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Photodetector based on two-dimensional (2D) materials is an ongoing quest in optoelectronics. These 2D photodetectors are generally efficient at low illuminating power but suffer severe recombination processes at high power, which results in the sublinear power dependence of photoresponse and lower optoelectronic efficiency. The desirable superlinear photocurrent is mostly achieved by sophisticated 2D heterostructures or device arrays, while 2D materials rarely show intrinsic superlinear photoresponse. Here, we report the giant superlinear power dependence of photocurrent based on multi-layer Ta$_2$NiS$_5$. While the fabricated photodetector exhibits good sensitivity ($3.1 mS/W$ per square) and fast photoresponse ($31 \mu$$s$), the bias-, polarization-, and spatial-resolved measurements point to an intrinsic photoconductive mechanism. By increasing the incident power density from $1.5 \mu$W/$\mu$$m^{2}$ to $200 \mu$W/$\mu$$m^{2}$, the photocurrent power dependence varies from sublinear to superlinear. At higher illuminating conditions, a prominent superlinearity is observed with a giant power exponent of $\gamma=1.5$. The unusual photoresponse can be explained by a two-recombination-center model where the distinct density of states of the recombination centers effectively closes all recombination channels. The fabricated photodetector is integrated into camera for taking photos with enhanced contrast due to the superlinearity. Our work provides an effective route to enable higher optoelectronic efficiency at extreme conditions.

We describe the electronic structure and spectroscopic properties of CuAlxFe1–xS2 nanocrystals and their core/shell structures. The as-synthesized CuAlxFe1–xS2 core exhibits a tetragonal chalcopyri...

In this work we study many-body 'steady states' that arise in the non-Hermitian generalisation of the non-interacting Su-Schrieffer-Heeger model at a finite density of fermions. We find that the hitherto known phase diagrams for this system, derived from the single-particle gap closings, in fact correspond to distinct non-equilibrium phases, which either carry finite currents or are dynamical insulators where particles are entrapped. Each of these have distinct quasi-particle excitations and steady state correlations and entanglement properties. Looking at finite-sized systems, we further modulate the boundary to uncover the topological features in such steady states -- in particular the emergence of leaky boundary modes. Using a variety of analytical and numerical methods we develop a theoretical understanding of the various phases and their transitions, and uncover the rich interplay of non-equilibrium many-body physics, quantum entanglement and topology in a simple looking, yet a rich model system., Comment: Published version

The anomalous Hall effect in time-reversal symmetry broken systems is underpinned by the concept of Berry curvature in band theory. However, recent experiments reveal that the nonlinear Hall effect can be observed in non-magnetic systems without applying an external magnetic field. The emergence of nonlinear Hall effect under time-reversal symmetric conditions can be explained in terms of non-vanishing Berry curvature dipole arising from inversion symmetry breaking. In this work, we availed realistic tight-binding models, first-principles calculations, and symmetry analyses to explore the combined effect of transverse electric field and strain, which leads to a giant Berry curvature dipole in the elemental buckled honeycomb lattices -- silicene, germanene, and stanene. The external electric field breaks the inversion symmetry of these systems, while strain helps to attain an asymmetrical distribution of Berry curvature of a single valley. Furthermore, the topology of the electronic wavefunction switches from the band inverted quantum spin Hall state to normal insulating one at the gapless point. This band gap closing at the critical electric field strength is accompanied by an enhanced Berry curvature and concomitantly a giant Berry curvature dipole at the Fermi level. Our results predict the occurrence of an electrically switchable nonlinear electrical and thermal Hall effect in a new class of elemental systems that can be experimentally verified., To appear in 2D Materials

In the presence of time reversal symmetry, a non-linear Hall effect can occur in systems without an inversion symmetry. One of the prominent candidates for detection of such Hall signals are Weyl semimetals. In this article, we investigate the Berry curvature induced second and third order Hall effect in multi-Weyl semimetals with topological charges $n =1, 2, 3$. We use low energy effective models to obtain general analytical expressions and discover the presence of a large Berry curvature dipole in multi-Weyl semimetals. We also study the Berry curvature dipole in a realistic tight-binding lattice model and observe two different kinds of variation with increasing topological charge -- these can be attributed to different underlying Berry curvature components. We provide estimates of the signatures of second harmonic of Hall signal in multi-Weyl semimetals, which can be detected experimentally. Furthermore, we predict the existence of a third order Hall signal in multi-Weyl semimetals. We derive the analytical expressions of Berry connection polarizability tensor, which is responsible for third order effects, using a low energy model and estimate the measurable conductivity. Our work can help guide experimental discovery of Berry curvature multipole physics in multi-Weyl semimetals., Comment: 22 pages, 6 figures. Comments welcome

