High-Pressure Phase Transitions and Structures of Topological

Nov 18, 2013 - College of Physics, Jilin University, Changchun 130012, Peoples ... Photon Sciences, Brookhaven National Laboratory, Upton, New York ...
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High-Pressure Phase Transitions and Structures of Topological Insulator BiTeI Yuanzheng Chen,†,‡ Xiaoxiang Xi,§ Wai-Leung Yim,ζ Feng Peng,† Yanchao Wang,*,† Hui Wang,† Yanming Ma,*,† Guangtao Liu,† Chenglin Sun,‡ Chunli Ma,†,# Zhiqiang Chen,& and H. Berger∥ †

State Key Lab of Superhard Materials and ‡College of Physics, Jilin University, Changchun 130012, Peoples Republic of China Photon Sciences, Brookhaven National Laboratory, Upton, New York 11973, United States ζ Institute of High Performance Computing, Agency for Science, Technology, and Research, 1 Fusionopolis Way, No. 16-16 Connexis, Singapore 138632 # Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20015, United States & Department of Geosciences, Stony Brook University, Stony Brook, New York 11794, United States ∥ Institute of Condensed Matter Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland §

S Supporting Information *

ABSTRACT: Being a giant bulk Rashba semiconductor, the ambient-pressure phase of BiTeI was predicted to transform into a topological insulator under pressure at 1.7−4.1 GPa [Nat. Commun. 2012, 3, 679]. Because the structure governs the new quantum state of matter, it is essential to establish the high-pressure phase transitions and structures of BiTeI for better understanding its topological nature. Here, we report a joint theoretical and experimental study up to 30 GPa to uncover two orthorhombic high-pressure phases of Pnma and P4/nmm structures named phases II and III, respectively. Phases II (stable at 8.8−18.9 GPa) and III (stable at >18.9 GPa) were first predicted by our first-principles structure prediction calculations based on the calypso method and subsequently confirmed by our high-pressure powder X-ray diffraction experiment. Phase II can be regarded as a partially ionic structure, consisting of positively charged (BiTe)+ ladders and negatively charged I− ions. Phase III is a typical ionic structure characterized by interconnected cubic building blocks of Te−Bi−I stacking. Application of pressures up to 30 GPa tuned effectively the electronic properties of BiTeI from a topological insulator to a normal semiconductor and eventually a metal having a potential of superconductivity.

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INTRODUCTION Bismuth acts both as an electron donor and acceptor interacting with other elements, thus initiating a refined interplay of electron delocalization and localization that results in a wide range of properties, from an insulator or a semiconductor to a metal or a semimetal. In the bismuthbased compound, bismuth is prone to possess three-center bondings involving both sides of the 6p orbitals and thus allowing for accommodation of up to six nearest neighbors, which is witnessed in the sandwiched layer structures of Bi2Q3 (Q = Se, Te),1−3 known as a topological insulator (TI).3−6 Besides the TI state, interestingly, the Bi2Q3 also possess superconducting properties tuned by high pressure (HP). For © 2013 American Chemical Society

example, Bi2Te3 was reported to transform into a topological superconductor with a highest Tc of 9.5 K at about 13.6 GPa.7,8 The similar unconventional superconducting phases were observed in Bi2Se3 and Bi4Te3.9−11 At higher pressures, Bi2Q3 compounds even can transform to substitutional alloys.12,13 Recently, a giant Rashba splitting of bulk bands has been reported in the ternary BiTeI compound,14,15 arousing renewed interest in bismuth tellurohalides. The BiTeI, which is structurally related to Bi2Q3, crystallizes in a trigonal layer Received: October 2, 2013 Revised: November 14, 2013 Published: November 18, 2013 25677

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Figure 1. Crystal structures of BiTeI: (a) the orthorhombic Pnma structure, (b) “zigzag” Bi−Te ladder structural motifs of the Pnma structure, and (c) the orthorhombic P4/nmm structure. The blue, red, and yellow spheres indicate Bi, Te, and I atoms, respectively.

