Unidirectional Charge Density Wave Research Articles

Atomic-scale visualization of a cascade of magnetic orders in the layered antiferromagnet GdTe3

GdTe3 is a layered antiferromagnet which has attracted attention due to its exceptionally high mobility, distinctive unidirectional incommensurate charge density wave (CDW), superconductivity under pressure, and a cascade of magnetic transitions between 7 and 12 K, with as yet unknown order parameters. Here, we use spin-polarized scanning tunneling microscopy to directly image the charge and magnetic orders in GdTe3. Below 7 K, we find a striped antiferromagnetic phase with twice the periodicity of the Gd lattice and perpendicular to the CDW. As we heat the sample, we discover a spin density wave with the same periodicity as the CDW between 7 and 12 K; the viability of this phase is supported by our Landau free energy model. Our work reveals the order parameters of the magnetic phases in GdTe3 and shows how the interplay between charge and spin can generate a cascade of magnetic orders.

Melting of Unidirectional Charge Density Waves across Twin Domain Boundaries in GdTe3.

Solids undergoing a transition from order to disorder experience a proliferation of topological defects. The melting process generates transient quantum states. However, their dynamic nature with a femtosecond lifetime hinders exploration with atomic precision. Here, we suggest an alternative approach to the dynamic melting process by focusing on the interface created by competing degenerate quantum states. We use a scanning tunneling microscope (STM) to visualize the unidirectional charge density wave (CDW) and its spatial progression ("static melting") across a twin domain boundary (TDB) in the layered material GdTe3. Combining the STM with a spatial lock-in technique, we reveal that the order parameter amplitude attenuates with the formation of dislocations and thus two different unidirectional CDWs coexist near the TDB, reducing the CDW anisotropy. Notably, we discovered a correlation between this anisotropy and the CDW gap. Our study provides valuable insight into the behavior of topological defects and transient quantum states.

Coexistence of Unidirectional Charge Density Waves in LaTe3

The classic rare-earth tritelluride provides an ideal platform to study the strong correlation state owing to its stable structures and abundance of orders. Here we report the observation of an undiscovered charge density wave (CDW) in LaTe3 under 4.2 K, the transition temperature of the CDW states is fitted to be 35 K, and confirmed by the evanishment of this CDW at 77 K via using temperature-dependent scanning tunneling microscope/spectroscopy. The coexistence of these CDWs is confirmed by the atomic resolution and beating pattern simulation. It is the first time to observe the coexistence of unidirectional charge density waves system, providing a new platform to understand the competition and evolution between strong correlation states, and get a deeper sight into the phase lag between different order parameters.

Real-Space Observation of Unidirectional Charge Density Wave and Complex Structural Modulation in the Pnictide Superconductor Ba1–xSrxNi2As2

Here we use low-temperature and variable-temperature scanning tunneling microscopy to study the pnictide superconductor, Ba1-xSrxNi2As2. In the low-temperature phase (triclinic phase) of BaNi2As2, we observe the unidirectional charge density wave (CDW) with Q = 1/3 on both the Ba and NiAs surfaces. On the NiAs surface of the triclinic BaNi2As2, there are structural-modulation-induced chain-like superstructures with distinct periodicities. In the high-temperature phase (tetragonal phase) of BaNi2As2, the NiAs surface appears as the periodic 1 × 2 superstructure. Interestingly, in the triclinic phase of Ba0.5Sr0.5Ni2As2, the unidirectional CDW is suppressed on both the Ba/Sr and NiAs surfaces, and the Sr substitution stabilizes the periodic 1 × 2 superstructure on the NiAs surface, which enhance the superconductivity in Ba0.5Sr0.5Ni2As2. Our results provide important microscopic insights for the interplay among the unidirectional CDW, structural modulation, and superconductivity in this class of pnictide superconductors.

