New Insights into the Diverse Electronic Phases of a Novel Vanadium Dioxide Polymorph: A Terahertz Spectroscopy Study

A remarkable feature of vanadium dioxide is that it can be synthesized in a number of polymorphs. The conductivity mechanism in the metastable layered polymorph VO2(B) thin films has been investigated by terahertz time-domain spectroscopy (THz-TDS). In VO2(B), a critical temperature of 240 K marks the appearance of a non-zero Drude term in the observed complex conductivity, indicating the evolution from a pure insulating state towards a metallic state. In contrast, the THz conductivity of the well-known VO2(M1) is well fitted only by a modification of the Drude model to include backscattering. We also identified two different THz conductivity regimes separated by temperature in these two polymorphs. The electronic phase diagram is constructed, revealing that the width and onset of the metal-insulator transition in the B phase develop differently from the M1 phase.

M ulti-polymorphic materials -compounds that can assume numerous, different crystal symmetries with the same chemical composition, show great promise as future electronic materials. This is because their structural diversity can give rise to a variety of electrical and optical responses that can be tuned for technological applications such as optical switches, batteries, solar cells, optical filters, spintronic devices, memory devices etc [1][2][3][4] . Vanadium dioxide is one of the most popular polymorphic materials that can assume several crystallographic structures [5][6][7] . Amongst the several stable and metastable VO 2 polymorphs, monoclinic VO 2 (B) and monoclinic VO 2 (M1) are particularly interesting, as these materials display more than thousand-fold changes in conductivity with temperature 8,9 . Understanding polymorphism in vanadium dioxide has tremendous practical importance in the design and control of electro-optic materials for future technologies.
The metastable monoclinic VO 2 (B) adopts a structure derived from V 2 O 5 and belongs to the space group C2/m (12) compared to the well-known VO 2 (M1), which takes up the space group P2 1 /c (14) [10][11][12] . The crystal structure of VO 2 (B) is illustrated in Figure 1(a). A salient structural difference between the monoclinic phases in VO 2 (B) and VO 2 (M1) is that VO 2 (B) has a smaller b inter-axial angle 11 (b vo2(B)~1 06:6 0 and b vo2(M1)~1 22:6 0 ) which may play an important role in the formation of defects and impurities in epitaxial growth of films. While metalinsulator transition (MIT) in VO 2 (M1) is associated with a corresponding reversible structural phase transition from a room temperature monoclinic to a high temperature tetragonal phase 9,13-16 , currently there is little understanding of the nature of the semimetal-to-insulator transition in VO 2 (B) which remains monoclinic with MIT 10 . It is also interesting to compare these polymorphs in context of V-V pairing mechanism, which strongly influences the conductivity pathways. VO 2 (M1) undergoes V-V dimerization in the monoclinic insulating phase with very short V-V bonds (,2.65 Å ) creating a large dimer-to-dimer distance (,3.12 Å ) 14 . This alternate long and short V-V separation inhibits conductivity. But when VO 2 (M1) undergoes a phase transition to the rutile structure all the V-V distances become the same (,2.87 Å ) and do not allow the formation of dimers 14 . In contrast, one doesn't see a significant change of V-V distance in the B phase 10 . One could plainly see that, even though these VO 2  are evidently distinct and a comparative study between these polymorphs is aptly motivated by an objective to get a better understanding on the correlation between MIT and structural phase transition. Furthermore, while a lot of progress has been made towards understanding the physics of metal-insulator transition in VO 2 (M1) by optical techniques [17][18][19][20][21][22][23][24][25][26][27][28] , no parallel efforts has been made so far to understand the mechanism in VO 2 (B). From a practical applications point of view, one of the key attractions of VO 2 (B) is that it is conducting at room temperature, compared to VO 2 (M1) which is insulating and may hold technological merits over VO 2 (M1) for devices at room temperature operation 8 . The drastic changes in conductivity with temperature for these VO 2 polymorphs are accompanied by a corresponding change in optical response, thereby making terahertz (THz) spectroscopy a viable technique to probe the nature of electronic properties in these systems. There have been several reports where THz spectroscopy has been employed to measure conductivity in VO 2 (M1) polymorphs 25,26,[29][30][31] . Although metal-insulator transition materials are generally characterized by standard four-point probe method, it provides information only about dc conductivities which can be distorted by surface defects due to electrode contacts 32 . On the other hand, THz spectroscopy is a contactless probe, providing frequency-dependent complex conductivity in the far-infrared region. Terahertz time-domain spectroscopy (THz-TDS) allows the amplitude and phase of the THz pulse to be obtained, without the need for Kramers-Kronig analysis in the extraction of complex conductivity [33][34][35] . Moreover, compared to traditional steadystate dc conductivity measurements which is limited to macroscopic conductivity paths, THz spectroscopy explores electron dynamics over nanometer length scales, possibly revealing conducting phases in this scale undetectable by long-range transport measurements 29 . Indeed, THz spectroscopy has been used to make comprehensive optical investigations in a host of materials rich in exotic conducting phases including graphene 36,37 , toplogical insulators 34,38 , superconductors 39-41 , oxide semiconductors 32,33 , quantum-confined semiconductors 42 , and percolating systems 43 .
