Chiral charge-density waves

We discovered the chirality of charge-density waves (CDW) in 1T-TiSe? by using STM and time-domain optical polarimetry. We found that the CDW intensity becomes Ia?∶Ia?∶Ia? = 1∶0.7 ± 0.1∶0.5 ± 0.1, where Ia(i) (i=1,2,3) is the amplitude of the tunneling current contributed by the CDWs. There were two states, in which the three intensity peaks of the CDW decrease clockwise and anticlockwise. The chirality in CDW results in the threefold symmetry breaking. Macroscopically, twofold symmetry was indeed observed in optical measurement. We propose the new generalized CDW chirality H(CDW) ≡ q?·(q?×q?), where q(i) are the CDW q vectors, which is independent of the symmetry of components. The nonzero H(CDW)-the triple-q vectors do not exist in an identical plane in the reciprocal space-should induce a real-space chirality in CDW system.     

Subgap collective tunneling and its staircase structure in charge density waves

Tunneling spectra of chain materials NbSe3 and TaS3 were studied in nanoscale mesa devices. Current-voltage I-V characteristics related to all charge density waves (CDWs) reveal universal spectra within the normally forbidden region of low V, below the electronic CDW gap 2Delta. The tunneling always demonstrates a threshold Vt approximately 0.2Delta, followed, for both CDWs in NbSe3, by a staircase fine structure. T dependencies of Vt(T) and Delta(T) scale together for each CDW, while the low T values Vt(0) correlate with the CDWs' transition temperatures Tp. Fine structures of CDWs perfectly coincide when scaled along V/Delta. The results evidence the sequential entering of CDW vortices (dislocations) in the junction area with the tunneling current concentrated in their cores. The subgap tunneling proceeds via the phase channel: coherent phase slips at neighboring chains.     

Indication of charge-density-wave formation in Bi(111)

Photoemission spectroscopy of Bi(111) reveals a small hexagonal two-dimensional Fermi surface (FS) associated with an electron band centered in the surface Brillouin zone. Along the hexagon the Fermi momentum k(F) ranges from 0.053 to 0.061 A(-1). Temperature dependent valence band spectra show an anisotropic energy gap Delta near the Fermi level. We find a transition temperature of about 75 K. At 11 K, the gap is Delta=4 meV at the corner and Delta=7.5 meV at the side of the hexagon. Arguments based on susceptibility chi(--> q) calculations of a hexagonal FS are used to discuss an incommensurate charge-density-wave (CDW) formation associated with a q(CDW)=0.106 A(-1).     

Adsorbate-induced pinning of a charge-density wave in a quasi-1D metallic chains: Na on the In/Si(111)-(4x1) surface

We find that foreign adsorbates acting as local impurities can induce a metal-insulator transition by pinning a charge-density wave (CDW) on the quasi-1D metallic In/Si(111)-(4x1) chain system. Our scanning tunneling microscopy image clearly reveals the presence of a new local 4x2 structure nucleated by Na adatoms at room temperature, which turns out to be insulating with a doubled periodicity along the chains. We directly determine a CDW gap energy Delta = 105+/-8 meV by identifying a characteristic loss peak in our high-resolution electron-energy-loss spectra. We thus report the first observation of a local impurity-derived Peierls-like reconstruction of a quasi-1D system.     

Observation of multiple charge density wave phases in epitaxial monolayer 1T-VSe2 film

As a special order of electronic correlation induced by spatial modulation, the charge density wave (CDW) phenomena in condensed matters attract enormous research interests. Here, using scanning—tunneling microscopy in various temperatures, we discover a hidden incommensurate stripe-like CDW order besides the ($sqrt{7}$ × $sqrt{3}$) CDW phase at low-temperature of 4 K in the epitaxial monolayer 1T-VSe₂} film. Combining the variable-temperature angle-resolved photoemission spectroscopic (ARPES) measurements, we discover a two-step transition of an anisotropic CDW gap structure that consists of two parts Δ₁ and Δ₂. The gap part Δ₁ that closes around ～ 150 K is accompanied with the vanish of the ($sqrt{7}$ × $sqrt{3}$) CDW phase. While another momentum-dependent gap part Δ₂ can survive up to ～ 340 K, and is suggested to the result of the incommensurate CDW phase. This two-step transition with anisotropic gap opening and the resulted evolution in ARPES spectra are corroborated by our theoretical calculation based on a phenomenological form for the self-energy containing a two-gap structure Δ₁ + Δ₂, which suggests different forming mechanisms between the ($sqrt{7}$ × $sqrt{3}$) and the incommensurate CDW phases. Our findings provide significant information and deep understandings on the CDW phases in monolayer 1T-VSe₂} film as a two-dimensional (2D) material.     