Charge density wave transitions, soft phonon, and possible electronic nematicity in BaNi2(As1−xPx)2

A detailed investigation of ${\mathrm{BaNi}}_{\text{2}}{({\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x})}_{\text{2}}$ single crystals using high-resolution thermal-expansion, heat-capacity, Young's-modulus, and resistivity measurements is presented. The phase diagram of ${\mathrm{BaNi}}_{\text{2}}{({\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x})}_{\text{2}}$ is shown to be much richer than suggested by the original data of Kudo et al. [Phys. Rev. Lett. 109, 097002 (2012)]. The transition to the commensurate charge density wave (C-CDW) is always preceded by a fourfold symmetry-breaking transition associated with the long-range ordering of a strongly fluctuating unidirectional incommensurate charge density wave (I-CDW). Significant precursors above the I-CDW and C-CDW transitions are seen in the thermal expansion and resistivity and are particularly evident in the temperature dependence of the $c/a$ ratio of the lattice parameters. Heat-capacity measurements of the crystals with a higher P content and a higher critical temperature of 3.2 K uncover a Debye-like behavior of a soft-phonon mode with a very low ${\mathrm{\ensuremath{\Theta}}}_{\text{Debye}}$ of roughly 50 K. Associated with this soft phonon are unusually large thermal-expansion anomalies, resulting in logarithmically diverging uniaxial phonon Gr\"uneisen parameters. Young's-modulus data of these higher-${T}_{c}$ crystals exhibit a significant softening in both ${B}_{1g}$ and ${B}_{2g}$ channels, which is argued to be incompatible with nematic criticality and is rather associated with a broad phase transition to an hitherto unknown structure. Possible origins of the increase in the superconducting critical temperature with P substitution are discussed.

Chirality locking charge density waves in a chiral crystal

In Weyl semimetals, charge density wave (CDW) order can spontaneously break the chiral symmetry, gap out the Weyl nodes, and drive the material into the axion insulating phase. Investigations have however been limited since CDWs are rarely seen in Weyl semimetals. Here, using scanning tunneling microscopy/spectroscopy (STM/S), we report the discovery of a novel unidirectional CDW order on the (001) surface of chiral crystal CoSi – a unique Weyl semimetal with unconventional chiral fermions. The CDW is incommensurate with both lattice momentum and crystalline symmetry directions, and exhibits an intra unit cell π phase shift in the layer stacking direction. The tunneling spectrum shows a particle-hole asymmetric V-shaped energy gap around the Fermi level that modulates spatially with the CDW wave vector. Combined with first-principle calculations, we identify that the CDW is locked to the crystal chirality and is related by a mirror reflection between the two enantiomers of the chiral crystal. Our findings reveal a novel correlated topological quantum state in chiral CoSi crystals and raise the potential for exploring the unprecedented physical behaviors of unconventional chiral fermions.

Origin and strain tuning of charge density wave in LaTe3

We study the origin of charge density wave (CDW) in rare-earth tritelluride LaTe3 and the strain tuning effect on CDW in monolayer LaTe3 by first-principles calculations. The calculations of the electronic structure, phonon spectrum, electron susceptibility, and electron-phonon coupling (EPC) matrix show that the origin of CDW in LaTe3 is momentum-dependent EPC rather than Fermi-surface nesting. The unidirectional CDW with a wave-vector QCDW≈2/7c∗ is the most stable state. We study the biaxial strain effect on CDW in monolayer LaTe3 by evaluating the total energy, CDW-related lattice distortions, and phonon spectra. Our results show that the tensile strain can enhance CDW order, while the compressive strain can inhibit CDW order. As the CDW order is fully suppressed, superconductivity could be induced. Our study may help to clarify the mechanism of CDW in LaTe3 and find the effective tuning method of CDW in monolayer or few-layer configuration.

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 2a 0 × 2a 0 CDW (charge density wave with in-plane 2 × 2 superlattice modulation) in AV3Sb5, an additional 1 × 4 (4a 0) unidirectional stripe order has been observed at the Sb surface of RbV3Sb5 and CsV3Sb5. However, the stability and electronic nature of the 4a 0 stripe order remain controversial and unclear. Here, by using low-temperature scanning tunneling microscopy/spectroscopy (STM/S), we systematically study the 4a 0 stripe order on the Sb-terminated surface of CsV3Sb5. We find that the 4a 0 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 4a 0 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.

