Anomalous Hall eect and two-dimensional Fermi surfaces in the charge-density-wave state of kagome metal RbV 3Sb5 Lingfei Wangx1Wei Zhangx1Zheyu Wangx1Tsz Fung Poon1Wenyan Wang1Chun Wai Tsang1

2025-04-30 0 0 722.8KB 8 页 10玖币

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Anomalous Hall eﬀect and two-dimensional Fermi surfaces

in the charge-density-wave state of kagome metal RbV3Sb5

Lingfei Wang§,1Wei Zhang§,1Zheyu Wang§,1Tsz Fung Poon,1Wenyan Wang,1Chun Wai Tsang,1

Jianyu Xie,1Xuefeng Zhou,2Yusheng Zhao,2Shanmin Wang,2Kwing To Lai,1, 3, ∗and Swee K. Goh1, †

1Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China

2Department of Physics, Southern University of Science and Technology, Shenzhen, Guangdong, China

3Shenzhen Research Institute, The Chinese University of Hong Kong, Shatin, Hong Kong, China

(Dated: February 10, 2023)

AV3Sb5(A=Cs, K, Rb) are recently discovered superconducting systems (Tc∼0.9−2.5 K) in

which the vanadium atoms adopt the kagome structure. Intriguingly, these systems enter a charge-

density-wave (CDW) phase (TCDW ∼80−100 K), and further evidence shows that the time-reversal

symmetry is broken in the CDW phase. Concurrently, the anomalous Hall eﬀect has been observed

in KV3Sb5and CsV3Sb5inside the novel CDW phase. Here, we report a comprehensive study of a

high-quality RbV3Sb5single crystal with magnetotransport measurements. Our data demonstrate

the emergence of anomalous Hall eﬀect in RbV3Sb5when the charge-density-wave state develops.

The magnitude of anomalous Hall resistivity at the low temperature limit is comparable to the

reported values in KV3Sb5and CsV3Sb5. The magnetoresistance channel further reveals a rich

spectrum of quantum oscillation frequencies, many of which have not been reported before. In

particular, a large quantum oscillation frequency (2235 T), which occupies ∼56% of the Brillouin

zone area, has been recorded. For the quantum oscillation frequencies with suﬃcient signal-to-noise

ratio, we further perform ﬁeld-angle dependent measurements and our data indicate two-dimensional

Fermi surfaces in RbV3Sb5. Our results provide indispensable information for understanding the

anomalous Hall eﬀect and band structure in kagome metals AV3Sb5.

I. INTRODUCTION

Kagome lattice intrinsically hosts the ﬂat electronic

band, van Hove singularities and the Dirac band1–3.

Thus, when the charge degree of freedom is enabled, a

kagome system provides an important platform to ex-

plore both the eﬀect of electronic correlation and topolog-

ical physics, and a rich variety of phenomena can be ex-

pected. The recently discovered kagome metals AV3Sb5

(A=K, Rb, Cs), in which the V atoms form a perfect

kagome net, are an ideal manifestation of the diverse phe-

nomena this structural class can oﬀer4–25. Indeed, calcu-

lations and experiments have revealed several Dirac-like

band crossings near the Fermi energy with a non-zero Z2

topological invariant5,11,26. Furthermore, these systems

exhibit interesting and intertwining electronic phases, in-

cluding a charge-density-wave (CDW) phase, electronic

nematicity as well as superconductivity4–25.

The CDW phase of AV3Sb5, which sets in at TCDW ∼

80 −100 K, has been argued to have an unconven-

tional origin. Chiral charge order, the absence of

acoustic phonon anomaly, and time-reversal symme-

try breaking (TRSB) have been observed in the CDW

phase8,15,20,27–35. Below TCDW, a giant anomalous Hall

eﬀect (AHE) has been reported in KV3Sb5and CsV3Sb5,

supporting the notion of TRSB20,21. Given that the su-

perconductivity, which sets in at Tc∼0.9−2.5 K, arises

from this unconventional metallic state, understanding

the CDW phase and the phenomena associated with the

CDW phase is essential for deepening the understanding

of the superconducting state. Further evidence of the

nontrivial interplay between the CDW state and super-

conductivity comes from pressure studies - while TCDW

is suppressed monotonically by pressure, Tcshows an un-

usual double dome dependence on pressure6,7,22,36.