In this paper we report a systematic investigation of THz complex conductivities of 60-nm thick VO 2 (B) thin films deposited on (001) SrLaAlO 4 (SLAO) substrate. There has been no literature report on the complex conductivities of this system. In our operational THz frequency range (0.3-2.3 THz), there are no observable optical phonon resonances of VO 2 (B), and hence it is possible to observe the conductivity response that arises solely from free carriers. These are then compared with that of 60-nm VO 2 (M1) thin films deposited on SLAO substrate. This study conclusively demonstrates clear signatures of different electronic orders in these two vanadium dioxide polymorphs.

Results
Sample growth, structural and transport characterization. The XRD spectra of VO 2 (B) thin film on SLAO is shown in Figure 1(b). We clearly see that the XRD reflections of VO 2 (B) are perfectly aligned with the substrate (azimuthal angle, x 5 0). This means that our film is highly oriented. Temperature-dependent electrical transport measurements are carried out in Physical Property Measurement system (Quantum Design) utilizing a four probe geometry. As shown in Figure 1(c), the resistivity of VO 2 (B) films grown on SLAO substrate undergo four orders-of-magnitude change (from 2 3 10 25 V-m to 0.35 V-m) in resistivity as the temperature changes from 400 K to 160 K, which is consistent with a previous report on VO 2 (B) nanorods 8 . There is a weak thermal hysteresis at low temperatures below 240 K.
THz-TDS. The transmittance, T(v) of the VO 2 film is defined as the ratio between complex electric field of the THz pulse from sample (film 1 substrate)Ẽ s (v) and reference (bare substrate)Ẽ r (v). In Figure 2(b) the frequency-dependent and temperature-dependent transmittance amplitudes through the VO 2 (B) film are shown. In the insulating state, at temperatures lower than the transition temperature, we find that the transmittance amplitude is close to unity. For VO 2 (B) film, as the temperature of the sample approaches ,240 K, there is THz absorption and a clear trend of increasing absorption at higher temperatures. The spectral shape is almost frequency independent for all runs. The frequency dependent complex refractive indexñ~nzik can be extracted from the experimental transmittance T(v) by fitting the formula 36,44 whereñ andñ sub are the complex refractive indices of VO 2 film and SLAO substrate, respectively, d is film thickness and DL is the thickness  difference between sample and reference substrates and c is the speed of light in vacuum. This above equation takes into account the multiple internal reflections inside the film. The extracted complex refractive indexñ is then used to calculate the complex optical conductivitys~s 1 zis 2 where s 1 (v) 5 2nkve 0 and s 2 (v) 5 (e ' 2 n 2 1 k 2 )ve 0 where e 0 is the permittivity of free space and e ' is the high frequency dielectric constant. For VO 2 (B), e ' is an unknown quantity and is initially set to 1. After the determination of complex conductivities, e ' will be used as a temperature-dependent fitting parameter in the conductivity models as discussed in the following sub-sections. On the other hand, we used e ' 5 9 based on previous studies for determining conductivities in VO 2 (M1) 45,46 .
Complex conductivity of VO 2 (B). The complex optical conductivities of the VO 2 (B) films for temperatures ranging from 240 K to 400 K are shown in Figures 3(a) and (b) as a function of frequency during the warming process (open symbols). Below 240 K, the transmission is ,100%, giving zero real conductivity, indicating that the films are clearly insulating. The onset of a positive s 1 (v) marks the transition from an insulating regime to a conducting one. We clearly observe s 1 (v) to increase with increasing temperature throughout our frequency range. Thermal excitation of electrons into the conduction band can account for this nature, that is, a Drude response where s 1 (v) is a maximum at low frequency and decreases with increasing frequency, while s 2 (v) are zero at low frequency and increases with increasing frequency.
