function with the electron energy respectively, and the dashed line rep- resents the position of the Fermi plane, letting the energy of the Fermi surface be zero. (c) and (d) indicate the local spin-up and spin-down density of states at the Fermi surface, respectively. Fano resonance causes the transfer function to change dramatically with the electron energy, which is bound to strengthen the thermoelectric effect. Compared with other energy points, the thermoelec- tric performance at the Fermi surface will attract more attention of researchers. In Figure 3(a), we give the change of spin-dependent Seebeck coef- ficient with temperature at the Fermi surface. It is found that the spin-up Seebeck coefficient is positive while the spin-down Seebeck coefficient is negative. This result can be well explained by the following equation. At low temperature, equation (3) can be simplified as: (6) This equation shows that Sσ at the Fermi surface is directly proportional to the negative value of the slope of the transmission probability τσ and inversely proportional to its size. At the same time, we also note that it is directly proportional to the temperature T. This equation can well explain the behavior of Sσ in the low temperature region (0 < T ≤ 50 K). How- ever, when the temperature further increases, we find that the spin-down Seebeck coefficient is significant- ly strengthened, and equation (6) becomes no longer applicable. It is mainly because more nonlinearity participates in the contribution to the spin Seebeck coefficient at high temperature[29]. In order to calcu- late the charge and spin thermoelectric quality fac- tors, in Figure 3(b), we give the contribution of the 15 electron and phonon part to the thermal conductivity. The thermal conductivity contributed by the phonon part κph and the thermal conductivity contributed by the electron part κel increase monotonically with the increase of temperature. Figure 3. Spin-dependent thermoelectric property. (a) Spin-de- pendent Seebeck coefficients; (b) Electron and phonon partial thermal conductivity; (c) Charge and spin Seebeck coefficients; (d) Trend of spin and charge thermoelectric quality factors with temperature. Moreover, it is important that the thermal con- ductivity of the phonon part is significantly lower than that of the electronic part, especially in the low temperature region (T < 100 K), and the thermal conductivity of the phonon part is one percent of the electronic part (See the embedded diagram in Figure 3(b)). Interestingly, the spin-down Seebeck coeffi- cient is significantly strengthened near the tempera- ture of 80 K, and the maximum value even reaches 2000 μV/K. The charge Seebeck coefficient Sc and spin Seebeck coefficient Ss are also significantly strengthened near the temperature of 80 K. In the high temperature region (near room temperature), we find that the value Ss is significantly larger than Sc, which indicates that the spin thermoelectric effect is significantly stronger than the corresponding charge thermoelectric effect. In Figure 3(d), we show the variation trend of spin thermoelectric quality factor ZST and charge thermoelectric quality factor ZCT with temperature T. The results show that their maximum value is close to 40, and the sizes of ZST and ZCT are the same in the whole temperature region. Generally speaking, if the thermoelectric quality factor is great- er than 3, it is considered that the material has high thermoelectric efficiency. It can be used as an ideal thermoelectric material. More interestingly, in the high temperature region (room temperature region), ZST is significantly larger than ZCT, and ZST is close to 3. This shows that this double probe model with carbon atoms can be used as an ideal thermoelectric device at room temperature. 4. Conclusion We designed a one-dimensional spin quantum device composed of graphene nanoribbons, carbon chains and graphene nanosheets. It is found that the spin-down transfer function at the Fermi surface is almost suppressed to zero, while the spin-up transfer function is close to 0.25, so it has obvious semi-me- tallic property. In addition, we also found that in this device, the thermal conductivity of the phonon part is significantly smaller than the corresponding elec- tronic partial conductance. In the low temperature re- gion, the phonon partial thermal conductance is only one percent of the electronic partial thermal conduc- tance. However, in the low temperature region (near 80 K), the spin Seebeck coefficient is significantly strengthened, resulting in the charge or spin quality factor close to 40. Moreover, in the whole tempera- ture range (0< T ≤ 400 K), the spin thermoelectric quality factor is always greater than the correspond- ing charge thermoelectric quality factor, and this effect becomes more obvious at room temperature. Therefore, this one-dimensional carbon-based na- noribbon can be used to design ideal spin thermo- electric devices at room temperature. Conflict of interest The authors declare that they have no conflict of interest. Acknowledgements National Natural Science Foundation of China “Research on theory and application of molecular thermoelectric devices” (11247028). 