Nodeless electron pairing in CsV3Sb5-derived
kagome superconductors

Laser and Synchrotron Research Center, The Institute for Solid States Physics
Yigui Zhong, Kozo Okazaki
Overview
Thekagomelattice,consisting ofcorner-shared

triangles (inset of Fig. 1), is an exciting platform for
emergent quantum phenomena, since its electronic
structure is featured with a flat band, a Dirac cone, andvan Hove singularities. Recently, superconductivity thatintertwines with charge density wave (CDW) has been
observed in kagome metals AV3Sb5 (A = K, Rb, Cs) [1-2].
Toilluminate

thepairing

mechanism

andtheinterplays between multiple phases, a fundamental
issue is to determine the superconducting (SC) gap

Fig. 1. Phase diagram of substituted CsV3Sb5. The inset
illustrates Ta or Nb substitutions by V atoms in V-Sb layer.

symmetry. However, it remains elusive owing to theexistence of several conflicting experimental results [2]Results

and lack of a momentum-dependent measurements of SC

We first map out the Fermi surface (FS). Fig. 2a shows agap structure. Angle-resolved photoemission spectroscopy

joint FS of the Ta0.14 sample by combing three(ARPES) has been proved to be a powerful tool to directly

segments, which is consistent with whole-FS mapping

measure the SC gap in the momentum space [3].

using a larger photon energy [4]. Three FS sheets – aNevertheless, the relatively low transition temperature

circular electron-like pocket (marked as α) and a(Tc) renders the precise ARPES determination of the gap

hexagonal hole-like pocket (marked as β) at Brillouinin the SC state extremely challenging.

Zone (BZ) center Γ point, and a triangle pocket (markedIn this work, we utilize an ultrahigh-resolution and lowtemperature laser-ARPES, together with a chemical
substitution of V in CsV3Sb5, that raises Tc, to preciselyas δ) at the BZ corner K point – are well distinguished.
This makes the determination of the Fermi momentum(kF) reliable.

measure the gap structure in the SC state. Considering

Before investigating the SC gap structure, we confirm

the accessibility in terms of temperature and possible

the spectral evidence of the superconductivity. Using theinfluence of CDW, we select Cs(V0.93Nb0.07)3Sb5 andTa0.14 sample as an example, the temperature-Cs(V0.86Ta0.14)3Sb5 for the SC gap measurement (denoteddependent EDCs of a cut on β FS are shown in Fig. 2b.

as Nb0.07 and Ta0.14, respectively). The Nb0.07 sample

Apparently, at T = 2 K, far below Tc, the emergent

exhibits Tc of 4.4 K and a CDW transition at TCDW = 58

quasiparticle peak around the Fermi level (EF) clearly

K, whereas the Ta0.14 sample exhibits a Tc of 5.2 K, butindicates the opening of an SC gap. With temperature

no clear CDW transition (Fig. 1). Our results uncover thegradually increasing, the growing intensity at EF and theSC gap structures of both samples are isotropic,

approaching peaks suggest that the SC gap becomes

regardless of the disappearance of CDW, hinting at asmaller and eventually closes. The fitted SC gap

robust nodeless pairing in CsV3Sb5-derived kagome

amplitudes versus temperature are summarized in thesuperconductors [4].

inset of Fig. 2b. The estimated Tc of approximately 5.2 K1

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Fig. 2. Isotropic superconducting gap in Cs(V0.86Ta0.14)3Sb5. a. Fermi surface mappings. b. Temperaturedependent EDCs at kF in a cut marked as a black line in a. c-e, EDCs at kF along with the a, b, and d FS,respectively. f, Positions of examined kF. g, SC gap amplitude from the fits to EDCs at kF. The shaded areas
represent the error bars.
is consistent with the bulk Tc determined by resistivity

isotropic (Fig. 3a). The averaged gap amplitude ∆Nb ismeasurements, demonstrating the high quality of the0.54 ± 0.06 meV, giving out a weaker ratio 2∆Nb/kBTc ofsamples and the high precision of our SC gap

2.83 ± 0.32. By turning the photon energy from 5.8 eV tomeasurements.