Table 1. Optimized Structural Parameters for the Predicted Pnma and P4/nmm Structures structure

pressure (GPa)

lattice parameters (Å, deg)

Pnma

10

P4/nmm

30

a = 8.3166, b = 3.9365 c = 10.2002 α = β = γ = 90° a = b = 3.9380 c = 12.2659 α = β = γ = 90°

atomic coordinates (x, y, z) Bi Te I Bi Te I

structure (phase I, space group: P3m1) at ambient pressure and acts as a noncentrosymmetric semiconductor. One might expect that BiTeI possesses similar HP states of Bi2Q3. Excitingly, BiTeI indeed has been predicted to undergo a transition into the TI phase at 1.7−4.1 GPa.16 However, no exact experiment has proven it thus far. Meanwhile, there is a debate on whether or not the TI state can exist in phase I once one considers HP structural phase transitions.17,18 Here, the HP phase transitions and structures of BiTeI have become the key to address these debates. Though the ambient-pressure phase I of BiTeI was extensively studied, the HP phases remain less explored. The only HP research work on phase transformations reported a structural transition at 8−9 GPa by HP X-ray diffraction (XRD)17 and Raman spectroscopy18 experiments, but the structure remain unsolved. Here, we report a joint theoretical and experimental study on investigation of HP structures of BiTeI at 0−30 GPa. The theoretical approach involved the use of our developed calypso methodology for structure prediction,19,20 which is unbiased by any prior known structural information. Our structure prediction revealed two HP structural phase transitions into orthorhombic Pnma and P4/nmm structures, respectively, with increasing pressure. Our subsequent HP XRD experiments confirmed our predicted structures through Rietveld refinements. Our joint theoretical and experimental research was able to establish that pressure tuning of BiTeI modifies significantly the electronic properties from a TI state to a semiconductor and eventually to a metal having a potential of superconductivity.

4c 4c 4c 8j 8j 8j

0.3415 0.1815 0.5148 0.5000 0.0000 0.0000

0.2500 0.2500 0.7500 0.0000 0.5000 0.5000

0.3626 0.0721 0.1583 0.7760 0.9038 0.6091

framework of density functional theory (DFT) using the Perdew−Burke−Ernzerhof (PBE) exchange−correlation functional28 within GGA as implemented in the Vienna ab initio simulation package (VASP) code.29 The projector augmented wave (PAW) pseudopotentials with 6s26p3, 6s26p4, and 6s26p5 valence electrons were adopted for Bi, Te, and I, respectively. A plane wave energy cutoff of 800 eV was employed. The accurate energies and band gaps were calculated using VASP within DFT by employing PBE or the Heyd−Scuseria− Ernzerhof (HSE) functional. The Monkhorst−Pack k grids30 of 10 × 10 × 5 for the P3m1 structure, 5 × 10 × 4 for the Pnma structure, and 10 × 14 × 5 for the P4/nmm structure, respectively, were used to ensure that all of the enthalpy calculations were well converged to better than 1 meV/atom. Phonon calculations were performed based on the supercell approach as implemented in the PHONOPY program,31 where the Hellmann−Feynman forces were calculated by DFT-PBE using VASP. Single crystals of BiTeI were grown by the Bridgman method. The HP angle-dispersive powder XRD experiments were performed at the X17C beamline at the National Synchrotron Light Source (Brookhaven National Laboratory). The sample was loaded in a 120 μm diameter cavity, and a 4:1 mixture of methanol−ethanol was used as the pressuretransmitting medium. Pressure was determined by laser-excited ruby fluorescence. Two-dimensional diffraction rings were collected for pressures up to 30 GPa, with the incident monochromatic X-ray wavelength set to 0.4066 Å. Integrating the diffraction rings yielded XRD patterns as a function of the diffraction angle 2θ.32 All data were collected at room temperature. The HP XRD patterns were fitted by Rietveld profile matching through the GSAS+EXPGUI programs.33,34 For every refinement cycle, the fractional coordinates, scale factors, background parameters, isotropic thermal parameters, profile functions, and lattice parameters were optimized.

