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Correction: 1 December 007 www.sciencemg.org/cgi/content/full/318/5857/1750/dc1 Supporting Online Mteril for Mott Trnsition in VO Reveled by Infrred Spectroscopy nd Nno- Imging M. M. Qzilbsh,* M.

1 Correction: 1 December Supporting Online Mteril for Mott Trnsition in VO Reveled by Infrred Spectroscopy nd Nno- Imging M. M. Qzilbsh,* M. Brehm, B. G. Che, P.-C. Ho, G. O. Andreev, B. J. Kim, S. J. Yun, A. V. Bltsky, M. B. Mple, F. Keilmnn, H. T. Kim, D. N. Bsov *To whom correspondence should be ddressed. -mil: mumtz@physics.ucsd.edu This PDF file includes: Mterils nd Methods SOM Text Tble S1 References Published 14 December 007, Science 318, DOI: /science Correction: Yellow highlighting nd red borders hve been removed.

2 Correction: 1 December 007 Supporting Online Mteril Mterils nd Methods Smples nd mesurements The VO films used in this study re 100 nm thick nd were grown on 101 oriented Al O 3 spphire substrtes. Detils of film growth nd chrcteriztion re given in Ref.S i. We chose thin films of VO for infrred mesurements in the phse trnsition regime insted of single crystls becuse the crystls frcture when tken cross the phse trnsition nd thereby crete problems of reproducibility nd significnt uncertinties in the quntittive results in the trnsition regime. Dt obtined for high qulity films grown on lttice mtched substrtes re free of the bove complictions nd thus enble studies of the intrinsic properties of VO. The dt nd results presented in this report were obtined while heting up the smple. The dt nd results for the cooling runs show the sme behvior s obtined for the heting runs for ll the mesurements but in reverse order. There is lso downwrd shift in T c by 8 K on cooling compred to the T c on heting due to hysteresis resulting from the first order nture of the phse trnsition see Ref. S i. The resistnce of the film plotted in Fig. 3 ws mesured by stndrd four-probe method. The technique of scnning ner-field infrred microscopy S ii,s iii,s iv is described in the following section. The fr-field complex opticl constnts or dielectric function

3 Correction: 1 December 007 = + i were obtined vi combintion of ellipsometry in the spectrl 1 rnge cm -1 nd ner-norml incidence reflectnce in the spectrl rnge cm -1 see below for detils. We note here tht in generl the complex conductivity = + i of mteril is relted to its complex opticl dielectric constnt 1 by 4πi = 1+. The effective medium theory MT ws employed to obtin the opticl constnts of the metllic puddles in the insultor-to-metl trnsition regime S v,s vi. The detils of the MT nd the extended Drude nlysis S vii re given in subsequent sections. Scnning ner-field infrred microscopy. Scttering scnning ner-field infrred microscopy ws performed with custom Atomic Force Microscope AFM using Ptcoted silicon tips in the tpping mode S ii,s iii. The = 930 cm -1 nd = 175 cm -1 infrred frequencies were provided by CO lser nd CO lser respectively. The pseudo-heterodyne scheme with second hrmonic demodultion ws employed to isolte nd detect the ner-field signl in mplitude nd phse S iv. The sptil resolution of the ner-field infrred probe is bout 10-0 nm nd is set by the rdius of curvture of the tip. The ner-field penetrtes bout 0 nm into the VO film nd is bulk probe of the insultor-to-metl trnsition compred to the scnning tunneling microscope, for exmple, which is surfce sensitive probe. The ner-field interction between the tip nd the smple is described by the dipole model. Within this model, the complex scttering signl t the second hrmonic of the tpping frequency is function of the opticl constnts of the tip nd the smple S ii,s iii. The scttering mplitude is higher for metllic regions which hve lrge negtive rel

