Supporting InformationShakhvorostov, et al. 10.1073/pnas.0812942106SI TextX-Ray Diffraction of Eutectic GeSb Under Pressure. Fig. S1 showscomparison of experimental and calculated X-ray diffractionspectra in eutectic GeSb under different pressures (with ran-domly placed Ge atoms substituting on the Sb sites): Peierls’distorted (Pd) at ambient pressure (see Results and Discussion),simple cubic (sc) at 12.8 GPa, and ‘‘host–guest’’ (hg) at 17.4 GPa.The low-pressure structure (Pd) is layered rhombohedral, withlattice parameters a � 4.240 Å and c � 11.424 Å to start (for pureSb, a � 4.308 Å and c � 11.274 Å; space group R3m). ThePeierls’ distortion is removed with pressure as witnessed by thecollapse of the Bragg peaks in Fig. 1C. The high-pressurehost–guest structure has a modified 4D space group I�4/mcm(00�)0000, where the host takes on I4/mcm symmetry with8 atoms in the unit cell occupying 8h positions and the guest takeson I4/mmm symmetry with 2 atoms in the 2a positions. X-rayspectra (at 30.55 keV; � � 0.4066 nm) were collected underisotropic compression at the high-energy, high-intensity super-conducting-wiggler X-ray beam line X17C of the NationalSynchrotron Light Source at Brookhaven National Laboratory,using symmetric piston-cylinder diamond anvil cell (DAC) with400-�m culet anvils. For the X-ray spectroscopy of pure Sb underpressure see ref. 1.

Raman Spectroscopy of Eutectic GeSb Under Pressure. Free-standingfilm composition was determined by Rutherford back-scatteringto be typically as Ge(12.2 � 0.5%):Sb(86.0 � 0.5%), withresidual (1.8 � 0.5%) amounts of Ar present. A commercialRenishaw Raman spectrometer (Model 2000) was used forpressure determination and Raman measurements, see Materialsand Methods. Fig. S2A shows integrated relative reflectivity andRaman shift corresponding to the low-pressure cycle. It showsthe change in optical reflectivity at 650 nm wavelength, consis-tent with closing of the gap at the Fermi energy EF, as also seenin the optical data under the temperature-sweep in Fig. 1. Fig.S2B shows Raman spectra measured during compression–decompression cycle of initially amorphous Ge-Sb to maximumpressure of 29 GPa show crystallization at slightly below �2 GPa.Increasing pressure to �12.7 GPa introduced shifts and broad-ening consistent with the incommensurate structure observed inX-ray diffraction (see Fig. 1C). Further compression narrows thespectra again, with the upshift to higher frequencies. Amorphousphase has 4 Raman active modes at 120, 142, 151, and 207 cm�1.The crystalline phase is Raman active at 121, 155, 168, and 276cm�1. There is seen in Fig. 1 a large amount of hysteresis inemerging from the host–guest structure upon decompression.The hysteresis means that the amorphous phase is not returnedto at ambient pressure. For the Raman spectroscopy of pure Sbunder pressure see ref. 2.

Ab Initio Molecular Dynamics Simulation Studies. The ab initiomolecular dynamics simulation studies presented in this paperwere performed using the Car–Parrinello method (3). A finitebasis set of plane waves is used to expand the Kohn–Shamorbitals of Kohn–Sham density functional theory (KS-DFT) (4)at an energy cutoff of Ecut � 35Ry such that (�2/2me)g2 � 35Ry. Because the exact KS-density functional is unknown, theB-LYP approximation was adopted (5, 6). The core electronswere eliminated by using norm-conserving nonlocal pseudopo-tentials of the Martins–Troullier type (7). Rather large systemswere examined (�192 atoms), and the computations wereperformed at the �-point of the Brillion zone. In the Car–

Parrinello method, the dynamics of the nuclei on the ground-state electronic surface given by the approximate KS-DFT isgenerated by the simultaneous propagation of a fictitious clas-sical dynamics associated with the plane wave expansion coef-ficients that acts to keep the functional approximately mini-mized, along with the nuclear dynamics. Given an appropriatechoice of parameters, an adiabatic separation is achieved andcorrect results generated. Nose–Hoover chain equations ofmotion (8) were used to drive both the nuclear and the plane-wave expansion coefficient time evolution, as opposed to New-ton’s equations because of the semimetallic nature of the systemsstudied. Note, the structure predicted by the Born–Oppenhei-mer approximation is expected to be reasonably accurate be-cause the low lying excited state surfaces in metals are approx-imately parallel. Finally, the standard Car–Parrinello methodwas further modified through the use of Euler exponential splinetechniques (9, 10) to achieve high scaling on large-scale parallelcomputers as described in ref. 11 without loss of numericalaccuracy.

