Density Wave State Research Articles

Detection of a pair density wave state in UTe2

Spin-triplet topological superconductors should exhibit many unprecedented electronic properties, including fractionalized electronic states relevant to quantum information processing. Although UTe2 may embody such bulk topological superconductivity1–11, its superconductive order parameter Δ(k) remains unknown12. Many diverse forms for Δ(k) are physically possible12 in such heavy fermion materials13. Moreover, intertwined14,15 density waves of spin (SDW), charge (CDW) and pair (PDW) may interpose, with the latter exhibiting spatially modulating14,15 superconductive order parameter Δ(r), electron-pair density16–19 and pairing energy gap17,20–23. Hence, the newly discovered CDW state24 in UTe2 motivates the prospect that a PDW state may exist in this material24,25. To search for it, we visualize the pairing energy gap with μeV-scale energy resolution using superconductive scanning tunnelling microscopy (STM) tips26–31. We detect three PDWs, each with peak-to-peak gap modulations of around 10 μeV and at incommensurate wavevectors Pi=1,2,3 that are indistinguishable from the wavevectors Qi=1,2,3 of the prevenient24 CDW. Concurrent visualization of the UTe2 superconductive PDWs and the non-superconductive CDWs shows that every Pi:Qi pair exhibits a relative spatial phase δϕ ≈ π. From these observations, and given UTe2 as a spin-triplet superconductor12, this PDW state should be a spin-triplet PDW24,25. Although such states do exist32 in superfluid 3He, for superconductors, they are unprecedented.

Pair density wave state in a monolayer high-Tc iron-based superconductor.

The pair density wave (PDW) is an extraordinary superconducting state in which Cooper pairs carry non-zero momentum1,2. Evidence for the existence of intrinsic PDW order in high-temperature (high-Tc) cuprate superconductors3,4 and kagome superconductors5 has emerged recently. However, the PDW order in iron-based high-Tc superconductors has not been observed experimentally. Here, using scanning tunnelling microscopy and spectroscopy, we report the discovery of the PDW state in monolayer iron-based high-Tc Fe(Te,Se) films grown on SrTiO3(001) substrates. The PDW state with a period of λ ≈ 3.6aFe (aFe is the distance between neighbouring Fe atoms) is observed at the domain walls by the spatial electronic modulations of the local density of states, the superconducting gap and the π-phase shift boundaries of the PDW around the vortices of the intertwined charge density wave order. The discovery of the PDW state in the monolayer Fe(Te,Se) film provides a low-dimensional platform to study the interplay between the correlated electronic states and unconventional Cooper pairing in high-Tc superconductors.

Multi- k magnetic structure and large anomalous Hall effect in candidate magnetic Weyl semimetal NdAlGe

The magnetic structure, magnetoresistance (MR), and Hall effect of the noncentrosymmetric magnetic semimetal NdAlGe are investigated, revealing an unusual magnetic state and anomalous transport properties that are associated with the electronic structure of this compound. The magnetization and MR measurements are both highly anisotropic and indicate an Ising-like magnetic system. The magnetic structure is complex in that it involves two magnetic ordering vectors, including an incommensurate spin density wave and commensurate ferrimagnetic state in zero field. We have discovered a large anomalous Hall conductivity that reaches $\ensuremath{\approx}430\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.28em}{0ex}}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$, implying that it originates from an intrinsic Berry curvature effect stemming from Weyl nodes found in the electronic structure. These electronic structure calculations indicate the presence of nested Fermi surface pockets with nesting wave vectors like the measured magnetic ordering wave vector and the presence of Weyl nodes in proximity to the Fermi surface. We associate the incommensurate magnetic structure with the large anomalous Hall response to be the result of the combination of Fermi surface nesting and the Berry curvature associated with Weyl nodes.

Moiré Kanamori-Hubbard model for transition metal dichalcogenide homobilayers

Ab initio and continuum model studies predicted that the $\mathrm{\ensuremath{\Gamma}}$ valley transition metal dichalcogenide (TMD) homobilayers could simulate the conventional multiorbital Hubbard model on the moir\'e honeycomb lattice. Here, we perform the Wannierization starting from the continuum model and show that a more general moir\'e Kanamori-Hubbard model emerges, beyond the extensively studied standard multiorbital Hubbard model, which can be used to investigate the many-body physics in the $\mathrm{\ensuremath{\Gamma}}$ valley TMD homobilayers. Using the unrestricted Hartree-Fock and Lanczos techniques, we study these half-filled multiorbital moir\'e bands. By constructing the phase diagrams we predict the presence of an antiferromagnetic state and in addition we found unexpected and dominant states, such as a $S=1$ ferromagnetic insulator and a charge density wave state. Our theoretical predictions made using this model can be tested in future experiments on the $\mathrm{\ensuremath{\Gamma}}$ valley TMD homobilayers.

