Charge Density Wave and Narrow Energy Gap at Room Temperature

Jul 17, 2017 - We report a new two-dimensional compound, Pb3–xSb1+xS4Te2−δ, that has a charge density wave (CDW) at room temperature. The CDW is ...
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Charge Density Wave and Narrow Energy Gap at Room Temperature in 2D Pb3−xSb1+xS4Te2−δ with Square Te Sheets Haijie Chen,†,‡ Christos D. Malliakas,†,‡ Awadhesh Narayan,§,⊥ Lei Fang,†,‡ Duck Young Chung,‡ Lucas K. Wagner,§ Wai-Kwong Kwok,‡ and Mercouri G. Kanatzidis*,†,‡ †

Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States § Department of Physics, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States ‡

S Supporting Information *

ABSTRACT: 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 qvector 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 P1̅(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.

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INTRODUCTION Charge density waves (CDWs), periodic modulations of conduction electron densities coupled with lattice distortions in solids, are broken-symmetry ground states in low-dimensional metals.1−3 Typically, the structure of a CDW forms a superlattice that results in weak satellite Bragg reflections in Xray diffraction around the main subcell reflections. The satellite reflections are often incommensurate with the underlying lattice. Incommensurate modulations can be properly described only with a multidimensional crystallographic approach. Quantum phenomena based on electron−phonon interactions, such as superconductivity, are often associated with the destabilization of a CDW state. In cuprates, it is accepted that the high transition temperature superconducting state coexists and competes with the CDW.4−6 In some other compounds, with the CDWs being suppressed, the superconducting state could be induced after suitable tuning methods, such as intercalation and high-pressure approaches in transition-metal chalcogenides,7−9 chemical doping in titanium oxypnictides,10−12 etc.13−17 Although the relationship between CDWs and superconductivity is not fully explored, CDW materials provide ideal model systems for studying highly cooperative phenomena.18 Theoretical predictions indicate that square sheet arrangements of main group atoms is unstable and prone to form CDWs.19 Polytelluride compounds with square Te sheets have been recognized to be excellent two-dimensional (2D) © 2017 American Chemical Society

materials with Fermi surface (FS) nesting-driven CDW formation. Classic example is the RETen family (RE = rare earth element; n = 2, 2.5, 3), which exhibits CDWs in the square Te sheets.20−26 Driven by FS nesting, RETe2−δ is semiconducting with a narrow band gap opened at the Fermi level.27,28 With the application of high physical pressure, emergent superconductivity was reported in CeTe2−δ (superconducting transition temperature (Tc) ≈ 2.7 K) and TbTe3 (Tc ≈ 4 K),29,30 whereas superconductivity could be induced by Pd intercalation in RETe2.5 and RETe3.31 Less explored materials with distorted Te sheets include K0.33Ba0.67AgTe2, KLaCuTe4, Cu0.66EuTe2, etc.32−35 Here we introduce an unusual layered compound, Pb3−xSb1+xS4Te2−δ, with CDWs in the square Te sheets, which have long-range ordered vacancies as indicated by δ. The cooling speed during synthesis can affect x and δ, as two different formulas with different q-vectors were found at room temperature. One stoichiometry is Pb2.70(8)Sb1.29(2)S4Te1.62(7) with q = 0.248(6)a* + 0.246(8)b* + 0.387(9)c* obtained by slow cooling; the other composition is Pb2.94(6)Sb1.05(4)S4Te1.76(4) with q = 0.222(1)a* + 0.223(5)b* + 0.375(5)c* synthesized by fast quenching. Detailed temperature-dependent studies of the Pb2.70(8)Sb1.29(2)S4Te1.62(7) revealed that the CDW transition temperature (TCDW) is around 345 K, above which Received: June 23, 2017 Published: July 17, 2017 11271

DOI: 10.1021/jacs.7b06446 J. Am. Chem. Soc. 2017, 139, 11271−11276

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Figure 1e shows the synthetic precession images from the Xray diffraction experiment along the c-axis ([0 0 1]) at 293, 340, and 400 K, respectively. As indicated by the arrows, there are many extra satellite peaks around the main Bragg diffraction peaks at 293 and 340 K, which are the consequence of the CDW distortion. When the temperature increases to 400 K, all the satellite spots disappear and only the strong Bragg reflections remain. To explore the detailed modulated structure, four-dimensional superspace crystallographic techniques, in which the position of the atoms is described with a combination of static waves using the atoms in the undistorted unit cell (subcell) as a reference, were used. For crystals obtained by slow cooling and the Te flux method (Table 1), the refined formula was

the long-range ordering of Te vacancies disappears. The crystallographically determined structure of CDWs along with the undistorted structure above TCDW were used to perform density functional theory (DFT) calculations, which show the existence of a CDW gap.

