VOLUME 50, +UMBER j7 PHYSICAL REVIEW LETTERS 25 APRIL 1983

A.yproaches for Reducing the Insulator-Metal Transition Pressure in Hydrogen

A. E. Carlsson and N. W. Ashcroft
I.abo~atoxy of Atomic and Solid State Physics and the Materials Science Cente~, Cornell University,
Ithaca, Nese Yowl 14853
(Received 7 February 1983)
Two possible techniques for reducing the external pressure required to induce the in-
sulator-metal transition in solid hydrogen are described. One uses impurities to lower
the energy of the metallic phase relative to that of the insulating phase. The other utilizes
a negative pressure induced in the insulating phase by electron-hole pairs, created either
with laser irradiation or pulsed synchrotron sources.
PACS numbers: 71.30.+h, 61.70.Rj, 64.70.Kb

The quest to synthesize a high-pressure metal- The effect of impurities on the relative stability
lic phase of hydrogen is motivated both by the of the two phases of hydrogen under discussion
fundamental interest of this "simplest" metal, is conveniently discussed in terms of their asso-
and by some of its predicted useful properties, ciated screening functions. The impurity screen-
such as a very high superconducting transition'' ing energy in the metallic phase is expected to
T, . Unfortunately, the corresponding predicted be larger than that in the insul. ating phase, be-
insulator-metal transition pressures, varying cause of the nonvanishing Fermi-level density of
from 100 to 1000 GPa in recent estimates, ' are states in the former. To obtain an estimate of
mostly above the range of pressure currently the magnitude of the energy difference, we con-
available in a static diamond-cell apparatus. For sider a trivalent impurity modeled by an empty-
this and other reasons chemical techniques for core pseudopotential (a valence of three is chosen
simulating the dissociative effect of external because we consider this to be the approximate
pressure have been suggested, such as the use l. imit of appl. icability of the linear screening theo-
of a proposed artificial. compound LiH, F in the ry to be used). Thus V;~ = -(4mZe'/q') cosqr,
place of pure hydrogen. In this Letter we specu- .
for some core radius x, The impurity screening
late on the applicability of two as yet untried energy is then given to second order in t/'; by
techniques which may also simulate the effects
E 111Ct, H1S

of external pressure. Both are based on the gen-

'„,
S(T

eral. observation that at least part of the energy =-e'/m J dq[1 —c (q)jcos'qr, ,
favoring insulating phases of elements and com-
pounds can be linked to the presence of an energy
where c „;„, are the metal. and insulator static
We take c~«(q) = 1+k,'/q'
gap between f illed and empty electron states. It
' dielectric functions.
and'
follows that processes which locally reduce the
gap (such as impurity or defect production), or c,„(q ) = 1+ (c, —1)/[1+ c,(q'/k. ,')],
reduce the &ffects of the gap (such as electron- where k, is the Thomas-Fermi wave vector, k;„,'
hole pair creation), should favor the metall. ic =k, 'c, /(c, —1) (both phases are taken to have the
phase. same density for ease of comparison), and c, is
(a) ImPurity stabilization. — It has been known the insulator's static dielectric constant. It is
for some time that impurities can have a destabi- obtained approximately from the band-structure
lizing effect on semiconducting phases of solids. calculations of Ref. 10, by use of the formula"
For example, a concentration of donor impurities ',
c, =1+ &v~'/8, where E, is the average direct
as low as O. leuc can cause a reduction in cer- gap and co~ is the plasma f requency. At x, = 1.75,
tain shear elastic constants of Si and Ge.' Fur-
5%%uc

a density roughly corresponding to the highest

thermore, it has been observed' that the equilib- pressures currently used in diamond-cell experi-
rium 2x1 reconstructed Si surface, which is ments, and with xp 1 1 a u corresponding to"
semiconducting, can be destabilized by the addi- Al, we have c, = 7 and F. , "-E',
"' =-5 eV. At
tion of 0.01-0.05 monolayers of Te. In addition, this density, the calculated energy difference"
we note that impurities can stabilize supercon- between the semiconducting phases is roughly 1
ducting compounds which are not stable in their eV. Thus for a 10'%%uo concentration of impurities,
pure forms, such as'615 Nb, Nb. about half of this energy difference can be elim-