To validate the simulation studies, comparisons were madeboth to experimental and theoretical studies in the literature aswell as our own experimental datasets. As can be seen in Fig. S4and Fig. S5, the functional does an excellent job predicting theexperimental structure factors for both amorphous and crystal-line materials. There is a 3% error in the location of the second(short-distance) peak and a more significant difference betweenthe shapes of the theoretical and experimental first (long-range)peaks.

We anticipate a larger uncertainty in the amorphous phaseowing to the finite system size and finite cooling rate used toquench the system. The optical conductivity, �(�) was evaluatedin the Born–Oppenheimer approximation using the Kubo–Greenwood (KG) formula (12) and the nuclear configurationsgenerated as described above. However, a grid of 4 � 4 � 4k-points was used to achieve convergence of the KS excited-statespectrum. Note, because the KS states are used in the evaluationof the KG expression for the conductivity, herein, even with theexact functional, the results would be inaccurate (13). Accurateresults would require the use of many-body techniques (14–19),whose computational cost is prohibitive for the systems ofinterest (TDDFT based approaches (13), although promisingwhen used with current functionals, suffer from self-interactionerrors that deter their ability to describe the bulk systems ofinterest.) Nonetheless, we expect the trends generated by KGformula to be correct. That is, the general phenomenon of gapinduced stabilization is contained in the KS spectrum but theresponse is off in magnitude. Indeed, the bare KS spectrum isknown to underestimate gaps and thus to overestimate themetallic behavior of some systems. It should be noted that theKG/KS formalism has been shown to lead to important insightsin many physical systems of interest (20, 21).

Some of the key structural aspects of the volume amorphiza-tion process can be seen in the movie of the AIMD simulationin Movie S1. At the beginning of the simulation, the structure isclearly layered, atoms having 3 short bonds to nearest neighborsin the same layer. As the simulation proceeds, interlayer bondsare seen to form, resulting in the presence of 4-coordinatedatoms (Fig. 2B, main text). Eventually, the layering motif isseverely weakened by the 4-coordinated sites as the systemapproaches the amorphous state.

Given the localized nature of the structural changes from 3- to4-coordination during amorphization, it is essential to search for

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signs of localized or virtual bound electronic states which mightbe associated with these localized structural centers. The pres-ence of such electronic localized states might indicate an alter-native way in which the electronic energy is lowered duringamorphization and suggest a hypothetical alternative drivingforce for the process.

A measure of the localization of each of the electronic statescan be obtained from the participation ratio

PREi � �V � drEi; r4 �1 , [s1]

where the wave function is normalized, �dr(Ei;r)2 � 1, andV is the volume of the simulation cell. The PR is computed in realspace.

The integral over the fourth power favors a wave functionhaving a large value in a small region of space, i.e., a localizedwave function, and because this is in the denominator of the PR,the smaller the PR, the more localized the state . For purelyextended modes, or completely delocalized states, PR � 1. Forhighly localized states, the PR will be a small numerical value onthe order of PR � 1/NS

TOT, where NSTOT is the total number of

electronic states in the system. The PR is calculated for theelectronic states of several frames along the time axis during theamorphization of the GeSb crystal using the pressure quenchtechnique, as shown in Fig. 4.

There is �5% drop in the average PR value of the amorphizedframes compared with the reference crystal value, a relatively

insignificant change. The value of the PR is steady across the 266highest occupied states as can be seen from the Inset of Fig. S3, and no significant localization of states (or lowering of the PRvalue) occurs for the states closest to the Fermi level, throughoutthe pressure induced amorphization run. These results indicatethat the drop in conductivity associated with the same frames ofthe pressure anneal (shown in Fig. 3B of the main article) is notdue to the localization of states resulting from site-specificorbital rehybridization. The information obtained from this testfor state localization goes to support the gap-driven scenariodeveloped in this article. It cannot be explained by a hypotheticalalternative picture in which bound-state resonances, or localizedstates, associated with the structurally rehybridized centers playa significant role as the driving force.

Similar structural and electronic changes as reported here forGeSb are observed in other chalcogenic materials, such as pureSb (although it is known to crystallize explosively near roomtemperature (23). Simulated pressure quenches on pure Sb alsoshow evidence for a gap-induced metal-insulator transition. Thesemimetallic crystal configuration subjected to volume quenchbecomes fully insulating upon relaxing to the amorphous struc-ture, where again, a noticeable percentage of antimony atomsbecome 4-coordinated in the equatorially vacant trigonal bipy-ramidal arrangement. Thermal quenches on this material alsoshow the opening of the gap, but need to be explored with longerquenching rates than we have currently accessed.

1. Degtyareva O, McMahon MI, Nelmes RJ (2004) High-pressure structural studies ofgroup-15 elements. High Pressure Res 24:319–356.

2. Degtyareva O, Struzhkin VV, Hemley RJ (2006) High-pressure Raman spectroscopy ofantimony: As-type, incommensurate host-guest, and bcc phases. Solid State Commun141:164–167.