The synergy between non-Hermitian concepts and topological ideas have led to very fruitful activity in the recent years. Their interplay has resulted in a wide variety of new non-Hermitian topological phenomena being discovered. In this review, we present the key principles underpinning the topological features of non-Hermitian phases. Using paradigmatic models -- Hatano-Helson, non-Hermitian Su-Schrieffer-Heeger and non-Hermitian Chern insulator -- we illustrate the central features of non-Hermitian topological systems, including exceptional points, complex energy gaps and non-Hermitian symmetry classification. We discuss the non-Hermitian skin effect and the notion of the generalized Brillouin zone, which allows restoring the bulk-boundary correspondence. Using concrete examples, we examine the role of disorder, present the linear response framework, and analyze the Hall transport properties of non-Hermitian topological systems. We also survey the rapidly growing experimental advances in this field. Finally, we end by highlighting possible directions which, in our view, may be promising for explorations in the near future., Comment: Topical review. Close to published version

Janus transition metal dichalcogenides, with intrinsic mirror asymmetry, exhibit a wide array of interesting properties. In this work, we study Janus monolayers derived from WTe$_2$ using first-principles and tight-binding calculations. We discover that WSeTe and WSTe are topologically trivial, in contrast to the parent quantum spin Hall insulator WTe$_2$. Motivated by the growing interest in non-linear Hall effect, which also requires asymmetric structures, we investigate the Berry curvature and its dipole in these Janus systems and find that they exhibit strikingly large values of Berry curvature dipole, despite being in the topologically trivial phase. We track down the origin of this behaviour and put forth a low-energy massive Dirac model to understand the central features of our ab initio computations. Our predictions introduce Janus monolayers as promising new platforms for exploring as well as engineering non-linear Hall effect., Comment: 18 pages, 4 figures. To appear in Materials Research Express Special Issue on Emerging Investigators in Materials Science

Symmetry-protected spectral topology in non-Hermitian systems has interesting manifestations such as dynamically anomalous chiral currents and skin effect. We study the interplay between symmetries and disorder in a paradigmatic model for spectral topology - the non-reciprocal Su-Schrieffer-Heeger model. We numerically study the effect of disorder in on-site and non-reciprocal hopping terms. Using a real-space winding number, we investigate the impact of disorder on the spectral topology and the anomalous chiral modes under periodic boundary conditions. We discover a remarkable robustness of chiral current under disorder. The value of the chiral current retains the clean system value, is independent of disorder strength and is tracked completely by the real-space winding number for class A which has no symmetries, and class AIII, which has a sub-lattice symmetry. In class $D^\dagger$, which has $PT$-symmetric on-site gain and loss terms, we find that the disorder-averaged current is not robust while the winding number is robust. We study the localization physics using the inverse participation ratio and local density of states. As the disorder strength is increased, a mobility-edge phase with a finite winding appears. The abrupt vanishing of the winding number marks a transition from a partially localized to a fully localized phase. Under open boundary conditions, we observe a series of transitions through skin effect-partial skin effect-no skin effect phases. Further, we study the non-Hermitian Anderson skin effect (NHASE) for different symmetry classes, where the system without skin effect develops a disorder-driven skin effect at intermediate disorder values. Remarkably while NHASE is present for different classes, the real-space winding number shows a direct correspondence with it only when all symmetries are broken., Comment: Published version

Two-dimensional (2D) ferromagnetic materials have been discovered with tunable magnetism and orbital-driven nodal-line features. Controlling the 2D magnetism in exfoliated nanoflakes via electric/magnetic fields enables a boosted Curie temperature (TC) or phase transitions. One of the challenges, however, is the realization of high TC 2D magnets that are tunable, robust and suitable for large scale fabrication. Here, we report molecular-beam epitaxy growth of wafer-scale Fe3+XGeTe2 films with TC above room temperature. By controlling the Fe composition in Fe3+XGeTe2, a continuously modulated TC in a broad range of 185–320 K has been achieved. This widely tunable TC is attributed to the doped interlayer Fe that provides a 40% enhancement around the optimal composition X = 2. We further fabricated magnetic tunneling junction device arrays that exhibit clear tunneling signals. Our results show an effective and reliable approach, i.e. element doping, to producing robust and tunable ferromagnetism beyond room temperature in a large-scale 2D Fe3+XGeTe2 fashion.

