Charge Density Wave Type Research Articles

Directly visualizing nematic superconductivity driven by the pair density wave in NbSe2

Pair density wave (PDW) is a distinct superconducting state characterized by a periodic modulation of its order parameter in real space. Its intricate interplay with the charge density wave (CDW) state is a continuing topic of interest in condensed matter physics. While PDW states have been discovered in cuprates and other unconventional superconductors, the understanding of diverse PDWs and their interactions with different types of CDWs remains limited. Here, utilizing scanning tunneling microscopy, we unveil the subtle correlations between PDW ground states and two distinct CDW phases — namely, anion-centered-CDW (AC-CDW) and hollow-centered-CDW (HC-CDW) — in 2H-NbSe2. In both CDW regions, we observe coexisting PDWs with a commensurate structure that aligns with the underlying CDW phase. The superconducting gap size, Δ(r), related to the pairing order parameter is in phase with the charge density in both CDW regions. Meanwhile, the coherence peak height, H(r), qualitatively reflecting the electron-pair density, exhibits a phase difference of approximately 2π/3 relative to the CDW. The three-fold rotational symmetry is preserved in the HC-CDW region but is spontaneously broken in the AC-CDW region due to the PDW state, leading to the emergence of nematic superconductivity.

Anomalous low-energy carrier dynamics of stripe-type charge ordered Pr0.5Sr0.5MnO3 thin film revealed by magneto-terahertz spectroscopy

The perovskite manganites host a range of charge- and orbital-ordered phases wherein the intrinsic and extrinsic controls of magnetic field, doping, epitaxial strain, chemical pressure, etc., induce subtleties of phase transition. The Pr0.5Sr0.5MnO3 (PSMO) is one such system that possesses a unique stripe-type charge-order manifesting in anisotropic transport. It exhibits a Drude-type and charge-density-wave (CDW) type of low-energy phases; the magnetic field is contemplated as a key control for both these phases; however, it has not yet been explored. Here, we have investigated the magnetic-field dependence of Drude-type terahertz (THz) carriers dynamics and the CDW type of low-energy excitations along two non-identical orthogonal in-plane axes of the (110) epitaxial thin film in the energy range of 1–7 meV using magneto-THz time-domain spectroscopy in Faraday geometry. While THz Drude conductivity expectedly increases with the increasing magnetic field, the CDW type of resonance absorption peak anomalously strengthens with the field. The origin of this unusual field-induced stabilization of the CDW-type mode is expected to lie in the d(x2–y2) orbital ordering in the A-type antiferromagnetic ordered state and anisotropic charge ordering. This study brings out a unique facet of the effect of magnetic field on orbital ordering of anisotropic stripe-type charge-ordered PSMO, which has potential THz modulation and switching applications.

Topological theory of inversion-breaking charge-density-wave monolayer 1T-TiSe2

A charge density wave (CDW) of a nonzero ordering vector q couple electronic states at k and k + q statically, giving rise to a reduced Brillouin zone due to the band folding effect. Its structure, referred to an irreducible representation of the little group of q, would change the symmetry of the system and electronic structure accompanying possible change of band inversion, offering a chance of the topological phase transition. Monolayer 1T-TiSe2 is investigated for it shows an unconventional CDW phase having a triple-q structure. Moreover, the coupling between the triple-q component of the CDW will inevitably produces a small CDW. The CDW yields a band inversion in 1T-TiSe2 but different types of CDW can affect the electronic structure and system topology differently. The impact of CDW of different types was studied by utilizing a symmetrization–antisymmetrization technique to extract the and CDW contributions in the density functional theory-based tight-binding model and study their effects. The results are consistent with the parity consideration, improving understanding of topology for a CDW system with and without parity.

Breakdown of charge homogeneity in the two-dimensional Hubbard model: Slave-boson study of magnetic order

We study the two-dimensional one-band Hubbard model on the square lattice through the spin rotation invariant Kotliar-Ruckenstein slave-boson method, with an emphasis on the electron-doped regime. The phase diagram determined within mean field approximation reveals three different magnetically ordered phases separated by first-order transitions, and a wide instability region as indicated by a negative compressibility. We show that this conundrum of the unstable mean field domain is resolved by spatially mixed phases of neighboring stable states. We also find charge density wave type instabilities in the antiferromagnetically ordered (AFM) state at wave vectors commensurate with the doping. The corresponding charge and spin density response functions are calculated from a Gaussian fluctuations formalism about a magnetic saddle point, for which we provide a detailed derivation. Further, we present density and spin excitation spectra in the AFM phase, allowing for a quantitative calculation of the spin wave parameters, the gap in the longitudinal spin excitation spectrum, and the density excitations in the upper Hubbard band.

