Fermiology and Origin of ${T}_{c}$ Enhancement in a Kagome Superconductor $\mathrm{Cs}({\mathrm{V}}_{1\ensuremath{-}x}{\mathrm{Nb}}_{x}{)}_{3}{\mathrm{Sb}}_{5}$

Fermiology and Origin of $T_{c}$ Enhancement in a Kagome Superconductor $Cs (V_{1 - x} {Nb}_{x})_{3} {Sb}_{5}$

Takemi Kato, Yongkai Li, Kosuke Nakayama, Zhiwei Wang, Seigo Souma, Fumihiko Matsui, Miho Kitamura, Koji Horiba, Hiroshi Kumigashira, Takashi Takahashi, Yugui Yao, and Takafumi Sato

Phys. Rev. Lett. 129, 206402 – Published 10 November 2022

Abstract

Kagome metals $A V_{3} {Sb}_{5}$ ( $A = K$ , Rb, and Cs) exhibit a characteristic superconducting ground state coexisting with a charge density wave (CDW), whereas the mechanisms of the superconductivity and CDW have yet to be clarified. Here we report a systematic angle-resolved photoemission spectroscopy (ARPES) study of $Cs (V_{1 - x} {Nb}_{x})_{3} {Sb}_{5}$ as a function of Nb content $x$ , where isovalent Nb substitution causes an enhancement of superconducting transition temperature ( $T_{c}$ ) and the reduction of CDW temperature ( $T_{CDW}$ ). We found that the Nb substitution shifts the Sb-derived electron band at the $Γ$ point downward and simultaneously moves the V-derived band around the $M$ point upward to lift up the saddle point (SP) away from the Fermi level, leading to the reduction of the CDW-gap magnitude and $T_{CDW}$ . This indicates a primary role of the SP density of states to stabilize the CDW. The present result also suggests that the enhancement of superconductivity by Nb substitution is caused by the cooperation between the expansion of the Sb-derived electron pocket and the recovery of the V-derived density of states at the Fermi level.

Received 9 March 2022
Revised 14 June 2022
Accepted 6 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.206402

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

Takemi Kato ^1,§, Yongkai Li^2,3,4,§, Kosuke Nakayama ^1,5,*, Zhiwei Wang ^2,3,4,†, Seigo Souma ^6,7, Fumihiko Matsui ⁸, Miho Kitamura ⁹, Koji Horiba ^9,10, Hiroshi Kumigashira ¹¹, Takashi Takahashi^1,6,7, Yugui Yao^2,3, and Takafumi Sato ^1,6,7,12,‡

¹Department of Physics, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
²Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, People’s Republic of China
³Beijing Key Lab of Nanophotonics and Ultrafine Optoelectronic Systems, Beijing Institute of Technology, Beijing 100081, People’s Republic of China
⁴Material Science Center, Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing 314011, People’s Republic of China
⁵Precursory Research for Embryonic Science and Technology (PRESTO), Japan Science and Technology Agency (JST), Tokyo 102-0076, Japan
⁶Center for Science and Innovation in Spintronics, Tohoku University, Sendai 980-8577, Japan
⁷Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, Sendai 980-8577, Japan
⁸UVSOR Synchrotron Facility, Institute for Molecular Science, Okazaki 444-8585, Japan
⁹Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
¹⁰National Institutes for Quantum Science and Technology (QST), Sendai 980-8579, Japan
¹¹Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University, Sendai 980-8577, Japan
¹²International Center for Synchrotron Radiation Innovation Smart (SRIS), Tohoku University, Sendai 980-8577, Japan

^*Corresponding author. k.nakayama@arpes.phys.tohoku.ac.jp
^†Corresponding author. zhiweiwang@bit.edu.cn
^‡Corresponding author. t-sato@arpes.phys.tohoku.ac.jp
^§T. K. and Y. L. contributed equally to this work.

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Vol. 129, Iss. 20 — 11 November 2022