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RESULTS AND DISCUSSION Average and Modulated Structure. The average structure of Pb3−xSb1+xS4Te2−δ (not accounting for the CDW modulation) is shown in Figure 1a. The elemental ratio of

Table 1. Crystallographic Data and Structure Refinement for Pb2.70(8)Sb1.29(2)S4Te1.62(7) at 293 K chemical formula fw space group crystal system unit cell dimens

q-vector volume, Z density (calcd) absorp coeff F(000) cryst size (mm3) θ range for data collection indep reflns data/constraints/params final R indices [I > 3σ(I)]a R indices [all data] final R main indices [I > 3σ(I)] R main indices (all data) final R first-order satellites [I > 3σ(I)] R first-order satellites (all data) Tmin and Tmax coeffs

Figure 1. (a) Average structure of Pb3−xSb1+xS4Te2−δ with alternating Pb3−xSb1+xS4 slabs and square Te2−δ sheets. (b) Side-view of the average structure. Bonds between the two different layers indicate a weak interlayer interaction. (c) Photo of an as-synthesized single crystal with a smooth surface. (d) Ideal perfect square Te sheets. (e) X-ray diffraction images along the [0 0 1] zone at 293, 340, and 400 K, respectively. The satellite reflections associated with CDW modulation are indicated with arrows at 293 and 340 K, and reflections disappear above 400 K.

Pb:Sb:S:Te from the wavelength dispersive spectroscopic analysis (WDS) results (Figure S2) is close to 3:1:4:2 with an ideal formula of Pb3SbS4Te2 ([Pb3SbS4]+[Te2]−). The formula can be charge-balanced with the valence states +2, +3, −2, and −1/2 for Pb, Sb, S, and Te, respectively. Deviating from the ideal case, the refined formula was determined to be Pb3−xSb1+xS4Te2−δ. One Pb site is partially substituted by Sb, and there are vacancies in the Te layers. This compound has alternating “Pb3−xSb1+xS4 double layers” and “Te2−δ layers”, Figure 1b. The Pb3−xSb1+xS4 layers can be considered as being composed of double distorted NaCl-type PbS layers. The Pb3−xSb1+xS4 and Te2−δ layers are connected by long bonds with a shortest distance of 3.597(2) Å (Pb1−Te). The shortest bond (Pb3/Sb1−S3) within the double Pb3−xSb1+xS4 layers is 3.445(9) Å. This implies that the interlayer coupling is weak and bonding interactions between Pb3−xSb1+xS4 and Te2−δ layers are weaker than those within the Pb3−xSb1+xS4 double layers. A photograph of a typical single crystal with a shiny and smooth mirror-like surface is shown in Figure 1c with a size of around 1 mm × 0.6 mm × 0.05 mm. In the most thermodynamically favored configuration, these Te layers prefer to be distorted, as they are more stable than the ideal square net structure (Figure 1d).19 The critical temperature necessary to overcome this distortion (TCDW) in Pb3−xSb1+xS4Te2−δ is above room temperature and can be determined using temperature-dependent X-ray diffraction.

Pb2.70(8)Sb1.29(2)S4Te1.62(7) 1054.28 P1(̅ αβγ)0 triclinic a = 5.8925(5) Å, α = 93.918(7)° b = 5.8999(5) Å, β = 97.070(7)° c = 15.1906(14) Å, γ = 90.255(7)° 0.248(6)a* + 0.246(8)b* + 0.387(9)c* 522.82(8) Å3, 2 6.6966 g/cm3 51.947 mm−1 874 0.934 × 0.429 × 0.022 2.35° to 29.29° 8500 [Rint = 0.1311] 8500/30/231 Robs = 0.0589, wRobs = 0.1191 Rall = 0.2377, wRall = 0.1329 Robs = 0.0586, wRobs = 0.1189 Rall = 0.1118, wRall = 0.1268 Robs = 0.0713, wRobs = 0.1566 Rall = 0.5934, wRall = 0.4395 0.0027 and 0.3308