4 Correction: 1 December 007 prt nd lrge positive imginry prt of the opticl constnts t = 930 cm -1 nd = 175 cm -1. Insultors like monoclinic VO yield lower scttering mplitudes becuse of the negligibly smll imginry prt of the opticl constnts nd positive rel prt somewht higher thn unity 1 [ = 930 cm -1 ] 5 nd 1 [ = 175 cm -1 ] 6 in insulting VO. This difference in scttering mplitudes llows us to imge the insultorto-metl trnsition in VO. The ner-field scttering mplitude imges obtined with = 175 cm -1 re similr to those shown in Fig. which were obtined with = 930 cm -1. The dipole model provides good quntittive description of the ner-field infrred scttering mplitudes ner the onset of the insultor-to-metl trnsition where the metllic puddles re seprted by the insulting host. The model lso cptures the observed nerfield contrst t higher frctions of the metllic regions but will need to be refined to quntify the continuously incresing scttering mplitude from the expnding metllic regions. However, this does not impct the determintion of the insulting nd metllic frctions from ner-field imges. We note tht repeted ner-field scns in the insultor-to-metl trnsition regime over the sme smple re nd t fixed temperture show nerly identicl ptterns of metllic puddles in the insulting host. This indictes tht the effect of possible dynmic fluctutions on the sttic ptterns is smll. The metllic islnds re most likely seeded nd controlled by stress t the interfce, defects, grin boundries etc. nd this is resonble scenrio for relistic smples. These nucletion centers would led to sttic nd reproducible ptterns of inhomogeneity t given temperture. Therefore, the frction of the sttic metllic nd insulting regions obtined from ner-field imges cn be used to

5 Correction: 1 December 007 interpret fr-field dt within the effective medium theory described in subsequent section. Fr-field infrred spectroscopy. Spectroscopic ellipsometry provides the rel nd imginry prts of the ellipsometric coefficients t ech mesured frequency S viii. This enbles us to obtin the opticl constnts of the VO film without recourse to Krmers- Kronig nlysis which breks down in the insultor-to-metl trnsition region of VO becuse of inhomogeneity nd phse-coexistence. Provided the incident wvelength is lrge compred to the size of the nno-scle metllic puddles, the inhomogeneous system cn be described by n effective dielectric function S v,s vi. This is certinly expected to be the cse for long wvelengths in the fr- nd mid-infrred regime between 40 cm -1 nd 5000 cm -1. In ccord with the Bruggemn effective medium theory MT S v,s vi, simple mixing of the dielectric functions of the insulting phse nd rutile metllic phse T = 360 K in the mid-infrred to visible regime cm -1 provides good description of the dt. Therefore, it is pproprite to ssign n effective dielectric function to the inhomogeneous, phse-seprted regime of VO even when the wvelength becomes comprble to the size of the metllic puddles. The effective dielectric function of the inhomogeneous, phse-seprted regime of VO is thus obtined vi the stndrd nlysis of the combined ellipsometric nd reflectnce dt bsed on two-lyer model of VO film with n effective dielectric function on spphire substrte S viii. The contributions of VO phonons to were modeled by Lorentzin oscilltors nd subsequently the phonon contributions were

6 Correction: 1 December 007 subtrcted so tht the electronic contribution to the opticl constnts could be unmbiguously presented nd nlyzed. ffective medium theory. A simple weighting of opticl constnts of the insulting phse nd of the metllic phse T = 360 K spectrum within the effective medium theory MT produces good description of the fr-field infrred dt ner the onset of the insultor-to-metl trnsition t frequencies between 3000 cm -1 nd 0000 cm -1. Devitions from this description become progressively stronger t longer wvelengths 40 to 3000 cm -1, regime where the MT formlism is expected to be most directly pplicble S v,s vi. This implies tht the opticl constnts of the metllic puddles when these first pper t the onset of the insultor-to-metl trnsition re different from the opticl constnts of the rutile metl T = 360 K. Therefore, we use the MT to extrct the opticl constnts of the metllic puddles. Within the Bruggemn effective medium theory S v,s vi, the effective complex opticl constnts of two-component inhomogeneous system re given by: b f + 1 f = 0 1 q 1 q + + b q q 1 In this eqution, nd b re the complex opticl constnts of the metllic nd insulting phses respectively, f nd 1 f re the volume frctions of the metllic nd insulting phses respectively, nd q is the depolriztion fctor tht depends on the shpe of the components which is inferred from ner-field imges. This fctor is tken to be ssuming nerly sphericl metllic regions t low concentrtions of the newborn metllic stte becuse their lterl dimensions re less thn the film thickness

