Fermi-Level Characteristics of Potential Chalcogenide Superconductors

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Fermi-Level Characteristics of Potential Chalcogenide Superconductors Kai S. Fries, and Simon Steinberg Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.7b04767 • Publication Date (Web): 20 Mar 2018 Downloaded from http://pubs.acs.org on March 20, 2018

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Chemistry of Materials

Fermi-Level Characteristics of Potential Chalcogenide Superconductors Kai S. Fries,a Simon Steinberga,* a

Institute of Inorganic Chemistry, RWTH Aachen University, Landoltweg 1, D-52074 Aachen, Germany Supporting Information Placeholder

ABSTRACT: Quantum chemical high-throughput screenings of compound libraries for the identifications of materials with the desired properties have emerged as beneficial tools to accelerate the discoveries of compounds of interest. The quantum chemical high-throughput screenings of compound libraries require the definitions of reliable descriptors enabling relationships between the observed physical properties and the computed electronic structures. The desire to enhance the discoveries of materials showing electronic instabilities which are related to possible metal-to-superconductor-transitions stimulated our impetus to probe the feasibility of a descriptor for the identifications of materials with the aforementioned electronic instabilities in the forms of flat bands crossing the Fermi levels. To evaluate the reliability of the projected descriptor based on the flat band/steep band scenario for superconductors, we inspected the characteristics of the electronic band structures near the Fermi levels for a series of chalcogenide superconductors, whose electronic structures were computed and analyzed by means of first-principles-based highthroughput techniques.

INTRODUCTION Since the discovery of superconductivity more than 100 years ago the full understanding of the occurrence of this phenomenon in solid-state materials has remained challenging to chemists as well as physicists.1-2 The very first explanation for the existence of superconducting states in solid-state materials based on attractive interactions between electrons mediated by virtual exchanges of specific phonons;3 yet, the findings of higher transition temperatures for superconducting states in cuprates4 have raised more questions and have initiated a search for unknown materials with even higher transition temperatures. More recent research on superconductivity revealed that, for instance, the suppressions of competing electronic collective states, i.e., charge density waves,5-6 and the presence of van Hove singularities at the Fermi level7-10 play essential roles in the accomplishments of superconducting states. According to the flat band/steep band scenario8-9 a structural instability which is generated by electrons in flat bands at the Fermi level in the forms of van Hove singularities is compensated by electrons located in highly dispersive bands such that a distortion of the structure is hindered. To date, the identifications of previously unknown materials showing metal-to-superconductor-transitions require the use of many synthetic attempts, because the physical properties of materials with different stoichiometry and crystal structures may vary widely for a given system. For instance, the binary and ternary compounds of the R−T−Te systems (R = rare-earth; T = Fe−Cu; Figure 1) differ widely in their temperature-dependent electrical conductivity behaviors and exhibit phase transitions due to the formations of superconducting states or charge density waves.11-25 To accelerate the discoveries of unknown materials with the desired properties, the quantum chemical high-throughput screenings of compound libraries based on appropriate descriptors and intelligent data mapping have emerged as powerful techniques.26

For example, the uses of high-throughput screenings of data bases by means of quantum chemical methods resulted in the accelerated detections of 18-electron ABX compounds,27 the forecast of 28 topological insulators,28 a map for phase-change materials,29 and the prediction of the performances of diverse materials for thermoelectric energy conversion.30-32

Figure 1. Overview of the hitherto determined temperaturedependent electrical conductivity behaviors reported for binary and ternary compounds of the R−T−Te systems. From an inspection of the map it is clear that the temperaturedependent electrical conductivity behaviors vary widely for the binary and ternary compounds of this prototypical system.11-25

Table 1. Overview of the Structure Types, Space Groups and Transition Temperatures (Tc) of Selected Chalcogenide Superconductors, for Which the Pres-

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ence of Van Hove Singularities (vHS) at the Fermi Levels Have Been Previously Identified, and Chalcogenide Superconductors, Whose Electronic Band Structures Were Examined in the Present Work.

by the flat band/step band scenario. In the context of the examinations of the band structures, we placed special emphasis on the positions of flat bands relative to the Fermi levels in the chalcogenides.