Pinned and bound modes of charge density wave type collective excitation in SmNiO3 as revealed by terahertz spectroscopy

The terahertz (THz) optical conductivity of charge-ordered nickelate ${\mathrm{SmNiO}}_{3}$ thin films depicts a unique dependence of the charge-density-wave (CDW) type instability on the film thickness. Here, we report a rare observation of two dominant resonance modes in the THz conductivity spectrum. Corroborated by structural and electrical conductivity data, we demonstrate that these doublet excitations are the attribution of the CDW type pinned and bound modes. Both the peak position and the peak strength can be controlled by the film thickness and the defect density associated with oxygen stoichiometry. The oxygen vacancies in these films act like defects/impurities and induce charge oscillation around them which get coupled with unperturbed CDW mode of the charge-ordered phase. Thus, an additional bound mode emerges alongside the pinned mode. The defect density as controlled by the film thickness allows modulation of the resonance excitations in the desired THz frequency range.

A New Type of Charge-Density-Wave Pinning in Orthorhombic TaS3 Crystals with Quenching Defects

Diminishing in the concentration of quenching defects during thermocycling of orthorhombic TaS$_3$ samples in the temperature range below the Peierls transition temperature $T <T_P$ is observed. It makes it possible to study the character of pinning of the charge density wave (CDW) by these defects. A number of fundamental differences from pinning by ordinary local pinning centers - impurities and point defects - have been found. We conclude that quenching defects are extended (non-local) objects (presumably, dislocations) that can diffuse from the crystal during low-temperature termocycling due to their strong interaction with the CDW, which is intrinsic for the Peierls conductors. The presence of these defects leads to a previously unknown non-local type of CDW pinning that acts on $T_P$ and the threshold field for the onset of the CDW sliding, $E_T$, differently in comparison with the local pinning centers.

Breathing charge density waves in intrinsic Josephson junctions

We demonstrate the creation of a charge density wave (CDW) along a stack of coupled Josephson junctions (JJs) in layered superconductors. Electric charge in each superconducting layer oscillates around some average value, forming a breathing CDW. We show the transformation of a longitudinal plasma wave to CDW in the state corresponding to the outermost branch. Transition between different types of CDW’s related to the inner branches of IV characteristic is demonstrated. The effect of the external electromagnetic radiation on the states corresponding to the inner branches differs crucially from the case of the single JJ. The Shapiro steps in the IV characteristics of the junctions in the stack do not correspond directly to the frequency of radiation ω. The system of JJs behaves like a single whole system: the Shapiro steps or their harmonics in the total IV characteristics appear at voltage \(\sum {V_l } = N_R \frac{m} {n}\omega\), where V l is the voltage in the lth junction, N R is the number of JJs in the rotating state, and m and n are integers.

Theory of subgap interchain tunneling in quasi 1D conductors

We suggest a theory of internal coherent tunneling in the pseudogap region when the applied voltage $U$ is below the free electron gap $2{\ensuremath{\Delta}}_{0}$. We address quasi-one-dimensional (quasi 1D) systems, where the gap is originated by spontaneous lattice distortions of the incommensurate charge density wave type. The results can be adjusted also to quasi 1D superconductors. The instanton approach allows one to calculate the interchain tunneling current both in single electron (amplitude solitons, i.e., spinons) and bielectron (phase slips) channels. Transition rates are governed by a dissipative dynamics originated by the emission of gapless phase excitations in the course of the instanton process. We find that the single-electron tunneling is allowed down to the true pair-breaking threshold at ${U}_{c1}=2{W}_{\mathit{as}}&lt;2{\ensuremath{\Delta}}_{0}$, where ${W}_{\mathit{as}}=2∕\ensuremath{\pi}{\ensuremath{\Delta}}_{0}$ is the amplitude soliton energy. Most importantly, the bielectronic tunneling stretches down to ${U}_{c2}=0$ (in the 1D regime). In both cases, the threshold behavior is given by power laws $J\ensuremath{\sim}{(U\ensuremath{-}{U}_{c})}^{\ensuremath{\beta}}$, where the exponent $\ensuremath{\beta}\ensuremath{\sim}{v}_{F}∕u$ is as large as the ratio of the Fermi velocity ${v}_{F}$ and the phase $u$. In the two-dimensional or three-dimensional ordered phases, at temperature $T&lt;{T}_{c}$, the one-electron tunneling current does not vanish at the threshold anymore, but saturates above it at $U\ensuremath{-}{U}_{c1}\ensuremath{\sim}{T}_{c}⪡{\ensuremath{\Delta}}_{0}$. Also the biparticle channel acquires a finite threshold ${U}_{c2}={W}_{2\ensuremath{\pi}}\ensuremath{\sim}{T}_{c}⪡{\ensuremath{\Delta}}_{0}$ at the energy of the $2\ensuremath{\pi}$ phase soliton.

