Unexpected High-Pressure Phase of GeTe with an ... - ACS Publications

Subscriber access provided by NAGOYA UNIV

C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Unexpected High-Pressure Phase of GeTe with an Origin of Low Ionicity and Electron Delocalization Hulei Yu, and Yue Chen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03984 • Publication Date (Web): 12 Jun 2018 Downloaded from http://pubs.acs.org on June 19, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Unexpected High-Pressure Phase of GeTe with an Origin of Low Ionicity and Electron Delocalization Hulei Yu and Yue Chen∗ Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China E-mail: [email protected]

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract First-principles evolutionary searches have been performed to systematically explore the high-pressure phases of germanium telluride. Two new phases are found to be both energetically and dynamically stable under moderate pressures. A Pnma orthorhombic phase with an uncommon “boat” conformation and a P4/nmm tetragonal phase are found to become stable at ∼15 and ∼37 GPa, respectively. The long-believed highpressure B2 phase, however, is found to be energetically unfavorable comparing to the P4/nmm phase. Our calculations of the electronic structures show that Pnma-boat GeTe and P4/nmm GeTe exhibit a semimetallic and a metallic behavior, respectively. Based on the electron-phonon coupling calculations, P4/nmm GeTe is shown to have a superconducting transition at low temperatures, resulting from its sudden decrease of ionicity and the more delocalized lone-pair electrons. The discovery of these new GeTe phases further enriches our knowledge of the high-pressure behaviors of the IVVI compounds.

Introduction Semiconductor-superconductor transitions are of great importance in both fundamental research and practical applications. The narrow band gap semiconductor GeTe was recently reported to possess a record high device thermoelectric performance, 1 making it an extremely attractive material for energy-related applications. It is also notable that the predictions of superconductivity in some highly doped and multiple-valley GeTe based semiconductors constitute the first studies of this type of superconducting transition. 2,3 However, the superconducting transition temperature (Tc ) of GeTe at ambient pressure is very low (∼0.2 K ), 2 although Tc can be slightly increased to ∼ 1.5 K in the GeTe thin films. 4 On the other hand, high-pressure studies of the IV-VI group semiconductors have shown that the metallization and superconductivity are associated with the pressure-induced phase transitions, which could lead to a fairly higher Tc (4 - 8 K). 5–7 The structural phase transition order 2


Page 2 of 20

Page 3 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of the group IV monochalcogenides with increasing pressure can generally be summarized as R3m - Fm¯3m (B1) - Pnma (GeS-type) - Cmcm - Pm¯3m (B2). 5,8–11 Particularly, α-GeTe which has a R3m structure undergoes a phase transition to the Fm¯3m (B1) structure below 10 GPa. 12–14 It was also reported that the body-centered cubic Pm¯3m (B2) phase of GeTe can be stabilized above 40 GPa based on X-ray diffraction (XRD) measurements, 15 and this B2 phase was believed to be superconducting above 44 GPa. 6,16 However, the structural phase transformations between the B1 and B2 phases are still controversial. Onodera et al proposed that a potential orthorhombic structure with a space group of Pbcn could exist between 18 and 39.4 GPa with a dramatically increased electrical resistivity. 14 In another study, 17 a rhombohedral to cubic transition was reported below 5 GPa, accompanied by an orthorhombic phase with a space group of Pnma or Cmcm. Serebryanaya et al also reported phase transitions of GeTe from B1 through orthorhombic B16 to B2 at 34 and 43 GPa, respectively. 15 Ab initio molecular dynamics simulations of GeTe were also carried out up to 38.9 GPa at room temperature and a reversible phase transition order of rhombohedral - rocksalt - orthorhombic - monoclinic was reported. 18 Therefore, a systematic study using state-of-the-art methods will help to clarify the above ambiguities in the high-pressure phases of GeTe and facilitate further explorations of its superconducting properties. Theory-assisted crystal structure prediction based on evolutionary algorithms was recently developed and proven to be an effective approach for discovering ground-state structures at high pressures. 19,20 Using this approach, Ma et al predicted that sodium undergoes a pressure-induced phase transition into an optically transparent insulator at ∼200 GPa, and the prediction was later confirmed in experiments. 21 High-pressure crystal structures of germane were theoretically explored by Gao et al ; a novel monoclinic phase was discovered at 220 GPa, showing a remarkable superconducting critical temperature of 64 K. 22 Our previous work also unveiled a novel Sn3 Se4 compound, which was later successfully synthesized under high pressures. 23 By means of first-principles structural search based on evolutionary algorithms, we have