Kondo-enhanced Andreev tunneling in InAs nanowire quantum dots

We report measurements of the nonlinear conductance of InAs nanowire quantum dots coupled to superconducting leads. We observe a clear alternation between odd and even occupation of the dot, with subgap peaks at |V(sd)| = Delta/e markedly stronger (weaker) than the quasiparticle tunneling peaks at |V(sd)| = 2Delta/e for odd (even) occupation. We attribute the enhanced Delta peak to an interplay between Kondo correlations and Andreev tunneling in dots with an odd number of spins, and we substantiate this interpretation by a poor man's scaling analysis.     

The influence of impurities on the quasiparticle tunneling current between weakly coupled quasi-one-dimensional charge density waves

The dc and ac conductivity of a tunneling junction between two impure quasi-one-dimensional charge density wave (CDW) systems is calculated. The non-magnetic impurities are considered in the self-consistent Born approximation (SCBA). Impurities modify the density of states (DOS) of the pure CDW system for quasiparticles inside the energy region of the gap 2(T). As in the pure case, the theory predicts in addition to a tunneling current which is proportional to the product of the DOS a term proportional to the cosine of the order parameter phase difference. In the case of a normal state/CDW junction, analytical expressions are obtained forT=0 showing deviations from the pure case. The linear ac conductivity is obtained by the scaling relation between the dc and the ac response.     

Tunable charge density wave in TiS_3 nanoribbons

Recently, modifications of charge density wave(CDW) in two-dimensional(2D) show intriguing properties in quasi-2D materials such as layered transition metal dichalcogenides(TMDCs). Optical, electrical transport measurements and scanning tunneling microscopy uncover the enormous difference on the many-body states when the thickness is reduced down to monolayer. However, the CDW in quasi-one-dimensional(1D) materials like transition metal trichalcogenides(TMTCs) is yet to be explored in low dimension whose mechanism is likely distinct from their quasi-2D counterparts.Here, we report a systematic study on the CDW properties of titanium trisulfide(TiS_3). Two phase transition temperatures were observed to decrease from 53 K(103 K) to 46 K(85 K) for the bulk and 15-nm thick nanoribbon, respectively,which arises from the increased fluctuation effect across the chain in the nanoribbon structure, thereby destroying the CDW coherence. It also suggests a strong anisotropy of CDW states in quasi-1D TMTCs which is different from that in TMDCs.Remarkably, by using back gate of-30 V ～ 70 V in 15-nm device, we can tune the second transition temperature from110 K(at-30 V) to 93 K(at 70 V) owing to the altered electron concentration. Finally, the optical approach through the impinging of laser beams on the sample surface is exploited to manipulate the CDW transition, where the melting of the CDW states shows a strong dependence on the excitation energy. Our results demonstrate TiS_3 as a promising quasi-1D CDW material and open up a new window for the study of collective phases in TMTCs.     

Interaction of both charge density waves in NbSe3 from interlayer tunneling experiments

An interlayer tunneling technique has been used for spectroscopy of charge density wave (CDW) energy gaps (Δ_1,2) in NbSe₃ subsequently opened at the Fermi surface on decreasing temperature at T _p1 = 145 K (CDW1) and at T _p2 = 60 K (CDW2). We found that the CDW2 formation is accompanied by an increase of the CDW1 gap below T _p2. The maximum enhancement of Δ₁, δΔ₁ is about 10%. The effect observed has been predicted theoretically as resulting from the joint phase locking of both CDWs with the underlying crystalline lattice below T _p2. The text was submitted by the authors in English.     