Multifold fermion systems feature free fermionic excitations, which have no counterparts in high-energy physics, and exhibit several unconventional properties. Using first-principles calculations, we predict that strain engineering can be used to control the distribution of topological charges in transition metal silicide candidate CoSi, hosting multifold fermions. We demonstrate that breaking the rotational symmetry of the system, by choosing a suitable strain, destroys the multifold fermions, and at the same time results in the creation of Weyl points. We introduce a low energy effective model to complement the results obtained from density functional calculations. Our findings suggest that strain-engineering is a useful approach to tune topological properties of multifold fermions., 23 pages, 8 figures

We systematically study the bulk and finite size effects on the band structure of prototypical line node materials using density functional theory based computations. For the bulk system, we analyze quantum oscillations with changes in the Fermi surface topology. We show that ultra thin slabs are gapped, with the first signatures of the line node appearing beyond a critical thickness. Further, motivated by possibility of tuning the bulk line node, we find that the line node radius is rather sensitive to bulk volume change. Based on this observation, we propose that application of pressure or suitable substrate engineering can be used as an effective means to control and tune the line node and the accompanying surface drumhead states., 14 pages, 8 figures. Contribution to special issue of J. Phys. Chem. Solids on spin-orbit materials

In two-dimensional (2D) systems, high mobility is typically achieved in low-carrier-density semiconductors and semimetals. Here, we discover that the nanobelts of Weyl semimetal NbAs maintain a high mobility even in the presence of a high sheet carrier density. We develop a growth scheme to synthesize single crystalline NbAs nanobelts with tunable Fermi levels. Owing to a large surface-to-bulk ratio, we argue that a 2D surface state gives rise to the high sheet carrier density, even though the bulk Fermi level is located near the Weyl nodes. A surface sheet conductance up to 5-100 S per □ is realized, exceeding that of conventional 2D electron gases, quasi-2D metal films, and topological insulator surface states. Corroborated by theory, we attribute the origin of the ultrahigh conductance to the disorder-tolerant Fermi arcs. The evidenced low-dissipation property of Fermi arcs has implications for both fundamental study and potential electronic applications.

Au–Ag nanostructures comprising of ∼1 nm Ag nanoparticles embedded into an Au matrix show several unconventional optical, electric and magnetic properties. Here, we review progress made towards the preparation of these materials as well as analysis of their structure. Further, electrical and magnetic transitions in these materials are discussed. Finally, we review the properties of these materials as revealed from optical and electron microscopic probes.

Discovered decades ago, the quantum Hall effect remains one of the most studied phenomena in condensed matter physics and is relevant for research areas such as topological phases, strong electron correlations and quantum computing1-5. The quantized electron transport that is characteristic of the quantum Hall effect typically originates from chiral edge states-ballistic conducting channels that emerge when two-dimensional electron systems are subjected to large magnetic fields2. However, whether the quantum Hall effect can be extended to higher dimensions without simply stacking two-dimensional systems is unknown. Here we report evidence of a new type of quantum Hall effect, based on Weyl orbits in nanostructures of the three-dimensional topological semimetal Cd3As2. The Weyl orbits consist of Fermi arcs (open arc-like surface states) on opposite surfaces of the sample connected by one-dimensional chiral Landau levels along the magnetic field through the bulk6,7. This transport through the bulk results in an additional contribution (compared to stacked two-dimensional systems and which depends on the sample thickness) to the quantum phase of the Weyl orbit. Consequently, chiral states can emerge even in the bulk. To measure these quantum phase shifts and search for the associated chiral modes in the bulk, we conduct transport experiments using wedge-shaped Cd3As2 nanostructures with variable thickness. We find that the quantum Hall transport is strongly modulated by the sample thickness. The dependence of the Landau levels on the magnitude and direction of the magnetic field and on the sample thickness agrees with theoretical predictions based on the modified Lifshitz-Onsager relation for the Weyl orbits. Nanostructures of topological semimetals thus provide a way of exploring quantum Hall physics in three-dimensional materials with enhanced tunability.

