Charge Density Wave State Research Articles

Strain-induced superconducting pair density wave states in graphene

Graphene is known to be nonsuperconducting. However, surprising superconductivity is recently discovered in a flat band in a twisted bilayer graphene. Here, we show that superconductivity can be more easily realized in topological flat bands induced by strain in graphene through periodic ripples. Specifically, it is shown that by including correlation effects, the chiral $d$-wave superconductivity can be stabilized under strain even for slightly doped graphene. The chiral $d$-wave superconductivity generally coexists with charge density waves (CDW) and pair density waves (PDW) of the same period. Remarkably, a pure PDW state with doubled period that coexists with the CDW state is found to emerge at a finite-temperature region under reasonable strain strength. The emergent PDW state is shown to be superconducting with nonvanishing superfluid density, and it realizes the long-sought-after superconducting states with nonvanishing center-of-mass momentum for Cooper pairs.

Charge Density Waves Driven by Peierls Instability at the Interface of Two-Dimensional Lateral Heterostructures.

The origin of charge density wave (CDW) observed in low-dimensional systems is, for long, a subject of intensive debate in contemporary condensed matter physics. Specifically, a simple and well established model, namely, the Peierls instability is often (but not always) used to clearly explain CDW states in real systems. Here, first-principles density functional theory calculations are used to show CDW formation at a one-dimensional interface embedded in a lateral heterostructure comprising blue and black phosphorene, even at room temperature. The CDW formation is fully explained by the Peierls mechanism, including a double-periodicity lattice distortion energy lowering and a bandgap opening. The lattice distortion also substantially modifies the band alignment of the heterostructure. Comparison with a freestanding P chain shows that the structural distortion is confined to one dimension within the heterostructures, ruling out competing non-Peierls-type distortions in two dimensions. In addition, similar Peierls-type distortions for other lateral heterostructures are shown by using the example of a graphene-hexagonal boron nitride heterostructure, which may stimulate related studies in different 2D systems. These findings not only shed more light on the Peierls mechanism, but also have important implications for devices based on 2D lateral heterostructures.

Observation of charge density waves in free-standing 1T-TaSe2 monolayers by transmission electron microscopy

While bulk 1T-TaSe2 is characterized by a commensurate charge density wave (CCDW) state below 473 K, the stability of the CCDW state in a 1T-TaSe2 monolayer, although theoretically predicted, has not been experimentally confirmed so far. As charge density waves and periodic lattice distortions (PLDs) always come together, we evaluate the PLD in a 1T-TaSe2 monolayer from low-voltage aberration-corrected high-resolution transmission electron microscopy experiments. To prevent fast degradation of 1T-TaSe2 during exposure to the electron-beam, a 1T-TaSe2/graphene heterostructure was prepared. We also perform the image simulations based on atom coordinates obtained using density functional theory calculations. From the agreement between the experimental and simulated images, we confirm the stability of the CCDW/PLD in a monolayer 1T-TaSe2/graphene heterostructure at room temperature in the form of a 13×13 superstructure. At the same time, we find that in comparison to multi-layer structures, the superstructure is less pronounced.

Transistor-Less Logic Circuits Implemented With 2-D Charge Density Wave Devices

We propose logic gates and circuits implemented with 2-D charge density wave (CDW) devices, which operate at room temperature. The 1T-TaS2 charge density wave devices exhibit a voltage triggered phase transition between the nearly commensurate and incommensurate CDW states, which is accompanied by an abrupt change of the resistance and hysteresis. The unique output characteristics of such devices allow for building logic gates and circuits without any transistors. Using the experimentally measured current–voltage characteristics, we model and numerically simulate the performance of the inverter and the OR logic gates consisting of CDW devices and regular resistors. Owing to the radiation-hard nature of the CDW devices and absence of transistors, the proposed circuits can be utilized in various harsh environments on earth or outer space.