1983 The American Physical Society 1305

VOLUME 50, NUMBER 17 PHYSICAL REVIEW LETTERS 25 APRIL 1983

inated, and correspondingly the structural transi- it is then possible to tune the Fermi level to
tion pressure is reduced substantially. coincide with peaks in the density of states. Thus
Existing band-theoretic techniques are not suffi- the molecul. ar phase itself can, in principle,
ciently accurate or fl. exible to point to the optimal support a superconducting transition. In this
impurity for stabilizing the metallic phase. How- regard, we note that the superconductivity in
ever, we regard transition-metal impurities to semiconductors with only -0.02 carriers per
be good choices, for two reasons: (1) Transition- atom has been both predicted" and observed. "
metal surfaces are known to effectivel. y disso- (b) Electron hole-pair creation. —
It is known
ciate hydrogen molecul. es. A transition-metal that the laser annealing process, involving in-
impurity in a hydrogen matrix might then be tense irradiation of semiconductors with photons
thought of as a small region of transition-metal at energies above the band-gap energy, can re-
surface in contact with the surrounding hydrogen sult in large-scale structural rearrangements. "
atoms. (2) Some transition metals are known to We propose that similar techniques may also be
form very hydrogen-rich compounds, such as used to help synthesize the metallic phase of
YH, . In these compounds the hydrogen atoms hydrogen by reducing the pressure required to
general. ly are found in a metallic crystal struc- compress the molecular phase. For the photons
ture, and characteristic hydrogen-associated to reach the hydrogen and be absorbed, the band

"
bands are found below the transition-metal. d
Their superconducting properties are
,
gap F, of the molecular hydrogen must be small-
"
bands. er than the gapE, of the diamond cell itself.
"
dissimilar to those predicted for metallic hydro-
gen because the density of transition-metal atoms "
This is not the case at zero pressure, where E,
=14.5 eV (Ref. 18) and E, "=5.4 eV. However,
is large. Accordingly, the electrons they con- Z, " will drop much more rapidly than E, "with
tribute raise the Fermi level above the hydrogen pressure, because of the large compressibility
bands into a gap between these and the transi- of the hydrogen. Using the calculations of Ref.
tion-metal. d bands, or into the d bands them- ",
10 for the volume dependence of E, the mol-
selves. If it were possible to synthesize a com- ecular hydrogen equation of state of Ref. 13, and
pound with a lower relative density of transition- the pressure dependence of F., " reported in
metal atoms, then the hydrogen atoms coul. d Ref. 19, we fi.nd coincidence in the band gap,
maintain their metallic crystal structure with " ,"
i.e. , F, =F. = 5.0 eV, at P = 30 QP a.
the Fermi level staying inside the hydrogen- The usual. picture of the transition to the metal-
associated bands. Such a compound might be l. ic crystal structure in hydrogen involves a sub-
created by first impl. anting a solid H, matrix stantial reduction of the band gap, followed by a
with transition-metal ions, and subsequently structural. transition at a pressure P„. It is not
applying external pressure. Al. ternatively, the known whether the structural transition occurs
physical mixing of a hydride with pure hydrogen before or after the bands overlap in the diatom-
might be attempted. Both of these techniques ically ordered structure (at a, pressure Pb„say).
have the desirable feature that they produce large The presence of a concentration x of electron-
numbers of defects, and these are also expected hole pairs is expected to shift the equation of
to favor the metallic phase by the screening- state of the molecular phase by an amount equal
energy arguments presented above. to p' "= x(dE /dA-„), where 0„ is the volume
Even if the impurities do not stabilize the per atom. Since F, drops with compression,
metallic crystal. structures, they are expected p' "(0. Using the E, H(Q„) values calculated in
to contribute carriers to the mol. ecul. ar phase, Ref. 10, we find a maximum value of dE, /0„
provided the band gap is not too large. For elec- equal to approximately 700 GPa, at the band-
tropositive impurities such as Cs, it is very like- overlap transition.
ly that these wil. l. be conduction-band electrons. This means that if it is possible to obtain a 5/0
Two of the features responsible for the predicted concentration of electron-hole pairs, an equiva-
high T, of the metal. lic phase, ' namely, the high lent excess pressure of roughly 35 GPa could be
characteristic (Debye) frequency and the large obtained. The resulting effect on the pressure
electron-phonon coupling, are present in the required to induce the structural. transition de-
molecular phase as well. If a sufficiently large
„) „
pends on whether P is greater or less than Pb, .
impurity concentration can be incorporated,
then the Fermi-level density of states in the de-
If P „
Pb„ then P is essential. ly unaffected by
the presence of the electron-hole pairs, since
fected molecular phase may also be high, and P' " vanishes along the trajectory leading from
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VOLUME 50, NUMBER 17 PHYSICAL REVIEW LETTERS 25 APRiL 198$