Compound

COMPUTATIONAL DETAILS

Structure Type

Space Group

KOs2O633 RbNiCrF6 Fd3തm YBa2Cu3O6.936 YBa2Cu3O6+x Pmmm YBa2Cu4O841 YBa2Cu4O8 Ammm HgBa2Ca2Cu3O8+x4 own P4/mmm

TC [K]

Inspected for vHS in

9.634 9237-38 8241 ~13342

35

12844

43

0.9347 0.849 2.251

48

39-40 39 43

2

HgBa2CaCu2O6+x44 YBa2Cu3O6+x P4/mmm * Sr2RuO445-46 K2NiF4 I4/mmm LiZrSe249-50 LiTiS2 P3തm1 Mo2SbS251 3D network P21/m ScSe52 YS52 YSe52 YTe52 LaS55 LaSe56 LaTe57 LuS52 LuSe52 PdTe58 IrTe58 CuSe260

NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NaCl NiAs NiAs pyrite

‫ ܨ‬m3ത m ‫ ܨ‬m3തm ‫ܨ‬m3ത m Fm3ത m ‫ ܨ‬m3ത m Fm3ത m Fm3ത m Fm3ത m Fm3ത m P6ଷ /݉݉ܿ P6ଷ /݉݉ܿ Pܽ3ത

CuTe260 RhSe261 RhTe258 PdSbSe65 La3Se468 La3Te468 Rh3Te269 PdTe258 In3Te473

pyrite pyrite pyrite ullmannite Th3P4 Th3P4 Rh3Te2 CdI2 layer

Pܽ3ത Pܽ3ത Pܽ3ത P2ଵ 3 I4ത3݀ I4ത3݀ C݉ܿ݉ P3ത݉1 R3ത݉

49 51

a) 3.753 1.3−1.952 a), 54 a) 2.552-53 2.0552-53 a) a) 0.8453 53 a) 1.02 a) 1.4853 0.8−1.152 a) 0.5652-53 a) a) 3.8559 a) 3.059 a) 2.3− 2.4360 a) 1.360 62-63 a) 1−6 a) 1.5164 a) 1.066-67 a) 7.868 a) 5.368 a) 0.4970 a), 71-72 1.6959 1.15−1.257 a) 3

FeS74-75

574-75

layer P4/݊݉݉ TaS277-78 layer P63 /mmc 0.877, 79 a) Present work. *Tetragonal modification

a), 76 a), 80

The screening of a data repository using quantum chemical high-throughput methods for the identification of materials of interests typically employs an appropriate descriptor whose definition has to establish a relationship between the computed microscopic features and the observed macroscopic physical properties.26 Our desire81 to accelerate the detections of tellurides in the R−T−Te systems (Figure 1) for which the achievements of superconducting states compete with the formations of charge density waves stimulated our impetus to develop a descriptor for the identifications of candidate systems by means of high-throughput quantum chemical techniques. In this connection, it should be recapped that the flat band/steep band scenario is expected to establish a relationship between the electronic band structures and the superconducting states for superconducting materials (see above). To probe the feasibility of an indicator based on the flat band/steep band scenario as a practicable guide to identify materials with possible superconducting states, we examined the electronic band structures of a series of chalcogenide superconductors for the conformance of the criteria classified

Full structural optimizations and electronic band structure computations for the diverse chalcogenide superconductors were performed using the projector augmented wave (PAW) method82 of Blöchl as coded in the Vienna ab-initio simulation package (VASP) by Kresse and Joubert.83-87 Correlation and exchange in all computations were described by the generalized gradient approximation of Perdew, Burke and Ernzerhof (GGA−PBE).88 Since this type of functional cannot fully describe the van der Waals interactions between layers of chalcogenide atoms which do not enclose any transition metal atoms, correction terms (DFT-D3 correction method) were included to represent the dispersive nature of interactions between the aforementioned layers.89-90 Lists of the diverse kpoints sets employed in the structural optimizations, band structure and densities-of-states (DOS) computations for the inspected chalcogenide superconductors are provided in the Supporting Information (Table S1). The energy cutoff of the plane wave basis sets was 500 eV and all calculations converged until the energy differences between two iterative steps fell below 10−8 (and 10−6) eV/cell for the electronic (and the ionic) relaxations. The coordinates of the high-symmetry k-paths in the Brillouin zones and the electronic band structures of the diverse inspected chalcogenide superconductors were generated with the aid of the AFLOW91 and Python Materials Genomics (pymatgen) codes, respectively,92 while the wxDragon software package93 was used for the visualizations of the DOS curves. Representations of the electronic band structures and DOS curves of selected examples are shown below (Figures 3−6), while the electronic band structures and DOS curves including illustrations of the band structures in the energy regions near the Fermi levels in all inspected chalcogenides may be extracted from the Supporting Information (Figures S1−S12).

