Charge Density Wave State Research Articles

Dirac spectroscopy of strongly correlated phases in twisted trilayer graphene.

Magic-angle twisted trilayer graphene (MATTG) hosts flat electronic bands, and exhibits correlated quantum phases with electrical tunability. In this work, we demonstrate a spectroscopy technique that allows for dissociation of intertwined bands and quantification of the energy gaps and Chern numbers C of the correlated states in MATTG by driving band crossings between Dirac cone Landau levels and energy gaps in the flat bands. We uncover hard correlated gaps with C = 0 at integer moiré unit cell fillings of ν = 2 and 3 and reveal charge density wave states originating from van Hove singularities at fractional fillings ν = 5/3 and 11/3. In addition, we demonstrate displacement-field-driven first-order phase transitions at charge neutrality and ν = 2, which are consistent with a theoretical strong-coupling analysis, implying C2T symmetry breaking. Overall, these properties establish a diverse electrically tunable phase diagram of MATTG and provide an avenue for investigating other related systems hosting both steep and flat bands.

Orthogonal Grade-Separated Nanowiring of Molecular Single Chains

Quasi-one-dimensional (1D) compounds are suitable models to develop future nanodevices. The critical issue is that most of the several hundred reported 1D compounds adopt parallel arrangements. Here, we report the first example of an orthogonal grade-separated arrangement of the halogen-bridged metal complex (MX-Chain) [PtII(en)2][PtIVCl2(en)2][FeIIICl5]2, abbreviated as [Pt(en)2Cl][FeIIICl5] (en = ethylenediamine), which is the first example of that arrangement of molecular single chains. The space group and topology are coincidentally same as alchemists’ gold, Hg3−δAsF6, which aligns as atomic single chains. This molecular nanostructure is very rare and valuable as a three-dimensional (3D) nanowiring model. The hydrogen bond network found in [Pt(en)2Cl][FeIIICl5] represents a new strategy for making such nanostructures. The structural and optical relationships are similar to those of typical Pt(II)/Pt(IV) mixed valent MX-Chains in charge-density-wave (CDW) states. Polarized Raman spectra strongly supported the presence of orthogonal grade-separated chains in CDW states. Thus, this work proved the concept of molecular single-chain grade-separated nanowiring.

Chern Fermi pocket, topological pair density wave, and charge-4e and charge-6e superconductivity in kagomé superconductors

The recent discovery of novel charge density wave (CDW) and pair density wave (PDW) in kagomé lattice superconductors AV3Sb5 (A = K, Rb, Cs) hints at unexpected time-reversal symmetry breaking correlated and topological states whose physical origin and broader implications are not understood. Here, we make conceptual advances toward a mechanism behind the striking observations and new predictions for novel macroscopic phase coherent quantum states. We show that the metallic CDW state with circulating loop currents is a doped orbital Chern insulator near van Hove filling. The emergent Chern Fermi pockets (CFPs) carry concentrated Berry curvature and orbital magnetic moment. We find that the pairing of electrons on the CFPs leads to a superconducting state with an emergent vortex-antivortex lattice and the formation of a complex triple-Q PDW. A plethora of correlated and topological states emerge, including a never-before-encountered chiral topological PDW superconductor, a loop-current pseudogap phase, and vestigial charge-4e and charge-6e superconductivity in staged melting of the vortex-antivortex lattice and hexatic liquid crystal. Our findings reveal previously unknown nature of the superconducting state of a current-carrying Chern metal, with broad implications for correlated and topological materials.

Angle-resolved photoemission spectroscopy study of charge density wave order in the layered semiconductor EuTe4

Layered tellurides have been extensively studied as a platform for investigating the Fermi surface (FS) nesting-driven charge density wave (CDW) states. EuTe4, one of quasi-two-dimensional (quasi-2D) binary rare-earth tetratellurides CDW compounds, with unconventional hysteretic transition, is currently receiving much attention. Here, the CDW modulation vector, momentum and temperature dependence of CDW gaps in EuTe4 are investigated using angle-resolved photoemission spectroscopy. Our results reveal that (i) a FS nesting vector q ~ 0.67 b* drives the formation of CDW state, (ii) a large anisotropic CDW gap is fully open in the whole FS, and maintains a considerable size even at 300 K, leading to appearance of semiconductor properties, (iii) an abnormal non-monotonic increase of CDW gap in magnitude as a function of temperature, (iv) an extra, larger gap opens at a higher binding energy due to the interaction between the different orbits of the main bands.