Phase-resolved frequency-domain analysis of the photoemission spectra for photoexcited 1T-TaS2 in the Mott insulating charge density wave state

We investigate the nonequilibrium electronic structure of 1T-TaS2 by time- and angle-resolved photoemission spectroscopy. We observe that strong photoexcitation induces the collapse of the Mott gap, leading to the photo-induced metallic phase. It is also found that the oscillation of photoemission intensity occurs as a result of the excitations of coherent phonons corresponding to the amplitude mode of the charge density wave (CDW). To study the dynamical change in the band dispersions modulated by the CDW amplitude mode, we perform analyses by using frequency-domain angle-resolved photoemission spectroscopy (FDARPES). We find that two different peak structures exhibit anti-phase oscillation with respect to each other by retrieving the amplitude and phase parts of the FDARPES spectra. They are attributed to the minimum and maximum band positions in energy, where the single band is oscillating between them synchronizing with the CDW amplitude mode. We further find that the flatband constructed as a result of CDW band folding survives during the oscillation while the Mott gap is significantly reduced. Our results suggest the CDW phase is robust, and the lattice modulation corresponding to the CDW amplitude mode dynamically modulates the Mott gap.

Manipulating charge density wave state in kagome compound RbV3Sb5

Owing to the unique electronic structure, kagome materials AV3Sb5 (A = K, Rb, Cs) provide a fertile platform of quantum phenomena such as the strongly correlated state and topological Dirac band. It is well known that RbV3Sb5 exhibits a 2 × 2 unconventional charge density wave (CDW) state at low temperature, and the mechanism is controversial. Here, by using scanning tunneling microscopy/spectroscopy (STM/STS), we successfully manipulated the CDW state in the Sb plane of RbV3Sb5, and realized a new modulation together with the ubiquitous 2 × 2 period in the CDW state of RbV3Sb5. This work provides a new understanding of the collective quantum ground states in the kagome materials.

Structure of the kagome superconductor CsV3Sb5 in the charge density wave state

The structure of charge density wave states in AV$_3$Sb$_5$ (A = K, Rb, Cs) kagome superconductors remains elusive, with three possible $2a\times2a\times2c$ candidates: tri-hexagonal, star-of-David, and their mixture. In this study, we conducted a systematic first-principles investigation of the nuclear quadrupole resonance (NQR) and nuclear magnetic resonance (NMR) spectra for the $2a\times2a\times2c$ CsV$_3$Sb$_5$ structures. By comparing our simulations with experimental data, we have concluded that the NQR spectrum indicates the tri-hexagonal structure as the proper structure for CsV$_3$Sb$_5$ after its charge density wave phase transition. The NMR calculation results obtained from the tri-hexagonal structure are also consistent with the experimental data.

Effect of pressure on the scattering of electrons by phonons in niobium triselenide at low temperatures

The paper analyzed the data on the temperature dependence in the region 4.2-300 K of the electrical resistance along the direction of the highest conductivity of the NbSe3 single crystal at different values of the uniaxial pressure perpendicular to the indicated direction. This pressure suppresses the charge density wave states without shifting their temperatures. In regions of metallic conductivity, the resistance can be approximated within the framework of the Bloch- Gruneisen-Wilson model. The Debye temperature decreases due to the size effect, which is stimulated by both cooling and pressure.

Crystal growth, characterization and electronic band structure of TiSeS

Layered semimetallic van der Waals material $\mathrm{Ti}{\mathrm{Se}}_{2}$ has attracted a lot of attention because of interplay of a charge density wave (CDW) state and superconductivity. Its sister compound ${\mathrm{TiS}}_{2}$, being isovalent to $\mathrm{Ti}{\mathrm{Se}}_{2}$ and having the same crystal structure, shows a semiconducting behavior. The natural question rises---what happens at the transition point in $\mathrm{Ti}{\mathrm{Se}}_{2\ensuremath{-}x}{\mathrm{S}}_{x}$, which is expected for x close to one. Here we report the growth and characterization of TiSeS single crystals and the study of the electronic structure using density functional theory (DFT) and angle-resolved photoemission (ARPES). We show that TiSeS single crystals have the same morphology as $\mathrm{Ti}{\mathrm{Se}}_{2}$. Transport measurements reveal a metallic state; no evidence of CDW was found. DFT calculations suggest that the electronic band structure in TiSeS is similar to that of $\mathrm{Ti}{\mathrm{Se}}_{2}$, but the electron and hole pockets in TiSeS are much smaller. The ARPES results are in good agreement with the calculations.

