# Optical Response of Chiral Multifold Semimetal PdGa

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results and Discussion

`optic`module [52]. Figure 3 shows the density of states (DOS) of PdGa, as well as the atomic densities of Pd and Ga separately. It can be clearly seen that the majority of carriers at the Fermi surface, as well as electrons involved in optical transitions far beyond the visible spectrum, are entirely contributed by Pd. Significant contributions to the DOS from Ga arise at energies only as low as $-15\phantom{\rule{3.33333pt}{0ex}}\mathrm{eV}$, and beyond.

## 3. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Yan, B.; Felser, C. Topological Materials: Weyl Semimetals. Annu. Rev. Condens. Matter Phys.
**2017**, 8, 337–354. [Google Scholar] [CrossRef][Green Version] - Murakami, S. Phase transition between the quantum spin Hall and insulator phases in 3D: Emergence of a topological gapless phase. New J. Phys.
**2007**, 9, 356. [Google Scholar] [CrossRef] - Wan, X.; Turner, A.M.; Vishwanath, A.; Savrasov, S.Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B
**2011**, 83, 205101. [Google Scholar] [CrossRef][Green Version] - Burkov, A.A.; Balents, L. Weyl Semimetal in a Topological Insulator Multilayer. Phys. Rev. Lett.
**2011**, 107, 127205. [Google Scholar] [CrossRef] [PubMed][Green Version] - Šmejkal, L.; Jungwirth, T.; Sinova, J. Route towards Dirac and Weyl antiferromagnetic spintronics. Phys. Status Solidi RRL
**2017**, 11, 1700044. [Google Scholar] [CrossRef] - Šmejkal, L.; Mokrousov, Y.; Yan, B.; MacDonald, A.H. Topological antiferromagnetic spintronics. Nat. Phys.
**2018**, 14, 242–251. [Google Scholar] [CrossRef] - Shi, Z.; Wang, M.; Wu, J. A spin filter transistor made of topological Weyl semimetal. Appl. Phys. Lett.
**2015**, 107, 102403. [Google Scholar] [CrossRef] - Grushin, A.G.; Bardarson, J.H. How to Make Devices with Weyl Materials. Physics
**2017**, 10, 63. [Google Scholar] [CrossRef][Green Version] - Hills, R.D.Y.; Kusmartseva, A.; Kusmartsev, F.V. Current-voltage characteristics of Weyl semimetal semiconducting devices, Veselago lenses, and hyperbolic Dirac phase. Phys. Rev. B
**2017**, 95, 214103. [Google Scholar] [CrossRef][Green Version] - Zhu, C.; Wang, F.; Meng, Y.; Yuan, X.; Xiu, F.; Luo, H.; Wang, Y.; Li, J.; Lv, X.; He, L.; et al. A robust and tuneable mid-infrared optical switch enabled by bulk Dirac fermions. Nat. Commun.
**2017**, 8, 1–7. [Google Scholar] [CrossRef] - Sun, Y.; Meng, Y.; Jiang, H.; Qin, S.; Yang, Y.; Xiu, F.; Shi, Y.; Zhu, S.; Wang, F. Dirac semimetal saturable absorber with actively tunable modulation depth. Opt. Lett.
**2019**, 44, 582–585. [Google Scholar] [CrossRef] [PubMed] - Müchler, L.; Zhang, H.; Chadov, S.; Yan, B.; Casper, F.; Kübler, J.; Zhang, S.C.; Felser, C. Topological Insulators from a Chemist’s Perspective. Angew. Chem. Int. Ed.
**2012**, 51, 7221–7225. [Google Scholar] [CrossRef] [PubMed] - Kong, D.; Cui, Y. Opportunities in chemistry and materials science for topological insulators and their nanostructures. Nat. Chem.
**2011**, 3, 845–849. [Google Scholar] [CrossRef] [PubMed] - Chen, H.; Zhu, W.; Xiao, D.; Zhang, Z. CO Oxidation Facilitated by Robust Surface States on Au-Covered Topological Insulators. Phys. Rev. Lett.
**2011**, 107, 056804. [Google Scholar] [CrossRef][Green Version] - Yan, B.; Stadtmüller, B.; Haag, N.; Jakobs, S.; Seidel, J.; Jungkenn, D.; Mathias, S.; Cinchetti, M.; Aeschlimann, M.; Felser, C. Topological states on the gold surface. Nat. Commun.
**2015**, 6, 1–6. [Google Scholar] [CrossRef] - Xiao, J.; Kou, L.; Yam, C.Y.; Frauenheim, T.; Yan, B. Toward Rational Design of Catalysts Supported on a Topological Insulator Substrate. ACS Catal.
**2015**, 5, 7063–7067. [Google Scholar] [CrossRef] - Lv, B.Q.; Weng, H.M.; Fu, B.B.; Wang, X.P.; Miao, H.; Ma, J.; Richard, P.; Huang, X.C.; Zhao, L.X.; Chen, G.F.; et al. Experimental Discovery of Weyl Semimetal TaAs. Phys. Rev. X
**2015**, 5, 031013. [Google Scholar] [CrossRef][Green Version] - Weng, H.; Fang, C.; Fang, Z.; Bernevig, B.A.; Dai, X. Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides. Phys. Rev. X
**2015**, 5, 011029. [Google Scholar] [CrossRef] - Sun, Y.; Zhang, Y.; Felser, C.; Yan, B. Strong Intrinsic Spin Hall Effect in the TaAs Family of Weyl Semimetals. Phys. Rev. Lett.
**2016**, 117, 146403. [Google Scholar] [CrossRef] - Aroyo, M.I. International Tables for Crystallography, Volume A, 6th ed.; Wiley: Hoboken, NJ, USA, 2013. [Google Scholar]
- Sohncke, L. Entwicklung einer Theorie der Kristallstruktur; B. G. Teubner: Leipzig, Germany, 1879. [Google Scholar]