Checkerboard charge density wave and pseudogap of high-Tccuprate

We consider the scenario where a 4-lattice constant, rotationally symmetric charge density wave (CDW) is present in the underdoped cuprates. We prove a theorem that puts strong constraint on the possible form factor of such a CDW. We demonstrate, within mean-field theory, that a particular form factor within the allowed class describes the angle-resolved photoemission and scan tunneling spectroscopy well. We conjecture that the ``large pseudogap'' in cuprates is the consequence of this type of charge density wave.

As–As dimerization, Fermi surfaces and the anomalous electrical transport properties of UAsSe and ThAsSe

A temperature dependent electron diffraction study has been carried out on UAsSe to search for evidence of As–As dimerization at low temperature. A highly structured characteristic diffuse intensity distribution, closely related to that recently reported for ThAsSe, has been observed at low temperature and interpreted in terms of a gradual charge density wave type phase transition upon lowering of temperature involving disordered As–As dimerization within (001) planes. Plausible models of the proposed As–As dimerization have been obtained using a group theoretical approach. Electronic band structure calculations of ThAsSe and UAsSe have been used to search for potential Fermi surface nesting wave-vectors. The results are in good agreement with the experimentally observed diffuse intensity distributions in both cases.

A low-temperature electron diffraction study of structural disorder and its relationship to the Kondo effect in ThAsSe

A low-temperature electron diffraction study has been carried out on ThAsSe to search for evidence of structural disorder associated with the low-temperature non-magnetic Kondo effect. A highly structured and extremely complex characteristic diffuse intensity distribution has been observed at low temperature and interpreted in terms of a gradual charge density wave type phase transition upon lowering of temperature involving disordered As–As dimerization within (001) planes. Plausible models of the proposed As–As dimerization have been obtained using a group theoretical approach.

Trifluoromethylsulfonyl-Based Salts of BEDT-TTF: Crystal and Electronic Structures and Physical Properties11

Three 2 : 1 salts of the organic donor molecule bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF or ET) with trifluoromethylsulfonyl-based anions N(SO 2CF 3) 2 −, CH(SO 2CF 3) 2 − and C(SO 2CF 3) 3 − were prepared by electrocrystallization. These salts were characterized by single-crystal X-ray diffraction, electron spin resonance (ESR) spectroscopy, electrical resistivity measurements and electronic band structure calculations. (ET) 2N(SO 2CF 3) 2 is a two-dimensional (2D) metal, but its ESR spin susceptibility above 150 K shows a weakly semiconducting behavior, presumably because during ESR measurements the sample cooling rate is slow hence allowing the disordered anions to readjust their positions. (ET) 2CH (SO 2CF 3) 2 is a 2D metal and undergoes a metal-to-insulator (MI) transition at 110 K due probably to a geometry change of the donor molecule layers. (ET) 2C(SO 2CF 3) 3 is a one-dimensional (1D) metal and undergoes an MI between 180 and 240 K, which is expected to be of charge density wave type.

Charge-density-wave transitions in the local-moment magnet Er5Ir4Si10

We report the observation of a new type of charge-density wave (CDW) in the large magnetic-moment rare-earth intermetallic compound, Er5Ir4Si10, which then orders magnetically at low temperatures. Single crystal x-ray diffraction shows the development of a 1D incommensurate CDW at 155 K, which then locks into a purely commensurate state below 55 K. The well-localized Er3+ moments are antiferromagnetically ordered below 2.8 K. We observe very sharp anomalies in the specific heat at 145 and 2.8 K, signifying the bulk nature of these transitions. Our data suggest the coexistence of strongly coupled CDW with local-moment antiferromagnetism in Er5Ir4Si10.

Effects of a transverse electric field on charge-density waves

A transverse electric field (a field perpendicular to the quasi-one-dimensional conducting chains) applied to a charge-density wave (CDW) causes frustration in the ordered state and has similar effects to a magnetic field applied to a superconductor. We study the equilibrium states of CDW in the transverse electric field paying attention to this similarity. Corresponding to type-I and type-II superconductivity, two types of CDW are investigated.