7 Correction: 1 December 007 nd the out-of-plne dimension is ssumed to be similr to the lterl dimensions. The depolriztion fctor continuously increses to 0.5 which is pproprite for thin flt disks t higher concentrtions of metllic clusters s their lterl dimensions exceed the out-ofplne dimension which is limited by the thickness of the film S vi. The volume frctions of the insulting nd metllic phses re obtined directly from the ner-field imges. The fr-field opticl constnts of the insulting phse nd the inhomogeneous trnsition regime hve lso been mesured see Fig. 1. The opticl constnts of the insulting phse re ssumed to be independent of temperture in this nlysis. This is supported by the ner-field imges which show little vrition of the scttering intensity from the insulting regions with incresing temperture. Since,, nd f re known wheres the rnge of q is constrined bsed on the knowledge of the metllic cluster size nd film thickness, the eqution cn be solved to obtin the opticl constnts of the metllic regions, nd hence the complex conductivity whose rel prt is plotted in Fig.3B. Vlues of f nd q t relevnt tempertures re listed in Tble S1. Uncertinties in the mgnitude of q do ffect the behvior of spectr t the lowest frequencies close to the experimentl cut-off of the dt. Specificlly, these uncertinties do not rule out non-monotonic form of the conductivity 1 : response consistent with Drude dynmics modified by locliztion. Irrespective of some mbiguity in the form of the conductivity in the limit of 0, the oscilltor strength of this low-energy mode is continuously decresing s the trnsition to the insultor is produced, signling n increse of the opticl effective mss. b b

8 Correction: 1 December 007 Interfcil scttering nd locliztion will become importnt when the size of the metllic puddles is comprble to or less thn the intrinsic men free pth of the chrge crriers within these puddles. Our estimte of the men free pth bsed on the scttering rte dt in Fig.3c is of the order of few nnometers. Thus the smllest puddles we cn detect limited by the 0 nm sptil resolution of our probe re still in the regime where the men free pth is shorter thn the sptil extent of metllic regions. Therefore, we believe interfcil scttering nd locliztion re unlikely to ffect chrge dynmics in the metllic puddles. However, we cnnot rule out signtures of locliztion below our experimentl cut-off frequency. xtended Drude formlism. The following equtions of the extended Drude formlism Svii completely describe the evlution of the scttering rte 1/τ nd the mss enhncement fctor m*/m b from the rel nd imginry prts of the opticl conductivity of the metllic regions 1 i + = : π τ p + = 4 * 1 π p m b m + = 3 The plsm frequency p = 000 cm -1 is nerly constnt within ten percent for the metllic sttes nd is obtined vi the prtil sum rule: d c p =

9 Correction: 1 December 007 Here, the frequency cut-off c = cm -1 is chosen to exclude contributions from higher-lying opticl trnsitions. The plsm frequency is relted to the crrier density n by the following expression: 4πne p = 5 m b Since the experimentlly determined plsm frequency is nerly constnt for the metllic sttes, we infer tht the crrier density is lso nerly constnt for the evolving metllic regions provided tht the bnd mss m b of the crriers does not chnge drsticlly.

10 Correction: 1 December 007 T K f q Tble S1. The vlues of the filling frction f nd depolriztion fctor q used to obtin the opticl constnts of the metllic regions t selected tempertures within the frmework of the MT formlism q.1. S i. B. G. Che et l., lectrochem. Solid-Stte Lett. 9, C S ii. B. Knoll, F. Keilmnn, Nture 399, S iii. F. Keilmnn, R. Hillenbrnd, Phil. Trns. R. Soc. Lond. A 36, S iv. N. Ocelic, A. Huber, R. Hillenbrnd, App. Phys. Lett. 89, S v. K. D. Cummings, J. C. Grlnd, D. B. Tnner, Phys. Rev. B 30, S vi. G. L. Crr, S. Perkowitz, D. B. Tnner, in Infrred nd millimeter wves, K. J. Button, d. Acdemic Press, Orlndo, 1985, vol. 13. S vii. D. N. Bsov, T. Timusk, Rev. Mod. Phys. 77, S viii. H. G. Tompkins,. A. Irene, d., Hndbook of llipsometry Willim Andrew Publishing/Springer Verlg 005.

Department of Electrical and Computer Engineering, Cornell University. ECE 4070: Physics of Semiconductors and Nanostructures.

Department of Electrical and Computer Engineering, Cornell University. ECE 4070: Physics of Semiconductors and Nanostructures. Deprtment of Electricl nd Computer Engineering, Cornell University ECE 4070: Physics of Semiconductors nd Nnostructures Spring 2014 Exm 2 ` April 17, 2014 INSTRUCTIONS: Every problem must be done in the