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題名 拓樸半金屬的非線性光電流
Nonlinear Photocurrent of Topological Semimetals
作者 許恆睿
Xu, Heng-Rui
貢獻者 許琇娟
Hsu, Hsiu-Chuan
許恆睿
Xu, Heng-Rui
關鍵詞 外爾半金屬
體光伏效應
量子幾何張量
Weyl semimetal
Bulk photovoltaic effect
Quantum geometric tensor
日期 2024
上傳時間 5-Aug-2024 15:06:43 (UTC+8)
摘要 能帶拓樸對外爾半金屬的體光伏效應電流有相當密切的關係，像是量子幾何張量的虛部---貝里曲率和圓偏振光注入電流之間的關聯已被熟知。在線性能帶的假設下，三個循環排列的圓偏振光注入電導率加總後會正比於外爾點的手性。然而黎曼度量身為量子幾何張量的實部與傳輸特性的關係卻尚未被人清楚了解。本論文聚焦在探討二階光響應在交流電場下所產生的直流注入電流是如何被量子幾何張量的分佈影響。線偏振光引起的注入電流是由黎曼度量給出的，因此本文分析動量空間中黎曼度量的分佈，並引入改變對稱性的參數以調控電流。 本論文以四能帶的緊束縛哈密頓量為例，引入延特定方向的磁化強度破壞時間反演對稱，計算其中一節點附近的注入電導率的所有分量。除了重現圓偏振光注入電導率與結點手性的關係，另外還發現於結點附近有兩類的線偏振光電導率皆與光頻率成正比關係。並透過分析動量空間的黎曼度量分佈，發現這些電流都是因為在節點附近的量子幾何張量切片上的不對稱所得出。 在接著依序加入空間反演對稱破缺和應變項的情形下，其中三項線偏振光電導率失去正比特性，除此之外其他分量的電導率皆不受到空間反演對稱破缺和應變項的影響． 透過了解外爾半金屬的線偏振光電導率特性，其線偏振光電流效應展現出作為低頻光感器的潛力。本論文強調了能帶拓樸對光電流的影響，也提供了計算量子幾何切片來探討能帶拓樸的作用。
The bulk photovoltaic effect of Weyl semimetals is related to its band topology, such as the well-known relationship between the imaginary part of the quantum geometric tensor, Berry curvature, and the circularly polarized light induced injection current. Under the assumption of linear bands, the sum of the circularly polarized light induced injection conductivities in three orthogonal directions is proportional to the chirality of the Weyl point. However, the relationship between the quantum metric as the real part of the quantum geometric tensor and the transport properties is less explored. This thesis explores the relationship between the DC injection current and the quantum geometric tensor. In addition to reproducing the relationship between the circularly polarized light injection conductivity and node chirality, the injection current induced by linearly polarized light, given by the quantum metric, is analyzed, and the distribution of the quantum metric in momentum space is examined. Parameters altering symmetry are introduced to modulate the current. Using a four-band tight-binding Hamiltonian as an example, time-reversal symmetry is broken by introducing magnetization in a specific direction, and all components of the injection conductivity are calculated. Nonzero components of the conductivity tensor induced by linearly polarized light are identified. One class of complements shows a positive linear relationship between conductivity and the incident light frequency, while the other class shows a negative linear relationship. By analyzing the distribution of the quantum metric in momentum space, it is found that these currents arise due to asymmetry in the quantum geometric tensor slices near the node. Upon introducing spatial inversion symmetry breaking, three components of linear injection conductivities are no longer linearly proportional to incident light frequency. In contrast, other components of linear injection conductivities still remain the linearity in incident light frequency. This thesis emphasizes the impact of band topology on photocurrents and the potential of Weyl semimetals as low-frequency photodetectors.