Smeared nematic quantum phase transitions due to rare-region effects in inhomogeneous systems

The concept of a vestigial nematic order emerging from a "mother" spin or charge density-wave state has been applied to describe the phase diagrams of several systems, including unconventional superconductors. In a perfectly clean system, the two orders appear simultaneously via a first-order quantum phase transition, implying the absence of quantum criticality. Here, we investigate how this behavior is affected by impurity-free droplets that are naturally present in inhomogeneous systems. Due to their quantum dynamics, finite-size droplets sustain long-range nematic order but not long-range density-wave order. Interestingly, rare droplets with moderately large sizes undergo a second-order nematic transition even before the first-order quantum transition of the clean system. This gives rise to an extended regime of inhomogeneous nematic order, which is followed by a density-wave quantum Griffiths phase. As a result, a smeared quantum nematic transition, separated from the density-wave quantum transition, emerges in moderately disordered systems.

Chemical Growth of 1T-TaS2 Monolayer and Thin Films: Robust Charge Density Wave Transitions and High Bolometric Responsivity.

Ultrathin two-dimensional (2D) charge density wave (CDW) materials, with sharp resistance change at the phase-transition temperature, yet with ultrathin thickness, hold great potential for electrical device applications. However, chemical synthesis of high-quality samples and observation of the CDW states down to the monolayer limit is still of great challenge. Chemical vapor deposition of 1T-TaS2 sheets on hexagonal boron nitride (h-BN) with robust CDW states even down to the monolayer extreme is reported here. Further, based on the near commensurate CDW to incommensurate CDW phase transition with a high temperature coefficient of resistance (TCR), highly responsive room-temperature bolometers are fabricated by suspending the as-grown 1T-TaS2 sheets.

Correlation between charge density waves and antiferromagnetism in Nd1−xGdxNiC2 solid solutions

We report a study on the evolution of a charge density wave and antiferromagnetism in the series of the polycrystalline solid solution Nd$_{1-x}$Gd$_x$NiC$_2$ (0 $\leq$ x $\leq$ 1) by means of magnetic and transport properties measurements. The experimental results reveal the violation of the de Gennes law and a strong correlation between the Peierls, N\'eel and Curie-Weiss temperatures, which strongly suggests a cooperative interaction between the charge density wave state and antiferromagnetism due to Fermi surface nesting enhancement of the RKKY interaction. We also find that, the obtained results for the Nd$_{1-x}$Gd$_x$NiC$_2$ (0 $\leq$ x $\leq$ 1) series overlap with the $T_{CDW}$ trend line in the phase diagram for RNiC$_2$ family.

Nontrivial metallic state of MoS2

The electrical conductivity and Raman spectroscopy measurements have been performed on MoS$_2$ at high pressures up to 90 GPa and variable temperatures down to 5 K. We find that the temperature dependence of the resistance in a metallic 2H$_a$ phase has an anomaly (a hump) which shifts with pressure to higher temperature. Concomitantly, a new Raman phonon mode appears in the metallic state suggesting that the electrical resistance anomaly may be related to a structural transformation. We suggest that this anomalous behavior is due to a charge density wave state, the presence of which is indicative for a possibility for an emergence of superconductivity at higher pressures.

Charge Density Wave States in 2H-MoTe2 Revealed by Scanning Tunneling Microscopy**Supported by the National Key Research and Development Program of China under Grant Nos 2016YFA0301003 and 2016YFA0300403, and the National Natural Science Foundation of China under Grant Nos 11521404, 11634009, U1632102, 11504230, 11674222, 11574202, 11674226, 11574201 and U1632272.

2H- and -phase monolayer MoTe2 films on highly oriented pyrolytic graphite are studied using scanning tunneling microscopy and spectroscopy (STM/STS). The phase transition of MoTe2 can be controlled by a post-growth annealing process, and the intermediate state during the phase transition is directly observed by STM. For 2H-MoTe2, inversion domain boundaries are presented as bright lines at high sample bias, but as dark lines at lower sample bias. The dI/dV mappings reveal the distinct distributions of electronic states between domain boundaries and interiors of domains. It should be noted that a 2 × 2 periodic structure is clearly discernable inside the domains, where the STS measurement shows a small dip of size ∼150 meV at the vicinity of the Fermi level, indicating that the 2 × 2 periodic structure may be an incommensurate charge density wave. Moreover, a 4 × 4 periodic structure appears in 2H-MoTe2 grown at a higher substrate temperature.