- Bradlyn, B.; Cano, J.; Wang, Z.; Vergniory, M.G.; Felser, C.; Cava, R.J.; Bernevig, B.A. Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals. Science
**2016**, 353. [Google Scholar] [CrossRef][Green Version] - Sanchez, D.S.; Belopolski, I.; Cochran, T.A.; Xu, X.; Yin, J.X.; Chang, G.; Xie, W.; Manna, K.; Süß, V.; Huang, C.Y.; et al. Topological chiral crystals with helicoid-arc quantum states. Nature
**2019**, 567, 500–505. [Google Scholar] [CrossRef] [PubMed] - Schröter, N.B.M.; Pei, D.; Vergniory, M.G.; Sun, Y.; Manna, K.; de Juan, F.; Krieger, J.A.; Süss, V.; Schmidt, M.; Dudin, P.; et al. Chiral topological semimetal with multifold band crossings and long Fermi arcs. Nat. Phys.
**2019**, 15, 759–765. [Google Scholar] [CrossRef] - Chang, G.; Xu, S.Y.; Wieder, B.J.; Sanchez, D.S.; Huang, S.M.; Belopolski, I.; Chang, T.R.; Zhang, S.; Bansil, A.; Lin, H.; et al. Unconventional Chiral Fermions and Large Topological Fermi Arcs in RhSi. Phys. Rev. Lett.
**2017**, 119, 206401. [Google Scholar] [CrossRef] [PubMed][Green Version] - Rao, Z.; Li, H.; Zhang, T.; Tian, S.; Li, C.; Fu, B.; Tang, C.; Wang, L.; Li, Z.; Fan, W.; et al. Observation of unconventional chiral fermions with long Fermi arcs in CoSi. Nature
**2019**, 567, 496–499. [Google Scholar] [CrossRef] [PubMed][Green Version] - Tang, P.; Zhou, Q.; Zhang, S.C. Multiple Types of Topological Fermions in Transition Metal Silicides. Phys. Rev. Lett.
**2017**, 119, 206402. [Google Scholar] [CrossRef][Green Version] - Takane, D.; Wang, Z.; Souma, S.; Nakayama, K.; Nakamura, T.; Oinuma, H.; Nakata, Y.; Iwasawa, H.; Cacho, C.; Kim, T.; et al. Observation of Chiral Fermions with a Large Topological Charge and Associated Fermi-Arc Surface States in CoSi. Phys Rev. Lett.
**2019**, 122, 076402. [Google Scholar] [CrossRef][Green Version] - Sessi, P.; Fan, F.R.; Küster, F.; Manna, K.; Schröter, N.B.M.; Ji, J.R.; Stolz, S.; Krieger, J.A.; Pei, D.; Kim, T.K.; et al. Handedness-dependent quasiparticle interference in the two enantiomers of the topological chiral semimetal PdGa. Nat. Commun.
**2020**, 11, 3507. [Google Scholar] [CrossRef] - Schröter, N.B.M.; Stolz, S.; Manna, K.; de Juan, F.; Vergniory, M.G.; Krieger, J.A.; Pei, D.; Schmitt, T.; Dudin, P.; Kim, T.K.; et al. Observation and control of maximal Chern numbers in a chiral topological semimetal. Science
**2020**, 369, 179. [Google Scholar] [CrossRef] - De Juan, F.; Grushin, A.G.; Morimoto, T.; Moore, J.E. Quantized circular photogalvanic effect in Weyl semimetals. Nat. Commun.
**2017**, 8. [Google Scholar] [CrossRef] - Le, C.; Zhang, Y.; Felser, C.; Sun, Y. Ab initio study of quantized circular photogalvanic effect in chiral multifold semimetals. Phys. Rev. B
**2020**, 102, 121111. [Google Scholar] [CrossRef] - Rees, D.; Manna, K.; Lu, B.; Morimoto, T.; Borrmann, H.; Felser, C.; Moore, J.E.; Torchinsky, D.H.; Orenstein, J. Helicity-dependent photocurrents in the chiral Weyl semimetal RhSi. Sci. Adv.
**2020**, 6, eaba0509. [Google Scholar] [CrossRef] [PubMed] - Ni, Z.; Wang, K.; Zhang, Y.; Pozo, O.; Xu, B.; Han, X.; Manna, K.; Paglione, J.; Felser, C.; Grushin, A.G.; et al. Giant topological longitudinal circular photo-galvanic effect in the chiral multifold semimetal CoSi. Nat. Commun.
**2021**, 12, 1–8. [Google Scholar] [CrossRef] [PubMed] - Maulana, L.Z.; Manna, K.; Uykur, E.; Felser, C.; Dressel, M.; Pronin, A.V. Optical conductivity of multifold fermions: The case of RhSi. Phys. Rev. Res.
**2020**, 2, 023018. [Google Scholar] [CrossRef][Green Version] - Neubauer, D.; Carbotte, J.P.; Nateprov, A.A.; Löhle, A.; Dressel, M.; Pronin, A.V. Interband optical conductivity of the [001]-oriented Dirac semimetal Cd
_{3}As_{2}. Phys. Rev. B**2016**, 93, 121202. [Google Scholar] [CrossRef][Green Version] - Schilling, M.B.; Schoop, L.M.; Lotsch, B.V.; Dressel, M.; Pronin, A.V. Flat Optical Conductivity in ZrSiS due to Two-Dimensional Dirac Bands. Phys. Rev. Lett.