16 References 1. Novoselov KS, Geim AK, Morozov SV. Electric field effect in atomically thin carbon films. Science 2004; 306: 666–669. 2. Son Y, Cohen ML, Louie SG. Energy gaps in graphene nanoribbons. Physical Review Letters 2007; 98(8). 3. Xu C, Luo G, Liu Q, et al. Giant magnetoresistance in silicene nanoribbons. Nanoscale 2012; 4: 3111– 3117. 4. Son Y, Cohen ML, Louie SG. Half-metallic graphene nanoribbons. Nature 2006; 444: 347. 5. Wu T, Wang X, Zhai M, et al. Negativedifferential spin conductance in doped zigzag graphenenanorib- bons. Applied Physical Letters 2012; 100(5): 2112. 6. Maunárriz J, Gaul C, Malyshev AV, et al. Strong spin-dependent negative differential resistance in composite graphene superlattices. Physical Review B Condensed Matter 2012; 88(15): 5423. 7. Jiang C, Wang X, Zhai M. Spin negative differential resistance in edge doped zigzag graphene nanorib- bons. Carbon an International Journal Sponsored by the American Carbon Society 2014; 68: 406. 8. Uchida K, Takahashi S, Harii K, et al. Observation of the spin Seebeck effect. Nature 2008; 455: 778. 9. Dubi Y, Di Ventra M. Thermo-spin effects in a quan- tum dot connected to ferromagnetic leads. Physical Review B Condensed Matter 2009; 79(8): 1302(R). 10. Jaworski CM, Yang J, Mack S, et al. Observation of spin-Seebeck effect in a ferromagnetic semiconduc- tor. Nature Mater 2010; 9: 898. 11. Uchida K, Adachi H, et al. Long-range spin Seebeck effect and acoustic spin pumping. Nature Mater 2011; 10: 737. 12. Adachi H, Ohe J, Takahashi S, et al. Linear-response theory of spin Seebeck effect in ferromagnetic insu- lators. Physical Review B 2011; 83(9): 4410. 13. Dubi Y, Di Ventra M. Colloquium: Heat flow and thermoelectricity in atomic and molecular junctions. Review of Modern Physics 2011; 83: 131. 14. Liu Y, Chi F, Yang X, et al. Pure spin thermoelectric generator based on a rashba quantum dot molecule. Journal of Applied Physics 2011; 109(5): 3712. 15. Liu Y, Yang X, Chi F, et al. A proposal for time-de- pendent pure-spin-current generators. Applied Phys- ics Letters 2012; 101(21): 3109. 16. Liu Y, Wang X, Chi F. Non-magnetic doping induced a high spin-filter efficiency and large spin Seebeck effect in zigzag graphene nanoribbons. Journal of Materials Chemistry C 2013; 2013(1): 3756–3776. 17. Yang X, Liu Y, Zhang X, et al. Perfect spin filter- ing and large spin thermoelectric effects in organic transition-metal molecular junctions. Physical Chem- istry Chemical Physics Cambridge Royal Society of Chemistry 2014; 16: 11349–11357. 18. Liu Y, Zhang X, Wang X, et al. Spin-resolved Fano resonances induced large spin Seebeck effects in grapheme carbon-chain junctions. Applied Physics Letters 2014; 104(24): 2412. 19. Yang X, Liu Y, Wang X, et al. Large spin Seebeck effects in zigzag-edge silicene nanoribbons. Aip Ad- vances 2014; 4(8): 7116. 20. Yang X, Zhang X, Hong X, et al. Temperature-con- trolled giant thermal magnetoresistance behaviors in doped zigzagedged silicene nanoribbons. Rsc Ad- vances 2014; 4: 48539–48546. 21. Yang X, Zhou W, Hong X, et al. Half-metallic prop- erties, single-spin negative differential resistance, and large singlespin Seebeck effects induced by chemical doping in zigzag-edged graphene nanoribbons. The Journal of Chemical Physics 2015; 142(2): 4706. 22. Jin C, Lan H, Peng L, et al. Deriving carbon atomic chains from graphene. Physical Review Letters 2009; 102(20): 5501. 23. Shen L, Zeng M, Yang S, et al. Electron transport properties of atomic carbon nanowires between graphene electrodes. Journal of the American Chemi- cal Society 2010; 132: 11481–11486. 24. Dong Y, Wang X, Zhai M, et al. Half-metallicity in aluminum-doped zigzag silicene nanoribbons. The Journal of Physical Chemistry C 2013; 117(37): 18845–18850. 25. Kobayashi K, Aikawa H, Katsumoto S, et al. Tun- ing of the Fano effect through a quantum dot in an Aharonov-bohm Interferometer. Physics Review Letters 2002; 88: 256806. 26. Liu Y, Yang X. Enhancement of thermoelectric effi- ciency in a double-quantum-dot molecular junction. 17 Journal of Applied Physics 2010; 108(2): 3710. 27. Taylor T, Guo H, Wang J. Ab initio modeling of quantum transport properties of molecular electronic devices. Physical Review B 2001; 63(24): 5407. 28. Brandbyge M, Mozos JL, Ordejon P, et al. Densi- ty-functional method for non-equilibrium electron transport. Physical Review B, Condensed Matter 2002; 65(16): 5401. 29. Yang X, Liu Y. Pure spin current in a double quantum dot device generated by thermal. Journal of Applied Physics 2013; 113(16): 4310.