Charge Density Wave and Spin Density Wave in Two-Orbital Model for Iron-Based Superconductors

We present a mean-field theoretical model study for the coexistence of the two strongly interacting charge density wave (CDW) and spin density wave (SDW) for iron-based superconductors in the under-doped region before the onset of the superconductivity in the system. The analytic expressions for the temperature dependence of the CDW and SDW order parameters are derived by using Zubarev’s technique of double-time single particle Green’s functions and solved self-consistently. Their interplay is studied by varying both the CDW and SDW coupling constants. Further, the electronic density of states (DOS) for the conduction electrons are studied in the pure CDW and SDW states and coexistence state for the cases, where the CDW transition temperature is greater than the SDW transition temperature and vice versa, which show two gap parameters.

Weak ergodicity breaking from quantum many-body scars

Certain wave functions of non-interacting quantum chaotic systems can exhibit "scars" in the fabric of their real-space density profile. Quantum scarred wave functions concentrate in the vicinity of unstable periodic classical trajectories. We introduce the notion of many-body quantum scars which reflect the existence of a subset of special many-body eigenstates concentrated in certain parts of the Hilbert space. We demonstrate the existence of scars in the Fibonacci chain -- the one- dimensional model with a constrained local Hilbert space realized in the 51 Rydberg atom quantum simulator [H. Bernien et al., arXiv:1707.04344]. The quantum scarred eigenstates are embedded throughout the thermalizing many-body spectrum, but surprisingly lead to direct experimental signatures such as robust oscillations following a quench from a charge-density wave state found in experiment. We develop a model based on a single particle hopping on the Hilbert space graph, which quantitatively captures the scarred wave functions up to large systems of L = 32 atoms. Our results suggest that scarred many-body bands give rise to a new universality class of quantum dynamics, which opens up opportunities for creating and manipulating novel states with long-lived coherence in systems that are now amenable to experimental study.

Single-crystal study of the charge density wave metal LuNiC2

We report on single crystal growth, single crystal x-ray diffraction, physical properties and density functional theory (DFT) electronic structure as well as Fermi surface calculations for two ternary carbides, LuCoC2 and LuNiC2. Electrical resistivity measurements reveal for LuNiC2 a charge density wave (CDW) transition at T_{CDW}~ 450 K and, for T > T_{CDW}, a significant anisotropy of the electrical resistivity, which is lowest along the orthorhombic a-axis. The analysis of x-ray superstructure reflections suggest a commensurate CDW state with a Peierls-type distortion of the Ni atom periodicity along the orthorhombic a-axis. DFT calculations based on the CDW modulated monoclinic structure model of LuNiC2 as compared to results of the orthorhombic parent-type reveal the formation of a partial CDW gap at the Fermi level which reduces the electronic density of states from N(E_{F})= 1.03 states/eV f.u. without CDW to N(E_{F})= 0.46 states/eV f.u. in the CDW state. The corresponding bare DFT Sommerfeld value of the latter, gamma_{DFT}^{CDW}= 0.90 mJ/molK^2, reaches reasonable agreement with the experimental value gamma= 0.83(5) mJ/mol\,K^2 of LuNiC2. LuCoC2 displays a simple metallic behavior with neither CDW ordering nor superconductivity above 0.4 K. Its experimental Sommerfeld coefficient, gamma= 5.9 (1) mJ/molK^2, is in realistic correspondence with the calculated, bare Sommerfeld coefficient, gamma_{DFT}= 3.82 mJ/molK^2, of orthorhombic LuCoC2.

Dc Resistivity of Quantum Critical, Charge Density Wave States from Gauge-Gravity Duality.

