Abstract
Topological semimetals have linear band dispersion around the band crossing which is near the Fermi level. Chiral topological semimetals have no spatial inversion symmetry, and they have non-vanishing second-order optical response. The band structure and nonlinear optical conductivity (NOC) \({\sigma }_{zxy}^{(2)}(0;\omega ,-\omega )\) of the isostructural chiral semimetals RhSn, HfSn, and PdGa are studied by the first-principles calculation in this work. Our calculation demonstrates that the maximal NOC \({\sigma }_{zxy}^{(2)}(0;\omega ,-\omega )\) of chiral semimetals RhSn is about \(\sim 1370\, \upmu \hbox {A/V}^{2}\) under terahertz optical field with photon energy of \(\sim \) 12 meV, while the maximal NOCs \({\sigma }_{zxy}^{(2)}(0;\omega ,-\omega )\) of HfSn and PdGa are \(600 \, \upmu \hbox {A/V}^{2}\) and \(240\, \upmu \hbox {A/V}^{2}\), respectively. The relatively large NOC of RhSn can be interpreted by its multiple band crossing on the Fermi level, while multiple band crossings in the band structures of HfSn and PdGa are not on the Fermi level. Our calculations also reveal that the calculated imaginary part of dielectric function decreases with increasing photon energy, while the absorption coefficient increases with increasing photon energy in the terahertz region. The relatively large NOC makes chiral topological semimetal RhSn suitable for terahertz detection.
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Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Data is available upon request from the Authors.]
References
J. Li, S. Ullah, R. Li, M. Liu, H. Cao, D. Li, Y. Li, X.-Q. Chen, Topological massive Dirac fermions in \(\beta \)-tungsten. Phys. Rev. B 99, 165110 (2019)
A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009)
B. Bradlyn, J. Cano, Z. Wang, M.G. Vergniory, C. Felser, R.J. Cava, B.A. Bernevig, Beyond Dirac and Weyl fermions: unconventional quasiparticles in conventional crystals. Science 353, aaf5037 (2016)
J.-P. Sun, D. Zhang, K. Chang, Coexistence of topological nodal lines, Weyl points, and triply degenerate points in TaS. Phys. Rev. B 96, 045121 (2017)
X. Yang, T.A. Cochran, R. Chapai, D. Tristant, J.-X. Yin, I. Belopolski et al., Observation of sixfold degenerate fermions in \(\text{PdSb}_{2}\). Phys. Rev. B 101 (2020)
X. Zhang, Q. Gu, H. Sun, T. Luo, Y. Chen, Y. Liu, Z. Shao, Z. Zhang, S. Li et al., Eightfold fermionic excitation in a charge density wave compound. Phys. Rev. B 102, 035125 (2020)
H.B. Nielsen, M. Ninomiya, Absence of neutrinos on a lattice: (I). Proof by homotopy theory. Nucl. Phys. B 185, 20–40 (1981)
H.B. Nielsen, M. Ninomiya, Absence of neutrinos on a lattice: (II). Intuitive topological proof. Nucl. Phys. B 193, 173–194 (1981)
D. Takane, Z. Wang, S. Souma, K. Nakayama, T. Nakayama, H. Oinuma, Y. Nakata, H. Iwasawa, C. Cacho, T. Kim, K. Horiba, H. Kumigashira, T. Takahashi, Y. Ando, T. Sato, Observation of chiral fermions with a large topological charge and associated fermi-arc surface states in cosi. Phys. Rev. Lett. 122, 076402 (2019)
Z. Li, T. Iitaka, H. Zeng, H. Su, Optical response of the chiral topological semimetal RhSi. Phys. Rev. B 100, 155201 (2019)
P. Tang, Q. Zhou, S.-C. Zhang, Multiple types of topological fermions in transition metal silicides. Phys. Rev. Lett. 119, 206402 (2017)