7eV, we further study the z-direction momentum (kz)dependence of the SC gap. We find that the SC gap

We then study the momentum dependence of the SC gap

remains nearly the same at these two kz planes withinin the Ta0.14 sample with the CDW order fully

our experimental uncertainties. Giving the direct

suppressed. The EDCs at kF of α, β and δ FSs are

momentum-resolved capability of ARPES and thepresented in Figs. 2c-e. Near EF, the leading edges of theprominent features of SC gap opening, our data reveal aEDCs at 2 K all show a shift compared to that at 7 K.

nodeless, nearly isotropic and orbital-independent SC

Moreover, they universally show a strong coherence peakgap in both Nb0.07 and Ta0.14 samples (Fig. 3a, b).

at the same binding energy, indicating an isotropic SC
gap structure. Fitting these EDCs to a Bardeen–Cooper–Discussion and outlook

Schrieffer (BCS) spectral function, the quantitatively

As shown in Fig. 3c, the isovalent substitutions of Nb/Ta

extracted gap amplitudes of the different FSs have rarely

for V atoms can be viewed as effective in-plane negative

fluctuated amplitudes with an average ∆Ta of 0.77 ± 0.06

pressure, which suppresses the CDW order while itmeV (Fig. 2g), yielding a ratio 2 ∆Ta/kBTc of 3.44 ± 0.27

enhances the superconductivity. Our results uncover a(where kB is the Boltzmann constant).

fact that the same isotropic SC gap structure on
suppression of CDW, different from the observation of aNext, we turn to examine the SC gap structure of thenodal-to-nodeless in the sister compounds KV3Sb5 andNb0.07 sample, where TCDW gets slightly suppressed.

RbV3Sb5 under hydrostatic pressure [5], suggesting a

After checking the FS topology like that of the Ta0.14

probably weak CDW-SC competition in CsV3Sb5.

sample, we take the EDCs at kF positions of three FSs.
By fitting them with a BCS spectral function,

Our results allow us further to discuss the pairing

quantitatively, the SC gap amplitudes remain nearly

symmetry. The robust isotropic SC gaps with small■■■■ ■■■

物性研だより第 64 巻第 1 号

2Innovation Program from the Japan Science andTechnology Agency (JST) and MEXT Quantum Leap
Flagship Program of Japan (MEXT Q-LEAP) (grant No.
JPMXS0118068681).

References[1] J. -X. Yin et al., Nature 612, 647 (2022).
[2] B. R. Ortiz et al., Phys. Rev. Mater. 3, 094407 (2019).
[3] J. A. Sobota et al., Rev. Mod. Phys. 93, 025006 (2021).
[4] Y. Zhong et al., Nature 617, 488 (2023).
[5] Guguchia Z. et al., Nature Commun. 14, 153 (2023).
[6] Y. Zhong et al., Nature Commun. 14, 1945 (2023).
[7] R. Gupta et al., Commun. Phys. 5, 232 (2022).

Fig. 3. Robust isotropic SC gap on suppression of CDW. a,b,Schematic momentum-dependent SC gap of the Nb0.07 andTa0.14 samples, respectively. c, Schematic phase diagram asfunction of the lattice expansion due to substitutions. Here,δa is the change of the in-plane lattice constant relative topristine CsV3Sb5.

2∆/kBTc seem to be consistent with a conventional s-wave
pairing. This is also supported by the observed band
dispersion

kinks

stemming

fromelectron-phonon

couplings, as well as the positive correlation between thecoupling strength and Tc [6]. Precisely, these results do
not rule out other nodeless pairing states due to the lackofphase

informationinARPES

measurements.

Particularly, the observation of increased muon spin
relaxation rate on CDW-suppressed CsV3Sb5 by pressure
provide evidence for the potential presence of timereversal-symmetry-breaking

superconductivity[7],highlighting the need for further examination. In
addition, a direct ARPES investigation on pristineCsV3Sb5 will be more helpful to further pin down thepairing symmetry.
Acknowledgements
This work was supported by the Grants-in-Aid for
Scientific Research (KAKENHI) (grant No. JP18K13498,
JP19H01818, JP19H00651 and JP21H04439) from theJapan Society for the Promotion of Science (JSPS), JSPS
KAKENHI on Innovative Areas “Quantum LiquidCrystals” (grant No. JP19H05826), the Center of3

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