In contrast to metals with weak disorder, the resistivity of weakly pinned charge density waves (CDWs) is not controlled by irrelevant processes relaxing momentum. Instead, the leading contribution is governed by incoherent, diffusive processes which do not drag momentum and can be evaluated in the clean limit. We compute analytically the dc resistivity for a family of holographic charge density wave quantum critical phases and discuss its temperature scaling. Depending on the critical exponents, the ground state can be conducting or insulating. We connect our results to dc electrical transport in underdoped cuprate high T_{c} superconductors. We conclude by speculating on the possible relevance of unstable, semilocally critical CDW states to the strange metallic region.

Exciton-phonon cooperative mechanism of the triple- q charge-density-wave and antiferroelectric electron polarization in TiSe2

We investigate the microscopic mechanisms of the charge-density-wave (CDW) formation in a monolayer TiSe$_2$ using a realistic multiorbital $d$-$p$ model with electron-phonon coupling and intersite Coulomb (excitonic) interactions. First, we estimate the tight-binding bands of Ti $3d$ and Se $4p$ orbitals in the monolayer TiSe$_2$ on the basis of the first-principles band structure calculations. We thereby show orbital textures of the undistorted band structure near the Fermi level. Next, we derive the electron-phonon coupling using the tight-binding approximation and show that the softening occurs in the transverse phonon mode at the M point of the Brillouin zone. The stability of the triple-$q$ CDW state is thus examined to show that the transverse phonon modes at the M$_1$, M$_2$, and M$_3$ points are frozen simultaneously. Then, we introduce the intersite Coulomb interactions between the nearest-neighbor Ti and Se atoms that lead to the excitonic instability between the valence Se $4p$ and conduction Ti $3d$ bands. Treating the intersite Coulomb interactions in the mean-field approximation, we show that the electron-phonon and excitonic interactions cooperatively stabilize the triple-$q$ CDW state in TiSe$_2$. We also calculate a single-particle spectrum in the CDW state and reproduce the band folding spectra observed in photoemission spectroscopies. Finally, to clarify the nature of the CDW state, we examine the electronic charge density distribution and show that the CDW state in TiSe$_2$ is of a bond-type and induces a vortex-like antiferroelectric polarization in the kagome network of Ti atoms.

Unveiling Charge-Density Wave, Superconductivity, and Their Competitive Nature in Two-Dimensional NbSe2.

Recently, charge-density wave (CDW) and superconductivity are observed to coexist in atomically thin metallic NbSe2. Lacking of knowledge on the structural details of CDW, however, prevents us to explore its interplay with superconductivity. Using first-principles calculations, we identify the ground state 3 × 3 CDW atomic structure of monolayer NbSe2, which is characterized by the formation of triangular Nb clusters and shows a scanning tunnelling microscopy (STM) image and Raman CDW modes in good agreement with experiments. We further demonstrate that from bulk to monolayer NbSe2, as the layer thickness decreases, the CDW order is gradually enhanced with rising energy gain and strengthened Fermi surface gapping, while superconductivity is weakened due to the increasingly reduced Fermi level density of states in the CDW state. These results well explain the observed opposite thickness dependencies of CDW and superconducting transition temperatures and uncover the nature of competitive interaction between the two collective orders in two-dimensional NbSe2.

First principles analysis of the CDW instability of single-layer 1T-TiSe2 and its evolution with charge carrier density