3



systematically investigated the ground-state crystal structures of GeTe under hydrostatic pressures up to 50 GPa in this work. Two new GeTe phases are predicted to be energetically preferable at high pressures. Most interestingly, the long-believed high-pressure B2 phase is found to be thermodynamically unstable comparing to the newly discovered P4/nmm phase. The dynamical stabilities of the new phases have also been examined via phonon calculations. Our chemical bond analysis unveils that a large decrease of ionicity and a more delocalized electron distribution of the P4/nmm phase may be related to its higher stability comparing to the B2 phase. Further investigations on the XRD pattern, electronic structure, and superconductivity of the newly found high-pressure phases have also been carried out.

Computational details Ab initio evolutionary structural prediction 24,25 based on density functional theory (DFT) 26 was performed with maximum 18 atoms in a unit cell. Structural relaxation and electronic properties were calculated within the projector-augmented wave method (PAW) 27 and the generalized gradient approximation (GGA) of Perdew-Burke and Ernzerhof (PBE). 28 A plane-wave energy cut-off of 350 eV and a Gamma-centered k-sampling of 0.03 × 2π Å−1 density in the Brillouin zone 29 were applied with a convergence criterion of 10−6 eV for the electronic self-consistent calculations. A 3 × 2 × 2 supercell containing 96 atoms of the Pnma phase and a 4 × 4 × 2 supercell containing 128 atoms of the P4/nmm phase were adopted to calculate the phonon dispersions using the small displacement method. 30 For accurate phonon calculations, a higher total energy convergence criterion of 10−8 eV was applied. Density-functional perturbation theory (DFPT) as implemented in the QUANTUM ESPRESSO package 31 was utilized to calculate the electron-phonon coupling (EPC). We used the Troullier-Martins norm-conserving pseudopotentials 32 with 4s2 4p2 and 5s2 5p4 treated as the valence electrons of Ge and Te, respectively. We adopted a 6 × 6 × 4 q-point mesh and a 24 × 24 × 16 k-sampling in the EPC calculations with a kinetic cutoff energy of

4


Page 4 of 20

Page 5 of 20

80 Ry. To obtain the electron-phonon coefficient λ, interpolation over the Brillouin Zone was applied. 33 The Gaussian broadening was set to 0.03 Ry.The Allen-Dynes modified McMillan equation 34 was used to calculate the Tc of GeTe with typical values of the Coulomb pseudopotential µ∗ (0.1 - 0.14).

Results and Discussion (a)

∆H (meV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


100 0 -100

R3m Fm3m(B1) Pnma-boat P4/nmm

-200 0

10

Pnma-chair Cmcm Pbcn Pm3m(B2) 20 30 P (GPa)

(b)

40

50

(c)

chair (GeS-type)

Pnma-boat

P4/nmm

boat

Pm3m

Figure 1: (a) Enthalpy differences of various competing phases of GeTe as functions of the hydrostatic pressures. (b) The crystal structure of the Pnma phase with boat conformation; the chair conformation of the GeS-type structure is also given for comparison. (c) Crystal structures of the P4/nmm and Pm¯3m phases. Ge and Te atoms are shown in purple and yellow, respectively.