D.S. Sanchez, I. Belopolski, T.A. Cochran, X. Xu, J.-X. Yin, G. Chang, W. Xie, K. Manna et al., Topological chiral crystals with helicoid-arc quantum states. Nature 567, 500–505 (2019)
N.B.M. Schröter, D. Pei, M.G. Vergniory, Y. Sun, K. Manna, F. de Juan et al., Chiral topological semimetal with multifold band crossings and long Fermi arcs. Nat. Phys. 15, 759–765 (2019)
S. Geller, E.A. Wood, The crystal structure of rhodium silicide. RhSi Acta Cryst. 7, 441–443 (1954)
L.E. Golub, E.L. Ivchenko, B. Spival, Semiclassical theory of the circular photogalvanic effect in gyrotropic systems. Phys. Rev. B 102, 085202 (2020)
E. Deyo, L. E. Golub, E. L. Ivchenko, B. Spival, Semiclassical theory of the circular photogalvanic effect in non-centrosymmetric systems, arXiv: 0904.1917
J.E. Sipe, A.I. Shkrebtii, Second-order optical response in semiconductors. Phys. Rev. B 61, 5337–5352 (2000)
N. Ogawa, M. Sotome, Y. Kaneko, M. Ogino, Y. Tokura, Shift current in the ferroelectric semiconductor SbSl. Phys. Rev. B 96, 241203 (2017)
B. Sadhukhan, Y. Zhang, R. Ray, J. van der Brink, First-principles calculation of shift current in chalcopyrite semiconductor \(\text{ ZnSnP}_{2}\). Phys. Rev. Mater. 4, 064602 (2020)
Z. Li, Y.-Q. Jin, T. Tohyama, T. Iitaka, J.-X. Zhang, H. Su, Second harmonic generation in the Weyl semimetal TaAs from a quantum kinetic equation. Phys. Rev. B 97, 085201 (2018)
Z. Li, A. Tudi, P. Ren, Y. Yang, T. Iitaka, T. Tohyama, Z. Yang, S. Pan, H. Su, NaPN2: Deep-ultraviolet nonlinear optical material with unprecedented strong second-harmonic generation coefficient. Phys. Rev. Mater. 3, 025201 (2019)
G.B. Osterhoudt, L.K. Diebel, M.J. Gray, X. Yang, J. Stanco, X. Huang, B. Shen, N. Ni, P.J.W. Moll, Y. Ran, K.S. Burch, Colossal mid-infrared bulk photovoltaic effect in a type-I Weyl semimetal. Nat. Mater. 18, 471–475 (2019)
S.M. Young, F. Zheng, A.M. Rappe, First-principles calculation of the bulk photovoltaic effect in the bismuth ferrite. Phys. Rev. Lett. 109, 236601 (2012)
L.Z. Tan, F. Zheng, S.M. Young, F. Wang, S. Liu, A.M. Rappe, Shift current bulk photovoltaic effect in polar materials-hybrid and oxide perovskites and beyond. npj Comput. Mater. 2, 16026 (2016)
Y. Chen, S. Wu, A.A. Burkov, Axion response in Weyl semimetals. Phys. Rev. B 88, 125105 (2013)
M.-C. Chang, M.-F. Yang, Chiral magnetic effect in a two-band lattice model of Weyl semimetal. Phys. Rev. B 91, 115203 (2015)
P. Goswami, G. Sharma, S. Tewari, Optical activity as a test for dynamic chiral magnetic effect of Weyl semimetals. Phys. Rev. B 92, 161110 (2015)
J. Liu, D. Vanderbilt, Weyl semimetals from noncentrosymmetric topological insulators. Phys. Rev. B 90, 155316 (2014)
K. Taguchi, T. Imaeda, M. Sato, Y. Tanaka, Photovoltaic chiral magnetic effect in Weyl semimetals. Phys. Rev. B 93, 201202 (2016)
I. Sodemann, L. Fu, Quantum nonlinear hall effect induced by berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015)
J.-S. You, S. Fang, S.-Y. Xu, E. Kaxiras, T. Low, Berry curvature dipole current in the transition metal dichalcogenides family. Phys. Rev. B 98, 121109 (2018)
S. Schmidt, D. Blaschke, G. Röpke, S.A. Smolyansky, A.V. Prozorkevich, V.D. Toneev, A quantum kinetic equation for particle production in the Schwinger mechanism. Int. J. Mod. Phys. E 7, 709–722 (1998)
I. Tavernelli, On the geometrization of quantum mechanics. Ann. Phys. 371, 239–253 (2016)
R.D. King-Smith, D. Vanderbilt, Theory of polarization of crystalline solids. Phys. Rev. B 47, 1651–1654 (1993)