RESULTS AND DISCUSSION Preliminary Considerations on a Search Parameter and a Test Data Set. Previous research on the electronic structures in the energy regions near the Fermi levels of certain chalcogenide superconductors revealed the presence of van Hove singularities at the Fermi levels (Table 1). This outcome provoked the conclusion that the occurrence of a superconducting state in a given material is related to the presence of a van Hove singularity at its Fermi level.48 Based on the flat band/steep band scenario, the occupations of flat bands in the forms of van Hove singularities at the Fermi level generate structural instabilities that are compensated by electrons residing in extremely dispersive bands.8-9 Therefore, the coincidence of bands with no as well as broad dispersions at the Fermi level is expected to be required for the occurrence of a superconducting state in a given material following the flat band/steep band scenario. As an outcome of the aforementioned scenario, it can be inferred that bands with no dispersion have to be located at the Fermi levels of superconductors; however, it should be noted that the existence of a van Hove singularity at the Fermi level for a particular material exclusively points to an electronic instability that is related to a superconducting state or a structural distortion within the crystal structure.94 Notably, these aforementioned distortions


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may be continuously suppressed by alternations of the temperature, pressure or chemical composition such that superconducting states emerge.94 To probe the capability of the localizations of van Hove singularities at the Fermi levels for the utilization in a descriptor to detect materials with the

aforementioned electronic instabilities by means of highthroughput quantum chemical techniques, we examined the electronic band structures of a series of chalcogenide superconductors for the features at the Fermi levels.

Figure 2. (a)−(i) Overview about the crystal structures of the chalcogenide superconductors, whose electronic band structures were examined: the transition-/post-transition-metal and chalcogenide atoms are represented by the blue and orange atoms, respectively. The very first examinations on the vibrational properties of layered crystals revealed three and four types of singularities for the two- and three-dimensional cases, respectively.10 Because of the relationship between the energy and the vibrational frequencies, the results extracted from the vibrational properties of layered crystals can also be transferred to the electronic band structures and densities-of-states.10 Previous inspections of the electronic structures for the presence of van Hove singularities at the Fermi levels in chalcogenide superconductors largely focused on the cuprate superconductors (Table 1). For an accelerated high-throughput screening of the electronic band structures for the presence of van Hove singu-

larities at the Fermi levels by using quantum chemical techniques, we chose a series of chalcogenide superconductors whose crystal structures were not reported to exhibit any structural disorders. Representations of the crystal structures for the inspected compounds are shown in Figure 2, while the references to the literature reporting on the determinations of the crystal structures and physical properties may be extracted from the Table 1. This limitation originates from the fact that structure models with atomic positions exhibiting positional as well as occupational disorders cannot be used as starting parameters for the first-principles-based computations and, thus, require the evaluations of diverse structure



models approximating the actual crystal structure to identify the most preferable structure model.95-99 In addition, we also examined the electronic band structures of certain chalcogenide superconductors whose electronic band structures have been reported elsewhere (Table 1) and compared them to the outcome derived from the previously computed electronic band structures to test the reliability of the selected quantum chemical technique. In the following, we will interpret the electronic band structures of eight prototypical examples. PdTe2 and FeS. To probe the reliability of the selected quantum chemical procedure, the electronic band structures were examined for the chalcogenide superconductors PdTe2 and FeS, whose electronic band structures have been previously inspected (references regarding the crystal structure determinations and the electronic band structure computations

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may be extracted from the Table 1). The crystal structures of FeS and PdTe2 are both composed of hexagonal closest packed layers of chalcogenide atoms (Figures 2f and 2h). In FeS, the iron atoms reside in all tetrahedral voids of every second layer enclosed by the chalcogenide atoms, while the palladium atoms occupy all octahedral vacancies of every second layer that is encapsulated by the tellurium atoms in PdTe2. An examination of the electronic band structure for FeS reveals that the states near the Fermi level, EF, originate primarily from the Fe-d atomic orbitals (AOs) with minor contributions from the S-p AOs, which are mainly located below −2 eV (Figure 3a). Furthermore, the position of EF at a maximum in the densities-of-states (DOS) of FeS indicates that this sulfide should be a metal. The sharp peak in the DOS at EF originates from a flat band propagating from the Γ- to the Z-point.

Figure 3. Electronic band structures and densities-of-states (DOS) curves of FeS (top, a) and PdTe2 (bottom, b); the Fermi levels, EF, are represented by the black horizontal lines. Detailed representations of the band structures in the energy regions near the Fermi levels, particularly, those regions comprising the flat bands, may be extracted from the Supporting Information (Figure S12).