Recently discovered 2M phase of bulk WS

We identify highly correlated hole pocket on the Fermi surface of colossal thermoelectric material ${\mathrm{K}}_{0.65}{\mathrm{RhO}}_{2}$, studied using high-resolution angle-resolved photoemission spectroscopy (ARPES) and density-functional theory (DFT) calculations. Most importantly, two kinks at binding energies of 75 and 195 meV have been observed below the Fermi level. While the low-energy kink at 75 meV can be understood as a result of the electron-phonon interaction, the high-energy kink at 195 meV is a discovery of this system, leading to anomalous band renormalization, possibly originated from the bosonic excitations at higher frequencies. We further notice that the high-energy anomaly has important implications on the colossal thermoelectric power of ${\mathrm{K}}_{0.65}{\mathrm{RhO}}_{2}$.

Non-Hermitian topological phases have gained widespread interest due to their unconventional properties, which have no Hermitian counterparts. In this work, we propose to use machine learning to identify and predict non-Hermitian topological phases, based on their winding number. We consider two examples -- non-Hermitian Su-Schrieffer-Heeger model and its generalized version in one dimension and non-Hermitian nodal line semimetal in three dimensions -- to demonstrate the use of neural networks to accurately characterize the topological phases. We show that for the one dimensional model, a fully connected neural network gives an accuracy greater than 99.9\%, and is robust to the introduction of disorder. For the three dimensional model, we find that a convolutional neural network accurately predicts the different topological phases., Published version

The low dielectric constant of organic semiconductors limits the efficiency of organic solar cells (OSCs). In an attempt to improve the dielectric constant of conjugated polymers, we report the synthesis of three semiconducting copolymers by combining the thiophene-substituted diketopyrrolopyrrole (TDPP) monomer with three different monomeric units with varying electron donating/accepting strengths: benzodithiophene (BBT-3TEG-TDPP), TDPP (TDPP-3TEG-TDPP), and naphthalene diimide (P(gNDI-TDPP)). Among the series, BBT-3TEG-TDPP and P(gNDI-TDPP) exhibited the highest dielectric constants (∼5) at 1 MHz frequency, signifying the contribution of dipolar polarization from TEG side-chains. Furthermore, transient absorption spectroscopic studies performed on these polymers indicated low exciton diffusion length as observed in common organic semiconducting polymers. Our findings suggest that utilizing the polar side-chains enhances the dielectric constant in a frequency regime of megahertz. However, it is not sufficient to reduce the Coulombic interaction between hole and electron in excitonic solar cells.

Using Floquet theory, we investigate the effect of light on triple fold fermions. We study a low energy model as well as a simplified tight binding model under illumination. We find that the three fold degeneracy remains symmetry protected even after applying light if the original band structure is rotationally symmetric around the degeneracy. Otherwise, light can lift the degeneracy and open up a gap. We further investigate the effect of light on the topological Fermi arcs by means of numerical computations. The changes caused by illumination are reflected in experimentally detectable signatures, such as the anomalous Hall conductivity, which we calculate., Comment: Published version

Non-Hermitian topological systems are the newest additions to the growing field of topological matter. In this work, we report of the light-driven exceptional physics in a multi-Weyl semi-metal. The driving is not only a key ingredient to control the position of the exceptional contours (ECs), light also has the ability to generate new ECs. Interestingly, we also demonstrate topological charge distribution and Lifshitz transition, which are controllable by the driving field in such generated ECs. Our findings present a promising platform for the manipulation and control over exceptional physics in non-Hermitian topological matter., 12 pages, 7 figures, Accepted for Publication in Phys. Rev. A Letts (Rapid communications)

An efficient photogeneration of free charge carriers has long been recognized as the paramount challenge in organic photovoltaic (OPV) devices. The low dielectric constant organic semiconductors fall short to reduce strong Coulombic interaction of tightly bound exciton and hence lead to a loss mechanism in OPVs due to charge-carrier recombination. To circumvent this problem, we adopt a strategy to enhance the dielectric constant of organic semiconductors by incorporating tetraethyleneglycol (TEG) side-chains. We report synthesis of three new semiconducting copolymers by combining thiophene substituted diketopyrrolopyrrole (TDPP) monomer with three other monomeric units with varying electron donating strength: benzodithiophene (BBT-3TEG-TDPP), TDPP (TDPP-3TEG-TDPP) and naphthalene diimide (PNDITEG-TDPP). BBT-3TEG-TDPP and PNDITEG-TDPP showed highest dielectric constants (~ 5) at 1MHz frequency suggesting efficient contribution of dipolar polarization from TEG side-chains. To understand the electronic contribution of the polymer backbone and the polarity of TEG side-chains, and the resulting enhancement of the dielectric constant, we further performed first-principles density functional theory calculations. Single-component organic solar cells (OSC) fabricated utilizing these polymers resulted in poor performance which is attributed to the absence of free charge generation. Furthermore, transient absorption spectroscopy studies show low exciton diffusion length as observed in donor-acceptor type conjugated polymers. Our results suggest that, the strategy of enhancing dielectric constant with polar side-chains is not sufficient to reduce Coulombic interaction between hole and electron in OSCs.