R = ∑∥Fo| − |Fc∥/∑|Fo|, wR = {∑[w(|Fo|2 − |Fc|2)2]/∑[w(| Fo|4)]}1/2 and w = 1/(σ2(I) + 0.0004I2). Wavelength 0.710 73 Å.

a

determined to be Pb2.70(8)Sb1.29(2)S4Te1.62(7) (a = 5.8925(5) Å, α = 93.918(7)°; b = 5.8999(5) Å, β = 97.070(7)°; c = 15.1906(14) Å, γ = 90.255(7)°). A (3 + 1)-dimensional approach was applied for the data integration using one independent incommensurate q-vector (0.248(6)a* + 0.246(8) b* + 0.387(9)c*). The modulated structure adopts the superspace group P1(̅ αβγ)0. A total of 8500 independent reflections were collected with 2829 main and 5671 satellites. The final agreement factor converged to the good value of 5.89% for all observed reflections (I > 3σ(I)). As listed in Table S1, crystallographic refinement at 340 K was also conducted successfully based on the average structure of Pb2.70(8)Sb1.29(2)S4Te1.62(7) with an agreement factor of 6.73%. The incommensurate q-vector at 340 K (0.247(7)a* + 0.248(2)b* + 0.373(1)c*) did not change significantly using the same superspace group. For the diffraction data collected at 350 and 400 K, the q-vector vanished and the structures were refined with the same P1̅ space group and agreement factors 11272

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Journal of the American Chemical Society were 6.75% (Table S2) and 6.45% (Table S3), respectively. This indicates that TCDW is between 340 and 350 K and without any structural changes above TCDW. Surprisingly, the quenched sample gave a different modulation vector than the one for the slow-cooled compound. Single-crystal X-ray diffraction analyses gave the refined formula of Pb2.94(6)Sb1.05(4)S4Te1.76(4) (a = 5.9201(5) Å, α = 93.928(7)°; b = 5.8979(5) Å, β = 97.054(8)°; c = 15.1572(15) Å, γ = 90.074(7)°) with a q-vector of 0.222(1)a* + 0.223(5)b* + 0.375(5)c* and the corresponding agreement factor of 8.54%, Table S4. The quenched structure adopts the same superspace group P1̅(αβγ)0 as the slow-cooled phase, but the relative lengths of a- and b-cell constants are switched where the a-axis in Pb 2.94(6)Sb 1.05(4)S4Te 1.76(4) is longer than the b-axis. Compared to Pb2.70(8)Sb1.29(2)S4Te1.62(7), it can be inferred that more Sb atoms substitute into the Pb3 site and more Te comes out from the square layers in the slow-cooling procedure, generating a higher Te vacancy level in Pb2.70(8)Sb1.29(2)S4Te1.62(7). The details about the Te occupancy waves in the modulated crystallographic model are plotted in Figure 2. At 293 K, Pb2.70(8)Sb1.29(2)S4Te1.62(7) has an average Te occupancy of around 80% with maximum 96.6% and minimum 66.1% for Te1 and maximum 94.4% and minimum 68.3% for Te2, Figure 2a. At 340 K, occupancy varies from 91.5% to 70.6% for Te1 and from 89.9% to 72.2% for Te2, Figure 2b. For Pb2.94(6)Sb1.05(4)S4Te1.76(4) at 300 K (Figure 2c), it can be modeled in terms of 100% and 0% occupancies. This indicates that Te bonding and vacancy ordering varies with different cooling rates, which generates different Te ordering patterns in the Te sheets. More structural details, such as the Te1−Te2 distances and displacement parameters along the a-axis (dx), b-axis (dy), and c-axis (dz) of Te atoms, are shown in Figure S3. A fragment of the incommensurately modulated CDW structure of the Te sheets projected onto the ab plane is also shown in Figure 2. Te atoms driven by the distortion feature a variety of [Ten]x− oligomers. Figure 2d illustrates the Te sheets in Pb2.70(8)Sb1.29(2)S4Te1.62(7) at 293 K with a bonding threshold of 3.040 Å that shows a periodic display of pink-colored (Te vacancies 80%) zones, which indicate periodic variances of Te atoms. For the structure at 340 K (Figure 2e) with a 3.090 Å threshold, Te sheets also show a similar periodic pattern. When the temperature increases to 400 K, no q-vector is observed, and Te atoms and vacancies are equivalent and disordered, forming perfect square sheets (Figure 2f). The Te sheets of the second-phase Pb2.94(6)Sb1.05(4)S4Te1.76(4) at 293 K display tetramers (marked in green and blue colors) and octamers (marked in orange color) together with fully vacant Te sites (as indicated with black arrows in Figure 2g). Figure 3a shows the temperature-dependent resistivity of Pb2.70(8)Sb1.29(2)S4Te1.62(7) from 300 to 2 K. The resistivity at 300 K is ∼0.09 Ω cm and increases with decreasing temperature. This thermally activated semiconductor behavior is consistent with the presence of a band gap. On the basis of the classical thermal excitation model,36 the fitted activation energy (Ea) is determined to be around ∼20 meV (see Supporting Information for the fitting details). There is a mild upturn around 125 K. The crystal structure at 100 K (Table S5 and Figure S6) is the same as that at 300 K, which excludes structural transition. The electronic absorption spectrum (Figure S7) indicates an energy band gap below 50 meV. Figure 3b shows the resistivity at higher temperature (300−400