**2017**, 119, 187401. [Google Scholar] [CrossRef][Green Version] - Hütt, F.; Yaresko, A.; Schilling, M.B.; Shekhar, C.; Felser, C.; Dressel, M.; Pronin, A.V. Linear-in-Frequency Optical Conductivity in GdPtBi due to Transitions near the Triple Points. Phys. Rev. Lett.
**2018**, 121, 176601. [Google Scholar] [CrossRef][Green Version] - Biswas, A.; Iakutkina, O.; Wang, Q.; Lei, H.C.; Dressel, M.; Uykur, E. Spin-Reorientation-Induced Band Gap in Fe
_{3}Sn_{2}: Optical Signatures of Weyl Nodes. Phys. Rev. Lett.**2020**, 125, 076403. [Google Scholar] [CrossRef] - Shao, Y.; Sun, Z.; Wang, Y.; Xu, C.; Sankar, R.; Breindel, A.J.; Cao, C.; Fogler, M.M.; Millis, A.J.; Chou, F.; et al. Optical signatures of Dirac nodal lines in NbAs
_{2}. Proc. Natl. Acad. Sci. USA**2019**, 116, 1168–1173. [Google Scholar] [CrossRef][Green Version] - Hosur, P.; Parameswaran, S.A.; Vishwanath, A. Charge Transport in Weyl Semimetals. Phys. Rev. Lett.
**2012**, 108, 046602. [Google Scholar] [CrossRef][Green Version] - Bácsi, A.; Virosztek, A. Low-frequency optical conductivity in graphene and in other scale-invariant two-band systems. Phys. Rev. B
**2013**, 87, 125425. [Google Scholar] [CrossRef][Green Version] - Polatkan, S.; Goerbig, M.O.; Wyzula, J.; Kemmler, R.; Maulana, L.Z.; Piot, B.A.; Crassee, I.; Akrap, A.; Shekhar, C.; Felser, C.; et al. Magneto-Optics of a Weyl Semimetal beyond the Conical Band Approximation: Case Study of TaP. Phys. Rev. Lett.
**2020**, 124, 176402. [Google Scholar] [CrossRef] [PubMed] - Mohelský, I.; Dubroka, A.; Wyzula, J.; Slobodeniuk, A.; Martinez, G.; Krupko, Y.; Piot, B.A.; Caha, O.; Humlíček, J.; Bauer, G.; et al. Landau level spectroscopy of Bi2Te3. Phys. Rev. B
**2020**, 102. [Google Scholar] [CrossRef] - Akrap, A.; Hakl, M.; Tchoumakov, S.; Crassee, I.; Kuba, J.; Goerbig, M.O.; Homes, C.C.; Caha, O.; Novák, J.; Teppe, F.; et al. Magneto-Optical Signature of Massless Kane Electrons in Cd
_{3}As_{2}. Phys. Rev. Lett.**2016**, 117, 136401. [Google Scholar] [CrossRef] [PubMed][Green Version] - Rodriguez, D.; Tsirlin, A.A.; Biesner, T.; Ueno, T.; Takahashi, T.; Kobayashi, K.; Dressel, M.; Uykur, E. Two Linear Regimes in Optical Conductivity of a Type-I Weyl Semimetal: The Case of Elemental Tellurium. Phys. Rev. Lett.
**2020**, 124, 136402. [Google Scholar] [CrossRef] [PubMed][Green Version] - Uykur, E.; Li, W.; Kuntscher, C.A.; Dressel, M. Optical signatures of energy gap in correlated Dirac fermions. NPJ Quantum Mater.
**2019**, 4, 1–8. [Google Scholar] [CrossRef][Green Version] - Xu, B.; Fang, Z.; Sánchez-Martínez, M.Á.; Venderbos, J.W.F.; Ni, Z.; Qiu, T.; Manna, K.; Wang, K.; Paglione, J.; Bernhard, C.; et al. Optical signatures of multifold fermions in the chiral topological semimetal CoSi. Proc. Natl. Acad. Sci. USA
**2020**, 117, 27104–27110. [Google Scholar] [CrossRef] - Blaha, P.; Schwarz, K.; Madsen, G.; Kvasnicka, D.; Luitz, J.; Laskowski, R.; Tran, F.; Marks, L.D. Wien2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties; Schwarz, K., Ed.; Vienna University of Technology: Vienna, Austria, 2019; ISBN 3-9501031-1-2. [Google Scholar]
- Blaha, P.; Schwarz, K.; Tran, F.; Laskowski, R.; Madsen, G.K.H.; Marks, L.D. WIEN2k: An APW+lo program for calculating the properties of solids. J. Chem. Phys.
**2020**, 152, 074101. [Google Scholar] [CrossRef] - Rarita, W.; Schwinger, J. On a Theory of Particles with Half-Integral Spin. Phys. Rev.
**1941**, 60, 61. [Google Scholar] [CrossRef] - Ambrosch-Draxl, C.; Sofo, J. Linear optical properties of solids within the full-potential linearized augmented planewave method. Comput. Phys. Commun.
**2006**, 175, 1–14. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**(