Most recent observation of topological Fermi arcs on the surface of manyfold degenerate B20 systems, CoSi and RhSi, have attracted enormous research interests. Although an another isostructural system, FeSi, has been predicted to show bulk chiral fermions, it is yet to be clear theoretically and as well experimentally that whether FeSi possesses the topological surface Fermi arcs associated with the exotic chiral fermions in vicinity of the Fermi level. In this contribution, using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), we present the low-energy electronic structure of FeSi. We further report the surface state calculations to provide insights into the surface band structure of FeSi near the Fermi level. Unlike in CoSi or RhSi, FeSi has no topological Fermi arcs near the Fermi level as confirmed both from ARPES and surface state calculations. Further, the ARPES data show spin-orbit coupling (SOC) band splitting of 40 meV, which is in good agreement with bulk band structure calculations. We noticed an anomalous temperature dependent resistivity in FeSi which can be understood through the electron-phonon interactions as we find a Debye energy of 80 meV from the ARPES data., 9 pages, 7 figures

We propose and show that application of light leads to an intriguing platform for controlling exceptional points in non-Hermitian topological systems. We demonstrate our proposal using three different non-Hermitian systems -- nodal line semimetals, semi-Dirac semimetals and Dirac semimetals -- and show that using illumination with light one can engineer the positions and stability of exceptional points. We illustrate the topological properties of these models and map out their light-driven topological phase transitions., 13 pages, 11 figures

Recently, many novel and exotic phases have been proposed by considering the role of topology in non-Hermitian systems, and their emergent properties are of wide current interest. In this work we propose the non-Hermitian generalization of semi-Dirac semimetals, which feature a linear dispersion along one momentum direction and a quadratic one along the other. We study the topological phase transitions in such two-dimensional semi-Dirac semimetals in the presence of a particle gain-and-loss term. We show that such a non-Hermitian term creates exceptional points originating out of each semi-Dirac point. We map out the topological phase diagram of our model, using winding number and vorticity as topological invariants of the system. By means of numerical and analytical calculations, we examine the nature of edge states for different types of semi-Dirac models and establish bulk-boundary correspondence and absence of the non-Hermitian skin effect, in one class. On the other hand, for other classes of semi-Dirac models with asymmetric hopping, we restore the non-Hermitian skin effect, an anomalous feature usually present in non-Hermitian topological systems., To appear in J. Phys.: Condens. Matter

Understanding the electronic behavior of Ni$^{2+}$ in a square planar environment of oxygen is the key to unravel the origin of the recently discovered superconductivity in the hole doped nickelate Nd$_{0.8}$Sr$_{0.2}$NiO$_2$. To identify the major similarities/dissimilarities between nickelate and cuprate superconductivity, the study of the electronic structure of Ni$^{2+}$ and Cu$^{2+}$ in an identical square planar environment is essential. In order to address these questions, we investigate the electronic structure of Sr$_2$CuO$_3$ and Ni doped Sr$_2$CuO$_3$ single crystals containing (Cu/Ni)O$_4$ square planar units. Our polarization dependent X-ray absorption spectroscopy experiments for Ni in Sr$_2$Cu$_{0.9}$Ni$_{0.1}$O$_3$ have revealed very large orbital polarization, which is a characteristic feature of high $T_c$ cuprate. This arises due to the low spin $S$=0 configuration with two holes in Ni 3$d_{x^2-y^2}$ orbitals - in contrast to the expected high spin $S$=1 state from Hund's first rule. The presence of such $S$=0 Ni$^{2+}$ in hole doped nickelate would be analogous to the Zhang Rice singlet. However, the Mott Hubbard insulating nature of the NiO$_4$ unit would point towards a different electronic phase space of nickelates, compared to high $T_c$ cuprates., Comment: 4 Figures