Figure 2. Te occupancy in the modulated crystallographic model as a function of t-coordinate for Pb2.70(8)Sb1.29(2)S4Te1.62(7) at (a) 293 K and (b) 340 K and (c) Pb2.94(6)Sb1.05(4)S4Te1.77(2) at 293 K. Evolution of the CDW in the Te sheets of Pb2.70(8)Sb1.29(2)S4Te1.62(7) at (d) 293 K (atoms vacancies below 80% are plotted in pink color and above 80% in green color) at a threshold of 3.040 Å, (e) 340 K at a threshold of 3.090 Å, and (f) 400 K at a threshold of 2.980 Å. It shows a disordered Te sheet due to vanishing of the CDW at 400 K. (g) Evolution of the CDW in the Te sheets of Pb2.94(6)Sb1.05(4)S4Te1.77(2) at 293 K with the 3.040 Å threshold (the black arrows indicate 100% Te vacancies, periodic tetramers are plotted in green and blue colors, and octamers are in orange color).

K). The resistivity kink at ∼345 K, indicated by the arrow in the inset, represents the TCDW point that is attributed to the disappearance of the q-vector and the crossing from the CDW state to the metallic state at TCDW. Heat capacity measurement shows one huge anomaly at around 345 K, which further confirms the CDW transition, Figure 3c. Differential scanning calorimetry on a large number of crystals also shows a kink around the same temperature, confirming the existence of the transition in the bulk. Hall effect measurements were conducted on the same single crystal (Figure S8) from which the resistivity was measured. As shown in Figure 3d, the in-plane Hall resistivity (ρxy) exhibits linear field dependence, and the positive sign reveals holes as the dominant charge carriers. The calculated carrier density (n) at 300 K is 1.75 × 1018 cm−3 and decreases with decreasing temperature (6.33 × 1014 cm−3 at 5 K, Figure 3e). The carrier mobility (μ) was evaluated by μ = 1/(nqρ). μ at 300 K is determined to be 41.0 cm2 V−1 s−1 and decreased to 4.1 cm2 V−1 s−1 at 5 K, Figure 3f. 11273

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Figure 4. (a) Calculated band structure using ideal Te nets in Pb3SbS4Te2 with no CDW distortion yields a metallic state; (b) corresponding density of states with different atomic contributions. (c) Side view and (d) top view of the Fermi surface topology for ideal Pb3SbS4Te2. (e) Calculated band structure using an approximate commensurate supercell (Pb6Sb2S8Te3 with modulated Te sheets) clearly shows the narrow energy band gap; (f) corresponding density of states around the Fermi energy with different atomic contributions.

Figure 3. Temperature-dependent resistivity of Pb2.70(8)Sb1.29(2)S4Te1.62(7) from (a) 300 to 2 K and (b) 300 to 400 K (inset: a magnification of the resistivity from 330 to 360 K). (c) Temperaturedependent heat capacity and differential scanning calorimetry of Pb2.70(8)Sb1.29(2)S4Te1.62(7). (d) In-plane Hall resistivities at different temperatures exhibit linear field dependence. Positive Hall resistivity indicates hole-type dominant behavior. Rxy versus magnetic field μ0H at different temperatures displays linear behavior. (e) Carrier density (n) and (f) mobility (μ) as a function of temperature.

distortion of the Te square sheets is responsible for the creation of the band gap.