Simultaneous formation of two-fold rotation symmetry with charge order in the kagome superconductor CsV3Sb5 by optical polarization rotation measurement

We report the observation of two-fold rotation symmetry in charge density wave (CDW) state in the newly discovered Kagome superconductor CsV$_3$Sb$_5$. Below its CDW transition temperature ($T_{CDW}$), the polarization rotation of the reflected laser beam promptly emerges and increases close to about 1 mrad, and the rotation angle shows two-fold rotation symmetry. With femtosecond laser pulse pumping, the rotation angle can be easily suppressed and then recovers in several picoseconds accompanied with coherent oscillations. Significantly, the oscillations in the signal also experience a 180 degree periodic change. Our investigation provides clear optical evidence for the formation of nematic order with two-fold rotation symmetry just below $T_{CDW}$. The results imply a immediate development of nematicity and possible time-reversal symmetry breaking in CDW state of CsV$_3$Sb$_5$.

Antiferromagnetic fluctuations and dominant dxy -wave pairing symmetry in nickelate-based superconductors

Motivated by recent experimental studies on superconductivity found in nickelate-based materials, we study the temperature dependence of the spin correlation and the superconducting pairing interaction within an effective two-band Hubbard model by the quantum Monte Carlo method. Based on parameters extracted from first-principles calculations, our intensive numerical results reveal that the pairing with a $d_{xy}$-wave symmetry firmly dominates over other pairings at low temperature, which is mainly determined by the Ni 3$d$ orbital. It is also found that the effective pairing interaction is enhanced as the on-site interaction increases, demonstrating that the superconductivity is driven by strong electron-electron correlation. Even though the $(\pi,\pi)$ antiferromagnetic correlation could be enhanced by electronic interaction, there is no evidence for long-range antiferromagnetic order exhibited in nickelate-based superconductors. Moreover, our results offer possible evidence that the pure electron correlation may not account for the charge density wave state observed in nickelates.

Anderson and many-body localization in the presence of spatially correlated classical noise

We study the effect of spatially correlated classical noise on both Anderson and many-body localization of a disordered fermionic chain. By analyzing the evolution of the particle density imbalance following a quench from an initial charge density wave state, we find prominent signatures of localization also in the presence of the time-dependent noise, even though the system eventually relaxes to the infinite temperature state. In particular, for sufficiently strong static disorder we observe the onset of metastability, which becomes more prominent the stronger the spatial correlations of the noise. In this regime we find that the imbalance decays as a stretched-exponential - a behavior characteristic of glassy systems. We identify a simple scaling behavior of the relevant relaxation times in terms of the static disorder and of the noise correlation length. We discuss how our results could be exploited to extract information about the localization length in experimental setups.

Evolution of superconductivity and charge density wave through Ta and Mo doping in CsV3Sb5

Here, we report the tunning study of superconductivity and charge density wave in $\mathrm{Cs}{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ through the V kagome net doping. Combining electrical transport and magnetic susceptibility measurements, we reveal the opposite effect of Ta and Mo doping. Ta doping promotes the superconductivity but suppresses charge density wave, which may be explained by the lift of van Hove singularity towards ${E}_{\mathrm{F}}$. On the contrary, Mo doping suppresses the superconductivity quickly and leads to a continuous increase of charge density wave temperature up to 100.7 K. Our result suggests that electron doping can also effectively tune charge density wave state in $\mathrm{Cs}{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$.

Kagome superconductors AV3Sb5 (A = K, Rb, Cs).