Electron-Exciton Coupling in 1T-TiSe2 Bilayer

Excitons in solid state are bosons generated by electron-hole pairs as the Coulomb screening is sufficiently reduced. The exciton condensation can result in exotic physics such as super-fluidity and insulating state. In charge density wave (CDW) state, 1T-TiSe2 is one of the candidates that may host the exciton condensation. However, to envision its excitonic effect is still challenging, particularly at the two-dimensional limit, which is applicable to future devices. Here, we realize the epitaxial 1T-TiSe2 bilayer, the two-dimensional limit for its 2 × 2 × 2 CDW order, to explore the exciton-associated effect. By means of high-resolution scanning tunneling spectroscopy and quasiparticle interference, we discover an unexpected state residing below the conduction band and right within the CDW gap region. As corroborated by our theoretical analysis, this mysterious phenomenon is in good agreement with the electron-exciton coupling. Our study provides a material platform to explore exciton-based electronics and opto-electronics.

Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands

Twisted double- and mono-bilayer graphene are graphene-based moiré materials hosting strongly correlated fermions in a gate-tunable conduction band with a topologically non-trivial character. Using unbiased exact diagonalization complemented by unrestricted Hartree-Fock calculations, we find that the strong electron-electron interactions lead to a non-coplanar magnetic state, which has the same symmetries as the tetrahedral antiferromagnet on the triangular lattice and can be thought of as a skyrmion lattice commensurate with the moiré scale, competing with a set of ferromagnetic, topological charge density waves featuring an approximate emergent O(3) symmetry, “rotating” the different charge density wave states into each other. Direct comparison with exact diagonalization reveals that the ordered phases are accurately described within the unrestricted Hartree-Fock approximation. Exhibiting a finite charge gap and Chern number |C|=1, the formation of charge density wave order which is intimately connected to a skyrmion lattice phase is consistent with recent experiments on these systems.

Competition of density waves and superconductivity in twisted tungsten diselenide

Evidence for correlated insulating and superconducting phases around regions of high density of states was reported in the strongly spin-orbit coupled van-der Waals material twisted tungsten diselenide (tWSe$_2$). We investigate their origin and interplay by using a functional renormalization group approach that allows to describe superconducting and spin/charge instabilities in an unbiased way. We map out the phase diagram as function of filling and perpendicular electric field, and find that the moir\'e Hubbard model for tWSe$_2$ features mixed-parity superconducting order parameters with $s/f$-wave and topological $d/p$-wave symmetry next to (incommensurate) density wave states. Our work systematically characterizes competing interaction-driven phases in tWSe$_2$ beyond mean-field approximations and provides guidance for experimental measurements by outlining the fingerprint of correlated states in interacting susceptibilities.

Electronic Instability of Kagome Metal CsV3Sb5 in the 2 × 2 × 2 Charge Density Wave State

Recently discovered kagome metals AV3Sb5 (A = K, Rb, and Cs) provide an ideal platform to study the correlation among nontrivial band topology, unconventional charge density wave (CDW), and superconductivity. The evolution of electronic structures associated with the change of lattice modulations is crucial for understanding of the CDW mechanism, with the combination of angle-resolved photoemission spectroscopy (ARPES) measurements and density functional theory calculations, we investigate how band dispersions change with the increase of lattice distortions. In particular, we focus on the electronic states around point, where the van Hove singularities are expected to play crucial roles in the CDW transition. Previous ARPES studies reported a spectral weight splitting of the van Hove singularity around point, which is associated with the 3D lattice modulations. Our studies reveal that this “splitting” can be connected to the two van Hove singularities at kz = 0 and kz = π/c in the normal states. When the electronic system enters into the CDW state, both van Hove singularities move down. Such novel properties are important for understanding of the CDW transition.

Signatures of the exciton gas phase and its condensation in monolayer 1T-ZrTe2

The excitonic insulator (EI) is a Bose-Einstein condensation (BEC) of excitons bound by electron-hole interaction in a solid, which could support high-temperature BEC transition. The material realization of EI has been challenged by the difficulty of distinguishing it from a conventional charge density wave (CDW) state. In the BEC limit, the preformed exciton gas phase is a hallmark to distinguish EI from conventional CDW, yet direct experimental evidence has been lacking. Here we report a distinct correlated phase beyond the 2×2 CDW ground state emerging in monolayer 1T-ZrTe2 and its investigation by angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). The results show novel band- and energy-dependent folding behavior in a two-step process, which is the signatures of an exciton gas phase prior to its condensation into the final CDW state. Our findings provide a versatile two-dimensional platform that allows tuning of the excitonic effect.