Time-resolved structural dynamics of the out-of-equilibrium charge density wave phase transition in GdTe3.

We use ultrafast electron diffraction to study the out-of-equilibrium dynamics of the charge density wave (CDW) phase transition in GdTe3, a quasi-two-dimensional compound displaying a unidirectional CDW state. Experiments were conducted at different incident fluences and different initial sample temperatures below Tc. We find that following photo-excitation, the system undergoes a non-thermal ultrafast phase transition that occurs in out-of-equilibrium conditions. The intrinsic crystal temperature was estimated at each time delay from the atomic thermal motion, which affects each Bragg peak intensity via the Debye Waller factor. We find that the crystal temperature stabilizes with a 6 ps timescale in a quasi-equilibrium state at temperature . We then relate the recovery time of the CDW and its correlation lengths as a function of . The charge density wave is suppressed in less than a picosecond while its recovery time increases linearly with incident fluence and initial temperature. Our results highlight that the dynamics is strongly determined by the initial sample temperature. In addition, the transient CDW phase recently observed along the transverse direction in LaTe3 and CeTe3 is not observed in GdTe3.

Stripe order enhanced superconductivity in the Hubbard model

Unidirectional ("stripe") charge density wave order has now been established as a ubiquitous feature in the phase diagram of the cuprate high-temperature superconductors, where it generally competes with superconductivity. Nonetheless, on theoretical grounds it has been conjectured that stripe order (or other forms of "optimal" inhomogeneity) may play an essential positive role in the mechanism of high-temperature superconductivity. Here, we report density matrix renormalization group studies of the Hubbard model on long four- and six-leg cylinders, where the hopping matrix elements transverse to the long direction are periodically modulated-mimicking the effect of putative period 2 stripe order. We find that even modest amplitude modulations can enhance the long-distance superconducting correlations by many orders of magnitude and drive the system into a phase with a substantial spin gap and superconducting quasi-long-range order with a Luttinger exponent, [Formula: see text].

Rotational symmetry breaking at the incommensurate charge-density-wave transition in Ba(Ni,Co)2(As,P)2 : Possible nematic phase induced by charge/orbital fluctuations

Nematic phase transitions in high-temperature superconductors have a strong impact on the electronic properties of these systems. BaFe$_2$As$_2$,\@ with an established nematic transition around 137 K induced by magnetic fluctuations, and BaNi$_2$As$_2$,\@ a non-magnetic analog of BaFe$_2$As$_2$ with a structural transition in the same temperature range,\@ share a common tetragonal aristotype crystal structure with space-group type $I4/mmm$.\@ In contrast to BaFe$_2$As$_2$ where collinear stripe magnetic order is found for the orthorhombic low-$T$ phase, a unidirectional charge density wave together with (distorted) zig-zag chains are observed for the triclinic low-$T$ phase of BaNi$_2$As$_2$.\@ Here we show that between the high- and low-$T$ phases of Ba(Ni,Co)$_2$(As,P)$_2$ an additional phase with broken fourfold symmetry and $d_{xz}$ orbital order exists which is a promising candidate for charge/orbital-fluctuation-induced nematicity. Moreover, our data suggest that the enhanced $T_{\rm c}$ found for Ba(Ni,Co)$_2$(As,P)$_2$ for higher Co or P substitution levels might result from suppression of the (distorted) zig-zag chains by reducing the contribution of the $d_{xy}$ orbitals.

Charge Density Wave and Electron-Phonon Interaction in Epitaxial Monolayer NbSe2 FilmsSupported by the National Natural Science Foundation of China (Grant Nos. 11774154, 11790311, and 12004172), the National Key Research and Development Program of China (Grant No. 2018YFA0306800), the Fundamental Research Funds for the Central Universities (Grant No. 0204-14380186), the Jiangsu Planned Projects for Postdoctoral Research Funds (Grant No. 2020Z172), the

