Manipulating charge density wave state in kagome compound RbV3Sb5

Yu-Xin Meng(孟雨欣), Cheng-Long Xue(薛成龍), Li-Guo Dou(竇立國), Wei-Min Zhao(趙偉民),Qi-Wei Wang(汪琪瑋), Yong-Jie Xu(徐永杰), Xiangqi Liu(劉祥麒),Wei Xia(夏威),4, Yanfeng Guo(郭艷峰),4,?, and Shao-Chun Li(李紹春),5,6,?

1National Laboratory of Solid State Microstructures,School of Physics,Nanjing University,Nanjing 210093,China

2Collaborative Innovation Center of Advanced Microstructures,Nanjing University,Nanjing 210093,China

3School of Physical Science and Technology,Shanghai Tech University,Shanghai 201210,China

4Shanghai Tech Laboratory for Topological Physics,Shanghai 201210,China

5Jiangsu Provincial Key Laboratory for Nanotechnology,Nanjing University,Nanjing 210093,China

6Hefei National Laboratory,Hefei 230088,China

Keywords: kagome material,charge density wave,scanning tunneling microscopy

Kagome lattice is a corner-shared triangular network,and has attracted great attentions due to the intriguing electronic features including flat bands, Dirac cones and van Hove singularity (vHs).This model system exhibits various exotic properties, such as quantum spin liquid,[1,2]topological electronic states,[3–6]superconductivity(SC),[7–9]and charge density wave (CDW) states,[8–11]etc.Recently, a new family of kagome materials, namelyAV3Sb5(A= K,Rb, Cs), was discovered, in which rich quantum phases have been revealed.[12,13]AV3Sb5undergoes both of the superconductivity transition (TC=～0.9 K–2.5 K) and the CDW (TCDW=～78 K–103 K).[12–14]During the CDW transition, an in-plane unit-cell doubling with the 2×2 periodicity[13,15–18]occurs, as also accompanied by a threedimensional 2×2×2/2×2×4 ordering[19,20]and a surface 1×4 superstructure.[15,21]It was considered that the CDW phase exhibits some complicated entanglement with the superconductivity transition.[22–24]The CDW electronic order was initially manifested in the transport measurement as a magnetic anomaly, and then explored through a myriad of experimental and theoretical methods.[16,25–32]Scanning tunneling microscopy/spectroscopy (STM/STS) studies reveled a chiral charge order in the three compounds with the 2×2 order,[33–35]and a rotational symmetry breaking of the electronic ground state from C6to C2at low temperatures.[36,37]This anisotropy was considered as a chiral charge order with broken time-reversal symmetry due to its magnetic field switching effect, and possibly related with the observed anomalous Hall effect without a magnetic order.[38,39]To unveil the driving force for the CDW transition is no doubt essential to the understanding of its interplay with the superconductivity and the kagome physics inAV3Sb5materials.However,the mechanism of the CDW transition remains still under debate.

First-principle calculation and measurements indicated that the CDW transition is driven by the van Hove singularityrelated Fermi surface(FS)nesting.[30,40]Angle-resolved photoelectron spectroscopy(ARPES)measurement demonstrated a substantial reconstruction of Fermi surface and the dominant role of the in-plane inter-saddle-point scattering to the CDW transition.[41]Optical characterization showed the importance of the saddle point nesting, in favor of the theoretical calculations as well.[26,29,42–44]Hard x-ray scattering revealed an unconventional CDW relevant to the kagome lattice nesting at vHs.[18]However,neutron scattering studies and other ARPES measurements indicated that the electron–phonon coupling plays a dominant role in generating the CDW phase.[45,46]In contrast,polarized Raman spectroscopic measurement did not show a phonon anomaly below and near the CDW transition temperature.[47]Even though quantum states with various periodic orders, such as spin charge density wave and charge bond wave, have been discussed in theoretical models, most of experimental studies have only reported the 2×2 order to date.[32,48–51]

The RbV3Sb5single crystals werein-situcleaved in ultrahigh vacuum (UHV) at room temperature, and then immediately transfered into the STM stage for measurement.Scanning tunneling microscopy and spectroscopy(STM/STS)measurements were carried out at low-temperature of～4.2 K or～77 K in UHV, with the base pressure of 1×10-10mbar(1 bar=105Pa).STM topographic images were acquired under the constant current mode.Differential conductance dI/dVspectra were obtained using the standard lock-in amplifier technique with an ac modulation of 10 mV at 1000 Hz.

RbV3Sb5crystallizes in a hexagonal kagome lattice with the space groupP6/mmm(a0= 5.47 ?A;c0= 9.07 ?A), as schematically illustrated in Fig.1(a).The two-dimensional(2D) kagome lattices are composed of V atoms coordinated by Sb atoms,which form interlayer V3Sb lattices sandwiched by two layers of alkali metal ions.The 2×2 CDW transition occurs at～103 K[14]and the superconductivity transition at～0.9 K.[14]