參考文獻 [1] M.-C.Chang. Lecture notes on topological insulators. (2017). [2] Hermann Weyl. Elektron und Gravitation. I. 56(5-6):330–352+, 1929. [3] B. Q. Lv, T. Qian, and H. Ding. Experimental perspective on three-dimensional topological semimetals. Rev. Mod. Phys., 93:025002, Apr 2021. [4] H.B. Nielsen and M. Ninomiya. Absence of neutrinos on a lattice: (i). proof by homotopy theory. Nuclear Physics B, 185(1):20–40, 1981. [5] H.B. Nielsen and M. Ninomiya. Absence of neutrinos on a lattice: (ii). intuitive topological proof. Nuclear Physics B, 193(1):173–194, 1981. [6] M. M. Vazifeh and M. Franz. Electromagnetic response of weyl semimetals. Phys. Rev. Lett., 111:027201, Jul 2013. [7] Jing Liu, Fengnian Xia, Di Xiao, F. Javier García de Abajo, and Dong Sun. Semimetals for high-performance photodetection. Nature Materials, 19(8):830–837, July 2020. [8] J. E. Sipe and A. I. Shkrebtii. Second-order optical response in semiconductors. Phys. Rev. B, 61:5337–5352, Feb 2000. [9] Päivi Törmä. Essay: Where can quantum geometry lead us? Phys. Rev. Lett., 131:240001, Dec 2023. [10] Fernando De Juan, Adolfo G Grushin, Takahiro Morimoto, and Joel E Moore. Quantized circular photogalvanic effect in weyl semimetals. Nature communications, 8(1):15995, 2017. [11] Tobias Holder, Daniel Kaplan, and Binghai Yan. Consequences of time-reversal- symmetry breaking in the light-matter interaction: Berry curvature, quantum metric, and diabatic motion. Phys. Rev. Res., 2:033100, Jul 2020. [12] D. Vanderbilt. Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators. Titolo collana. Cambridge University Press, 2018. [13] Alberto Cortijo, Dmitri Kharzeev, Karl Landsteiner, and Maria AH Vozmediano. Strain-induced chiral magnetic effect in weyl semimetals. Physical Review B, 94(24):241405, 2016. [14] Yu-Ping Lin and Wei-Han Hsiao. Dual haldane sphere and quantized band geometry in chiral multifold fermions. Physical Review B, 103(8), February 2021. [15] Junyeong Ahn, Guang-Yu Guo, and Naoto Nagaosa. Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals. Phys. Rev. X, 10:041041, Nov 2020. [16] Claudio Aversa and J. E. Sipe. Nonlinear optical susceptibilities of semiconductors: Results with a length-gauge analysis. Phys. Rev. B, 52:14636–14645, Nov 1995. [17] Qiong Ma, Su-Yang Xu, Ching-Kit Chan, Cheng-Long Zhang, Guoqing Chang, Yuxuan Lin, Weiwei Xie, Tomás Palacios, Hsin Lin, Shuang Jia, Patrick A. Lee, Pablo Jarillo-Herrero, and Nuh Gedik. Direct optical detection of weyl fermion chirality in a topological semimetal. Nature Physics, 13(9):842–847, May 2017. [18] Hsiu-Chuan Hsu, Jhih-Shih You, Junyeong Ahn, and Guang-Yu Guo. Nonlinear photoconductivities and quantum geometry of chiral multifold fermions. Physical Review B, 107(15), April 2023. [19] Hassan Shapourian, Taylor L. Hughes, and Shinsei Ryu. Viscoelastic response of topological tight-binding models in two and three dimensions. Phys. Rev. B, 92:165131, Oct 2015. [20] S. X. Xu, H. Q. Pi, R. S. Li, T. C. Hu, Q. Wu, D. Wu, H. M. Weng, and N. L. Wang. Linear-in-frequency optical conductivity over a broad range in the three-dimensional dirac semimetal candidate ir2in8Se. Phys. Rev. B, 106:115121, Sep 2022.