STM studies of TbTe3: evidence for a fully incommensurate charge density wave

We observe unidirectional charge density wave (CDW) ordering on the quasi-2D material TbTe3 with a scanning tunneling microscope at approximately 6 K. Our analysis indicates that the CDW is fully incommensurate, with wave vector qCDW approximately 0.71x2pi/c. By imaging at various tip-sample voltages, we highlight effects of the subsurface layer and its effect on the CDW. We also observe an additional (possibly surface) dimerization and approximately 0.68x2pi/a ordering perpendicular to the CDW.     

Robustness of the unidirectional stripe order in the kagome superconductor CsV3Sb5

V-based kagome materials AV₃Sb₅ (A=K, Rb, Cs) have attracted much attention due to their novel properties such as unconventional superconductivity, giant anomalous Hall effect, charge density wave (CDW) and pair density wave. Except for the 2a₀×2a₀ CDW (charge density wave with in-plane 2×2 superlattice modulation) in AV₃Sb₅, an additional 1×4 (4a₀) unidirectional stripe order has been observed at the Sb surface of RbV₃Sb₅ and CsV₃Sb₅. However, the stability and electronic nature of the 4a₀ stripe order remain controversial and unclear. Here, by using low-temperature scanning tunneling microscopy/spectroscopy (STM/S), we systematically study the 4a₀ stripe order on the Sb-terminated surface of CsV₃Sb₅. We find that the 4a₀ stripe order is visible in a large energy range. The STM images with positive and negative bias show contrast inversion, which is the hallmark for the Peierls-type CDW. In addition, below the critical temperature about 60 K, the 4a₀ stripe order keeps unaffected against the topmost Cs atoms, point defects, step edges and magnetic field up to 8 T. Our results provide experimental evidences on the existence of unidirectional CDW in CsV₃Sb₅.     

Incommensurate magnetic order in TbTe3

We report a neutron diffraction study of the magnetic phase transitions in the charge-density wave (CDW) TbTe(3) compound. We discover that in the paramagnetic phase there are strong 2D-like magnetic correlations, consistent with the pronounced anisotropy of the chemical structure. A long-range incommensurate magnetic order emerges in TbTe(3) at T(mag1) = 5.78 K as a result of continuous phase transitions. We observe that near the temperature T(mag1) the magnetic Bragg peaks appear around the position (0, 0, 0.24) (or its rational multiples), that is fairly close to the propagation vector (0,0,0.29) associated with the CDW phase transition in TbTe(3). This suggests that correlations leading to the long-range magnetic order in TbTe(3) are linked to the modulations that occur in the CDW state.     

Direct observation of melted Mott state evidenced from Raman scattering in 1T-TaS_2 single crystal

The evolution of electron correlation and charge density wave(CDW)in 1T-TaS_2 single crystal has been investigated by temperature-dependent Raman scattering,which undergoes two obvious peaks of A_(1g) modes about 70.8 cm~(-1) and 78.7 cm~(-1) at 80 K,respectively.The former peak at 70.8 cm~(-1) is accordant with the lower Hubbard band,resulting in the electron-correlation-driven Mott transition.Strikingly,the latter peak at 78.7 cm~(-1) shifts toward low energy with increasing the temperature,demonstrating the occurrence of nearly commensurate CDW phase(melted Mott phase).In this case,phonon transmission could be strongly coupled to commensurate CDW lattice via Coulomb interaction,which likely induces appearance of hexagonal domains suspended in an interdomain phase,composing the melted Mott phase characterized by a shallow electron pocket.Combining electronic structure,atomic structure,transport properties with Raman scattering,these findings provide a novel dimension in understanding the relationship between electronic correlation,charge order,and phonon dynamics.     

Tri-hexagonal charge order in kagome metal CsV3Sb5 revealed by 121Sb nuclear quadrupole resonance

We report ¹²¹Sb nuclear quadrupole resonance(NQR)measurements on kagome superconductor CsV₃Sb₅ with Tc=2.5 K.¹²¹Sb NQR spectra split after a charge density wave(CDW)transition at 94 K,which demonstrates a commensurate CDW state.The coexistence of the high temperature phase and the CDW phase between 91 K and 94 K manifests that it is a first order phase transition.The CDW order exhibits tri-hexagonal deformation with a lateral shift between the adjacent kagome layers,which is consistent with 2×2×2 superlattice modulation.The superconducting state coexists with CDW order and shows a conventional s-wave behavior in the bulk state.     