Interesting ground state crystal structures are predicted from our ab initio evolutionary structure searches. With increasing pressure, GeTe is found to go through a structural phase transition order of R3m - Fm¯3m - Pnma-boat - P4/nmm, as shown in FIG. 1(a). De5



Frequency (THz)

(a)

Pnma-boat 15GPa 8 6 4 2 0 Γ

(b) Frequency (THz)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 20

X

S

Y

Γ

Z

U

R

T

Z

P4/nmm 40GPa 8 6 4 2 0 Γ

X

M

Γ Z

R

A

Z

Phonon Wave Vector q Figure 2: Phonon dispersions of the Pnma-boat and P4/nmm phases under hydrostatic pressures. tailed structural information on the predicted high-pressure phases is summarized in Table S1 in Supporting Information. The experimentally observed rhombohedral to cubic (R3m - Fm¯3m) phase transition below 10 GPa is successfully reproduced from our calculations. The superposition of the enthalpies of the R3m (α-GeTe) and Fm¯3m phases demonstrates a continuous phase transition, which is consistent with previous experiments. 17 With increasing pressure, GeTe undergoes a phase transition from Fm¯3m to an orthorhombic structure with a space group of Pnma at approximate 15 GPa. As shown in FIG. 1(b), this new orthorhombic GeTe phase is isostructural to the high-pressure SnTe phase 35 and the recently reported β-GeSe 36 phase with an uncommon boat conformation, whereas the previously reported GeS-type Pnma structure 37 has a chair conformation. Similar to the GeS-type Pnma phase, this new Pnma phase can also be considered to have a distorted rock-salt crystal

6


Page 7 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


structure. To distinguish the two Pnma crystal structures, we designate the newly predicted orthorhombic GeTe structure as Pnma-boat and the GeS-type structure as Pnma-chair. By further compressing GeTe to about 37 GPa, a novel tetragonal phase with a space group of P4/nmm surprisingly becomes the ground state, having a lower enthalpy than the longbelieved Pm¯3m (B2) phase. This P4/nmm phase has a similar crystal structure as that of B2 but a different atomic stacking order, as shown in FIG. 1(c). The different stacking order results in that the P4/nmm phase is about 0.5% more compact in volume (V ) than the B2 phase. The difference of the internal energy between these two competing phases is very small (E(P 4/nmm) − E(P m¯3m) = 0.86meV ), but the more compact P4/nmm phase has a significantly smaller P V term at high pressures (P V (P 4/nmm) − P V (P m¯3m) = −21.52meV , where P and V represent pressure and volume, respectively.). As a result, the enthalpy (H = E + P V ) of the P4/nmm phase becomes lower than that of B2. The P4/nmm phase has a prototype crystal structure of γ-CuTi, which usually forms in binary compounds containing only transition metal elements. This is the first time that the P4/nmm phase is found to be stable in a binary system containing metalloid elements. In addition to the energetics, the dynamical stabilities of the newly discovered Pnma-boat and P4/nmm phases of GeTe have also been studied. It is seen from the phonon dispersions (FIG. 2) that there is no imaginary frequency, indicating that both of the Pnma-boat and P4/nmm phases are dynamically stable under high pressures. To better understand the formation of these high-pressure GeTe phases, we have analyzed their chemical bonding based on the calculations of electronic structures. Due to the symmetries of the stable high-pressure phases, all the Ge or Te atoms are in equivalent lattice sites. Therefore, the number of electrons that each Ge donates or each Te accepts is identical. It is seen from the Bader charge analysis 38 that GeTe shows slowly weakening ionicity as pressure increases (FIG. 3 (a)). At 0 GPa, the number of electrons that each Ge donates in the R3m phase is equal to 0.39 e, suggesting obvious ionic bonding. 18 As pressure increases, the Ge atom is found to donate fewer electrons to Te, which indicates

7


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(a)

(b)

Bader Charge of Ge (e)


Page 8 of 20

0.4 0.3 0.2

R3m Fm3m

Pnma-boat

P4/nmm

0.1 0 0 1

10

20 30 P (GPa)