Detection of a Pair Density Wave State in UTe2

Detection of a Pair Density Wave State in UTe2

Detection of a Pair Density Wave State in UTe2

Detection of a Pair Density Wave State in UTe2

Unidirectional coherent quasiparticles in the high-temperature rotational symmetry broken phase of AV3Sb5 kagome superconductors

Kagome metals AV3Sb51 (where the A can stand for K, Cs or Rb) display a rich phase diagram of correlated electron states, including superconductivity2–4 and density waves5–7. Within this landscape, recent experiments have revealed signs of a transition below approximately 35 K attributed to an electronic nematic phase that spontaneously breaks the rotational symmetry of the lattice8. Here we show that the rotational symmetry breaking initiates universally at a high temperature in these materials, towards the 2 × 2 charge density wave transition temperature. We do this via spectroscopic-imaging scanning tunnelling microscopy and study the atomic-scale signatures of the electronic symmetry breaking across several materials in the AV3Sb5 family: CsV3Sb5, KV3Sb5 and Sn-doped CsV3Sb5. Below a substantially lower temperature of about 30 K, we measure the quantum interference of quasiparticles, a key signature for the formation of a coherent electronic state. These quasiparticles display a pronounced unidirectional feature in reciprocal space that strengthens as the superconducting state is approached. Our experiments reveal that high-temperature rotation symmetry breaking and the charge ordering states are separated from the superconducting ground state by an intermediate-temperature regime with coherent unidirectional quasiparticles. This picture is phenomenologically different compared to that in high-temperature superconductors, shedding light on the complex nature of rotation symmetry breaking in AV3Sb5 kagome superconductors. The charge density wave state in kagome superconductors is not fully understood. Now, evidence suggests that the rotational symmetry of the lattice is broken before coherence of unidirectional quasiparticles is established at a lower temperature.

Giant Angular Nernst Effect in the Organic Metal α-(BEDT-TTF)2KHg(SCN)4

We have detected a large Nernst effect in the charge density wave state of the multiband organic metal α-(BEDT-TTF)2KHg(SCN)4. We find that apart from the phonon drag effect, the energy relaxation processes that govern the electron–phonon interactions and the momentum relaxation processes that determine the mobility of the q1D charge carriers have a significant role in observing the large Nernst signal in the CDW state in this organic metal. The emphasised momentum relaxation dynamics in the low field CDW state (CDW0) is a clear indicator of the presence of a significant carrier mobility that might be the main source for observation of the largest Nernst signal. The momentum relaxation is absent with increasing angle and magnetic field, i.e., in the high-field CDW state (CDWx) as evident from the much smaller Nernst effect amplitude in this state. In this case, only the phonon drag effect and electron–phonon interactions are contributing to the transverse thermoelectric signal. Our findings advance and change previous observations on the complex properties of this organic metal.

Novel electrical properties of moiré graphene systems

In this review, we discuss the electronic structures, topological properties, correlated states, nonlinear optical responses, as well as phonon and electron-phonon coupling effects of moiré graphene superlattices. First, we illustrate that topologically non-trivial flat bands and moiré orbital magnetism are ubiquitous in various twisted graphene systems. In particular, the topological flat bands of magic-angle twisted bilayer graphene can be explained from a zeroth pseudo-Landau-level picture, which can naturally explain the experimentally observed quantum anomalous Hall effect and some of the other correlated states. These topologically nontrivial flat bands may lead to nearly quantized piezoelectric response, which can be used to directly probe the valley Chern numbers in these moiré graphene systems. A simple and general chiral decomposition rule is reviewed and discussed, which can be used to predict the low-energy band dispersions of generic twisted multilayer graphene system and alternating twisted multilayer graphene system. This review further discusses nontrivial interaction effects of magic-angle TBG such as the correlated insulator states, density wave states, cascade transitions, and nematic states, and proposes nonlinear optical measurement as an experimental probe to distinguish the different “featureless” correlated states. The phonon properties and electron-phonon coupling effects are also briefly reviewed. The novel physics emerging from band-aligned graphene-insulator heterostructres is also discussed in this review. In the end, we make a summary and an outlook about the novel physical properties of moiré superlattices based on two-dimensional materials.

Charge instability of topological Fermi arcs in chiral crystal CoSi

Topological boundary states emerged at the spatial boundary between topological non-trivial and trivial phases, are usually gapless, or commonly referred as metallic states. For example, the surface state of a topological insulator is a gapless Dirac state. These metallic topological boundary states are typically well described by non-interacting fermions. However, the behavior of topological boundary states with significant electron–electron interactions, which could turn the gapless boundary states into gapped ordered states, e.g., density wave states or superconducting states, is of great interest theoretically, but is still lacking evidence experimentally. Here, we report the observation of incommensurable charge density wave (CDW) formed on the topological boundary states driven by the electron–electron interactions on the (001) surface of CoSi. The wavevector of CDW varies as the temperature changes, which coincides with the evolution of topological surface Fermi arcs with temperature. The orientation of the CDW phase is determined by the chirality of the Fermi arcs, which indicates a direct association between CDW and Fermi arcs. Our finding will stimulate the search of more interactions-driven ordered states, such as superconductivity and magnetism, on the boundaries of topological materials.