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CONCLUSIONS The new layered material Pb3−xSb1+xS4Te2−δ has a stable CDW with a narrow indirect energy gap at room temperature. The cooling speed during the synthesis is effective in tuning the positional and occupational long-range ordering of Te atoms in the sheets, giving rise to slightly different CDWs. DFT calculations on undistorted and CDW modulated structures confirm that the semiconducting property arises from the CDW in the Te sheets, in agreement with the thermally activated behavior of the electrical resistivity. Pb3−xSb1+xS4Te2−δ provides a good platform for fundamental investigations of CDW distortion at room temperature. This finding should further motivate direct measurements of the band structure in this novel material using angle-resolved photoemission spectroscopy or transmission electron microscopy for exploration of the true origin of the CDW states in this compound. Because Pb3−xSb1+xS4Te2−δ is stable at room temperature, it is a good candidate for studying the effects of fluctuation on transport properties of CDW materials, the interaction with magnetic fields, and the investigation of novel devices.39,40

In RETe2−δ, CDW distortions are driven by Fermi surface nesting.37 To explore the effect of the CDW on the electronic structure of this compound, first-principles DFT calculations were carried out on both the undistorted (Pb3SbS4Te2 with ideal square Te nets) and modulated commensurate model structure with Te vacancies (Pb6Sb2S8Te3 with modulated Te sheets). For the undistorted structure, in which perfect Te square sheets exist, we find no band gap and a metallic behavior (Figure 4a and b). Similar to that of RETe2,38 only Te 5p orbitals contribute to the band structure crossing the Fermi level (Figure S9). Side and top views of the Fermi surface topology are displayed in Figure 4c and d, respectively. Different colors represent different bands crossing the Fermi level. We find a total of five bands crossing the Fermi level, with prominently hole-like pockets around the Brillouin zone center. Overall, the Fermi surface structure is characteristic of a twodimensional material, with cylindrical features that are nearly dispersionless along the corresponding real space stacking direction. It also appears to favor formation of several nesting vectors between the nearly parallel Fermi sheets. On the other hand, the modulated CDW structure has a narrow band gap of approximately 58 meV (Figure 4e and f). The density of states (DOS) near the Fermi energy is only associated with the Te 5p orbitals, while the contributions of Pb and Sb atoms are above and the S atom is below the Fermi level (Figure S10). Our first-principles calculations thus reveal a contrasting situation between the average and modulated structures. This strongly lends support to the idea that the

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EXPERIMENTAL DETAILS

Crystal Growth. Method 1. Single crystals of Pb3−xSb1+xS4Te2−δ were grown using the self-flux method. High-purity Pb nuggets (99.999%, American Elements), Sb lumps (99.999%, American Elements), S powders (99.999%, American Elements), and Te granules (99.999%, American Elements) were weighed according to a ratio of 3:1:4:2. The total weight of the starting materials is ∼0.8 g. These starting materials were sealed in an evacuated fused silica tube 11274

