Hole-lattice Coupling and Photo-induced Insulator-Metal Transition in VO$_2$

0.41 MB·English

by  Xun Yuan

Hole-lattice Coupling and Photo-induced Insulator-Metal Transition in VO
2
Xun Yuan,1 Wenqing Zhang,2,1 and Peihong Zhang3
1State Key Laboratory of High Performance Ceramics and Superfine Microstructures,
Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China
2School of Chemistry & Chemical Engineering, and Sate Key Laboratory
of Coordination Chemistry, Nanjing University, Jiangsu 210093, China
3Department of Physics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
(Dated: January 29, 2013)
3 Photo-induced insulator-metal transition in VO2 and the related transient and multi-timescale
1 structuraldynamics uponphotoexcitation are explained within a unifiedframework. Holes created
0
byphotoexcitationweakentheV-VbondsandeventuallybreakV-VdimersintheM1 phaseofVO2
2
when the laser fluence reaches a critical value. The breaking of the V-V bonds in turn leads to an

n immediateelectronicphasetransitionfromaninsulatingtoametallicstatewhilethecrystallattice
a remainsmonoclinicinshape. Thecouplingbetweenexcitedelectronsandthe6.0THzphononmode
J is found to be responsible for the observed zig-zag motion of V atoms upon photoexcitation and is

6 consistent with coherent phonon experiments.
2

] Despite decades of intensive research, the physics be- multi-timescale structural evolution ranging from subpi-
i
c hind the metal-insulator transition in VO2 at about cosecondtonanosecondswasuncovered. Thefirststepof
s 340 K[1] remains a subject of unabated debate. The the structural change shortly after photoexcitation was
-
l electronic phase transition is accompanied by a seem- identified as a rapid (subpicosecond) separation of the
r
t ingly “simultaneous” structural change from a low tem- initially paired V atoms (i.e., V-V dimers) in the M
m 1
perature monoclinic (M ) to a high temperature rutile phase VO . It is natural to associate this subpicosec-
1 2
t. (R) structure. It is likely that the phase transition in- ond displacements of V atoms with the observed ultra-
a
volves multiple intermediate states that occur at dis- fast ( 100 fs) photo-induced insulator-metal transition.
m ∼
tinct timescales. Unfortunately, the delicate and tran- Unfortunately, there is no direct evidence that supports
-
sientinterplaybetweentheatomicandelectronicdegrees this connection.
d
n of freedom, which determines the dynamics and the ki- In this letter, results from first-principles electronic
o netic pathway of the phase transition in VO , cannot
2 structurecalculationsareusedto establisha theorythat
c be easily accessed within time averaged or equilibrium
is able to explain the ultrafast photo-induced insulator-
[
measurements. Therefore, recent advances in ultrafast metal transition and the the multi-timescale structural
1 spectroscopyhavebroughtmuchexcitementandinspired
dynamics associated with photoexcitations. The strong
v a new wave of investigations [2–12] with unprecedented
coupling between the lattice and the excited holes is re-
5
time resolution and accuracy.
1 sponsible for the observed rapid separation of V-V pairs
2 These new experiments reveal a great deal of details after photoexcitation. The atomic motion is found to be
6 on the ultrafast dynamics and intermediate states asso- primarilyassociatedwitha339cm−1 (10.2THz)phonon
.
1 ciated with the phase transition, offering rare insights mode, instead of the much discussed 6.0 THz ( 200
0 into the intriguing physics of VO . For example, an ul- cm−1) mode. The separation of the V-V pair in∼-turn
2
3 trafast ( 100 fs) photo-induced insulator-metal transi- leads to an immediate electronic phase transition. al-
1 ∼
tion was observed [2–9]. The observed response cannot though the crystal lattice remains monoclinic in shape.
:
v be explained by simply considering the effects of the ex- The longer timescale ( a few picoseconds) structural
i ∼
X cited carriers, and a structurally driven phase transition dynamics observed in experiment is associated with a
mechanism was proposed[4]. The structural change was phonon mode at 200 cm−1 ( 6.0 THz) often observed
r ∼
a ascribed to coherently generated optical phonons at ul- incoherentphononexperiments[4,5,8,11]. Thisphonon
trashort time scales. Indeed, a coherent phonon mode modeinvolveszig-zagmovementsofVatomsandisfound
withfrequenciesatabout6.0THz ( 200cm−1) isoften to couple primarily with the excited electrons. However,
∼
observed [4, 5, 8, 11]. Other coherent phonons at about the excitationofthis phononmode is notresponsible for
4.5THz( 150cm−1)[11]and6.75THz( 225cm−1)[4] the subpicosecond photo-induced insulator-metal transi-
∼ ∼
have also been observed. However,the precise role these tion. Instead,itis justanimportantsteptowardthe full
coherentlygeneratedphononsplayandthemechanismof structural phase transition from the monoclinic to the
their generation upon photoexcitation are still not well rutile phase.
understood.