Ge

Te

Te

40 Te

50

Te

Te

Te 0.5

Ge

Ge Te

Ge

Te

Te Te

Te 0

Ge Pnma-boat 35GPa

Ge

Ge

P4/nmm 40GPa

Figure 3: (a) Bader charge of Ge atom in different phases as a function of pressure. (b) Electron localization functions of Pnma-boat GeTe at 35 GPa and P4/nmm GeTe at 40 GPa. The purple isosurface value is equal to 0.86. weakening ionic bonding in the phase transitions from R3m through Fm¯3m to Pnma-boat. Most interestingly, a significant fall of the Bader charge is observed when the Pnma-boat phase transforms into the P4/nmm phase at about 40 GPa. The extremely low electron transfer in the P4/nmm phase indicates a weak ionic characteristic. From the electron localization function (ELF) shown in FIG. 3 (b), it is found that the lone pair electrons of Ge atoms become more delocalized in the P4/nmma phase at 40 GPa. The decrease of ionicity and the more delocalized electrons suggest dominant metallic bonding under high pressures, rationalizing the energetically preferable P4/nmm phase, which usually forms in transition metal compounds. The stabilities of these two new phases are also confirmed from ab initio molecular dynamics (AIMD) simulations at 300 K (see FIG. S2-S3 in Supporting Information).

8


Page 9 of 20

P4/nmm Pm3-m(B2) Pnma-boat

XRD-CuKα Intensity (A.U.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10

20

30

40

50 2θ (°)

60

70

80

90

Figure 4: Simulated XRD patterns, using Cu Kα radiation with λ = 1.54 Å for P4/nmm, Pm¯3m (B2) and Pnma-boat GeTe at 40 GPa. To provide further guidelines for identifying the predicted P4/nmm phase, we have computed the XRD patterns of the competing high-pressure phases (see FIG. 4). It is found that most of the characteristic XRD peaks of the P4/nmm and B2 phases overlap, while the main distinctions between them are the XRD peaks in the vicinity of 30◦ . Nonetheless, it should be noted that the Pnma-boat phase also produces XRD peaks near 30◦ at 40 GPa. Thus, it may be more difficult to differentiate the B2 and the P4/nmm phase if the Pnma-boat phase co-exists in the sample. The projected electronic band structures and density of states (DOS) of Pnma-boat and P4/nmm GeTe are calculated and shown in FIG. 5. It is found that both phases have gapless band structures. The DOS at the Fermi level of Pnma-boat GeTe at 15 GPa is very small; the pseudo gap suggests a semi-metal behavior with only a few bands crossing the Fermi level. For Pnma-boat GeTe, the electronic bands above the Fermi level mostly consist of the Ge 4p and Te 5p states while the bands below the Fermi level mostly consist of the Te 5p states. On the other hand, the DOS at the Fermi level of P4/nmm GeTe is large, consisting of mainly the Te 5p and Ge 4p states. The metallic behavior of the P4/nmm phase is consistent with the above observation of low ionicity and electron delocalization. To explore the superconducting property of the metallic P4/nmm phase, we have further 9



Pnma-boat 15GPa

(a)

8

Total Ge 4s Ge 4p Te 5s Te 5p

E (eV)

4 0 -4 -8 (b)

Γ

X S

Y Γ Z

U R

T Z 0

0.3

0.6

0.9

DOS (states/eV/atom)

P4/nmm 40GPa 8 4

E (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 20

0

-4 -8

Γ

X

M

ΓZ

R

A

Z 0

0.3

0.6

0.9


Figure 5: Projected band structures and density of states of the Pnma-boat and P4/nmm phases of GeTe at selected hydrostatic pressures. Fermi level is located at 0 eV. Different circle sizes correspond to the projected weights of different orbitals. calculated its electron-phonon coupling, as shown in FIG. 6. It is found that the highfrequency optical phonon modes in the range of 4 - 8 THz have larger phonon linewidths, indicating their stronger coupling to electrons. The total EPC parameter λ of the P4/nmm phase at 40 GPa and the weighted logarithmic average of the phonon frequency are found to be 0.65 and 164.8 K, respectively. The predicted superconducting transition temperature Tc is in the range of 3.1 - 4.7 K. We have also found that the Tc of P4/nmm decreases as pressure is further increased; e.g., the Tc becomes 2.4 - 3.9 K at 45 GPa.