The quasi-two-dimensional kagome materials AV3Sb5 (A = K, Rb, Cs) were found to be a prime example of kagome superconductors, a new quantum platform to investigate the interplay between electron correlation effects, topology and geometric frustration. In this review, we report recent progress on the experimental and theoretical studies of AV3Sb5 and provide a broad picture of this fast-developing field in order to stimulate an expanded search for unconventional kagome superconductors. We review the electronic properties of AV3Sb5, the experimental measurements of the charge density wave state, evidence of time-reversal symmetry breaking and other potential hidden symmetry breaking in these materials. A variety of theoretical proposals and models that address the nature of the time-reversal symmetry breaking are discussed. Finally, we review the superconducting properties of AV3Sb5, especially the potential pairing symmetries and the interplay between superconductivity and the charge density wave state.

Revealing the order parameter dynamics of 1T-TiSe_2 following optical excitation

The formation of a charge density wave state is characterized by an order parameter. The way it is established provides unique information on both the role that correlation plays in driving the charge density wave formation and the mechanism behind its formation. Here we use time and angle resolved photoelectron spectroscopy to optically perturb the charge-density phase in 1T-TiSe_2 and follow the recovery of its order parameter as a function of energy, momentum and excitation density. Our results reveal that two distinct orders contribute to the gap formation, a CDW order and pseudogap-like order, manifested by an overall robustness to optical excitation. A detailed analysis of the magnitude of the the gap as a function of excitation density and delay time reveals the excitonic long-range nature of the CDW gap and the short-range Jahn–Teller character of the pseudogap order. In contrast to the gap, the intensity of the folded Se_{4p}* band can only give access to the excitonic order. These results provide new information into the the long standing debate on the origin of the gap in TiSe_2 and place it in the same context of other quantum materials where a pseudogap phase appears to be a precursor of long-range order.

Steady off-diagonal long-range order state in a half-filled dimerized Hubbard chain induced by a resonant pulsed field

We show that a resonant pulsed field can induce a steady superconducting state even in the deep Mott insulating phase of the dimerized Hubbard model. The superconductivity found here in the non-equilibrium steady state is due to the $\eta $-pairing mechanism, characterized by the existence of the off-diagonal long-range order (ODLRO), and is absent in the ground-state phase diagram. The key of the scheme lies in the generation of the field-induced charge density wave (CDW) state that is from the valence bond solid. The dynamics of this state resides in the highly-excited subspace of dimerized Hubbard model and is dominated by a $\eta $-spin ferromagnetic model. The decay of such long-living excitation is suppressed because of energy conservation. We also develop a dynamical method to detect the ODLRO of the non-equilibrium steady state. Our finding demonstrates that the non-equilibrium many-body dynamics induced by the interplay between the resonant external field and electron-electron interaction is an alternative pathway to access a new exotic quantum state, and also provides an alternative mechanism for enhancing superconductivity.

Lattice-driven chiral charge density wave state in 1T−TaS2

We use scanning tunneling microscopy to study the domain structure of the nearly commensurate charge density wave (NC-CDW) state of $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$. In our subangstrom characterization of the state, we find a continual evolution of the CDW lattice from domain wall to domain center, instead of a fixed CDW arrangement within a domain. Further, we uncover an intradomain chirality characterizing the NC-CDW state. Unlike the orbital-driven chirality previously observed in related transition-metal dichalcogenides, the chiral nature of the NC-CDW state in $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ appears driven by a strong coupling of the NC-CDW state to the lattice.

Competing magnetic and nonmagnetic states in monolayer VSe2 with charge density wave

The field of two-dimensional ferromagnets has been reinvigorated by the discovery of ${\mathrm{VSe}}_{2}$ monolayer grown on van der Waals substrates, which is reported to be ferromagnetic with a Curie point higher than 330 K. However, the ferromagnetic and nonmagnetic states of pristine monolayer ${\mathrm{VSe}}_{2}$ are highly debated. Here, employing density functional theory, Wannier function calculations, and the band unfolding method, we explore the electronic structure of monolayer ${\mathrm{VSe}}_{2}$ with a $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{7}$ charge density wave (CDW). Certain qualitative aspects of the calculated unfolded band dispersion and unfolded Fermi surface of monolayer ${\mathrm{VSe}}_{2}$ with the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{7}$ CDW in the nonmagnetic state agree well with previous angle-resolved photoemission spectroscopy results, albeit with uncertainty about whether these experiments probed single or multiple domains. Specifically, we find that an isolated CDW domain naturally induces a strong breaking of the threefold symmetry of the electronic structure. In addition we find that, relative to the undistorted structure, the CDW structure shows a strong competition between nonmagnetic and various magnetic states, with an energy difference less than 5 meV/f.u. For the CDW structure in the antiferromagnetic state, the band dispersions and Fermi surface are similar to those in the nonmagnetic state, while the unfolded bands of the ferromagnetic CDW state display a sizable exchange splitting. These results indicate the possibility of various antiferromagnetic fluctuations in ${\mathrm{VSe}}_{2}$ to coexist and compete with ferromagnetic order and the experimentally reported CDW order. Our calculations build insights for exploring the interplay between magnetism and CDW behaviors more generally in transition metal dichalcogenides.

