Coexistence of Bulk-Nodal and Surface-Nodeless Cooper Pairings in a Superconducting Dirac Semimetal

Xian P. Yang, Yigui Zhong, Sougata Mardanya, Tyler A. Cochran, Ramakanta Chapai, Akifumi Mine, Junyi Zhang, Jaime Sánchez-Barriga, Zi-Jia Cheng, Oliver J. Clark, Jia-Xin Yin, Joanna Blawat, Guangming Cheng, Ilya Belopolski, Tsubaki Nagashima, Sahand Najafzadeh, Shiyuan Gao, Nan Yao, Arun Bansil, Rongying Jin, Tay-Rong Chang, Shik Shin, Kozo Okazaki, and M. Zahid Hasan

Phys. Rev. Lett. 130, 046402 – Published 25 January 2023

Abstract

The interplay of nontrivial topology and superconductivity in condensed matter physics gives rise to exotic phenomena. However, materials are extremely rare where it is possible to explore the full details of the superconducting pairing. Here, we investigate the momentum dependence of the superconducting gap distribution in a novel Dirac material PdTe. Using high resolution, low temperature photoemission spectroscopy, we establish it as a spin-orbit coupled Dirac semimetal with the topological Fermi arc crossing the Fermi level on the (010) surface. This spin-textured surface state exhibits a fully gapped superconducting Cooper pairing structure below $T_{c} \sim 4.5 K$ . Moreover, we find a node in the bulk near the Brillouin zone boundary, away from the topological Fermi arc. These observations not only demonstrate the band resolved electronic correlation between topological Fermi arc states and the way it induces Cooper pairing in PdTe, but also provide a rare case where surface and bulk states host a coexistence of nodeless and nodal gap structures enforced by spin-orbit coupling.

Received 25 April 2022
Accepted 3 January 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.046402

Physics Subject Headings (PhySH)

Electrical properties Fermi surface Superconducting gap Topological superconductors

Dirac semimetal Topological materials

Angle-resolved photoemission spectroscopy First-principles calculations Tight-binding model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xian P. Yang ^1,*, Yigui Zhong², Sougata Mardanya³, Tyler A. Cochran¹, Ramakanta Chapai⁴, Akifumi Mine ², Junyi Zhang ^5,†, Jaime Sánchez-Barriga ^6,7, Zi-Jia Cheng¹, Oliver J. Clark ⁶, Jia-Xin Yin⁸, Joanna Blawat^4,9, Guangming Cheng ¹⁰, Ilya Belopolski¹, Tsubaki Nagashima², Sahand Najafzadeh², Shiyuan Gao⁵, Nan Yao ¹⁰, Arun Bansil¹¹, Rongying Jin ^4,9, Tay-Rong Chang^3,12,13, Shik Shin^2,14,15, Kozo Okazaki ^2,15,16, and M. Zahid Hasan^1,10,17,‡

¹Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
²Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
³Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
⁴Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
⁵Institute for Quantum Matter and Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
⁶Helmholtz-Zentrum Berlin für Materialien und Energie, Elektronenspeicherring BESSY II, Albert-Einstein Strasse 15, Berlin 12489, Germany
⁷IMDEA Nanoscience, C/ Faraday 9, Campus de Cantoblanco, Madrid 28049, Spain
⁸Department of Physics, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
⁹Center for Experimental Nanoscale Physics, Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina 29208, USA
¹⁰Princeton Institute for Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
¹¹Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
¹²Center for Quantum Frontiers of Research and Technology (QFort), Tainan 701, Taiwan
¹³Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
¹⁴Office of University Professor, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
¹⁵Material Innovation Research Center, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
¹⁶Trans-scale Quantum Science Institute, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
¹⁷Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

^*xiany@princeton.edu
^†jzhan312@jhu.edu
^‡mzhasan@princeton.edu

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Vol. 130, Iss. 4 — 27 January 2023

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Images

Figure 1
Superconductivity and crystal structure of PdTe. (a) The crystal structure of PdTe, with Pd in blue and Te in cyan. (b) Bulk and surface Brillouin zones of PdTe. High symmetry points are marked. (c) Temperature-dependence zero-field electrical resistivity of PdTe at low temperature between 2 and 10 K. The dashed line is a guide for the eye. (d) Calculated bulk electronic structure of PdTe with spin-orbit coupling included. The bulk Dirac crossing is marked by the circle. The Fermi level is adjusted according to the experimental data. (e) Side surface scanning transmission electron microscope (STEM) image of PdTe. The unit cell is superimposed on top of the STEM image. (f) Semi-infinite Green’s function surface calculations along the high symmetry directions on the (010) Pd-terminated surface.
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Figure 2
Dirac crossing and Fermi arc state in PdTe above $T_{c}$ . (a) ARPES constant energy contour at binding energy of 100 meV corresponding to the Dirac crossing on the Te-terminated (010) surface. Red dotted lines indicate ARPES dispersion cuts 1–3 in (c)–(e). Purple dots represent the projection of the Dirac cone and the yellow dotted lines connecting these dots are Fermi arc surface states. (b) Calculated constant energy contour of (a). (c) ARPES dispersion map (i) along cut 1 in (a). Black arrow is the Fermi arc state. Corresponding semi-infinite Green’s function surface calculations including (ii) and excluding (iii) surface states contributions. (d) ARPES dispersion map (i) and corresponding DFT calculations (ii, iii) along cut 2 in (a). Black arrow in (i) indicates the surface state connecting to the bulk Dirac crossing. (e) ARPES dispersion map (i) and corresponding DFT calculations (ii, iii) along cut 3 in (a). Black arrow in (i) represents the bulk Dirac crossing.
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Figure 3
Spin polarization of the Fermi arc state above $T_{c}$ . (a) ARPES dispersion map of the Fermi arc state [same position as cut 1 in Fig. 2]. The yellow dotted lines represent the two momenta selected for spin-resolved photoemission measurements. (b)–(c) Spin-resolved intensity and polarization along the in-plane direction ( $k_{z}$ direction) for $k 1$ and $k 2$ .
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Figure 4
Fully gapped surface states and gapless bulk node in the superconducting state of PdTe. (a) Comparison between laser ARPES Fermi surface map (right) and slab calculation (left) for the Pd termination in PdTe. Several points marked by red dots (red stars) along the Fermi arc (on the bulk states) are selected for superconducting gap measurements. $Ø$ defines the angles used in (b)–(c). (b)–(c) Symmetrized energy distribution curves (EDCs) corresponding to the red dots and stars in (a) below and above the critical temperature. The specific momentum locations of EDCs are marked by the Fermi surface angles defined in (a). All symmetrized EDCs reveal the opening of the superconducting gap below the critical temperature. Solid black lines represent fits to the Dynes’ function. Experimental Fermi level position is determined by measuring a gold reference. (d) VUV ARPES Fermi surface map on the (010) surface. Laser ARPES Fermi surface map with much smaller momentum range is embedded on the VUV ARPES result. High symmetry points are marked in red. The location of the gapless node is indicated by the red square. (e) Temperature dependence of the EDC corresponding to the red square marked in (d) showing a node in the bulk band structure below the critical temperature. (f) Symmetrized EDCs in (e) indicating the existence of a nodal point.
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