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Journal of the American Chemical Society in high vacuum (10−4 mbar) followed by transferring into a tube furnace. The furnace was heated to 850 °C in 15 h, dwelled at this temperature for 2 h, slowly cooled to 600 °C in 80 h, and then turned off. Single crystals of Pb3−xSb1+xS4Te2−δ were found on the surface of the final ingot. The crystals are planar shaped with metallic dark and mirror-like surfaces. PbS is observed as the dominant byproduct. For comparison, some tubes were taken out immediately and quickly cooled to room temperature. Method 2. A large quantity of Pb3−xSb1+xS4Te2−δ single crystals could be obtained via the Te flux approach. The same starting materials as those in method 1 were weighed with a ratio of 3:1:4:20, followed by the sample heating process as above. After dwelling at 600 °C for 5 h, the tubes were taken out and centrifuged to get rid of the extra molten Te. The same shiny single crystals were obtained in the bottom of the tubes. The obtained Pb3−xSb1+xS4Te2−δ single crystals are stable in air. Energy Dispersive X-ray Spectroscopy, Wavelength Dispersive X-ray Spectroscopy, and Scanning Electron Microscopy (EDS/WDS/SEM). Elemental analysis of the synthesized crystals was performed by EDS/WDS/SEM using a Hitachi S3400N-II scanning electron microscope equipped with an Oxford Instruments INCAx-act SDD EDS detector and Wave 500 WDS spectrometer. Unpolished crystals mounted with carbon tape on an aluminum stub were examined at an accelerating voltage of 20 kV. Analytical results are shown in Figure S2. Single-Crystal X-ray Diffraction. Pb3−xSb1+xS4Te2−δ single crystals were carefully separated from the ingot and cut to an appropriate size for X-ray diffraction study. They were screened for quality using a small number of diffracted frames on a STOE IPDS 2 single-crystal diffractometer equipped with graphite-monochromatized Mo Kα radiation (λ = 0.710 73 Å). Full-sphere data were collected on the best high-quality crystal. The data were reduced, integrated, and corrected for absorption using the STOE X-Area suite.41 The crystal structure was solved and refined by full-matrix least-squares on F2 using the Jana2006 package.42,43 Crystallographic data and structure refinement for the sample obtained by slow cooling or method 2 at 293 K are listed in Table 1. More refinement results at 100, 340, 350, and 400 K together with the results at 293 K on the sample synthesized by fast quenching are listed in Tables S1−S6. Intensity data for the supercell of Pb2.70(8)Sb1.29(2)S4Te1.62(7) were also collected at 293, 340, and 400 K using ω and φ series of 0.3° scans on a Bruker Kappa APEX CCD area detector diffraction system using Quazar optics and Mo Kα microfocused radiation (λ = 0.710 73 Å) operating at 50 kV and 1 mA. The crystal-to-detector distance was 50 mm, and the exposure time was 10 s/frame. The APEX3 software package44 was used for data collection. Differential Scanning Calorimetry (DSC). DSC was performed in a Netzsch STA 449 F3 Jupiter simultaneous thermal analysis (STA) instrument. The sample was sealed in an aluminum pan by cold welding in air. Measurement was performed under ultra-high-purity He gas (flow of 50 mL/min). The temperature was increased at a rate of 2 °C/min. Transport Properties. Transport property measurements including resistivity, Hall effect, and heat capacity were carried out on a Quantum Design PPMS. Contacts were made with gold wires attached to the sample surface using Dupont 4929N silver paste, and sample dimensions were measured using SEM images. For accuracy, resistivity and Hall effect were measured on the same sample to exclude sample difference. The Hall resistivity, Rxy = [R(+H) − R(−H)]/2, was obtained by switching the magnetic field at each point to reduce the effect of Hall electrode misalignment. Absorption Spectra. Diffuse-reflectance IR absorption spectra were measured using a Nicolet 6700 FT-IR spectrometer on powder samples obtained by crushing a few large single crystals. The reflectance was converted to absorption using the Kubelka−Munk function α/S = (1 − R)2/2R, where R is the reflectance and α and S are the absorption and scattering coefficients, respectively.45 Computational Methods. First-principle density functional theory calculations were carried out using the Quantum-Espresso package.46 The Perdew−Burke−Ernzerhof form of the exchange−

correlation functional was employed.47 Experimentally obtained average and distorted geometries were used. A grid of 6 × 6 × 3 kpoints was used for self-consistent calculations, along with a plane wave cutoff of 40 Ry. XCrySDen48 was used to plot Fermi surfaces, which were obtained by sampling over a dense grid of 2601 reciprocal space points.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b06446. Refinement details of modulated structure, fitting details of resistivity, EDS result, crystallographic data and structure refinements, Te1−Te2 distances and displacement parameters (Å) along the three axis in the modulated crystallographic model as a function of tcoordinate, contour plots of Te atoms in Pb2.94(6)Sb1.05(4)S4Te1.77(2), diffuse-reflectance IR absorption spectrum, prepared electrode contacts, and band structure with projected contributions from different atoms (PDF) X-ray crystallographic data for Pb2.70(8)Sb1.29(2)S4Te1.62(7) at 100, 293, 340, 350, and 400 K and Pb2.94(6)Sb1.05(4)S4Te1.77(2) at 300 K (CIF)

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AUTHOR INFORMATION

Corresponding Author

*[email protected] ORCID

Haijie Chen: 0000-0003-3567-1763 Mercouri G. Kanatzidis: 0000-0003-2037-4168 Present Address ⊥

A.N.: Materials Theory, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH 8093 Zurich, Switzerland

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Center for Emergent Superconductivity, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award No. DEAC0298CH1088. Computational resources were provided by the University of Illinois Campus Cluster. This work made use of the Integrated Molecular Structure Education and Research Center (IMSERC) at Northwestern University, which has received support from the Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF NNCI-1542205); the State of Illinois and International Institute for Nanotechnology (IIN).

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REFERENCES

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DOI: 10.1021/jacs.7b06446 J. Am. Chem. Soc. 2017, 139, 11271−11276