Atomic-scale thermopower in charge density wave states

The microscopic origins of thermopower have been investigated to design efficient thermoelectric devices, but strongly correlated quantum states such as charge density waves and Mott insulating phase remain to be explored for atomic-scale thermopower engineering. Here, we report on thermopower and phonon puddles in the charge density wave states in 1T-TaS2, probed by scanning thermoelectric microscopy. The Star-of-David clusters of atoms in 1T-TaS2 exhibit counterintuitive variations in thermopower with broken three-fold symmetry at the atomic scale, originating from the localized nature of valence electrons and their interlayer coupling in the Mott insulating charge density waves phase of 1T-TaS2. Additionally, phonon puddles are observed with a spatial range shorter than the conventional mean free path of phonons, revealing the phonon propagation and scattering in the subsurface structures of 1T-TaS2.

Charge Density Wave Order and Fluctuations above T_{CDW} and below Superconducting T_{c} in the Kagome Metal CsV_{3}Sb_{5}.

The phase diagram of the kagome metal family AV_{3}Sb_{5} (A=K, Rb, Cs) features both superconductivity and charge density wave (CDW) instabilities, which have generated tremendous recent attention. Nonetheless, significant questions remain. In particular, the temperature evolution and demise of the CDW state has not been extensively studied, and little is known about the coexistence of the CDW with superconductivity at low temperatures. We report an x-ray scattering study of CsV_{3}Sb_{5} over a broad range of temperatures from 300 to ∼2 K, below the onset of its superconductivity at T_{c}∼2.9 K. Order parameter measurements of the 2×2×2 CDW structure show an unusual and extended linear temperature dependence onsetting at T^{*}∼160 K, much higher than the susceptibility anomaly associated with CDW order at T_{CDW}=94 K. This implies strong CDW fluctuations exist to ∼1.7×T_{CDW}. The CDW order parameter is observed to be constant from T=16 to 2K, implying that the CDW and superconducting order coexist below T_{c}, and, at ambient pressure, any possible competition between the two order parameters is manifested at temperatures well below T_{c}, if at all. Anomalies in the temperature dependence in the lattice parameters coincide with T_{CDW} for c(T) and with T^{*} for a(T).

Coexistence of two intertwined charge density waves in a kagome system

Materials with a kagome lattice structure display a wealth of intriguing magnetic properties due to their geometric frustration and intrinsically flat band structure. Recently, topological and superconducting states have also been observed in kagome systems. The kagome lattice may also host a ``breathing'' mode that leads to charge density wave (CDW) states, if there is strong electron-phonon coupling, electron-electron interaction, or external excitation of the material. This ``breathing'' mode can give rise to candidate distortions such as the star of David (SoD) or its inverse structure [trihexagonal (TrH)]. To date, in most materials, only a single type of distortion has been observed. Here, we present angle-resolved photoemission spectroscopy measurements on the kagome superconductor ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ at multiple temperatures and photon energies to reveal the nature of the CDW in this material. It is shown that ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ displays two intertwined CDW orders corresponding to the SoD and TrH distortions. These two distinct types of distortions are stacked along the $c$ direction to form a three-dimensional CDW order where the two 2-fold CDWs are phase shifted along the $c$ axis. The presented results provide not only key insights into the nature of the unconventional CDW order in ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$, but also an important reference for further studies on the relationship between the CDW and superconducting order.