3. Car R, Parrinello M (1985) unified approach for molecular dynamics and density-functional theory. Phys Rev Lett 55:2471–2474.

4. Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlationeffects. Phys Rev 140:A1133.

5. Beck, AD (1988) Density-functional exchange-energy approximation with correct as-symptotic behavior. Phys Rev A 38:3098.

6. Lee C, Yang W, Parr RG (1988) Development of the Calle–Salvetti correlation energyinto a functional of the electron density. Phys Rev B 37:785.

7. Troullier N, Martins JL (1991) Efficient pseudopotentials for plane wave calculations.Phys Rev B 43:1993.

8. Martyna GJ, Tuckerman ME, Klein ML (1992) Nose–Hoover chains: The canonicalensemble via continuous dynamics. J Chem Phys 97:2635.

9. Yarne DA, Tuckerman ME, Martyna GJ (2001) A dual length scale method for plane-wave-based, simulation studies of chemical systems modeled using mixed ab initio/empirical force field descriptions. J Chem Phys 115:3531.

10. Lee HS, Tuckerman ME, Martyna GJ (2005) Efficient evaluation of nonlocal pseudopo-tentials via Euler exponential spline interpolation. Chem Phys Chem 6:1827.

11. Bohm E, et al. (2008) Fine grained parallelization of the Car–Parrinello ab-initiomolecular dynamics method on the IBM BlueGene/L supercomputer. IBM J Res Dev52:159–179.

12. Mahan GD (2000) Many-Particle Physics (Plenum, New York).13. Runge E, Gross EKU (1984) Density-functional theory of time-dependent systems. Phys

Rev Lett 52:997.14. Hedin L, Lundqvist S (1969) Solid State Physics, eds Seitz F, Turnbull D, Erhenreich H

(Academic, New York), Vol 23, p 1.15. Hybertsen MS, Louie SG (1985) 1st-Principles theory of quasiparticles–Calculation of

band-gaps in semiconductors and insulators. Phys Rev Lett 55:1418.16. Hybertsen MS, Louie SG (1986) Electron correlation in semiconductors and insulators:

Band gaps and quasiparticle energies. Phys Rev B 34:5390.17. Strinati G (1984) Effects of dynamical screening on resonances at inner-shell thresholds

in semiconductors. Phys Rev B 29:5718.18. Rohlfing M, Louie SG (1998) Excitonic effects and the optical absorption spectrum of

hydrogenated Si clusters. Phys Rev Lett 80:3320.19. Grossman JC, Rohlfing M, Mitas L, Louie SG, Cohen ML (2001) High accuracy many-body

calculational approaches for excitations in molecules. Phys Rev Lett 86:472–475.20. Galli G, Martin RM, Car R, Parrinello M (1989) Carbon. The nature of the liquid state.

Phys Rev Lett 63:988–991.21. Galli G, Martin RM, Car R, Parrinello M (1989) Structural and electronic properties of

amorphous carbon. Phys Rev Lett 62:555–558.22. Bell RJ, Dean P (1971) Atomic vibrations in vitreous silica. Discuss Faraday Soc 50:55–61.23. Wickersham CE, Bajor G, Greene JE (1978) Impulse stimulated ‘explosive’ crystallization

of sputter deposited amorphous (In,Ga) Sb films. Solid State Commun 27:17–20.

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2θ(°)

XR

D in

tens

ity (

arbi

trary

uni

ts) experiment

ambient pressure

P = 12.8 GPa

P = 17.4 GPa

simulation

242220181614121086

Pd

sc

hg

Fig. S1. A comparison of experimental and calculated X-ray diffraction spectra in eutectic GeSb under different pressures.

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Pressure (GPa)048121620242420161284

Pda

Pdsc

hg

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an s

hift

(cm

-1)

100

150

200

Ram

an in

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max

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compression decompression

Reflectivity

Raman shift (cm-1) 400

250

100

2.6

01.1

1.50

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(GPa

)

100%

85%

a

b

Fig. S2. Raman optical spectroscopy of eutectic GeSb alloy films under pressure.

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0 1 2 3 4 5 6 7t (ps)

0.5

0.6

0.7

0.8

0.9<

PR >

50 100 150 200 250NS

0.50.60.70.80.9

PR

CrystalABCD

Crystal

A B C D

Fig. S3. Average participation ratio �PR� for several frames during the pressure quench. The Inset shows the PR for the 266 highest occupied states, labeledby state number NS, of the first 5 frames. Labeling A–D in Inset refers to the frames illustrated in main image.

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2θ(deg)20181614121086

simulation

XR

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Fig. S4. A comparison of experimental and simulation structure factors for a crystalline phase.

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Fig. S5. A comparison of experimental and simulation structure factors for amorphous phase.

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Movie S1 (MPG)

Movie S1. Movie of AIMD run illustrating volume amorphization of Ge0.850.15.

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