10


Page 11 of 20

λ(ω) 0

8 Frequency (THz)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.4

0.8

6 4 2

2

α F(ω) λ(ω)

0 Γ X M

ΓZ R A

Z

0.05 0.1

PHDOS

0

0.4

α2F(ω)

0.8

Figure 6: Phonon dispersions with linewidths of individual phonon modes, phonon density of states, and Eliashberg spectral function α2 F (ω) and the integrated electron-phonon coupling parameter λ(ω) of P4/nmm GeTe at 40 GPa.

Conclusions In summary, we have performed ab-initio evolutionary structural searches and discovered two new high-pressure phases of GeTe; i.e., the Pnma-boat phase and the P4/nmm phase which are stable in the range of 15 - 37 GPa and above 37 GPa, respectively. Most notably, the P4/nmm phase is found to have a lower enthalpy than the B2 phase, which has long been believed to be a stable phase at high pressures. We find that the low ionicity and delocalization of electrons in the high-pressure P4/nmm phase lead to its higher stability. The P4/nmm and the B2 phases have similar XRD patterns, and it becomes difficult to differentiate them when the Pnma-boat phase co-exists. Further electronic structure and electron-phonon coupling calculations indicate that the Pnma-boat phase is a semi-metal, while the P4/nmm phase is metallic and shows a superconducting transition at low temperatures. This work enriches our knowledge of the high-pressure structural phase transitions of GeTe, and suggests the potential existence of other hidden phases of the IV-VI group compounds.

11



Acknowledgement This work is supported by the Research Grants Council of Hong Kong under project numbers 27202516 and 17200017, and the National Natural Science Foundation of China under project number 51706192. The authors are grateful for the research computing facilities offered by ITS, HKU.

Supporting Information Available The following files are available free of charge. • Supporting Information.pdf : Table S1: Structural parameters of the predicted highpressure GeTe phases at selected pressures. FIG. S1: Enthalpy differences of various competing phases of GeTe calculated with the rVV10 vdW correction. FIG. S2-S3: Ab initio molecular dynamics simulations at 300 K for the Pnma-boat phase at 15 GPa and the P4/nmm phase at 40 GPa. This material is available free of charge via the Internet at http://pubs.acs.org/.

References (1) Li, J.; Zhang, X.; Chen, Z.; Lin, S.; Li, W.; Shen, J.; Witting, I. T.; Faghaninia, A.; Chen, Y.; Jain, A. et al. Low-Symmetry Rhombohedral GeTe Thermoelectrics. Joule 2018, 2, 976–987. (2) Hein, R. A.; Gibson, J. W.; Mazelsky, R.; Miller, R. C.; Hulm, J. K. Superconductivity in Germanium Telluride. Phys. Rev. Lett. 1964, 12, 320–322. (3) Blase, X.; Bustarret, E.; Chapelier, C.; Klein, T.; Marcenat, C. Superconducting GroupIV Semiconductors. Nat. Mater. 2009, 8, 375.

12


Page 12 of 20

Page 13 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(4) Narayan, V.; Nguyen, T.-A.; Mansell, R.; Ritchie, D.; Mussler, G. Interplay of Spin– orbit Coupling and Superconducting Correlations in Germanium Telluride Thin Films. Phys. Status Solidi RRL 2016, 10, 253–259. (5) Timofeev, Y. A.; Vinogradov, B. V.; Begoulev, V. B. Superconductivity of Tin Selenide at Pressures up to 70 GPa. Phys. Solid State 1997, 39, 207–207. (6) Narozhnyi, V.; Stepanov, G.; Semenova, E. Superconductivity of Si, GaP, GeTe at High Pressures. Investigation in Superconducting Anvils. High Press. Res. 1992, 10, 496–499. (7) Zhou, D.; Li, Q.; Ma, Y.; Cui, Q.; Chen, C. Pressure-Induced Superconductivity in SnTe: A First-Principles Study. J. Phys. Chem. C 2013, 117, 12266–12271. (8) Liebmann, M.; Rinaldi, C.; Sante, D. D.; Kellner, J.; Pauly, C.; Wang, R. N.; Boschker, J. E.; Giussani, A.; Bertoli, S.; Cantoni, M. et al. Giant Rashba-Type Spin Splitting in Ferroelectric GeTe(111). Adv. Mater. 2015, 28, 560–565. (9) Chattopadhyay, T.; Werner, A.; Von Schnering, H.; Pannetier, J. Temperature and Pressure Induced Phase Transition in IV-VI Compounds. Rev. Phys. Appl. (Paris) 1984, 19, 807–813. (10) Yu, H.; Dai, S.; Chen, Y. Enhanced Power Factor Via the Control of Structural Phase Transition in SnSe. Sci. Rep. 2016, 6, 26193. (11) Do, G.-S.; Kim, J.; Jhi, S.-H.; Park, C.-H.; Louie, S. G.; Cohen, M. L. Ab Initio Calculations of Pressure-induced Structural Phase Transitions of GeTe. Phys. Rev. B 2010, 82, 054121. (12) Redon, A.; Leger, J. The Rhombohedral-cubic Transition in the IV-VI Semiconductor GeTe under High Pressure. High Press. Res. 1990, 4, 315–317.