Allcalculationsarecarriedoutusingtheprojectoraug-
More recently, a 4D visualization of the transitional mentedwavemethod[14]implementedinVASP[15],and
structures of VO after photoexcitation was carried out the Perdew-Burke-Ernzerhof (PBE) functional is used.
2
usingafemtosecondelectrondiffractiontechnique[10]. A ItisworthmentioningthatalthoughthePBEfunctional
2
0.9 Whereas the V-V separation is nearly unchanged upon
electron doping, hole doping results in a gradual elonga-
0.6 tion of the V-V bond length below a critical level of
∼
eV) 0.3 0.15 holes per VO2 formula unit, above which a sudden
y ( jump in V-V separation is observed. The existence of a
g
er 0 criticalholelevelandthesuddenjumpinV-Vseparation
n
E
may be related to the requiredcritical excitation fluence
-0.3
in experiments [5, 10]. Therefore, we conclude that the
-0.6 observedrapidV-Vseparationuponphotoexcitationisa
Γ Y C Z Γ A E Z D B Γ
result of a strong lattice-hole coupling in this system.
In order to relate our results to the observed multi-
FIG. 1: (Color online) Calculated band structure of the M1 timescale atomic motion after photoexcitations [10], we
phase VO2 using theoretically relaxed crystal structure.
compare the experimentally observed atomic displace-
ments[Figs.3(a)and3(b)]attwodistincttimescalesand
the directions of the calculated initial forces [Figs. 3(c)
is not able to produce an insulating ground state for the
and 3(d)] on atoms with electron or hole doping with a
M phaseVO iftheexperimentalstructureisused,upon
1 2 “doping” level (carrier density) of 0.15 per VO formula
structuralrelaxation,asmallbandgap( 0.13eV)actu- 2
∼ unit. The calculation starts with the relaxed M1 struc-
ally develops, as shown in Fig 1. The use of the theoret-
ture before introducing carriers into the system. Car-
ically relaxed structure also gives a satisfactory descrip-
riers are then introduced, the forces on atoms are then
tionofthelatticedynamicsoftheM phaseVO . TableI
1 2 calculated. Upon hole doping, the calculated forces on
compares the calculated zone-center phonon frequencies
V atoms are directed primarily along the direction of V-
withexperiment. Theagreementbetweentheoryandex-
V pairs [the two V atoms in the middle Fig. 3(c)] and
periment is very good.
they tend to elongate the V-V bonds. This result co-
Photoexcitationsnaturallyintroducehotelectronsand
incides nicely with the observed [10] subpicosecond dis-
holesintothesystem. However,asmentionedearlier,the
placement of V atoms upon photoexcitation of VO as
2
observed optical response upon photoexcitation cannot
shown in Fig. 3(a). Electron doping, on the other hand,
be explained by simply considering the effects of these
results in forces on V atoms that are nearly parallel to
excited electrons/holes [4], and the transient lattice dy-
the lattice c direction and zig-zag along the lattice a di-
namics must be taken into account. In order to sepa-
rection,as shownin Fig. 3(d). This resultcompareswell
rate the effects of the excited electrons and holes on the
with the observed subnanosecond atomic displacements
transient lattice dynamics of the system, in particular,
asshowninFig.3(b). Therefore,ourresultsclearlyillus-
the observedrapidseparationofV-Vpairs,weintroduce
tratethatthe subpicosecondV-Vseparationcomes from
electronsandholeintothesysteminourcalculationsep-
the coupling between lattice and holes, whereas the sub-
arately. Our calculations start with a fully relaxed M
1 nanosecond structural dynamics should be attributed to
structure. Additional electrons or holes are then intro-
the electron-latticecoupling andis relatedto the zig-zag
duced into the system, and the structures are fully re-
motion of the V atoms.
laxed for a given electron (or hole) “doping” level while
This disparate structural responses to electrons and
keeping the monoclinic lattice vectors.
Figure 2 illustrates the drastically different effects of
electrons and holes on the calculated V-V separation:
TABLE I: Calculated zone-center phonon modes of the M1
phase VO2. Zone-center phonons are grouped into Raman
active (Ag or Bg) and infrared active (Au or Bu) modes.