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Figure 1
(a), (b) Crystal structure and bulk Brillouin zone (BZ) of $Cs (V_{1 - x} {Nb}_{x})_{3} {Sb}_{5}$ (CVNS), respectively. (c) Superconducting ( $T_{c}$ ) and CDW ( $T_{CDW}$ ) transition temperatures of CVNS plotted against $x$ [66]. (d) ARPES-intensity map at $E_{F}$ plotted as a function of $k_{x}$ and $k_{y}$ , measured at $T = 120 K$ with $h ν = 106 eV$ . Red, purple, and blue dashed lines are guides for the eye to trace the experimental Fermi surfaces. (e) ARPES intensity at $T = 120 K$ measured along a yellow dotted line in (d).
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Figure 2
(a) ARPES-intensity plot along the $Γ K M$ cut for $x = 0.07$ measured at $T = 120 K$ with $h ν = 106 eV$ . Crosses show experimental band dispersion extracted from the peak position in EDCs and MDCs. (b) Same as (a) but for $x = 0$ . (c) Comparison of band dispersions between $x = 0.07$ and $x = 0$ [same as red and black crosses in (a) and (b)]. (d),(e) Comparison of MDCs at $E_{F}$ and EDCs at $k_{y} = 0$ [the cuts are indicated by white dashed lines in (a)], respectively, between $x = 0.07$ (red) and $x = 0$ (black). The horizontal axis in (d), $k_{y} / | k_{Γ K} |$ , is defined as the $k_{y}$ value in units of the $Γ K$ length where the $Γ$ and $K$ points correspond to 0 and 1, respectively. Red dashed lines in (d) are a guide for the eye to trace the peak position of $x = 0.07$ . Triangles in (e) indicate the peak position. (f)–(h) ARPES intensity near $E_{F}$ around the $M$ point for $x = 0$ , 0.03, and 0.07, respectively, plotted as a function of binding energy and the $k_{y}$ value in units of the $M K$ length, $k_{y} / | k_{M K} |$ . Temperature of the measurement was set above $T_{CDW}$ (120, 90, 120 K for $x = 0$ , 0.03, and 0.07, respectively). (i) Comparison of experimental band dispersions in the $E - k_{y}$ window shown by a black dashed box in (f) among $x = 0$ (black circles), 0.03 (blue circles), and 0.07 (red circles). Inset shows the representative fitting result (green curve) to the EDC at the $k_{F}$ point for $x = 0.07$ (red circles). The $k_{F}$ point is indicated by black arrow in (i). The fitting assumes a single Lorentzian peak (black curve) multiplied by the Fermi-Dirac distribution (FD) function convoluted with a resolution function.
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Figure 3
(a) Plot of ARPES intensity near $E_{F}$ along the $M K$ cut for $x = 0.07$ measured at $T = 10 K$ . Red arrows indicate the $κ$ and $δ$ bands. (b) Experimental band dispersion obtained by numerical fittings to the EDCs in (c) with double Lorentzian peaks multiplied by the FD function convoluted with the resolution function. (c) Corresponding EDCs of (a). Dots show experimental dispersion of the $κ$ and $δ$ bands [same as red circles in (b)]. (d) Schematic Fermi surface in the surface BZ together with the $k_{F}$ points ( $P 1 - P 6$ ) where the EDCs in (e) were obtained. (e), (f) EDCs and symmetrized EDCs at $T = 10 K$ at $P 1 - P 6$ in (d). (g) Temperature dependence of the EDC at $P 1$ for $x = 0.07$ . (h)–(j) Temperature dependence of the symmetrized EDC at $P 1$ for $x = 0.07$ , 0.03, and 0, respectively. (k) Plots of $Δ_{δ}$ (squares) and $Δ_{κ}$ (triangles) against temperature for each $x$ . Curves represent the fitting result with the mean-field form $Δ \tanh [1.74 (T_{CDW} / T - 1)^{1 / 2}]$ with $T_{CDW} = 93 K$ , 77 K, and 58 K for $x = 0$ , 0.03, and 0.07, respectively. (l) EDC at $P 1$ at $T = 10 K$ for $x = 0.07$ , 0.03, and 0. Solid squares and triangles show the CDW gap of the SP band $Δ_{δ}$ and the shallow electron pocket $Δ_{κ}$ obtained by the same fittings as that in (b). (m) Plots of $Δ_{δ}$ (red squares) and $Δ_{κ}$ (red triangles) against $x$ , compared with the experimental $T_{CDW}$ from ARPES (black circles) and transport (white circles) measurements.
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Physical Review Letters

Fermiology and Origin of Tc Enhancement in a Kagome Superconductor Cs(V1−xNbx)3Sb5

Takemi Kato, Yongkai Li, Kosuke Nakayama, Zhiwei Wang, Seigo Souma, Fumihiko Matsui, Miho Kitamura, Koji Horiba, Hiroshi Kumigashira, Takashi Takahashi, Yugui Yao, and Takafumi Sato

Phys. Rev. Lett. 129, 206402 – Published 10 November 2022

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Fermiology and Origin of $T_{c}$ Enhancement in a Kagome Superconductor $Cs (V_{1 - x} {Nb}_{x})_{3} {Sb}_{5}$