13



(13) Nonaka, T.; Ohbayashi, G.; Toriumi, Y.; Mori, Y.; Hashimoto, H. Crystal structure of GeTe and Ge2 Sb2 Te5 meta-stable phase. Thin Solid Films 2000, 370, 258–261. (14) Onodera, A.; Sakamoto, I.; Fujii, Y.; Moˆri, N.; Sugai, S. Structural and Electrical Properties of GeSe and GeTe at High Pressure. Phys. Rev. B 1997, 56, 7935. (15) Serebryanaya, N.; Blank, V.; Ivdenko, V. GeTe-phases under Shear Deformation and High Pressure up to 56 GPa. Phys. Lett. A 1995, 197, 63–66. (16) Ravindran, R.; Asokamani, R. Electronic Structure and Pressure Induced Superconductivity in Ge, Sn and Pb Tellurides. AIP Conf. Proc. 1994, 309, 669–672. (17) Leger, J.; Redon, A. Phase Transformations and Volume of the IV-VI GeTe Semiconductor under High Pressure. J. Phys. Condens. Matter 1990, 2, 5655. (18) Sun, Z.; Zhou, J.; Mao, H.-K.; Ahuja, R. Peierls Distortion Mediated Reversible Phase Transition in GeTe under Pressure. Proc. Natl. Acad. Sci. 2012, 109, 5948–5952. (19) Chen, Y.; Hu, Q.-M.; Yang, R. Predicted Suppression of the Superconducting Transition of New High-Pressure Yttrium Phases with Increasing Pressure from First-Principles Calculations. Phys. Rev. Lett. 2012, 109, 157004. (20) Zhang, X.; Yang, Z.; Chen, Y. Novel Two-dimensional Ferroelectric PbTe under Tension: A First-Principles Prediction. J. Appl. Phys. 2017, 122, 064101. (21) Ma, Y.; Eremets, M.; Oganov, A. R.; Xie, Y.; Trojan, I.; Medvedev, S.; Lyakhov, A. O.; Valle, M.; Prakapenka, V. Transparent Dense Sodium. Nature 2009, 458, 182–185. (22) Gao, G.; Oganov, A. R.; Bergara, A.; Martinez-Canales, M.; Cui, T.; Iitaka, T.; Ma, Y.; Zou, G. Superconducting High Pressure Phase of Germane. Phys. Rev. Lett. 2008, 101, 107002.