Experimental results are taken from Ref.[16] (Raman) and
2.80
Å) hole doping Ref.[17] (infrared). The projections η of the Ag modes are
e ( discussed in the text.
c
stan 2.70 Ag Bg Au Bu
di Cal. Exp. η Cal. Exp. Cal. Exp. Cal. Exp.
mer 2.60 152 149 0.54 212 ... ... ... ... ...
V di electron doping 197 199 2.72 231 259 187 189 ... ...
− 224 225 0.96 247 265 265 270 253 227
V
2.50
331 313 0.59 374 395 304 310 295 285
0 0.1 0.2 0.3 339 339 1.58 432 444 333 340 324 324
doping concentration (1/f.u.) 389 392 0.82 447 453 415 392 374 355
508 503 0.79 495 489 508 505 490 478
FIG. 2: (Color online) Relaxed V-V dimer distance after in- 605 618 0.26 593 595 560 600 572 530
troducing holes or electrons to thesystem. 675 670 0.11 758 830 721 710 721 700
3
FIG. 3: (Color online) Atomic displacements upon photoexcitation: comparison between theory and experiment. Left panels:
theobservedsubpicosecond(a)andsubnanosecond(b)movementofVatomsintheM1 phaseVO2 uponphotoexcitation[10].
Middle panels: calculated initial forces on V atoms with additional holes (c) and electrons (d). Right panels: atomic displace-
ment (schematic) of the 339 cm−1 (e) and the 197 cm−1 phonon modes (f). The directions of the displacements of V atoms
are shown for comparison. The V and O atoms are shown with large (dark blue) and small (red) balls, respectively. Atoms
after displacement are shown with light colors.
holes can be understood by investigating the bonding and N is total number of atoms. We double the size of
character of the valence band maximum (VBM) and the the unit cell of the R phase so that there is one-to-one
conduction band minimum (CBM) states as shown in correspondencebetweenatomsinbothphases. Asitwas
Fig. 4. The VBM states are primarily of V-V bonding suggested experimentally [10], changes in internal struc-
character[Fig.4(a)]. Therefore,removingelectronsfrom ture after photoexcitations happen much faster than the
the VBM states (adding holes) results in a weakening change in the shape of the lattice. Therefore, in order
of V-V bonds. When this weakening reaches a critical toanalyzetheinitialstructuralevolution,weusethelat-
point, the V-V dimerization is no longer intact. This ticevectorsoftheM phase. Symmetryrequiresthatthe
1
explains the sudden jump in the V-V separation when displacement vector ∆R has the A symmetry. There-
g
hole level reaches a critical value of about 0.15 holes per fore,this displacementvectorcanonlybeprojectedonto
VO formula unit as shown in Fig. 2. This critical hole
2
density may also be related to the critical lase fluence in
experiment. TheCBMstates,ontheotherhand,involve
an antibonding character of the shortest V-O bonds, as
showninFig.4(b). TheseshortV-Obondsarerelatedto
the zig-zagarrangementofthe V atomsalongthe lattice
a direction as shown in Fig. 3. Therefore, adding elec-
trons to the antibonding V-O states tends to alleviate
the zig-zag arrangement of the V atoms. These results
areconsistentwith the force analysisshowninFigs. 3(c)
and 3(d); they also agree with the measured atomic dis-
placement as shown in Figs. 3(a) and 3(d).
Although the transient structural dynamics involved
inthephoto-inducedinsulator-metaltransitionofVO is
2
verydifferentfromtheconventionaldescriptionoflattice
dynamics in terms of phonons, it is still instructive to
map the structural change onto polarization vectors of
relevant phonon modes. Here we define a displacement
vector from the M to the R phase:
1
FIG. 4: (Color online) Charge density of the VBM (a) and
∆R R~ R R~ M1 ; i=1,2,...,N, (1) theCBM(b)statesonthe(-110)planeoftheM1 phase. The
i i
≡{ − } shortestV-OandV-Vbondsareapproximatelyonthe(-110)
where R~ is the position of the ith atom in the unit cell plane and are shown with dashed lines.