In particular, that flat band originates from the iron ݀௫మି௬మ atomic orbitals which can hybridize with each other between the iron atoms assembling square sheets within the ab plane (Figure S13). The outcome of this investigation is in good agreement with previous examinations on the electronic band

structure of the superconducting FeS, for which a flat band was also identified at the Fermi level.76, 100-101 An analysis of the regions of the DOS near EF in PdTe2 bares that these states stem from the Te-p as well as Pd-d AOs (Figure 3b). Because the Fermi level in PdTe2 lies close to a maximum of the DOS curves, this telluride should be a metal. A


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close inspection of the electronic band structure for PdTe2 reveals the presence of diverse singularities at the Fermi level: a saddle point at the M-point, a minimum at the L-point and a maximum at the Γ-point. More specifically, these bands arise from the tellurium px, py (at the Γ- and L-point), and pz (at the M-point) atomic orbitals, which hybridize with the palladium p and d atomic orbitals, respectively. The occurrence of different singularities at the Fermi level in PdTe2 was also recognized by previous investigations72 of the electronic band

structure of PdTe2 and, hence, agrees well with the present results. In summary, the results of the electronic band structure computations are in good agreement with those derived from previous first-principles-based calculations for these chalcogenide superconductors. Therefore, we followed up with an analysis of the electronic band structures for a series of chalcogenide superconductors.

Figure 4. Electronic band structures and densities-of-states (DOS) curves of CuTe2 (top, a) and RhTe2 (bottom, b); the Fermi levels, EF, are represented by the black horizontal lines. Detailed representations of the band structures in the energy regions near the Fermi levels, particularly, those regions comprising the flat bands, may be extracted from the Supporting Information (Figure S7).

CuTe2 and RhTe2. The tellurides crystallize with the pyrite type of structure, in which the tellurium atoms assemble dumbbells that are tilted relative to the crystallographic axes and surrounded by the transition-metal atoms in an octahedral fashion (Table 1 and Figure 2c). Additional research on the temperature-dependent electrical conductivity behaviors for both ditellurides identified transitions from metallic to superconducting states at 1.3 K for CuTe2 and 1.5 K for RhTe2 (Table 1). An analysis of the electronic band structures and DOS curves for CuTe2 (Figure 4) bares that the states near EF originate primarily from the Te-p atomic orbitals with minor contributions from the Cu-d atomic orbitals. In the band structure of the copper-containing telluride, flat bands cross the Fermi level between the M-point and Γ-point as well as between the M-point and R-point. In the case of the rhodiumcontaining telluride, the states around the Fermi level arise

from both the rhodium-d as well as tellurium-p atomic orbitals. Furthermore, a flat band crosses the Fermi level in RhTe2 between the X-point and M-point (detailed representations of the electronic band structures near EF in both tellurides may be extracted from the Figure S7). IrTe and La3Se4. The chalcogenides IrTe and La3Se4 were previously identified to crystallize with the NiAs-type and Th3P4-type, respectively (Table 1 and Figure 2). In particular, the crystal structure of IrTe is composed of hexagonal closest packed layers of tellurium atoms with iridium atoms residing in all octahedral voids between the tellurium layers, whereas the selenium atoms are enclosed by lanthanum octahedrons that are tilted to each other in the crystal structure of La3Se4. Investigations on the temperature-dependent electrical conductivity behaviors of IrTe and La3Se4 revealed metal-to-



superconductor-transitions at 3.0 K for the telluride and at 7.8 K for the selenide (Table 1). An analysis of the DOS curves for the selenide (Figure 5a) indicates that the Fermi level falls at a maximum of the DOS, which originates from flat bands at the Fermi level, particularly, one flat band crossing the Fermi level between the H-point and N-point. An additional inspection of the electronic struc-

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ture in the energy regions near the Fermi level denotes that the states near EF mainly arise from the lanthanum-d orbitals. In the case of the NiAs-type IrTe (Figure 5b), the states near EF originate largely from the iridium-d atomic orbitals. Furthermore, flat bands are evident at the Fermi level in IrTe at the Γpoint and between the A-point and L-point.

Figure 5. Electronic band structures and densities-of-states (DOS) curves of La3Se4 (top, a) and IrTe (bottom, b); the Fermi levels, EF, are represented by the black horizontal lines. Detailed representations of the band structures in the energy regions near the Fermi levels, particularly, those regions comprising the flat bands, may be extracted from the Supporting Information (Figures S5 and S10).

