Quasi-two-dimensional Fermi surface of superconducting line-nodal metal CaSb₂

[1] Y. S. Hor, A. J. Williams, J. G. Checkelsky, P. Roushan, J. Seo,Q. Xu, H. W. Zandbergen, A. Yazdani, N. P. Ong, and R. J. Cava, Superconductivity in CuxBi2Se3 and its Implications for Pairing in the Undoped Topological Insulator, Phys. Rev. Lett. 104, 057001 (2010).

[2] L. Fu and E. Berg, Odd-Parity Topological Superconductors: Theory and Application to CuxBi2Se3, Phys. Rev. Lett. 105, 097001 (2010).

[3] S. Sasaki, M. Kriener, K. Segawa, K. Yada, Y. Tanaka, M. Sato, and Y. Ando, Topological Superconductivity in CuxBi2Se3, Phys. Rev. Lett. 107, 217001 (2011).

[4] K. Matano, M. Kriener, K. Segawa, Y. Ando, and G.-q. Zheng, Spin-rotation symmetry breaking in the superconducting state of CuxBi2Se3, Nat. Phys. 12, 852 (2016).

[5] S. Yonezawa, K. Tajiri, S. Nakata, Y. Nagai, Z. Wang, K. Segawa, Y. Ando, and Y. Maeno, Thermodynamic evidence for nematic superconductivity in CuxBi2Se3, Nat. Phys. 13, 123 (2017).

[6] S. Kobayashi and M. Sato, Topological Superconductivity in Dirac Semimetals, Phys. Rev. Lett. 115, 187001 (2015).

[7] L. Aggarwal, A. Gaurav, G. S. Thakur, Z. Haque, A. K. Ganguli, and G. Sheet, Unconventional superconductivity at mesoscopic point contacts on the 3D Dirac semimetal Cd3As2, Nat. Mater. 15, 32 (2016).

[8] L. He, Y. Jia, S. Zhang, X. Hong, C. Jin, and S. Li, Pressure- induced superconductivity in the three-dimensional topological Dirac semimetal Cd3As2, npj Quantum Mater. 1, 16014 (2016).

[9] M. Oudah, A. Ikeda, J. N. Hausmann, S. Yonezawa, T. Fukumoto, S. Kobayashi, M. Sato, and Y. Maeno, Superconduc- tivity in the antiperovskite Dirac-metal oxide Sr3−xSnO, Nat.Commun. 7, 13617 (2016).

[10] G. Xu, B. Lian, P. Tang, X.-L. Qi, and S.-C. Zhang, Topological Superconductivity on the Surface of Fe-Based Superconduc- tors, Phys. Rev. Lett. 117, 047001 (2016).

[11] P. Zhang, K. Yaji, T. Hashimoto, Y. Ota, T. Kondo, K. Okazaki,Z. Wang, J. Wen, G. D. Gu, H. Ding, and S. Shin, Observation of topological superconductivity on the surface of an iron-based superconductor, Science 360, 182 (2018).

[12] C. Fang, Y. Chen, H.-Y. Kee, and L. Fu, Topological nodal line semimetals with and without spin-orbital coupling, Phys. Rev. B 92, 081201(R) (2015).

[13] C. Fang, H. Weng, X. Dai, and Z. Fang, Topological nodal line semimetals, Chin. Phys. B 25, 117106 (2016).

[14] H. Shapourian, Y. Wang, and S. Ryu, Topological crystalline superconductivity and second-order topological superconduc- tivity in nodal-loop materials, Phys. Rev. B 97, 094508 (2018).

[15] R. Yu, H. Weng, Z. Fang, X. Dai, and X. Hu, Topological Node- Line Semimetal and Dirac Semimetal State in Antiperovskite Cu3PdN, Phys. Rev. Lett. 115, 036807 (2015).

[16] A. Yamakage, Y. Yamakawa, Y. Tanaka, and Y. Okamoto, Line-node dirac semimetal and topological insulating phase in noncentrosymmetric pnictides CaAgX (X P, As), J. Phys. Soc. Jpn. 85, 013708 (2016).

[17] S. Kobayashi, Y. Yamakawa, A. Yamakage, T. Inohara, Y. Okamoto, and Y. Tanaka, Crossing-line-node semimetals: Gen- eral theory and application to rare-earth trihydrides, Phys. Rev. B 95, 245208 (2017).

[18] S. Kobayashi, Y. Yanase, and M. Sato, Topologically stable gapless phases in nonsymmorphic superconductors, Phys. Rev. B 94, 134512 (2016).

[19] K. Funada, A. Yamakage, N. Yamashina, and H. Kageyama, Spin-orbit-coupling-induced type-I/type-II Dirac nodal-line metal in nonsymmorphic CaSb2, J. Phys. Soc. Jpn. 88, 044711 (2019).