i
4
Raman active A phonons. The overlap between a Ra- 0.9
g
man active phonon i and the displacement vector ∆R is 0.6
calculated via 0.3
1 0
where mj is the ηmia=ssXojf t√hemjjt~ehija·t∆omR,,~eij is jth atom(2ic) Energy (eV) -- 0000....6963 ((aa))
component of the polarization vector of the ith phonon
0.3
mode. The result of this projection of the atomic dis-
placement is shown in Table I. 0
Interestingly, two phonon modes with wave numbers -0.3 ((bb))
197 cm−1 ( 6.0 THz) and 339 cm−1 ( 10.2 THz) -0.6
∼ ∼ Γ Y C Z Γ A E Z D B Γ
show the greatest projection amplitudes. Polarization
vectors of these two phonon modes are also shown in
FIG. 5: (Color online) (a) Calculated band structure using a
Figs. 3(e) and 3(f), and the vibration patterns of these distortedM1structureinwhichatomsaredisplacedaccording
two phonon modes also match nicely with the observed to the projection of the atomic displacement from the M1 to
firsttwostagesofthestructuralevolutionafterphotoex- theRphaseontothe339cm−1 phononmode. (b)Calculated
citations [10]. band structure using the crystal structure relaxed with 0.15
Combining this result with the analysis of forces ex- holes per VO2 formula. The Fermi level is indicated by the
dashed horizontal line at E=0.
erted onindividual atoms upon “opticaldoping” of elec-
trons and holes, we have clearly identified the active
phonon modes involved in the photo-induced insulator-
calculation is then carried out using the distorted struc-
metaltransitionofVO . Inaddition,ourresultindicates
2
that the strong coupling between the 339 cm−1 (10.2 ture. In the second calculation, we introduce 0.15 holes
per VO formula unit into the system. The internal co-
THz) phonon and hole states is responsible for the rapid 2
ordinates are then relaxed while the lattice vectors are
V-V separation upon photoexcitation, whereas the cou-
pling between the 197 cm−1 ( 6.0 THz) phonon and fixed. A band structure calculation is then carried out
∼ using the relaxed structure with the presence of holes.
electrons explains the zag-zig motion of V atoms at a
Since photo-induced ultrafast insulator-metal transition
longertimescale. The 6.0 THz phononmode is often ob-
occurs long before a full conversion of the lattice geom-
served in coherent phonon experiment. However, the V-
etry from monoclinic to rutile, our calculations are car-
V separation happens at a much faster timescale [10] so
ried out using the lattice vectors of the M phase. The
that the corresponding phonon mode (10.2 THz) cannot 1
resultingbandstructuresareshowninFig.5. Bothband
be observedin coherentphonon experiment. In addition
structures clearly show a metallic behavior beyond what
tothesetwophononmodes,thereareseveralothermodes
is expected for a simple semiconductor with small struc-
that have large projectionamplitudes. In particular,the
224 cm−1 ( 6.72 THz) phonon mode may be related to turaldistortions: Thereisamassivereorganizationofthe
∼ electronic states are the V-V bonds break. These results
the6.75THzphononmodesobservedincoherentphonon
clearly illustrate the much discussed strong coupling be-
experiments [4].
tweenthelatticeandelectronicdegreesoffreedominthis
There are still puzzles that need to be resolved before
system. However, not all lattice degrees of freedom are
wecanfullyuntangletheexperimentalfindings. Asmen-
coupled equally with electrons. It is the phonon mode
tionedabove,itisverylikelythattheultrafast( 100fs)
∼ involvingthe separationof V-V dimer that has the most
photo-induced insulator-metal transition and the rapid
importantimpactonthe underlyingelectronicstructure.
V-Vseparationuponphotoexcitationarecloselyrelated,
It is the rapid separation of V-V pairs (i.e., breaking of
and uncovering their cause-effect relationship is the last
theV-Vdimers),whichitselfisadirectresultofastrong
step toward a full understanding of the physics of the
phonon-holecoupling,thatisresponsiblefortheobserved
phasetransitioninVO . Sofarourresultsareconsistent
2
ultrafast photo-induced insulator-metal transition.
with experiments, but we have not addressed the issue
regarding the possible connection between the observed Theprocessofultrafastphoto-inducedinsulator-metal
rapid V-V separation and the ultrafast photo-induced transition in VO can now be summarized as follows:
2
insulator-metal transition. photoexcitation results in a depletion of electrons in the
To this end, we have carried out two additional cal- bonding states which are critical for V-V dimerization
culations. In the first calculation, the ideal M crystal and the insulating behavior of the M phase. When this
1 1
structure is displaced according to the projection of the weakeningof the V-V bonds reachesa criticalpoint (un-
displacement vector ∆R in Eq. (1) onto the 339 cm−1 der critical laser fluence), the V-V bond breaks. This
(10.2 THz) phonon mode. This procedure naturally re- bond breaking (V-V separation) is a result of a strong
sults in a separation of V-V dimers. A band structure lattice-hole coupling in this system. The breaking of the
5
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This work is supported in part by NSFC under
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grant numbers 11234012 and 50821064, by Shanghai
fer, M. A. El Khakani, and F. A. Hegmann,
Key Basic Research Project (3109DJ1400201), and by Phys. Rev.B 85, 155120 (2012).
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