We present a density functional theory study of the electronic structure of single-layer TiSe2, and focus on the charge density wave (CDW) instability present on this 2D material. We explain the periodicity of the CDW from the phonon band structure of the undistorted crystal, which is unstable under one of the phonon modes at the M point. This can be understood in terms of a partial band gap opening at the Fermi level, which we describe on the basis of the symmetry of the involved crystal orbitals, leading to an energy gain upon the displacement of the atoms following the phonon mode in a 2 × 1 structure. Furthermore, the combination of the corresponding phonons for the three inequivalent M points of the Brillouin zone leads to the 2 × 2 distortion characteristic of the CDW state. This leads to a further opening of a full gap, which reduces the energy of the 2 × 2 structure compared to the 2 × 1 one of a single M point phonon, and makes the CDW structure the most stable one. We also analyze the effect of charge injection into the layer on the structural instability. We predict that the 2 × 2 structure only survives for a certain range of doping levels, both for electrons and for holes, as doping reduces the energy gain due to the gap opening. We predict the transition from the commensurate 2 × 2 distortion to an incommensurate one with increasing wavelength upon increasing the doping level, followed by the appearance of the undistorted 1 × 1 structure for larger carrier concentrations.

Strong Electron–Phonon Interaction Establishes Correlation between Superconducting and Charge Density Wave States in NbSe<sub>2</sub>

Strong Electron–Phonon Interaction Establishes Correlation between Superconducting and Charge Density Wave States in NbSe<sub>2</sub>

Charge density wave states in tantalum dichalcogenides

Using density functional theory, we explore a range of charge density wave states (CDWs) in tantalum-based transition-metal dichalcogenide monolayers. The high-symmetry states of the $1H$ phases of $\mathrm{Ta}{X}_{2}$ ($X$ = S, Se, Te) are lower in total energy compared to the $1T$ variants, while the $1T$ phases exhibit a much stronger tendency for CDW formation. The stability of several CDWs is found to be stronger as the chalcogenide is changed in the sequence (S, Se, Te), with the tellurium-based systems exhibiting several CDWs with binding energy per formula unit in the range of $100\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$. These $1T$ CDW phases are lower in energy than the corresponding $1H$ CDW phases. The diversity of CDWs exhibited by these materials suggests that many ``hidden'' states may occur on ultrafast excitation or photodoping. Changes in electronic structure across the $\mathrm{Ta}{X}_{2}$ series are also elucidated.

Impact of the charge density wave state in the electrodynamic response of ZrTe3−xSex : Optical evidence for a pseudogap phase

The emergence of superconductivity upon progressively suppressing the long-range, charge-density-wave (CDW) order characterizes the phase diagram of several materials of interest in the on-going solid-state physics research. Se-doped ${\mathrm{ZrTe}}_{3}$ compounds provide the most recent, suitable arena in order to investigate the interplay of otherwise competing orders in layeredlike two-dimensional systems. We present an optical study of the CDW state in ${\mathrm{ZrTe}}_{3\ensuremath{-}x}{\mathrm{Se}}_{x}$ at selected Se dopings, based on the measurement of the reflectivity from the far-infrared up to the ultraviolet, as a function of temperature. We particularly focus our attention to the redistribution of the spectral weight, which images the impact of the CDW state within the optical conductivity across the phase diagram of the title compounds. The electrodynamic response is consistent with a scenario based on a long-range CDW condensate at low Se doping. Upon increasing the Se content, this then gives way to local, short-range order CDW segments. Our spectral weight analysis reveals the presence of a pseudogap phase, as fingerprint of the CDW precursor effects and thus shaping the charge dynamics of the title compounds in their normal state, preceding the onset of superconductivity.

Extended phase diagram of RNiC2 family: Linear scaling of the Peierls temperature

Physical properties for the late-lanthanide-based RNiC2 (R = Dy, Ho, Er, and Tm) ternary compounds are reported. All the compounds show antiferromagnetic ground state with the N\'eel temperature ranging from 3.4 K for HoNiC2 to 8.5 K for ErNiC2. The results of the transport and galvanomagnetic properties confirm a charge density wave state at and above room temperature with transition temperatures TCDW = 284, 335, 366, and 394 K for DyNiC2, HoNiC2, ErNiC2, and TmNiC2, respectively. The Peierls temperature TCDW scales linearly with the unit cell volume. A similar linear dependence has been observed for the temperature of the lock-in transition T1 as well. Beyond the intersection point of the trend lines, the lock-in transition is no longer observed. In this Rapid Communication we demonstrate an extended phase diagram for the RNiC2 family.