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COMPUTATIONAL AND EXPERIMENTAL DETAILS We performed global minimization of the free energy of BiTeI at T = 0 K by merging ab initio total energy calculations and the calypso technique on structural predictions,19 as implemented in the CALYPSO code.20 The CALYPSO method has been successful to correctly predict HP structures for various systems.21−27 The underlying ab initio electronic structure calculations and geometry relaxations were performed in the 25678

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Figure 2. Enthalpy curves (relative to the P3m1 structure) of various structures as a function of pressure in BiTeI. Enthalpies are given per formula unit.

Figure 4. Diffraction profiles of HP phases of BiTeI (a) 15.5 and (b) 22.9 GPa. The solid lines and open circles represent the Rietveld fits and observed data, respectively, and the solid lines at the bottom are the residual intensities. The vertical bars indicate the peak positions.

Figure 3. Selected XRD patterns of BiTeI at various pressures (λ = 0.4066 Å). The background in the XRD patterns was subtracted. The peaks marked with asterisks and solid diamonds are the diffraction peaks for phases II and III, respectively.

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RESULTS AND DISCUSSION Structural predictions for the BiTeI compound were performed using the CALYPSO code with simulation cells containing 1−4 formula units (f.u.) of BiTeI at pressure ranges of 0−50 GPa. We typically generated several hundred structures to ensure the convergence of the global structural searches. The structural searches successfully reproduced the experimental ambientpressure P3m1 structure, validating our method adopted here. At 10 GPa, we predicted an orthorhombic Pnma structure (4f.u./cell, denoted as phase II, Figure 1a) with the lowest enthalpy. At 50 GPa, another orthorhombic structure (space group P4/nmm, 2f.u./cell, denoted as phase III, Figure 1c) was found as the most stable structure. The detailed structural parameters of these two predicted phases are summarized in Table 1. Phase II has a unique structure, where onedimensional (1D) zigzag Bi−Te ladders (Figure 1b) occupy the vertex lattice sites and I atoms stay in the interstitials. Phase

Figure 5. Volumes as a function of pressure for different phases. The symbols are experimental data. The solid lines are theoretical results.

III forms atomic stacking in a Te−Bi−I−I−Bi−Te sequence along its crystallographic c axis, which can be characterized by interconnected cubic building blocks consisting of Te−Bi−I 25679

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Figure 6. (a) The ambient pressure structure of phase I; (b) the band structure of phase I at 4.5 GPa with the inclusion of SOI; (c) pressure dependence of the calculated band gaps of phase I by using the PBE or HSE functional (inset: the total DOS of phase I at 4.5 GPa); (d) pressure dependence of the c/a ratio of lattice parameters in phase I (inset: the electronic charge density distribution projected onto the (0,1,1.26) plane for phase I at 4.5 GPa).

conditions, the diffraction peaks can be indexed to the ambient hexagonal P3m1 structure by the Rietveld refinement. There was no obvious spectral change below 8.8 GPa. At 8.8 GPa, the diffraction pattern suddenly changed, and new peaks emerged, as marked by asterisks, signifying the formation of HP phase II. When the pressure reached 18.9 GPa, new Bragg peaks marked as solid diamonds emerged, indicating that phase II was transformed into phase III. The observed phase transitions are in apparent agreement with our theoretical prediction. After decompression from phase III, we did not observe the XRD patterns of the ambient-pressure phase I. We emphasize that by only relying on the experimental data, the structural solution of these two HP phases is not possible because the XRD peaks are rather weak and broad. However, we have the predicted structures at hand, allowing us to refine the observed XRD data at 15.5 and 22.9 GPa by using the predicted Pnma and P4/nmm structures, respectively. It is remarkably that the uses of the predicted structures gave excellent Rietveld fittings (Figure 4), therefore leading to the unambiguous determination of phases II and III as the predicted Pnma and P4/nmm structures, respectively. Figure 5 shows the experimental and theoretical volume data as a function of pressures for phases I, II, and III. There is excellent agreement between the theory and experiment. It is obvious that the two phase transitions can be characterized by first