YTe and LaTe. The monotellurides RTe of the rare-earth elements yttrium and lanthanum crystallize both with the cubic rock salt type of structure and show transitions to superconducting states at 2.05 K for R = Y and at 1.48 K for R = La (Figure 2a and Table 1). An examination of the electronic band structure for the yttrium-containing telluride indicates that a number of bands crosses the Fermi level (Figure 6a). Accordingly, these characteristics at EF in YTe clearly denote that this telluride should be a metal. The states near the Fermi level in YTe arise mainly from the Y-d AOs with minor contributions from the Te-p states, which are largely located between ~−6 eV and ~−2 eV. A closer inspection of the valence bands for YTe reveals the presence of a minimum in the vicinity of the Fermi level (~−0.1 eV) at the Γ-point. Although this outcome may evoke a discrepancy between the observed superconducting state and the computed location of the van

Hove singularity below instead of at EF for YTe in the eye of the reader,102 yet, subsequent examinations of the electronic band structure (below) will provide an insight into the origin of this assumed inconsistency. In the case of the lanthanum-containing telluride, an inspection of the bands in the energy regions near the Fermi level bares that a minimum crosses EF at the Γ-point (Figure 6b). In particular, the bands corresponding to the minima at the Γpoint at the Fermi level originate from the lanthanum dxy, dxz, and dyz atomic orbitals which may hybridize to La−La interactions. Because the Fermi level in LaTe falls in a maximum of the DOS curves, this telluride should be a metal. The states near the Fermi level in LaTe stem chiefly from the La-d AOs, whereas the Te-p AOs primarily reside below −2 eV. Based on the fact that a flat band/steep band scenario is present in the lanthanum-containing monotelluride, the existence of a singu-


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larity at the Fermi level in the computed electronic band structure of LaTe agrees well with the metal-tosuperconductor-transition observed for this telluride; however, a survey of the features around EF for the electronic band structures of a series of chalcogenide superconductors (see Table 1 for a complete list) reveals that van Hove singularities are located in the vicinity of the Fermi levels (≤ ±0.2 eV) for 91 % and at EF for 57 % of all inspected chalcogenide superconductors (Figure 7). Representations of the band structures and DOS curves, which also include detailed illustrations of the band structures in the energy regions near the Fermi levels, particularly, those regions containing flat bands, are

provided for all inspected chalcogenides in the SI (Figures S1−S12). At a first glance, this result implies that there is a disagreement between the observed metal-to-superconductortransitions and the positions of the singularities relative to the Fermi levels in the calculated electronic band structures of the inspected chalcogenide superconductors (see above). To understand the reason for this obvious discrepancy, we continued with an inspection of the band structure for YTe, whose electronic band structure was prototypically analyzed.

Figure 6. Electronic band structures and densities-of-states (DOS) curves of YTe (top, a) and LaTe (bottom, b), which crystallize with the NaCl type of structure; the Fermi level, EF, is represented by the black horizontal line. Detailed representations of the band structures in the energy regions near the Fermi levels, particularly, those regions comprising the flat bands, may be extracted from the Supporting Information (Figure S11).



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electronic instabilities in the forms of singularities at the Fermi levels.

CONCLUSIONS

Figure 7. Percentages of the inspected chalcogenide superconductors which show van Hove singularities near or at the Fermi levels, EF, respectively. The Influence of Vacancies on the Position of the Van Hove Singularity. Previous research on the temperature- and composition-dependent electrical conductivities of superconducting materials forming over certain homogeneity ranges revealed a clear interdependence between the compositions of the compounds and temperatures of the metal-tosuperconductor-transitions.103-104 Additional examinations on the electronic structures bared that the positions of the van Hove singularities relative to the Fermi levels are also affected by the respective compositions of the superconducting materials existing over particular homogeneity ranges.39, 48 Under consideration of the afore determined position of the singularity relative to EF in YTe (and those in other NaCl-type chalcogenides; see Supporting Information), it should be mentioned that the presence of vacancies has also been identified for the crystal structures of a series of NaCl-type chalcogenide superconductors.52-53 To probe the influence of vacancies on the positions of the van Hove singularities relative to the Fermi level, we inspected the electronic band structure of a hypothetical “Y32Te31” which was derived from a superstructure of the NaCl-type YTe corresponding to 2 × 2 × 2 expansions of the original unit cell. Because the Fermi level in “Y32Te31” ≡ “YTe0.97” falls in a local maximum in the DOS (Figure S1), the yttrium telluride, whose crystal structure features tellurium vacancies relative to that corresponding to a YTe composition, should be metallic. This maximum at EF stems from a flat band that is located at the M-point (Figure S1). An inspection of the energy regions near the Fermi level in “Y32Te31” indicates that these bands originate from Te-p as well as Y-d atomic orbitals. The presence of the van Hove singularity as well as steep bands crossing the Fermi level in “Y32Te31” are indicative for a flat band/steep band scenario which corresponds well with the metal-to-superconductor-transition observed for yttrium telluride. Furthermore, the result of this probe also provides justification for the assumed discrepancy between the occurrence of a metal-to-superconductor-transition and the presence of a van Hove singularity in the near of EF (see above); yet, this outcome also implies that minor deviations from the exact compositions related to slight amounts of vacancies within a given crystal structure are significant and, hence, must be taken into consideration for the electronic band structure computations of materials with the pronounced