Understanding the interplay between superconductivity and charge-density wave (CDW) in NbSe2 is vital for both fundamental physics and future device applications. Here, combining scanning tunneling microscopy, angle-resolved photoemission spectroscopy and Raman spectroscopy, we study the CDW phase in the monolayer NbSe2 films grown on various substrates of bilayer graphene (BLG), SrTiO3(111), and Al2O3(0001). It is found that the two stable CDW states of monolayer NbSe2 can coexist on NbSe2/BLG surface at liquid-nitrogen temperature. For the NbSe2/SrTiO3(111) sample, the unidirectional CDW regions own the kinks at ±41 meV and a wider gap at 4.2 K. It is revealed that the charge transfer from the substrates to the grown films will influence the configurations of the Fermi surface, and induce a 130 meV lift-up of the Fermi level with a shrink of the Fermi pockets in NbSe2/SrTiO3(111) compared with the NbSe2/BLG. Combining the temperature-dependent Raman experiments, we suggest that the electron-phonon coupling in monolayer NbSe2 dominates its CDW phase transition.

Interplay of charge density wave states and strain at the surface of CeTe2

We use scanning tunneling microscopy (STM) to study charge density wave (CDW) states in the rare-earth di-telluride, CeTe$_{2}$. In contrast to previous experimental and first-principles studies of the rare-earth di-tellurides, our STM measurements surprisingly detect a unidirectional CDW with $\textit{q}$ ~ 0.28 $\textit{a}$*, which is very close to what is found in experimental measurements of the related rare-earth tri-tellurides. Furthermore, in the vicinity of an extended sub-surface defect, we find spatially-separated as well as spatially-coexisting unidirectional CDWs at the surface of CeTe$_{2}$. We quantify the nanoscale strain and its variations induced by this defect, and establish a correlation between local lattice strain and the locally-established CDW states. Our measurements probe the fundamental properties of a weakly-bound two-dimensional Te-sheet, which experimental and theoretical work has previously established as the fundamental component driving much of the essential physics in both the rare-earth di- and tri-telluride compounds.

Light-induced charge density wave in LaTe3

When electrons in a solid are excited with light, they can alter the free energy landscape and access phases of matter that are beyond reach in thermal equilibrium. This accessibility becomes of vast importance in the presence of phase competition, when one state of matter is preferred over another by only a small energy scale that, in principle, is surmountable by light. Here, we study a layered compound, LaTe$_3$, where a small in-plane (a-c plane) lattice anisotropy results in a unidirectional charge density wave (CDW) along the c-axis. Using ultrafast electron diffraction, we find that after photoexcitation, the CDW along the c-axis is weakened and subsequently, a different competing CDW along the a-axis emerges. The timescales characterizing the relaxation of this new CDW and the reestablishment of the original CDW are nearly identical, which points towards a strong competition between the two orders. The new density wave represents a transient non-equilibrium phase of matter with no equilibrium counterpart, and this study thus provides a framework for unleashing similar states of matter that are "trapped" under equilibrium conditions.

Interplay between band crossing and charge density wave instabilities

Our measurements of the Hall coefficient in rare-earth tritelluride compounds reveal a strong hysteresis between cooling and warming in the low temperature range where a second unidirectional charge density wave (CDW) occurs. We show that this effect results from the interplay between two instabilities: band crossing of the Te $p_{x}$ and $p_{y}$ orbitals at the Fermi level and CDW, which have a close energy gain and compete. Calculation of the electron susceptibility at the CDW wave vector with and without band anticrossing reconstruction of the electron spectrum yields a satisfactory estimation of the temperature range of the hysteresis in Hall effect measurements.

Fermi surface reconstruction by a charge density wave with finite correlation length

Even a small amplitude charge-density-wave (CDW) can reconstruct a Fermi surface, giving rise to new quantum oscillation frequencies. Here, we investigate quantum oscillations when the CDW has a finite correlation length $\xi$ -- a case relevant to the hole-doped cuprates. By considering the Berry phase induced by a spatially varying CDW phase, we derive an effective Dingle factor that depends exponentially on the ratio of the cyclotron orbit radius, $R_c$, to $\xi$. In the context of YBCO, we conclude that the values of $\xi$ reported to date for bidirectional CDW order are, prima facie, too short to account for the observed Fermi surface reconstruction; on the other hand, the values of $\xi$ for the unidirectional CDW are just long enough.