[20] K. Momma and F. Izumi, VESTA 3 for three-dimensional visu- alization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, 1272 (2011).

[21] U. Ayachit, The ParaView Guide: A Parallel Visualization Ap- plication (Kitware Inc., Clifton Park, NY, USA, 2015)

[22] A. Ikeda, M. Kawaguchi, S. Koibuchi, T. Hashimoto, T. Kawakami, S. Yonezawa, M. Sato, and Y. Maeno, Supercon- ductivity in the nonsymmorphic line-nodal compound CaSb2, Phys. Rev. Materials 4, 041801(R) (2020).

[23] H. Takahashi, S. Kitagawa, K. Ishida, M. Kawaguchi, A. Ikeda,

onezawa, and Y. Maeno, S-wave superconductivity in the Dirac line-nodal material CaSb2, J. Phys. Soc. Jpn. 90, 073702 (2021).

[24] S. Kitagawa, K. Ishida, A. Ikeda, M. Kawaguchi, S. Yonezawa, and Y. Maeno, Peak in the superconducting transition tempera- ture of the nonmagnetic topological line-nodal material CaSb2 under pressure, Phys. Rev.B 104, L060504 (2021).

[25] S. Ono, H. C. Po, and K. Shiozaki, Z2-enriched symme-try indicators for topological superconductors in the 1651 magnetic space groups, Phys. Rev. Research 3, 023086 (2021).

[26] M. Oudah, J. Bannies, D. A. Bonn, and M. C. Aronson, Su- perconductivity and quantum oscillations in single crystals of the compensated semimetal CaSb2, Phys. Rev. B 105, 184504 (2022).

[27] See Supplemental Material at http://link.aps.org/supplemental/ 10.1103/PhysRevB.106.075151 for basic properties of the crys- tals: x-ray diffraction pattern, AC susceptibility, resistivity, and calculated band structure.

[28] S. Yonezawa, T. Higuchi, Y. Sugimoto, C. Sow, and Y. Maeno, Compact AC susceptometer for fast sample characterization down to 0.1 K, Rev. Sci. Instrum. 86, 093903 (2015).

[29] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri,L. Martin-Samos et al., QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).

[30] P. Giannozzi Jr, O. Andreussi, T. Brumme, O. Bunau,M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A. D. Corso, S. de Gironcoli, P. Delugas, R. A. D. Jr, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo et al., Ad- vanced capabilities for materials modelling with QUAN- TUM ESPRESSO, J. Phys.: Condens. Matter 29, 465901 (2017).

[31] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gra- dient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996).

[32] G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).

[33] A. Dal Corso, Pseudopotentials periodic table: From H to Pu, Comput. Mater. Sci. 95, 337 (2014).

[34] M. Buongiorno Nardelli, F. T. Cerasoli, M. Costa, S. Curtarolo,R. De Gennaro, M. Fornari, L. Liyanage, A. R. Supka, andH. Wang, PAOFLOW: A utility to construct and operate on ab initio Hamiltonians from the projections of electronic wave functions on atomic orbital bases, including characteri- zation of topological materials, Comput. Mater. Sci. 143, 462 (2018).

[35] F. T. Cerasoli, A. R. Supka, A. Jayaraj, M. Costa, I. Siloi,J. Sławin´ska, S. Curtarolo, M. Fornari, D. Ceresoli, and M. Buongiorno Nardelli, Advanced modeling of materials with PAOFLOW 2.0: New features and software design, Comput. Mater. Sci. 200, 110828 (2021).

[36] P. Rourke and S. Julian, Numerical extraction of de Haas–van Alphen frequencies from calculated band energies, Comput. Phys. Commun. 183, 324 (2012).

[37] D. Shoenberg, Magnetic Oscillations in Metals (Cambridge University Press, Cambridge, 1984).

[38] T. Ando, A. B. Fowler, and F. Stern, Electronic properties of two-dimensional systems, Rev. Mod. Phys. 54, 437 (1982).

[39] N. R. Werthamer, E. Helfand, and P. C. Hohenberg, Tempera- ture and purity dependence of the superconducting critical field, Hc2. III. Electron spin and spin-orbit effects, Phys. Rev. 147, 295 (1966).

[40] A. Gurevich, Enhancement of the upper critical field by non- magnetic impurities in dirty two-gap superconductors, Phys. Rev. B 67, 184515 (2003).

[41] M. Tinkham, Introduction to Superconductivity (Dover Publica- tions, New York, 2004).

[42] A. A. Abrikosov, Fundamentals of the Theory of Metals (Else- vier Science, Amsterdam, 1988).