Herein, we inspected the electronic band structures and DOS curves of a series of chalcogenide superconductors with special emphasis on the presence of van Hove singularities at the Fermi levels. The positions of the singularities relative to the Fermi levels in the chalcogenide superconductors were examined to probe the ability of the localizations of singularities at the Fermi levels for a descriptor to detect materials with such electronic instabilities. The presence of these electronic instabilities in solid-state-materials indicates a structural instability, which is counterbalanced by electrons in steep bands as expected for superconductors, or can be prevented to achieve a metal-to-superconductor-transition.94 Based on the step band/flat band scenario, which is used to explain the occurrence of metal-to-superconductor-transitions, singularities are expected to be present at the Fermi levels in the inspected chalcogenide superconductors. Indeed, the outcome of our survey reveals that van Hove singularities are evident at EF for 57 % and close to the Fermi levels (≤ ±0.2 eV) for 91 % of the inspected chalcogenide superconductors. Provided that all selected chalcogenides exhibit metal-tosuperconductor-transitions, the apparent discrepancy between the occurrence of superconductivity and the locations of the van Hove singularities in the near of the Fermi levels may be rationalized based on the presence of certain vacancies in the crystal structures that influence the positions of the van Hove singularities relative to the Fermi levels. Accordingly, the occurrence of a slight number of vacancies in a given crystal structure, which correspond to minor deviations from an exact composition and influence the positions of singularities relative to the Fermi level, must be taken into account for an indicator to identify materials with the aforementioned electronic instabilities. Because the examinations of the electronic band structures of the inspected chalcogenides denote metallic conductivity for all of them, it might be most advantageous to combine the detections of bands crossing the Fermi level as well as bands with minima, saddle points and maxima in the near of EF within one tool for the high-throughput screenings of materials libraries by means of quantum chemical methods. Such a descriptor represents a perspective to identify previously unknown materials showing the afore described electronic instabilities which hint to feasible metalto-superconductor-transitions; however, further research based on a larger test set with particular regard to the presence of vacancies in a given crystal structure is required to optimize such a search tool.

ASSOCIATED CONTENT Supporting Information Lists of the k-points sets employed in the structural optimizations, electronic band structure and DOS calculations of the inspected chalcogenide superconductors; representations of the DOS curves and the electronic band structures containing separate illustrations which show the energy regions of the band structures, particularly, those regions comprising singularities, close to the Fermi levels in all inspected chalcogenide superconductors (a list of all inspected chalcogenide superconductors is provided in the Table 1). This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION


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Corresponding Author [email protected]

Author Contributions K. S. F. carried out the first-principles-based computations, S. ST. supervised the project and prepared the manuscript. All authors have given approval to the final version of the manuscript.

Funding Sources This work was supported by Fonds der Chemischen Industrie (VCI) e. V., Frankfurt a. M., through a Liebig-Stipend to S. ST.

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENTS We wish to express thanks to Prof. Dr. R. Dronskowski for fruitful advice and the allocation of the computer cluster of the Chemistry Department of RWTH Aachen University, P. Konze, M. Sc., and Janine George, M. Sc., for technical assistance regarding the pymatgen code, and the IT Center of RWTH Aachen University (JARA-HPC project jara0167) for the granted computing time.

DEDICATION Dedicated to Prof. Wolfgang Schnick on the Occasion of his 60th Birthday

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Fermi-Level Characteristics of Potential Chalcogenide Superconductors

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