atoms to form 3D networks (Figure 1c). In comparison with the Pnma structure, the P4/nmm structure offers nearly perfect atomic arrangement with alternating opposite faces, leading to the densest possible atomic packing. As a result, there is a larger spherical packing efficiency (30.45%) in the P4/nmm structure than that of the Pnma structure (28.56%) at 25 GPa. The enthalpy difference curves for the predicted phases are shown in Figure 2. The energetic stabilities of the newly predicted Pnma (6−23 GPa) and P4/nmm (>23 GPa) structures were confirmed. Due to the heavy atomic masses of Bi, Te, and I, large atomic spin−orbtial interaction (SOI) is expected; therefore, it is necessary to study the SOI effect on the structural transformation. We therefore performed the energy calculations after considering SOI and found that the SOI effect did not change the phase transition sequence but slightly shifted (2−3 GPa) the phase transition pressure. It thus is plausible to perform the structure search and enthalpy calculations without SOI. Dynamical structural stabilities of these two predicted structures were investigated by calculating phonon dispersion curves.35 No imaginary frequency was found for the two structures, suggesting that they are dynamically stable. We subsequently performed the HP XRD experiments on BiTeI up to 30 GPa with pressure steps of 1−2 GPa. Selected diffraction patterns are shown in Figure 3. At ambient 25680

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Figure 7. (a) The ELF plots in the section for Pnma (0 1 0); (c) the ELF plots in the section for P4/nmm (1 0 0); (b) the electronic band structure of Pnma at 10 GPa; (d) the electronic band structure of the P4/nmm phase at 25 GPa.

lattice constants of phase I were optimized, and we found that the c/a ratio reaches the minimum at about 4−5 GPa (Figure 6d). The coincidence of the minimization of the c/a ratio with the band gap closure indicates a close correlation between the c/a ratio and the electronic band gap. The previous structural analysis study14 suggested that the bonding of phase I is semi-ionic and polar along the c-axis. At 4.5 GPa, metallic bonding occurs involving the pz orbitals of Bi and Te due to their band inversion, which leads to charge fluctuation along the c-axis (see inset of Figure 6d). As a result, the c-axis becomes more compressible. The correlation between the c/a ratio and the electronic band gap could be attributed to the fact that a topological quantum phase transition takes place at 4.5 GPa with an enhanced bonding along the c-axis through band crossing. A similar trend of pressure dependence of the c/ a ratio was extracted from the experimental XRD data,17 which validates our theoretical calculations. Our confirmation of the existence of a TI state in phase I helps to clarify the current debate.17,18 For phase II, we found that the structure consists of positively charged (BiTe)+ ladders surrounded by I− ions, as supported by the Bader charge analysis. A charge of

orders accompanying 4 and 7% volume drops at the transitions, respectively. Our theoretical and experimental study revealed that phase I, characterized by a sequence of triangular layers, as shown in Figure 6a, can only exist in a narrow pressure range (0−8.8 GPa). Within this stable pressure range, we have re-evaluated the electronic band structure of phase I and examined the influence of pressure on the electronic band gap, which is a crucial physical parameter for understanding the topological insulating state in BiTeI. The electronic band structures derived from the standard PBE-GGA with the inclusion of SOI are shown in Figure 6b. The GGA calculations predicted essentially zero band gap along the H−A direction at 4.5 GPa (Figure 6b and c), and the band gap reopens beyond 4.5 GPa. Thus, a band gap inversion character was thus confirmed.16 It is well recognized that the Kohn−Sham density functional calculations within the semilocal approximation may fail to describe the band gaps. Thus, we adopted a more precise hybrid functional of HSE36 for band gap calculations. Our HSE calculations yielded similar electronic band gaps and confirmed a full band gap closure at ∼4.5 GPa, as seen by the finite electronic density of states at the Fermi level (inset of Figure 6c). Moreover, the 25681