14


Page 14 of 20

Page 15 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(23) Yu, H.; Lao, W.; Wang, L.; Li, K.; Chen, Y. Pressure-stabilized Tin Selenide Phase with an Unexpected Stoichiometry and a Predicted Superconducting State at Low Temperatures. Phys. Rev. Lett. 2017, 118, 137002. (24) Oganov, A. R.; Glass, C. W. Crystal Structure Prediction Using Ab Initio Evolutionary Techniques: Principles and Applications. J. Chem. Phys. 2006, 124, 244704. (25) O., L. A.; R., O. A.; Mario, V. Modern Methods of Crystal Structure Prediction; WileyBlackwell: Weinheim, 2010; Chapter 7, pp 147–180. (26) Kresse, G.; Furthmüller, J. Efficiency of Ab-initio Total Energy Calculations for Metals and Semiconductors Using a Plane-wave Basis Set. Comput. Mater. Sci. 1996, 6, 15–50. (27) Blöchl, P. E. Projector Augmented-wave Method. Phys. Rev. B 1994, 50, 17953. (28) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. (29) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-zone Integrations. Phys. Rev. B 1976, 13, 5188. (30) Togo, A.; Oba, F.; Tanaka, I. First-principles Calculations of the Ferroelastic Transition between Rutile-type and CaCl2 -type SiO2 at High Pressures. Phys. Rev. B 2008, 78, 134106. (31) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I. et al. QUANTUM ESPRESSO: a Modular and Open-source Software Project for Quantum Simulations of Materials. J. Phys. Condens. Matter 2009, 21, 395502. (32) Troullier, N.; Martins, J. L. Efficient Pseudopotentials for Plane-wave Calculations. Phys. Rev. B 1991, 43, 1993.

15



(33) Wierzbowska, M.; de Gironcoli, S.; Giannozzi, P. Origins of low-and high-pressure discontinuities of Tc in niobium. arXiv preprint cond-mat/0504077 2005, (34) Allen, P. B.; Dynes, R. C. Transition Temperature of Strong-coupled Superconductors Reanalyzed. Phys. Rev. B 1975, 12, 905–922. (35) Zhou, D.; Li, Q.; Ma, Y.; Cui, Q.; Chen, C. Unraveling Convoluted Structural Transitions in SnTe at High Pressure. J. Phys. Chem. C 2013, 117, 5352–5357. (36) Von Rohr, F. O.; Ji, H.; Cevallos, F. A.; Gao, T.; Ong, N. P.; Cava, R. J. High-Pressure Synthesis and Characterization of β-GeSe—A Six-Membered-Ring Semiconductor in an Uncommon Boat Conformation. J. Am. Chem. Soc. 2017, 139, 2771–2777. (37) Shelimova, L.; Karpinskii, O. Phase Transitions and Crystal Chemical Features of GeTeAIV BV I (AIV =Sn, Pb; BV I =Se) Solid Solutions. Inorg. Mater. 1991, 27, 2170–2174. (38) Tang, W.; Sanville, E.; Henkelman, G. A Grid-based Bader Analysis Algorithm without Lattice Bias. J. Phys. Condens. Matter 2009, 21, 084204.

16


Page 16 of 20

Page 17 of 20

Graphical TOC Entry Bader Charge of Ge (e)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.4 0.3 0.2

Pnma-boat Fm3m (B1) R3m

0.1

P4/nmm

0 0

10

20 30 P (GPa)

17

40


50

(a)

Pnma-boat 15GPa

The Journal of Physical Chemistry Page 18 of 20

8

Total Ge 4s Ge 4p Te 5s Te 5p

4 E (eV)

1 0 2 3-4 4 5-8 Γ 6 (b) 78 8 94 10 0 11 12 -4 13 -8 14 Γ 15

X S

Y Γ Z

U R

T Z 0

0.3

0.6

0.9


E (eV)

P4/nmm 40GPa

ACS Paragon Plus Environment X

M

ΓZ

R

A

Z 0

0.3

0.6

0.9


Page 19 ofThe 20 Journal of Physical Chemistry 0

Frequency (THz)

8

16 2 4 3 42 5 60 7 Γ 8

ACS Paragon Plus Environment X M

ΓZ R A

Z

0.05 0.1

PHDOS

0

λ(ω) 0.4

0.8

α2F(ω) λ(ω) 0.4

α2F(ω)

0.8

Bader Charge of Ge (e

0.4

Pnma-boat The Journal of Physical Page Chemistry 20 of 20 0.3 0.2

Fm3m R3m (B1)

1 2 0.1 ACS Paragon Plus Environment P4/nmm 3 0 0 10 20 30 40 50 4 P (GPa)

Unexpected High-Pressure Phase of GeTe with an ... - ACS Publications

Recommend Documents