**a**) The crystal structure of PdGa. The Pd and Ga atoms are arranged chirally along the c-axis, with a distinct handedness, giving rise to chiral properties in the band structure and optical interactions. (

**b**) Fermi surface of PdGa. (

**c**) Brillouin zone of PdGa representing the high symmetry points used in the band structure plots. (

**d**) Contributions of the different bands to the Fermi surface, sorted from lowest to highest energy going from left to right.

**Figure 2.**Band structure of PdGa (

**a**) with spin-orbit coupling (SOC). Bands that cross the Fermi surface are labeled in pairs ${A}_{\pm}$ to ${D}_{\pm}$, with respect to their energy. The Fermi energy is positioned at ${E}_{F}=0$ eV. The label ± refer to spin pairs, which split away from high symmetry points. This splitting, due to lack of inversion and mirror symmetries, gives rise to a 4-fold intersection at $\Gamma $ and 6-fold intersection at R, both with Chern numbers of magnitude $\left|\chi \right|=4$. (

**b**) Magnified view of the band structure around the $\Gamma $-point without SOC. (

**c**) Magnified view around $\Gamma $ with SOC.

**Figure 3.**Density of states of PdGa and the atoms Pd and Ga separately. The Gd contribution is negligible, and has been magnified by a factor of 10. Most bands around the Fermi energy are thus contributed by the Pd atoms, underlining the relevance of chirality among carriers and optical transition. The Fermi level is positioned at ${E}_{F}=0$ eV as indicated by the blue dotted line.

**Figure 4.**(

**a**) The calculated real part of the interband optical conductivity ${\sigma}_{1}\left(\omega \right)$ with weight analysis. The features were sorted according to the labelling in Figure 2a. (

**b**) Intra-, interband, and total optical conductivity ${\sigma}_{1}\left(\omega \right)$ of PdGa for parameters $\Gamma =2.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{meV}$ and ${\omega}_{p}=4.43\phantom{\rule{3.33333pt}{0ex}}\mathrm{eV}$.

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Polatkan, S.; Uykur, E.
Optical Response of Chiral Multifold Semimetal PdGa. *Crystals* **2021**, *11*, 80.
https://doi.org/10.3390/cryst11020080

**AMA Style**

Polatkan S, Uykur E.
Optical Response of Chiral Multifold Semimetal PdGa. *Crystals*. 2021; 11(2):80.
https://doi.org/10.3390/cryst11020080

**Chicago/Turabian Style**

Polatkan, Sascha, and Ece Uykur.
2021. "Optical Response of Chiral Multifold Semimetal PdGa" *Crystals* 11, no. 2: 80.
https://doi.org/10.3390/cryst11020080