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*E-mail: [email protected]. Tel: +86-431-85168276. Fax: 86431-85168276. Webpage: http://mym.calypso.cn (Y.M.).

approximately −0.49 qe/atom are stripped off from the Bi atom and transferred to the I atom. This charge transfer stems from the large difference in electronegativity between I (2.66) and Bi (2.02). The electron localization function (ELF) of phase II is illustrated in Figure 7a, clearly showing the rectangle-like nature of Bi−Te ladders possessing weak Bi−Te covalent bonds. Two types of Bi−Te bond lengths were seen. At 10 GPa, one type of bond is 2.90 Å in length, whereas the other one is 2.91 Å, both of which are evidently close to the ideal Bi−Te covalent bond (∼2.82 Å). Phase II can thus be described as a partially ionic phase and is a semiconductor (Figure 7b). Its band gap tends to monotonically decrease with increasing pressure. Besides, the SOI has a significant impact on the band gap of phase II. Turning on SOI, the band gap decreases drastically. For example, the SOI reduces the band gap from 1.12 to 0.53 eV at 10 GPa. In phase III, the Bi, Te, and I atoms are ordered to share the orthorhombic lattice sites. There is no covalent bonding any more, and a clear charge transfer from Bi to Te and I is evident, as deduced from Bader analysis. Further, we did not find any charge localization in the interstitial areas of the lattice from the ELF plot in Figure 7c. Phase III can be well-recognized as a typical ionic structure. The band structure of phase III reveals a metallic character (Figure 7d). The electronic bands near the Fermi level along the R−Z and X−Γ directions are nearly flat, which gives rise to large electronic density of states near the Fermi level. The corresponding confined conduction electrons near the Fermi level possess large effective mass with their group velocities approaching zero, while the electronic bands along the Z−A, A−M, and M−Γ directions steeply cross the Fermi level, revealing the itinerant-like electrons with high conduction velocity. These electronic features apparently satisfy the “flat band−steep band” conditions, which have been suggested to favor the occurrence of superconductivity.37−41

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the China 973 Program (2011CB808200), Natural Science Foundation of China (NSFC) under 51202084, 11274136, 11104104, 11025418, and 91022029, NSFC awarded Research Fellowship for International Young Scientists under Grant No. 11250110051, the 2012 Changjiang Scholars Program of China, Changjiang Scholar, and the Innovative Research Team in University (IRT1132). The authors also acknowledge the High Performance Computing Center of Jilin University for supercomputer time. The work at BNL was also supported by the U.S. Department of Energy through Contract DE-AC0298CH10886. The use of the X17C beamline was partially supported by COMPRES (the Consortium for Materials Properties Research in Earth Sciences) under NSF Cooperative Agreement EAR 11-57758.