Two-band superconductivity in MgB2

The study of the anisotropic superconductor MgB2 using a combination of scanning tunneling microscopy and spectroscopy reveals two distinct energy gaps at Delta(1)=2.3 meV and Delta(2)=7.1 meV at 4.2 K. Different spectral weights of the partial superconducting density of states are a reflection of different tunneling directions in this multiband system. Temperature evolution of the tunneling spectra follows the BCS scenario [Phys. Rev. Lett. 3, 552 (1959)]] with both gaps vanishing at the bulk T(c). The data confirm the importance of Fermi-surface sheet dependent superconductivity in MgB2 proposed in the multigap model by Liu et al. [Phys. Rev. Lett. 87, 087005 (2001)]].     

The Tunneling Effect Between Two Weakly Coupled CD W Materials

Using the tunneling Hamiltonian method we have studied the Josephson type effect occuring in a junction composed of two weakly coupled CDW materials. We have found that the tunneling effect in CDW junction has great resemblance to the Josephson effect, but there are also basic differences between them. For example, in CDW junction there is a special pair-single particle tunneling current term which is absent in the superconducting tunneling junction. It is just this term that gives rise to the narrow band noise. This is a kind of contact effect, but its mechanism is probably different from the vortex theory.     

Observation of quantum coherence in mesoscopic molecular magnets

By applying a transverse magnetic field B( perpendicular) of sufficient strength to the uniaxial molecular magnets Fe8 and Mn12, the tunneling splitting Delta(t) of their S = +/-10 magnetic ground states can be made large compared to perturbations such as hyperfine and dipolar interactions. We present evidence for such a Delta(t) from magnetic specific heat data below 1 K that is consistent with coherent quantum mechanical tunneling in a "mesoscopic" system under such conditions.     

Energy gap of a charge density wave in NbSe3 induced by a high magnetic field above the Peierls transition temperature

The effect of a magnetic field on the energy gap of the charge density wave (CDW) in NbSe₃ near the temperature T _p2 of the lower Peierls transition has been investigated using interlayer tunneling spectroscopy. It has been shown that the magnetic field increases the energy gap and can even induce it at temperatures higher than T _p2 by 15–20 K. As the field strength increases, the peak amplitude of the gap singularity of the tunneling spectrum first increases, reaches its maximum at 20–30 T, and then decreases. The increase in the gap peak amplitude is attributed to the field-induced improvement of the condition of the CDW nesting, while the decrease in the amplitude in high fields, to the breakdown of the ground state caused by its Zeeman splitting.     

Charge density wave transport in NbSe<Subscript>3</Subscript> at low temperatures under high magnetic field

Charge density wave (CDW) depinning and sliding regimes have been studied in NbSe₃ at low temperatures down to 1.5 K under magnetic field of 19 T oriented along the c-axis. We found that the threshold field for CDW depinning becomes temperature independent below T ₀ ≈ 15 K. Also CDW current to frequency ratio characterizing CDW sliding regime increases by factor 1.7 below this temperature. The results are discussed as a crossover from thermal fluctuation to tunneling CDW depinning at T < T ₀. Besides, we found that CDW sliding strongly suppresses the amplitude of Shubnikov-de Haas oscillations of magnetoresistance.     

Charge density wave states in phase-engineered monolayer VTe2

Charge density wave (CDW) strongly affects the electronic properties of two-dimensional (2D) materials and can be tuned by phase engineering. Among 2D transitional metal dichalcogenides (TMDs), VTe$_{2}$ was predicted to require small energy for its phase transition and shows unexpected CDW states in its T-phase. However, the CDW state of H-VTe$_{2}$ has been barely reported. Here, we investigate the CDW states in monolayer (ML) H-VTe$_{2}$, induced by phase-engineering from T-phase VTe$_{2}$. The phase transition between T- and H-VTe$_{2}$ is revealed with x-ray photoelectron spectroscopy (XPS) and scanning transmission electron microscopy (STEM) measurements. For H-VTe$_{2}$, scanning tunneling microscope (STM) and low-energy electron diffraction (LEED) results show a robust $2\sqrt 3 \times 2\sqrt 3 $ CDW superlattice with a transition temperature above 450 K. Our findings provide a promising way for manipulating the CDWs in 2D materials and show great potential in its application of nanoelectronics.