Multiple energy scales and anisotropic energy gap in the charge-density-wave phase of the kagome superconductor ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$

Letter

Multiple energy scales and anisotropic energy gap in the charge-density-wave phase of the kagome superconductor ${CsV}_{3} {Sb}_{5}$

Kosuke Nakayama, Yongkai Li, Takemi Kato, Min Liu, Zhiwei Wang, Takashi Takahashi, Yugui Yao, and Takafumi Sato

Phys. Rev. B 104, L161112 – Published 21 October 2021

Abstract

Kagome metals $A V_{3} {Sb}_{5}$ ( $A = K$ , Rb, and Cs) exhibit superconductivity at 0.9–2.5 K and charge-density wave (CDW) at 78–103 K. Key electronic states associated with the CDW and superconductivity remain elusive. Here, we investigate low-energy excitations of ${CsV}_{3} {Sb}_{5}$ by angle-resolved photoemission spectroscopy. We found an energy gap of 50–70 meV at the Dirac-crossing points of linearly dispersive bands, pointing to an importance of spin-orbit coupling. We also found a signature of strongly Fermi-surface and momentum-dependent CDW gap characterized by the larger energy gap of maximally 70 meV for a band forming a saddle point around the $M$ point, the smaller (0–18 meV) gap for a band forming massive Dirac cones and a zero gap at the $Γ / A$ -centered electron pocket. The observed highly anisotropic CDW gap which is enhanced around the $M$ point signifies an importance of scattering channel connecting the saddle points, laying foundation for understanding the nature of CDW and superconductivity in $A V_{3} {Sb}_{5}$ .

Received 16 April 2021
Revised 18 August 2021
Accepted 6 October 2021

DOI:https://doi.org/10.1103/PhysRevB.104.L161112

Physics Subject Headings (PhySH)

Charge density waves Electronic structure Superconductivity Topological materials

Kagome lattice

Angle-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Kosuke Nakayama ^1,2,*,†, Yongkai Li^3,4,*, Takemi Kato¹, Min Liu^3,4, Zhiwei Wang ^3,4,†, Takashi Takahashi^1,5,6, Yugui Yao^3,4, and Takafumi Sato^1,5,6,7,†

¹Department of Physics, Faculty of Science, Tohoku University, Sendai 980-8578, Japan
²Precursory Research for Embryonic Science and Technology (PRESTO), Japan Science and Technology Agency (JST), Tokyo 102-0076, Japan
³Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China
⁴Beijing Key Lab of Nanophotonics and Ultrafine Optoelectronic Systems, Beijing Institute of Technology, Beijing 100081, China
⁵Center for Spintronics Research Network, Tohoku University, Sendai 980-8577, Japan
⁶WPI Research Center, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
⁷International Center for Synchrotron Radiation Innovation Smart (SRIS), Tohoku University, Sendai 980-8577, Japan

^*These authors contributed equally to this work.
^†Corresponding authors: k.nakayama@arpes.phys.tohoku.ac.jp; zhiweiwang@bit.edu.cn; t-sato@arpes.phys.tohoku.ac.jp

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 104, Iss. 16 — 15 October 2021

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) ARPES-intensity maps at binding energies ( $E_{B}$ 's) of $E_{F}$ , 0.3 eV, and 0.6 eV plotted as a function of $k_{x}$ and $k_{y}$ , for ${CsV}_{3} {Sb}_{5}$ measured at $T = 20$ K with 106-eV photons. (b) Photon-energy dependence of the normal-emission energy distribution curves (EDCs). The inner potential $V_{0}$ was estimated to be 10 eV. (c), (d) ARPES intensity as a function of wave vector and $E_{B}$ measured along the $Γ KM$ ( $k_{z} = 0$ ) and AHL ( $k_{z} = π$ ) cuts, respectively. Solid curve in (d) is a guide to the eyes to trace the experimental $γ$ band dispersion. (e) Calculated band structure along the $Γ KM Γ$ (AHLA) cut (top) without and (bottom) with SOC. Calculated $E_{F}$ is shifted downward by 50 meV to obtain a better matching with the experimental data. (f) EDCs at the Dirac-crossing points.
Reuse & Permissions
Figure 2
(a), (b) ARPES intensity along the MK cut ( $h ν = 106$ eV) measured at $T = 120$ K and 20 K, respectively. (c) EDCs at the k $_{F}$ point of the $δ$ band along the MK cut (magenta) and the $γ$ band along the LH cut (green). (d) Same as (b) but measured along the LH cut ( $h ν = 120$ eV). (e), (f) Same as (a) and (b) but measured at 21.2-eV photons. (g) Corresponding EDCs of (f). (h) Experimental band dispersion at $T = 10$ and 120 K extracted by tracing the peak position of EDCs in (e) and (f). Filled and open circles represent original and symmetrized data. (i) Temperature dependence of the EDC at the k $_{F}$ point of the shallow electron band measured across $T_{CDW}$ . Inset shows the magnified view for the EDC at 10 K. Black arrow indicates the peak position. (j) Same as (i) but symmetrized with respect to $E_{F}$ .
Reuse & Permissions
Figure 3
(a) Schematic FS in the surface BZ together with k cuts (cuts 1–6) and k points (points 1–6) where the intensity in (b) and the EDCs in (c) were obtained. Definition of the FS angle $θ$ is also indicated. (b) ARPES intensity measured at $T = 10$ K along cuts 1–6 in (a). (c), (d) EDCs and symmetrized EDCs at $T = 10$ K, respectively, at points 1–6 in (a). (e) Plots of the CDW-gap magnitude $Δ_{CDW}$ as a function of $θ$ . Magenta, red, blue, and green circles represent the CDW gaps for the saddle-point band, triangular FS centered at the $K / H$ point, hexagonal FS centered at the $Γ / A$ point, and electron band at the $Γ / A$ , respectively.
Reuse & Permissions
Figure 4
(a) ARPES intensity at $E_{F}$ measured at the $k_{z} \sim 0$ plane, together with the experimental FSs (solid curves) and the momentum region where the saddle point of the $δ$ band is present (magenta). (b) Original FSs extracted in (a) (solid curves) and their folded counterparts by the $2 \times 2$ CDW wave vector (dashed curves). Original and folded saddle-point regions are shown by magenta and light magenta, respectively.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Multiple energy scales and anisotropic energy gap in the charge-density-wave phase of the kagome superconductor ${CsV}_{3} {Sb}_{5}$

Kosuke Nakayama, Yongkai Li, Takemi Kato, Min Liu, Zhiwei Wang, Takashi Takahashi, Yugui Yao, and Takafumi Sato

Phys. Rev. B 104, L161112 – Published 21 October 2021

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

Supplemental Material (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review B

covering condensed matter and materials physics

Multiple energy scales and anisotropic energy gap in the charge-density-wave phase of the kagome superconductor CsV3Sb5

Kosuke Nakayama, Yongkai Li, Takemi Kato, Min Liu, Zhiwei Wang, Takashi Takahashi, Yugui Yao, and Takafumi Sato

Phys. Rev. B 104, L161112 – Published 21 October 2021

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

Supplemental Material (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Multiple energy scales and anisotropic energy gap in the charge-density-wave phase of the kagome superconductor ${CsV}_{3} {Sb}_{5}$