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(1) Rauhi, H.; Geickt, R.; Kohleri, H.; Nucker, N.; Lehner, N. Generalised Phonon Density of States of The Layer Compounds Bi2Se3, Bi2Te3, Sb2Te3 and Bi2(Te0.5Se0.5)3, (Bi0.5Sb0.5)2Te3. J. Phys. C: Solid State Phys. 1981, 14, 2705−2712. (2) Frangis, N.; Kuypers, S.; Manolikas, C.; Tendeloo, G. V.; Landuy, J. V.; Amelinck, S. Continuous Series of One-Dimensional Structures in Compounds Based on M2X3 (M = Sb, Bi; X = Se, Te). J. Solid. State. Chem. 1990, 84, 314−334. (3) Chen, Y. L.; Analytis, J. G.; Chu, J. H.; Liu, Z. K.; Mo, S. K.; Qi, X. L.; Zhang, H. J.; Lu, D. H.; Dai, X.; Fang, Z.; et al. Experimental Realization of a Three-Dimensional Topological Insulator, Bi2Te3. Science 2009, 325, 178−181. (4) Xia, Y.; Qian, D.; Hsieh, D.; Wray, L.; Pal, A.; Lin, H.; Bansil, A.; Grauer, D.; Hor, Y. S.; Cava, R. J.; et al. Observation of a Large-Gap Topological-Insulator Class with a Single Dirac Cone on the Surface. Nat. Phys. 2009, 5, 398−402. (5) Hsieh, D.; Xia, Y.; Qian, D.; Wray, L.; Meier, F.; Dil, J.; Osterwalder, J.; Patthey, L.; Fedorov, A.; Lin, H.; et al. Observation of Time-Reversal-Protected Single-Dirac-Cone Topological-Insulator States in Bi2Te3 and Sb2Te3. Phys. Rev. Lett. 2009, 103, 146401. (6) Zhang, H.; Liu, C.-X.; Qi, X.-L.; Dai, X.; Fang, Z.; Zhang, S.-C. Topological Insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a Single Dirac Cone on the Surface. Nat. Phys. 2009, 5, 438−442. (7) Zhang, C.; Sun, L.; Chen, Z.; Zhou, X.; Wu, Q.; Yi, W.; Guo, J.; Dong, X.; Zhao, Z. Phase Diagram of a Pressure-Induced Superconducting State and Its Relation to the Hall Coefficient of Bi2Te3 Single Crystals. Phys. Rev. B 2011, 83, 140504. (8) Zhang, J. L.; Zhang, S. J.; Weng, H. M.; Zhang, W.; Yang, L. X.; Liu, Q. Q.; Feng, S. M.; Wang, X. C.; Yu, R. C.; Cao, L. Z.; et al. Pressure-Induced Superconductivity in Topological Parent Compound Bi2Te3. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 24−28. (9) Kirshenbaum, K.; Syers, P. S.; Hope, A. P.; Butch, N. P.; Jeffries, J. R.; Weir, S. T.; Hamlin, J. J.; Maple, M. B.; Vohra, Y. K.; Paglione, J. Pressure-Induced Unconventional Superconducting Phase in the Topological Insulator Bi2Se3. Phys. Rev. Lett. 2013, 111, 087001. (10) Jeffries, J. R.; Lima Sharma, A. L.; Sharma, P. A.; Spataru, C. D.; McCall, S. K.; Sugar, J. D.; Weir, S. T.; Vohra, Y. K. Distinct Superconducting States in the Pressure-Induced Metallic Structures of the Nominal Semimetal Bi4Te3. Phys. Rev. B 2011, 84, 092505. (11) Zhang, C.; Sun, L.; Chen, Z.; Zhou, X.; Wu, Q.; Yi, W.; Guo, J.; Dong, X.; Zhao, Z. Phase Diagram of a Pressure-Induced Superconducting State and Its Relation to the Hall Coefficient of Bi2Te3 Single Crystals. Phys. Rev. B 2011, 83, 140504.

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CONCLUSION In summary, we have explored the HP structural phase transitions of BiTeI at 0−30 GPa by a joint theoretical and experimental study. Using the CALYPSO technique on structure prediction, we predicted two new HP phases having the orthorhombic Pnma (8.8−18.9 GPa) and P4/nmm structures (>18.9 GPa), as confirmed by our subsequent HP XRD experiments. We have examined the TI possibility of phase I. An inverted band gap and a correlated inverted c/a ratio of phase I at ∼4.5 GPa were found and can serve as key parameters for identifying the TI state. We uncovered that both phases II and III are ionic. Our work established that pressure enables the formation of a TI, a normal semiconductor, and eventually a metal having a superconducting potential in BiTeI. The current study represents a step forward in understanding the HP behaviors of BiTeI.

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ASSOCIATED CONTENT

S Supporting Information *

The phonon dispersion curves for the Pnma and P4/nmm structures under high pressure. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Tel: +86-431-85168276. Fax: 86431-85168276 (Y.W). 25682

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