描述 碩士
國立政治大學
應用物理研究所
110755005
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0110755005
資料類型 thesis
dc.contributor.advisor 許琇娟zh_TW
dc.contributor.advisor Hsu, Hsiu-Chuanen_US
dc.contributor.author (Authors) 許恆睿zh_TW
dc.contributor.author (Authors) Xu, Heng-Ruien_US
dc.creator (作者) 許恆睿zh_TW
dc.creator (作者) Xu, Heng-Ruien_US
dc.date (日期) 2024en_US
dc.date.accessioned 5-Aug-2024 15:06:43 (UTC+8)-
dc.date.available 5-Aug-2024 15:06:43 (UTC+8)-
dc.date.issued (上傳時間) 5-Aug-2024 15:06:43 (UTC+8)-
dc.identifier (Other Identifiers) G0110755005en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/152961-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用物理研究所zh_TW
dc.description (描述) 110755005zh_TW
dc.description.abstract (摘要) 能帶拓樸對外爾半金屬的體光伏效應電流有相當密切的關係，像是量子幾何張量的虛部---貝里曲率和圓偏振光注入電流之間的關聯已被熟知。在線性能帶的假設下，三個循環排列的圓偏振光注入電導率加總後會正比於外爾點的手性。然而黎曼度量身為量子幾何張量的實部與傳輸特性的關係卻尚未被人清楚了解。本論文聚焦在探討二階光響應在交流電場下所產生的直流注入電流是如何被量子幾何張量的分佈影響。線偏振光引起的注入電流是由黎曼度量給出的，因此本文分析動量空間中黎曼度量的分佈，並引入改變對稱性的參數以調控電流。 本論文以四能帶的緊束縛哈密頓量為例，引入延特定方向的磁化強度破壞時間反演對稱，計算其中一節點附近的注入電導率的所有分量。除了重現圓偏振光注入電導率與結點手性的關係，另外還發現於結點附近有兩類的線偏振光電導率皆與光頻率成正比關係。並透過分析動量空間的黎曼度量分佈，發現這些電流都是因為在節點附近的量子幾何張量切片上的不對稱所得出。 在接著依序加入空間反演對稱破缺和應變項的情形下，其中三項線偏振光電導率失去正比特性，除此之外其他分量的電導率皆不受到空間反演對稱破缺和應變項的影響． 透過了解外爾半金屬的線偏振光電導率特性，其線偏振光電流效應展現出作為低頻光感器的潛力。本論文強調了能帶拓樸對光電流的影響，也提供了計算量子幾何切片來探討能帶拓樸的作用。zh_TW
dc.description.abstract (摘要) The bulk photovoltaic effect of Weyl semimetals is related to its band topology, such as the well-known relationship between the imaginary part of the quantum geometric tensor, Berry curvature, and the circularly polarized light induced injection current. Under the assumption of linear bands, the sum of the circularly polarized light induced injection conductivities in three orthogonal directions is proportional to the chirality of the Weyl point. However, the relationship between the quantum metric as the real part of the quantum geometric tensor and the transport properties is less explored. This thesis explores the relationship between the DC injection current and the quantum geometric tensor. In addition to reproducing the relationship between the circularly polarized light injection conductivity and node chirality, the injection current induced by linearly polarized light, given by the quantum metric, is analyzed, and the distribution of the quantum metric in momentum space is examined. Parameters altering symmetry are introduced to modulate the current. Using a four-band tight-binding Hamiltonian as an example, time-reversal symmetry is broken by introducing magnetization in a specific direction, and all components of the injection conductivity are calculated. Nonzero components of the conductivity tensor induced by linearly polarized light are identified. One class of complements shows a positive linear relationship between conductivity and the incident light frequency, while the other class shows a negative linear relationship. By analyzing the distribution of the quantum metric in momentum space, it is found that these currents arise due to asymmetry in the quantum geometric tensor slices near the node. Upon introducing spatial inversion symmetry breaking, three components of linear injection conductivities are no longer linearly proportional to incident light frequency. In contrast, other components of linear injection conductivities still remain the linearity in incident light frequency. This thesis emphasizes the impact of band topology on photocurrents and the potential of Weyl semimetals as low-frequency photodetectors.en_US
dc.description.tableofcontents 第 一 章 緒論 1 第 二 章 介紹 3 第 一 節 有效哈密頓量 3 第 二 節 緊束縛模型 (Tight-binding Model) 5 第 三 節 量子幾何張量 (Quantum Geometry Tensor) 7 第 四 節 非線性光效應 8 第 一 小節 k · p 模型的圓偏振光電流效應 9 第 二 小節 k · p 模型的線偏振光電流 10 第 三 章 時間反演對稱破缺下的注入電流 12 第 一 節 圓偏振光伏效應 (CPGE) 12 第 二 節 CPGE 的數值結果觀察和假設 12 第 三 節 注入電導率的數值結果 13 第 一 小節 CPGE 14 第 二 小節 線偏振電導率 15 第 四 節 小結 21 第 四 章 空間反轉對稱性破缺 23 第 一 節 加入 b0 項 23 第 一 小節 CPGE 24 第 二 小節 線偏振電導率 25 第 二 節 加入應變項 26 第 一 小節 CPGE 27 第 二 小節 線偏振電導率 28 第 五 章 結論 30 參考文獻 31zh_TW