Localization effects in the charge density wave state [4]of the quasi-two-dimensional monophosphate tungsten bronzes

The monophosphate tungsten bronzes (PO 2 ) 4 (WO 3 ) 2m are quasi-two-dimensional conductors which show charge density wave type electronic instabilities. We report electrical resistivity and magnetoresistance measurements down to 0.30 K and in magnetic fields up to 16 T for the m = 7, 8 and 9 members of this family. We show that these compounds exhibit at low temperature an upturn of resistivity and field dependences of the magnetoresistance characteristic of localization effects. We discuss the dimensionality of the regime of localization as m is varied. We show that for m =7, the regime is quasi-two-dimensional and three-dimensional for m = 8, 9.

Charge density wave in a transverse electric field

A transverse electric field (a field perpendicular to the quasi-one-dimensional conducting chains) applied to a charge density wave (CDW) has similarities with a magnetic field applied to a superconductor: both cause frustration in the ordered state and, thus, can induce various intriguing states. We study the equilibrium states of CDW in a transverse electric field employing Ginzburg-Landau type effective free energy of the ordered state. We found that there are two types of CDW, corresponding to type-1 and type-II superconductivity: in type-I CDW, the order is completely destroyed in the surface region as we increase the transverse field, whereas in type-II CDW, the dislocations (topological defects) are created, thus avoiding the complete destruction of the order. We discuss the condition for type-I and type-II CDW.

Electronic Instabilities and Localization Effects in the Quasi-Two-Dimensional Monophosphate Tungsten Bronzes (PO2)4(WO3)2m and KxP4W8O32

The monophosphate tungsten bronzes (PO2)4(WO3)2m with pentagonal tunnels are quasi-two-dimensional conductors that show charge density wave type electronic instabilities. These series of compounds provide a model system where the low-dimensional character and the average electron concentration are functions of the m parameter. The low m compounds (m=4, 6) show conventional charge density wave instabilities. The m=5 compound exists with two different crystal structures and shows instabilities with slightly different properties. We report measurements of transport properties for the compounds m=5, 7, 8, 9. We show that, for m>7, these compounds exhibit an upturn of resistivity and field dependence of the magnetoresistance characteristic of quantum interference effects. We also report transport properties of the compounds KxP4W8O32 with pseudo-hexagonal tunnels that show electronic instabilities with critical temperatures depending on x.

Localization effects in the charge density wave state of the quasi-two-dimensional conductors (PO 2) 4(WO 3) 2 m ( m=7)

The quasi-two-dimensional conductors (PO 2) 4(WO 3) 2 m show charge density wave type electronic instabilities. The average number of conduction electrons per W atom is 2/ m, decreasing with m. We report resistivity and magnetoresistance measurements for the m=7 compound. The upturn of resistivity at low temperature and the field dependence of the magnetoresistance are discussed in terms of weak localization effects.

Tunneling spectroscopy around the boundary of a small impurity phase on the surface of 2H-NbSe 2

single crystal were studied at 4.2 K in an ultra-high vacuum using scanning tunneling microscopy. Small domains with \(\)×\(\) surface modulation were found adjacent to the flat 2H-type surface with the 3×3 intrinsic charge density wave (CDW). Using tunneling spectroscopy, density of states around the Fermi energy at the domains was found to be lower than that at the 2H-type surface. The \(\)×\(\) modulation is considered to originate from another type of CDW. The observed proximity of superconductivity of 2H-crystal to the highly modulated domain was very small. These results suggest that the crystal structure of the highly-modulated domain is the 4Hd polytype.

Resolution of the 66-Fold Superstructure of DySe1.84 by X-ray Diffraction and Second-Moment Scaled Hückel Calculations

We report the superlattice of the modulated structure DySe1.84. The modulation is of the charge density wave type, associated with electronic states on selenium atoms arranged in two-dimensional square nets. The complete modulated structure can be described in the superspace group formalism in a 3+2 dimensional space group . The basic cell observed by single-crystal X-ray diffraction is orthorhombic with a = 3.9912(3) Å, b = 3.9863(1) Å, and c = 8.206(1) Å. The modulation wave vectors are q1 = αa*+βb* + 1/2c* and q2 = αa* − βb* + 1/2c*, where α = 0.33338(16) and β = 0.27284(6). Structure refinement based on first- and second-order satellites as well as main lattice reflections produced solutions in four different space groups that could not be differentiated on the basis of agreement factors. A best solution was sought by use of second-moment scaled, tight-binding band calculations. The lowest energy model found was similar to but not identical with two of those refined for X-ray data. This lowest energy structure can be rationalized by analysis of second-nearest-neighbor interactions within the selenium square nets.