the band-overlap transition to the metallic crys- for the structural transition to take place, nei-
tal structure. However, if Pb, &P„, then the ther time being known accurately. However,
external pressure required to compress the we observe that room-temperature recombina-
diatomic phase to the volume at which the struc- tion, times in semiconductors range from 10 '
tural transition occurs is reduced by an amount '
to 10 sec, '4 and that martensitic phase trans-
iP' "i. Furthermore, the energy of the molecu- formations have been observed to nucleate in
'
lar phase at a given volume is raised relative to
that of the metallic phase by the electron-hole "
times as short as 10 sec, with subsequent
growth at a rate of 10' cm/sec.
pairs. Therefore we expect the structural transi- A second possibility is the use of pulsed radia-
tion to occur at a pressure l. ess than P„— iP' "i. tion from a synchrotron radiation source. As-
It might be argued that as soon as the transition suming an absorption length of 1 p, m, an external
to the monatomic crystal structure occurs, the pressure sufficient to reduce the band gap to 1
el. ectron-hole pairs will recombine, and if P eV, and using a favorable electron-hole recom-
„
&P the solid will immediately revert to the
molecular crystal. structure. Here we argue the
bination lifetime of 10 ' sec, we find that the
incident power intensity required to maintain an
importance of kinetic considerations. It has been electron-hole pair density of 5% is of order 10'
known for some time that nonequil. ibrium metal- W/cm'. It should be noted in this regard that the
lic phases of certain III-V semiconductors can heat supplied to the sample through the use of

even at zero external pressure. ""

be metastable at liquid-nitrogen temperatures,
Further-
these techniques is expected to lower the struc-
tural transition pressure, simply because the
more, the insulating phase may nucleate and metallic crystal structure has greater entropy
actually grow less rapidly than the metallic than the diatomic one. This effect has been ob-
phase. Such an effect is seen, for instance, at served in the semiconductor diamond to P-tin
the o. -P transition in Sn (Ref. 22) and even possi- structural transitions, in which the transition
bly at the metal-insulator transition in VO„ pressure is typically reduced by roughly 20% at
which shows an asymmetry in the growth rates the melting temperature. '

heating experiments. "