Anisotropy of 2H-NbSe2 in the superconducting and charge density wave states

Anisotropy is an important feature of layered materials, and a large anisotropy is usually related to the two-dimensional characteristics. We investigated the anisotropy of the layered transition metal dicalcogenide 2H-NbSe2 in the superconducting and charge density wave (CDW) states using magnetotransport measurements. In the superconducting state, the normalized is independent of the thickness of 2H-NbSe2, while increases significantly with decreasing thickness, where H p is the Pauli limiting magnetic field and and are the upper critical fields in the c and ab directions, respectively. It is found that the superconducting anisotropy parameter increases with reduction in the thickness of 2H-NbSe2. In the CDW state, the angular (θ) dependence of magnetoresistance, R(H,θ) scales with , which decreases with increasing temperature and disappears at about 40 K. It is found that the CDW anisotropy parameter γ CDW is much larger than the effective mass anisotropy but does not change a lot for ultrathin and bulk samples. Our results suggest the existence of three-dimensional superconductivity and quasi-two dimensional CDWs in bulk 2H-NbSe2.

Tuning charge density wave order and superconductivity in the kagome metals KV3Sb5−xSnx and RbV3Sb5−xSnx

The family of $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A$ = K, Rb, Cs) kagome metals exhibits charge density wave (CDW) order, proposed to be chiral, followed by a lower temperature superconducting state. Recent studies have proposed the importance of band structure saddle points proximal to the Fermi energy in governing these two transitions. Here we show the effects of hole doping achieved via chemical substitution of Sn for Sb on the CDW and superconducting states in both ${\mathrm{KV}}_{3}{\mathrm{Sb}}_{5}$ and ${\mathrm{RbV}}_{3}{\mathrm{Sb}}_{5}$ and generate a phase diagram. Hole doping lifts the $\mathrm{\ensuremath{\Gamma}}$ pocket and van Hove singularities toward ${E}_{F}$ causing the superconducting ${T}_{C}$ in both systems to increase to about 4.5 K, while rapidly suppressing the CDW state.

Controlling hysteretic transitions in quasi-one-dimensional TiS3 microribbons

Understanding the occurrence of charge density wave (CDW) states in quasi-one-dimensional (quasi-1D) transition metal trichalcogenides has attracted substantial research interest. Here, we report the systematic control of hysteretic transitions in quasi-1D TiS3 microribbons by changing the thickness and the cooling rate. Two distinguished resistance hysteresis loops are observed at a high temperature of ∼290 K and a low temperature of ∼60 K, respectively. In addition, two hysteretic transitions exhibit different behaviors under the external perturbations, in which the high temperature hysteretic transition is sensitive to TiS3 microribbons thickness, while the low temperature hysteretic transition is probably related to the CDW state and is robust against external perturbations. Our findings will offer a new frontier of exploration of the hysteretic transitions in the quasi-1D transition metal trichalcogenides.

Weak electronic correlations in the kagome superconductor AV3Sb5 ( A=K , Rb, Cs)

The kagome metals $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{K}$, Rb, Cs) have recently received enormous attention as they exhibit nontrivial topological electronic structure, flat band, unconventional intertwined charge density wave (CDW), anomalous Hall effect, and superconductivity. However, it is still controversial whether or not electronic correlations play an important role in these novel phenomena. Here we perform an extensive investigation on $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{K}$, Rb, Cs) with density functional theory plus dynamical mean field theory calculations. Our results indicate the electronic correlations effects are in the weak regime in both the normal state and the CDW state. The value of effective mass-enhancement ${m}^{*}/{m}_{\mathrm{DFT}}$ is about 1.3, and it is barely changed at temperatures ranging 50--900 K in the normal state. Our static susceptibility calculations with the normal structure show that static susceptibility has a weak ${q}_{z}$ dependence and the Fermi-surface nesting mechanism does not work in this system. In the CDW state with the inverse Star of David structure, the spectral function opens a CDW gap at the Fermi level below ${T}_{\mathrm{CDW}}$ (50 K) compared with the normal state above ${T}_{\mathrm{CDW}}$ (300 K). We find that there exists orbital multiplicity at the Fermi level owing to two nonequivalent V atoms in CDW states, which may have an important role in forming the CDW order.