Although all three AV3Sb5compounds show similar

physical properties, CsV3Sb5is currently the most heav-

ily studied, probably because it has the highest Tc. How-

ever, both KV3Sb5and RbV3Sb5should also be investi-

gated to build an overall picture for understanding this

family of V-based kagome superconductors. For instance,

aµSR experiment shows that the superconducting energy

gap can be tuned from nodal at ambient pressure to node-

less under pressure in RbV3Sb5and KV3Sb532, but this

tunability is absent in CsV3Sb5where the gap is found

to be nodeless over a large pressure range37. Whether

the observed nodal gap is related to TRSB needs to be

addressed. However, the anomalous Hall eﬀect (AHE),

a signature of TRSB, has not been comprehensively re-

ported in RbV3Sb5, to the best of our knowledge.

Detailed studies of the Fermi surface via quan-

tum oscillations have also been lacking in RbV3Sb5,

again in stark contrast to the progress made in

CsV3Sb520,22,26,38–45. In the pioneering work by Yin et

al.46, only two quantum oscillation frequencies at a single

ﬁeld angle are reported. In particular, these frequencies

are rather small – Fα= 34 T and Fβ= 117 T, indicating

the detection of small Fermi surface sheets. However,

much larger frequencies up to 9930 T when the mag-

netic ﬁeld is parallel to the c-axis have been reported

in CsV3Sb544. Therefore, it is urgently needed to re-

investigate the Fermi surface of RbV3Sb5via quantum

oscillations.

In this manuscript, we focus on RbV3Sb5and con-

duct a series of magnetotransport experiments on high-

quality single crystals. We ﬁrst patch the gap in the

arXiv:2210.13250v2 [cond-mat.supr-con] 9 Feb 2023

literature by reporting the observation of a large AHE

in RbV3Sb5. Next, we analyze the magnetoresistance,

uncovering quantum oscillations (the Shubnikov-de Haas

(SdH) eﬀect) with 12 frequencies. Notably, the largest

frequency detected is 2235 T, nearly 20 times larger

than the largest frequency reported by Yin et al.46. Fi-

nally, our ﬁeld angle dependent data establish that these

frequencies are associated with quasi-two-dimensional

Fermi surface sheets.

II. METHODS

ρ (µΩ·cm)

3002001000

T (K)

(b)

RbV3Sb5

RRR = 76.6

Tc = 1.3 K

0.5

0.4

0.3

0.2

0.1

0.0

dρ/dT (µΩ·cm/K)

1601208040 T (K)

Intensity (a.u.)

908070605040302010

2θ (deg.)

(001)

(002)

(003)

(004)

(005)

(006)

(007)

(008)

(a)

0.5

ρ (µΩ·cm)

20 T (K)

FIG. 1. (a) X-ray diﬀraction pattern of a RbV3Sb5single

crystal showing only (00L) peaks. (b) Temperature depen-

dence of the resistivity of RbV3Sb5under a zero external

magnetic ﬁeld. The RRR is 76.6. The inset displays the

superconducting transition starting at 1.3 K. (c) Tempera-

ture dependence of dρ/dT, displaying a sharp peak at TCDW

= 96.3 K.

Single crystals of RbV3Sb5were synthesized from Rb

(ingot, 99.95 %), V (powder, 99.9 %) and Sb (shot,

99.9999 %) using self-ﬂux method similar to Ref. [46].

Raw materials with the molar ratio of Rb:V:Sb = 5.5:7:14

were sealed in a quartz tube. To avoid the possible in-

ﬂuence of the ambient environment, all preparation pro-

cesses were performed in an argon-ﬁlled glovebox, before

the quartz tube was moved to the furnace for heat treat-

ment. The mixture was ﬁrst heated to 1000◦C with the

rate of 20◦C/h. After being held at 1000 ◦C for 24 h,

it was cooled to 900◦C at 50 ◦C/h, followed by a fur-

ther cooling to 400◦C at 2 ◦C/h. The excess ﬂux was

removed by distilled water and ethanol. The as-grown

single crystals were millimeter-sized shinny plates.