of the metallic and insulating phases in dynamic
If nucleation is centered
We conclude by observing that the feasibility of
the techniques described above depends crucially
around defects, then the arguments presented on parameters whose values we are unable to
above on screening energies would suggest that, calculate precisely. For this reason, it might
other factors being equal, the nucleation of the be useful to develop the techniques suggested in
metallic phase is favored. Finally, if it is possi- systems whose transition pressures are current-
ble to obtain pressures greater than P„ in the ly in the experimentally attainable range. One
laboratory, but nucleation and growth of the such system is I„which is believed~ to have a
metallic phase are insufficiently fast, then it second-order band-overlap transition at 18 Gpa,
can be accelerated by the presence of electron- and a subsequent first-order transition at 21 GPa, .
hole pairs. Br, and Cl, are expected to have similar transi-
Achieving a sufficiently high density of electron- tions at higher pressures, which are still in the
hole pairs in hydrogen wil. l be a difficult experi- experimentally accessible range. Another usef ul
mental challenge, but a possible approach is to precursor experiment is the investigation of ef-
use a very short burst of very high intensity fects of the dopant impurity concentration on the
radiation, as in the usual. semiconductor laser diamond to P-tin transition pressures in semi-
annealing process. For high enough external. conductors, these ranging from roughly 0 to 25
pressures, the hydrogen band gap will be of a GPa. Although the effects have generally been
scale that a readily available laser in the 2-eV assumed to be small, it may be possible to ob-
range can be used. At lower pressures, a fre- tain observable effects with the use of modern
quency doubler together with a focusing arrange- ion implantation techniques, which allow the
ment to increase the incident power density is
immediately suggested. Alternatively, a color- rium value."
dopant concentration to greatly exceed its equilib-

center laser might match the appropriate inter- We appreciate useful conversations with
band absorption edge. The effectiveness of this I. Silvera and K. C. Hass. This work was partly
approach hinges on the ratio of the lifetime of the supported by the National Aeronautics and Space
electrons and holes produced to the time required Administration, under Grant No. NAG 2-159,

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VOLUME 50, NUMBER 17 PHYSICAL REVIEW LETTERS 25 APRIL 1983

which is gratefull. y acknow'. edged. ' M. L. Cohen, Phys. Rev. 134, A511 (1964).
R. A. Hein, J. W. Gibson, R. Mazelski, R. C. Miller,
and J. K. Hulm, Phys. Rev. Lett. 12, 320 (1964).
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'N. W. Ashcroft, Phys. Rev. Lett. 21, 1748 (1968). New York, 1980).
T. Schneider and E. Stoll, Physica (Utrecht) 55, 702 ' A. Gedanken, B. Raz, and J. Jortner, J. Chem.
(1971). Phys. 59, 2752 (1973).
3For a compi1ation of such estimates, see, E. (6st- ' K. Syassen, Phys. Rev. B 25, 6548 (1982). We note
gaard, Phys. Lett. 45A, 371 (1973). that in Syassen's experiment, the strain in the diamond
4J. J. Gilman, Phys. Rev. Lett. 26, 546 (1971). is not hydrostatic, and the measured absorption may
5J. A. Van Vechten, Phys. Rev. 170, 773 (1968). not necessarily corr espond to the bulk diamond band
R. W. Keyes, in Solid State Physics: Advances in gap. However, Syassen's results do give the depen-
Research and Applications, edited by F. Seitz, D. Turn- dence of the diamond-cell-apparatus absorption edge
bull, and H. Ehrenreich {Academic, New York, 1967), on the pressure applied to the sample, which is the
Vol. 20, p. 37. It is not possible to get the doping con- relevant quantity here.
centration high enough to make the elastic constants P. B. McWhan, G. W. Hull, Jr. , T. R. McDonald,
vanish and destabilize the solid. and E. Gregory, Science 147, 1441 {1965).
D. E. Eastman, J.
Vac. Sci. Technol. 17, 492 (1980). 'H. E. Bommel, A. J. Darnell, W. F. Libby, and
86. R. Stewart, L. R. Newkirk, and F. A. Valencia, B. R. Tittman, Science 139, 1301 (1963).
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~J. C. Inkson, J. Phys. C 5, 2599 (1972). Soc. 23, 183 (1957).
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(1977). W. F. Fallmann, Phys. Status Solidi (a) 68, K101 (1981).
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(Academic, New York, 1972), Chap. 2. We have taken (Wiley, New York, 1981), Appendix H.
the dimensionless constant A in Phillips's Eq. (2.20) to 2~J. W. Christian, The Theory of Transformations in
be equal to unity. Metals and Alloys (Pergamon, New York, 1965),
' N. W. Ashcroft, Phys. Lett. 23, 48 {1966). Chap. 21.
'~S. Chakravarty, J. H. Rose, D. Wood, and N. W. ~6K. Takemura, S. Minomura, O. Shimomura, and
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