dc.format.extent 2323657 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0110755005en_US
dc.subject (關鍵詞) 外爾半金屬zh_TW
dc.subject (關鍵詞) 體光伏效應zh_TW
dc.subject (關鍵詞) 量子幾何張量zh_TW
dc.subject (關鍵詞) Weyl semimetalen_US
dc.subject (關鍵詞) Bulk photovoltaic effecten_US
dc.subject (關鍵詞) Quantum geometric tensoren_US
dc.title (題名) 拓樸半金屬的非線性光電流zh_TW
dc.title (題名) Nonlinear Photocurrent of Topological Semimetalsen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] M.-C.Chang. Lecture notes on topological insulators. (2017). [2] Hermann Weyl. Elektron und Gravitation. I. 56(5-6):330–352+, 1929. [3] B. Q. Lv, T. Qian, and H. Ding. Experimental perspective on three-dimensional topological semimetals. Rev. Mod. Phys., 93:025002, Apr 2021. [4] H.B. Nielsen and M. Ninomiya. Absence of neutrinos on a lattice: (i). proof by homotopy theory. Nuclear Physics B, 185(1):20–40, 1981. [5] H.B. Nielsen and M. Ninomiya. Absence of neutrinos on a lattice: (ii). intuitive topological proof. Nuclear Physics B, 193(1):173–194, 1981. [6] M. M. Vazifeh and M. Franz. Electromagnetic response of weyl semimetals. Phys. Rev. Lett., 111:027201, Jul 2013. [7] Jing Liu, Fengnian Xia, Di Xiao, F. Javier García de Abajo, and Dong Sun. Semimetals for high-performance photodetection. Nature Materials, 19(8):830–837, July 2020. [8] J. E. Sipe and A. I. Shkrebtii. Second-order optical response in semiconductors. Phys. Rev. B, 61:5337–5352, Feb 2000. [9] Päivi Törmä. Essay: Where can quantum geometry lead us? Phys. Rev. Lett., 131:240001, Dec 2023. [10] Fernando De Juan, Adolfo G Grushin, Takahiro Morimoto, and Joel E Moore. Quantized circular photogalvanic effect in weyl semimetals. Nature communications, 8(1):15995, 2017. [11] Tobias Holder, Daniel Kaplan, and Binghai Yan. Consequences of time-reversal- symmetry breaking in the light-matter interaction: Berry curvature, quantum metric, and diabatic motion. Phys. Rev. Res., 2:033100, Jul 2020. [12] D. Vanderbilt. Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators. Titolo collana. Cambridge University Press, 2018. [13] Alberto Cortijo, Dmitri Kharzeev, Karl Landsteiner, and Maria AH Vozmediano. Strain-induced chiral magnetic effect in weyl semimetals. Physical Review B, 94(24):241405, 2016. [14] Yu-Ping Lin and Wei-Han Hsiao. Dual haldane sphere and quantized band geometry in chiral multifold fermions. Physical Review B, 103(8), February 2021. [15] Junyeong Ahn, Guang-Yu Guo, and Naoto Nagaosa. Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals. Phys. Rev. X, 10:041041, Nov 2020. [16] Claudio Aversa and J. E. Sipe. Nonlinear optical susceptibilities of semiconductors: Results with a length-gauge analysis. Phys. Rev. B, 52:14636–14645, Nov 1995. [17] Qiong Ma, Su-Yang Xu, Ching-Kit Chan, Cheng-Long Zhang, Guoqing Chang, Yuxuan Lin, Weiwei Xie, Tomás Palacios, Hsin Lin, Shuang Jia, Patrick A. Lee, Pablo Jarillo-Herrero, and Nuh Gedik. Direct optical detection of weyl fermion chirality in a topological semimetal. Nature Physics, 13(9):842–847, May 2017. [18] Hsiu-Chuan Hsu, Jhih-Shih You, Junyeong Ahn, and Guang-Yu Guo. Nonlinear photoconductivities and quantum geometry of chiral multifold fermions. Physical Review B, 107(15), April 2023. [19] Hassan Shapourian, Taylor L. Hughes, and Shinsei Ryu. Viscoelastic response of topological tight-binding models in two and three dimensions. Phys. Rev. B, 92:165131, Oct 2015. [20] S. X. Xu, H. Q. Pi, R. S. Li, T. C. Hu, Q. Wu, D. Wu, H. M. Weng, and N. L. Wang. Linear-in-frequency optical conductivity over a broad range in the three-dimensional dirac semimetal candidate ir2in8Se. Phys. Rev. B, 106:115121, Sep 2022.zh_TW