X-ray diﬀraction (XRD) data were collected at room

temperature by using a Rigaku X-ray diﬀractometer with

CuKαradiation. The chemical compositions were char-

acterized by a JEOL JSM-7800F scanning electron micro-

scope equipped with an Oxford energy-dispersive X-ray

EDX spectrometer.

For magnetotransport measurements, the sample was

ﬁrstly exfoliated from a bulk crystal and then transferred

to a diamond surface pre-patterned with Au/Ti elec-

trodes in a standard six-probe Hall bar conﬁguration. A

polydimethylsiloxane (PDMS) ﬁlm were used to perform

the transfer and Dupont 6838 silver paste was used to

connect external leads with the electrodes. The transfer

process was also performed in the glove box, and in or-

der to protect the sample, we capped the sample with a

thin layer (∼500 nm) of h-BN. The thickness of the thin

ﬂakes and h-BN was determined by a dual-beam focused

ion beam system (Scios 2 DualBeam by Thermo Scien-

tiﬁc). These steps are similar to procedures optimized by

us in Refs. 47 and 48.

Low-temperature and high-ﬁeld measurements were

carried out in a commercial Physical Property Measure-

ment System (PPMS) by Quantum Design. A Stanford

Research 830 lock-in ampliﬁer was used for Shubnikov-de

Haas measurements, while the standard PPMS Resistiv-

ity option was used for recording magnetoresistance and

Hall eﬀect. The rotator insert option by Quantum Design

was used to tilt the angle between magnetic ﬁeld and the

ab plane of the sample. During the rotation, the current

direction is kept perpendicular to the magnetic ﬁeld. A

dilution fridge was additionally employed to measure the

superconducting transition in RbV3Sb5.

III. RESULTS

Figure 1(a) displays the XRD pattern of an as-grown

single crystal of RbV3Sb5. The data can be indexed

by the (00L) patterns from the crystal structure of

RbV3Sb5(space group: P6/mmm) reported in previous

studies4,46. This shows that our sample has a preferred

orientation, as expected for a single crystal of layered ma-

terials. The chemical composition of the single crystal is

obtained to be Rb:V:Sb = 0.94:2.86:5 via EDX (see the

Supplementary Information), which further conﬁrms the

result of XRD in Fig. 1(a).

Figure 1(b) shows the temperature dependence of

the electrical resistivity (ρ(T)) of our RbV3Sb5sam-

ple. The residual resistivity ratio (RRR) (deﬁned as

ρ(300K)/ρ(2K)) is about 77, currently one of the highest

reported values. The dρ/dTvs. Trelation is shown in

Fig. 1(c), where an anomaly can be clearly identiﬁed at

96.3 K. We associate this anomaly with TCDW, and our

value is slightly lower than the reported value for this

compound 46,49,50.

The availability of high-quality single crystals enables

us to investigate the important transport phenomena in

RbV3Sb5. We are particularly interested in anomalous

Hall eﬀect and quantum oscillations. We have performed

Hall measurements over a wide range of temperatures.

Figure 2(a) shows the Hall response below TCDW while

Fig. 2(b) shows that at temperatures higher than TCDW.

The magnetic ﬁeld (B) is parallel to the c-axis. At

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AnomalousHalleectandtwo-dimensionalFermisurfacesinthecharge-density-wavestateofkagomemetalRbV3Sb5LingfeiWangx,1WeiZhangx,1ZheyuWangx,1TszFungPoon,1WenyanWang,1ChunWaiTsang,1JianyuXie,1XuefengZhou,2YushengZhao,2ShanminWang,2KwingToLai,1,3,andSweeK.Goh1,y1DepartmentofPhysics,TheChineseUniversityofHo...

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Anomalous Hall eect and two-dimensional Fermi surfaces in the charge-density-wave state of kagome metal RbV 3Sb5 Lingfei Wangx1Wei Zhangx1Zheyu Wangx1Tsz Fung Poon1Wenyan Wang1Chun Wai Tsang1

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