In order to directly envision the CDW modulation in the underneath Sb planes,we turned toin-situremove the surface Rb atoms by applying high tunneling current and low bias voltage.Figure 2(a)shows a typical STM image collected on the pristine as-cleaved surface with a normal tunneling current and bias voltage.By increasing the tunneling current and lowering the bias voltage, the STM tip was pushed much closer to the surface to enhance the tip-surface coupling.The surface Rb atoms can be thus swiped away by STM tip during the scan with a high current and low bias voltage.In this way,the clean Sb plane underneath the Rb plane was successfully exposed without Rb atoms.Figures 2(a)–2(c)show the series of STM images collected at the same area during atom swiping.As shown in Fig.2(c), the 2×2 modulation is clearly identified as the characteristic of the CDW phase, which is consistent with the previous studies.[13,15–18]The dI/dVspectra taken on the Sb terminated plane is plotted in Fig.2(d).According to the previous studies,[15,21]in the Sb plane spectrum we attribute the peaks at-400 mV and-150 mV to the van Hove singularity(vHs)of the electronic states atMpoint,and the local minimum near-600 mV is related to the Dirac point(DP)atKpoint.The V-shaped energy dip located near the Fermi level may correspond to the CDW gap, and is considered to be connected with the electronic states near theMpoint.[53]For comparison, the dI/dVspectrum taken on the Rb terminated plane is also plotted in Fig.2(d).The dI/dVspectrum taken on the two terminations looks very similar except for an energy shift of～130 mV,suggesting that upon removing the alkali layer,the Fermi energy is moved downward induced by an effective hole doping.[54]

Fig.2.(a)–(c) STM images (12 nm×12 nm) in-situ collected on the RbV3Sb3 surface during swiping surface Rb atoms by STM tip.(a)Vs=-500 mV,It=-100 pA;(b)Vs=-80 mV,It=-100 pA;(c)Vs=-200 mV,It=-100 pA.(d)Differential conductance dI/dV spectrum taken on the Rb(black)and Sb(red)terminated planes.The data are taken before and after removing the surface Rb atoms,respectively.The peaks of van Hove singularity in Rb and Sb planes are marked by black and red triangles,respectively.The local minimum is denoted by red arrow.The red curve is shifted upward by 3 for clarity.(e)–(f) Topographic images (10 nm×10 nm) of the Sb plane prior to and after the STM voltage pulses.Vs=+80 mV(e)and+120 mV(f),It=100 pA.The insets show the corresponding fast Fourier transform images of the defect-free region.The red,blue,and green circles mark the vectors of Bragg lattice,2×2 and modulations,respectively.

It is well known that the saddle points of the Dirac bands are located at theMpoint in the Brillouin zone, closing to the Fermi level.[26,44]The vectors connecting the van Hove singularities atMpoints were believed to be responsible for the formation of 2×2 order, thus in favor of the Fermi surface nesting mechanism.[29,42]Moreover, the Kagome Hubbard model at van Hove filling, with the onsite repulsionUand the nearest-neighbor Coulomb interactionV, were also adopted to theoretically predict the electronic phases of kagome materials.[8,55–58]Within this theoretical model,the adopted Fermi surface and vHs,as schematically illustrated in Fig.4(a), is consistent with the experimental results.[26,27,29,32,50]The Bloch states connected by the nesting vectors are distributed among the three diverse sublattices, as illustrated in Fig.4(b).[7–9]The nearest-neighbor interactionVis found to lead to a different electron density on the neighboring lattice sites.AsVis promoted,the 2×2 modulation firstly appears.Since the nesting vector connects the electronic states of different sublattices, each sublattice hosts a uniform electron density.[28,32]However, asVis increased to a larger value, electrons tend to accumulate in fewer sites,and the electron intensity does not need to remain uniform at the different sublattices.Thus the 2×2 modulation turns tomodulation as a consequence to reduce the nesting effects for a local Hubbard interaction.

Even though the physical nature that drives the formation ofmodulation is still unknown,we believe it is possibly due to a tip-induced local deformation that tunes the nearest-neighbor interactionV, or a local doping effect that shifts the position of vHs.According to the previous theoretical work, our observation of both theand 2×2 orders may suggest that the nearest-neighbor interactionVis important to lead to the rich CDW ground states, via tuning the electronic states of the sub-lattices.The emergence of themodulation may be also related to the removing of the upper Rb atoms,the deficiency of Rb atoms can affect the electronic states of the lower Sb layer.For instance, to remove the Rb plane can induce an effective hole doping and shift the Fermi level downward by～130 mV,as demonstrated in Fig.2(d).The vHs can be thus shifted away from theMpoints,which weakens the Fermi surface nesting effect.

Fig.3.(a) Topographic image (6.8 nm×4.8 nm) taken on the Sb plane of the RbV3Sb5 sample. Vs =-200 mV, It =-150 pA.(b) Linescan dI/dV spectra taken along the symmetric direction as marked by the black arrowed line in panel(a).(c)Spatial variation of the dI/dV intensity extracted at+0.45 V and-0.3 V from the spectra in panel(b).The blue and green triangles mark the 2×2 and modulations,respectively.The black curve is shifted upward by 1 for clarity.(d)The FFT graphs of the two line scan profile in panel(c)with corresponding color.The peaks of two modulations are denoted by red triangles.

Fig.4.(a) Momentum-space illustration of the kagome AV3Sb5.The outer black hexagon is the original Brillouin zone, the middle blue one the schematic Fermi surface,and the inner red one the new Brillouin zone under 2×2 modulation.The high symmetry points are marked as Γ, M, and K.The nesting wave vectors are illustrated by the three black arrowed lines as marked by q1,q2,and q3.(b)Real-space illustration of the atomic structure in the kagome lattice.The labels 1 to 3 denote the three different sublattices.

Acknowledgements

Project supported by the National Key Research and Development Program of China(Grant No.2021YFA1400403),the National Natural Science Foundation of China (Grant Nos.92165205, 11790311, and 11774149), and Innovation Program for Quantum Science and Technology (Grant No.2021ZD0302800).Y F Guo acknowledges the support by the open project of Beijing National Laboratory for Condensed Matter Physics (Grant No.ZBJ2106110017) and the Double First-Class Initiative Fund of Shanghai Tech University.