Main > Acta Physica Sinica >  Volume 68 >  Issue 24 >  Page 247202-1 > Article
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  • Received: Aug. 22, 2019

    Accepted: --

    Posted: Sep. 17, 2020

    Published Online: Sep. 17, 2020

    The Author Email: Xu Yi (1739391094@qq.com), Tang Chao (tang_chao@xtu.edu.cn)

    DOI: 10.7498/aps.68.20191276

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    Yi Xu, Xiao-Yan Xu, Wei Zhang, Tao Ouyang, Chao Tang. Thermoelectric properties of polycrystalline graphene nanoribbons[J]. Acta Physica Sinica, 2019, 68(24): 247202-1

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$ H = \varepsilon \sum\limits_{\left\langle i \right\rangle } {c_i^ + } {c_i} - t\sum\limits_{\left\langle {i,j} \right\rangle } {{{\rm e}^{{\rm i}{\theta _{ij}}}}} c_i^ + {c_i}, $ (1)

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$ {G^{\rm{r}}}\left( E \right) = {\left[ {\left( {E + {\rm{i}}{0^ + }} \right)I - {H_{\rm{c}}} - \varSigma _{\rm{L}}^r - \varSigma _{\rm{R}}^r} \right]^{ - 1}}, $ (2)

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$ {T_{\rm{e}}}\left( E \right) = {T_{\rm{r}}}{\rm{[}}{G^{\rm{r}}}\left( E \right){{{\varGamma }}_{\rm{L}}}{G^{\rm{a}}}\left( E \right){\varGamma _{\rm{R}}}{\rm{]}}, $ (3)

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$ {L_{(m)}} = \frac{{\rm{2}}}{\hbar }\mathop \int \nolimits_{{\rm{ - }}\infty }^\infty {T_{\rm{e}}}\left( E \right){\left( {E - \mu } \right)^m}\left( { - \frac{{\partial f(E,\mu,T)}}{{\partial E}}} \right){\rm{d}}E, $ (4)

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$ \sigma (\mu,T) = {e^2}{L_0}(\mu,T), $ (5)

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$ S(\mu,T) = \frac{1}{{eT}}\frac{{{L_1}(\mu,T)}}{{{L_0}(\mu,T)}}, $ (6)

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$ {k_{\rm{e}}}\left( {\mu,T} \right) = \frac{1}{T}\left[ {{L_2}\left( {\mu,T} \right) - \frac{{{L_1}{{(\mu,T)}^2}}}{{{L_0}\left( {\mu,T} \right)}}} \right]. $ (7)

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$ {G^{\rm{r}}}\left( \omega \right) = {\left[ {{{\left( {\omega {\rm{ + i}}{0^+}} \right)}^{\rm{2}}}{{I - }}{K_{\rm{c}}} - \varSigma _{\rm{L}}^{\rm{r}} - \varSigma _{\rm{R}}^{\rm{r}}} \right]^{{\rm{ - 1}}}}. $ (8)

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$ {k_{\rm{p}}} = \frac{\hbar }{{{\rm{2{\text{π}}}}}}\mathop \int \nolimits_{\rm{0}}^\infty {T_{\rm{p}}}\left( \omega \right)\omega \frac{{\partial {f_{\rm{p}}}(\omega )}}{{\partial T}}{\rm{d}}\omega, $ (9)

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$ {\rho _\alpha }\left( \omega \right) =-\frac{{\rm{1}}}{{\text{π}}}{\mathop{\rm Im}\nolimits} G_{\alpha \alpha }^r(\omega {\rm{)}}. $ (10)

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$ ZT = \frac{{\sigma {S^2}T}}{{{k_{\rm{e}}}+{k_{\rm{p}}}}}. $ (11)

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