Recently discovered 2M phase of bulk WS$_2$ was observed to exhibit superconductivity with a critical temperature of 8.8 K, the highest reported among superconducting transition metal dichalcogenides. Also predicted to support protected surface states, it could be a potential topological superconductor. In the present study, we perform a detailed first-principles analysis of bulk and bilayer 2M WS$_2$. We report a comprehensive investigation of the bulk phase, comparing structural and electronic properties obtained from different exchange correlation functionals to the experimentally reported values. By calculation of the $Z_2$ invariant and surface states, we give support for its non-trivial band nature. Based on the insights gained from the analysis of the bulk phase, we predict bilayer 2M WS$_2$ as a new two-dimensional topological material. We demonstrate its dynamical stability from first-principles phonon computations and present its electronic properties, highlighting the band inversions between the W $d$ and S $p$ states. By means of $Z_2$ invariant computations and a calculation of the edge states, we show that bilayer 2M WS$_2$ exhibits protected, robust edge states. The broken inversion symmetry in this newly proposed bilayer also leads to the presence of Berry curvature dipole and resulting non-linear responses. We compute the Berry curvature distribution and the dipole as a function of Fermi energy. We propose that BCD signals, which are absent in the centrosymmetric bulk 2M WS$_2$, can be signatures of the bilayer. We hope our predictions lead to the experimental realization of this as-yet-undiscovered two-dimensional topological material., Comment: Added results on Berry curvature dipole

The search for proximity-induced superconductivity in topological materials has generated widespread interest in the condensed matter physics community. The superconducting states inheriting nontrivial topology at interfaces are expected to exhibit exotic phenomena such as topological superconductivity and Majorana zero modes, which hold promise for applications in quantum computation. However, a practical realization of such hybrid structures based on topological semimetals and superconductors has hitherto been limited. Here, we report the strong proximity-induced superconductivity in type-II Weyl semimetal WTe2, in a van der Waals hybrid structure obtained by mechanically transferring NbSe2 onto various thicknesses of WTe2. When the WTe2 thickness (tWTe2) reaches 21 nm, the superconducting transition occurs around the critical temperature (Tc) of NbSe2 with a gap amplitude (Δp) of 0.38 meV and an unexpected ultralong proximity length (lp) up to 7 μm. With the thicker 42 nm WTe2 layer, however, the proxi...

We report the discovery of two ternary Zintl phases Ba3Sn3Sb4 and Ba7–xSn11Sb15–y (x = 0.4, y = 0.6). Ba3Sn3Sb4 adopts the monoclinic space group P21/c with a = 14.669(3) A, b = 6.9649(14) A, c = 13.629(3) A, and β = 104.98(3)°. It features a unique corrugated two-dimensional (2D) structure consisting of [Sn3Sb4]6– layers extending along the ab-plane with Ba2+ atoms sandwiched between them. The nonstoichiometric Ba6.6Sn11Sb14.4 has a complex one-dimensional (1D) structure adopting the orthorhombic space group Pnma, with unit cell parameters a = 37.964(8) A, b = 4.4090(9) A, and c = 24.682(5) A. It consists of large double Sn–Sb ribbons separated by Ba2+ atoms. Ba3Sn3Sb4 is an n-type semiconductor which has a narrow energy gap of ∼0.18 eV and a room temperature carrier concentration of ∼4.2 × 1018 cm–3. Ba6.6Sn11Sb14.4 is determined to be a metal with electrons being the dominant carriers.

We report a new two-dimensional compound, Pb3–xSb1+xS4Te2−δ, that has a charge density wave (CDW) at room temperature. The CDW is incommensurate with q-vector of 0.248(6)a* + 0.246(8)b* + 0.387(9)c* for x = 0.29(2) and δ = 0.37(3) due to positional and occupational long-range ordering of Te atoms in the sheets. The modulated structure was refined from the single-crystal X-ray diffraction data with a superspace group P1(αβγ)0 using (3 + 1)-dimensional crystallography. The resistivity increases with decreasing temperature, suggesting semiconducting behavior. The transition temperature (TCDW) of the CDW is ∼345 K, above which the Te square sheets become disordered with no q-vector. First-principles density functional theory calculations on the undistorted structure and an approximate commensurate supercell reveal that the gap is due to the structure modulation.