T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, Y. Tokura, Magnetic control of ferroelectric polarization. Nature 426, 55–58 (2003)
P. Bruno, V.K. Dugaev, M. Taillefumier, Topological hall effect and berry phase in magnetic nanostructures. Phys. Rev. Lett. 93, 096806 (2004)
J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1997)
P. Giannozzi, O. Baseggio, P. Bonfà, D. Brunato, R. Car, I. Carnimeo, C. Cavazzoni, S. de Gironcoli, P. Delugas, F. Ferrari Ruffino, A. Ferretti, N. Marzari, I. Timrov, A. Urru, S. Baroni, QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Chem. Phys. 152, 154105 (2020)
H. Li, S. Xu, Z.-C. Rao, L.-Q. Zhou, Z.-J. Wang, S.-M. Zhou, S.-J. Tian, S.-Y. Gao, J.-J. Li, Y.-B. Huang, H.-C. Lei, H.-M. Weng, Y.-J. Sun, T.-L. Xia, T. Qian, H. Ding, Chiral fermion reversal in chiral crystals. Nat. Common. 10, 5505 (2019)
O. Schob, E. Parthé, The structure of HfSn. Acta Cryst. 17, 452–453 (1964)
N.B.M. Schröter, S. Stolz, K. Manna, F. de Juan, M.G. Vergniory, J.A. Krieger, D. Pei, T. Schmitt, P. Dudin, T.K. Kim, C. Cacho, B. Bradlyn, H.T. Borrmann, M. Schmidt, R. Widmer, V.N. Strocov, C. Felser, Observation and control of maximal Chern numbers in a chiral topological semimetal. Science 369, 179–183 (2020)
N. Marzari, A.A. Mostofi, J.R. Yates, I. Souza, D. Vanderbilt, Maximally localized Wannier functions: theory and applications. Rev. Mod. Phys. 84, 1419–1475 (2012)
G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, J. Ibañez-Azpiroz, H. Lee, J.-M. Lihm, D. Marchand, A. Marrazzo, Y. Mokrousov, J.I. Mustafa, Y. Nohara, Y. Nomura, L. Paulatto, S. Poncé, T. Ponweiser, J. Qiao, F. Thöle, S.S. Tsirkin, M. Wierzbowska, D. Nicola Marzari, I. Vanderbilt, A.A. Souza, A. Mostofi, J.R. Yate, Wannier90 as a community code: new features and applications. J. Phys. Condens. Matter 32, 165902 (2020)
L.Z. Maulana, K. Manna, E. Uykur, C. Felser, M. Dressel, A.V. Pronin, Optical conductivity of multifold fermions: the case of RhSi. Phys. Rev. Res. 2, 023018 (2020)
A.V. Pronin, M. Dressel, Nodal semimetals: a survey on optical conductivity. Phys. Status Solidi B 258, 2000027 (2021)
Z. Ni, B. Xu, M.-Á. Sánchez-Martínez, Y. Zhang, K. Manna, C. Bernhard, J.W.F. Venderbos, F. de Juan, C. Felser, A.G. Grushin, L. Wu, Linear and nonlinear optical responses in the chiral multifold semimetal RhSi. npj Quantum Mater. 5, 96 (2020)
A.-Q. Wang, X.-G. Ye, D.-P. Yu, Z.-M. Liao, Topological semimetal nanostructures: from properties to topotronics. ACS Nano 14, 3755–3778 (2020)
J. Liu, F. Xia, D. Xiao, F. Javier García de Abajo, D. Sun, Semimetals for high-performance photodetection. Nat. Mater. 19, 830–837 (2020)
Y. Zhang, L. Fu, Terahertz Detection Based on Nonlinear Hall Effect Without Magnetic Field, arXiv:2101.05842v1
Acknowledgements
This work is supported by the National Natural Science Foundation of China. T.I. is supported by MEXT via Exploratory Challenge on Post-K Computer (Frontiers of Basic Science: Challenge the Limits). The calculations were performed on the Hokusai system of Riken.
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Gao, Y., Iitaka, T. & Li, Z. Terahertz nonlinear optics of chiral semimetals RhSn, HfSn, and PdGa. Eur. Phys. J. B 94, 95 (2021). https://doi.org/10.1140/epjb/s10051-021-00093-z
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DOI: https://doi.org/10.1140/epjb/s10051-021-00093-z