Suppression of charge density wave order by disorder in Pd-intercalated ErTe3

Disorder is generically anticipated to suppress long range charge density wave (CDW) order. We report transport, thermodynamic, and scattering experiments on Pd$_x$ErTe$_3$, a model CDW system with disorder induced by intercalation. The pristine parent compound ($x=0$) shows two separate, mutually perpendicular, incommensurate unidirectional CDW phases setting in at 270 K and 165 K. Here we track the suppression of signatures corresponding to these two parent transitions as the Pd concentration increases. At the largest values of $x$, we observe complete suppression of long range CDW order in favor of superconductivity. We also report evidence from electron and x-ray diffraction which suggests a tendency toward short-range ordering along both wavevectors which persists even well above the crossover temperature. Pd$_x$ErTe$_3$ provides a promising model system for the study of the interrelation of charge order and superconductivity in the presence of quenched disorder.

Unconventional Charge Density Wave Order in the Pnictide Superconductor Ba(Ni_{1-x}Co_{x})_{2}As_{2}.

Ba(Ni_{1-x}Co_{x})_{2}As_{2} is a structural homologue of the pnictide high temperature superconductor, Ba(Fe_{1-x}Co_{x})_{2}As_{2}, in which the Fe atoms are replaced by Ni. Superconductivity is highly suppressed in this system, reaching a maximum T_{c}=2.3 K, compared to 24K in its iron-based cousin, and the origin of this T_{c} suppression is not known. Using x-ray scattering, we show that Ba(Ni_{1-x}Co_{x})_{2}As_{2} exhibits a unidirectional charge density wave (CDW) at its triclinic phase transition. The CDW is incommensurate, exhibits a sizable lattice distortion, and is accompanied by the appearance of α Fermi surface pockets in photoemission [B. Zhou etal., Phys. Rev. B 83, 035110 (2011)PRBMDO1098-012110.1103/PhysRevB.83.035110], suggesting it forms by an unconventional mechanism. Co doping suppresses the CDW, paralleling the behavior of antiferromagnetism in iron-based superconductors. Our study demonstrates that pnictide superconductors can exhibit competing CDW order, which may be the origin of T_{c} suppression in this system.

Evidence for topological defects in a photoinduced phase transition

Upon excitation with an intense ultrafast laser pulse, a symmetry-broken ground state can undergo a non-equilibrium phase transition through pathways dissimilar from those in thermal equilibrium. Determining the mechanism underlying these photo-induced phase transitions (PIPTs) has been a long-standing issue in the study of condensed matter systems. To this end, we investigate the light-induced melting of a unidirectional charge density wave (CDW) material, LaTe$_3$. Using a suite of time-resolved probes, we independently track the amplitude and phase dynamics of the CDW. We find that a quick ($\sim\,$1$\,$ps) recovery of the CDW amplitude is followed by a slower reestablishment of phase coherence. This longer timescale is dictated by the presence of topological defects: long-range order (LRO) is inhibited and is only restored when the defects annihilate. Our results provide a framework for understanding other PIPTs by identifying the generation of defects as a governing mechanism.

Generation and detection of edge magnetoplasmons in a quantum Hall system using a photoconductive switch

Edge magnetoplasmons (EMPs) are unidirectional charge density waves travelling in an edge channel of a two-dimensional electron gas in the quantum Hall regime. We present both generation and detection schemes with a photoconductive switch (PCS) for EMPs. Here, the conductance of the PCS is modulated by irradiation with a laser beam, whose amplitude can be modulated by an external signal. When the PCS is used as a generator, the electrical current from the PCS is injected into the edge channel to excite EMPs. When the PCS is used as a detector, the electronic potential induced by EMPs is applied to the PCS with a modulated laser beam so as to constitute a phase-sensitive measurement. For both experiments, we confirm that the time of flight for the EMPs increases with the magnetic field in agreement with the EMP characteristics. Combination of the two schemes would be useful in investigating and utilizing EMPs at higher frequencies.