According to the Drude model, the frequency dependent complex optical conductivity is given bỹ where v P is the Drude plasma frequency, c is the free carrier scattering rate and e ' is the high frequency dielectric constant as defined earlier. Both s 1 (v)and s 2 (v) at each temperature measurement are simultaneously fitted to Equation 2, as shown by the dash red lines in We observe a similar trend in both the plasma frequency and the scattering rate -both parameters increases as we increase the temperature up to ,280 K, and tends to saturate beyond 280 K. This common trend in v P and c describe two different temperature-dependent conductivity mechanisms. To address this issue and to make a distinction, we describe the temperature regions 240 K # T # 280 K and 280 K ,T # 400 K as conductivity regimes I and II respectively.
In regime I, v P /2p rises from (8 6 1) THz to (49 6 8) THz, while in regime II this parameter has a mean value of , (54 6 5) THz. The plasma frequency is closely related to the number of charge carriers (N) in the system via v 2 P~N e 2 =m Ã e 0 where m* is the effective mass. The scattering rate, (c) is associated with the mobility of the carriers, (m) via the expression c 5 e/(m*m). Without the knowledge of the carriers' effective mass, accurate values of N and m in VO 2 (B) cannot be determined. In the later sub-sections, more discussions regarding the nature of m* will be presented.
The Boltzmann dc conductivity s 0 can be obtained from the expression  The plot shows s 0 increasing with increasing temperatures, but the rate of change is significantly smaller at higher frequencies. We recall that while v P and c start saturating at 280 K, s 0 does not. However, for T . 280 K and T # 280 K, s 0 changes with different slopes and hence can be correlated with our description of conductivity regimes I and II. If we compare, our estimated dc conductivity from the THz measurements are consistent with the electrical transport measurements shown in Figure 1(c). Figure 5(b) shows the logarithmic conductivity, ln(s) plotted against reciprocal temperature, 1000/T. The activation energy, E a can be estimated from the thermal activation model of dc conductivity which has the following temperature dependence Comparison with VO 2 (M1). The THz conductivity spectra of 60-nm thick VO 2 (M1) film grown on SLAO are shown in Figure 6 plotted as the temperature of the system is gradually increased from 343 K to 400 K. In contrast to VO 2 (B), throughout this temperature range, s 1 (v) increases with increasing frequency, while s 2 (v) starts at zero at low frequencies, becomes negative, then crosses over to positive with increasing frequency. This is consistent with the previous reported THz studies of VO 2 (M1) films 25,26,30 .
In classical VO 2 (M1) systems it has been reported that the complex conductivities can be effectively modelled by Drude-Smith theory, which is a generalisation of the Drude model proposed by Smith, in order to account for the conductivity suppression due to charge localization 33,43,47,48 . In this polymorph, it is widely considered that the transition from a highly transparent insulating phase to an absorbing metallic phase occurs through a percolating network 29,46,49 . Near the threshold of this transition, phase separation and domain formation dictate the electronic pathways. The frequency-dependent optical conductivity in the Drude-Smith model is given by 47 The additional terms described by c j represents the fraction of the carrier's initial velocity retained after j number of scattering events 47 .
In various systems such as poor conductors, metal-insulator transition materials and various nanomaterials where the Drude-Smith model is successfully applied, only the first scattering term is considered (i.e. j 5 1) 30,48,[50][51][52] . In this scenario, carrier transport transitions from ballistic to diffusive after one scattering event, leading to complete momentum randomization 47 . In our fitting analysis also we will only consider the first c j term and in this case we take c 1 5 c. The parameter c can take up any values anywhere between 0 (free Drude  carrier conduction) and 21 (full carrier backscattering) 43 . There have been other reports of using effective medium theory (EMT) models to fit THz conductivities of VO 2 (M1) with varying degrees of success 29,31 . Our attempts to model the optical conductivities using the effective medium models gave inconsistent results (Supplementary Information). On the other hand, as shown by the fitting lines in the Figures 6 (a) and (b), the Drude-Smith formalism given by Equation (5) when j 5 1 gives excellent fits to our measured conductivities of s 1 (v) and s 2 (v). We could see that even at high temperatures the conductivity does not follow an ideal Drude behaviour which indicates that the nanogranular boundaries persist even after the transition. In highly granular systems, the Drude-Smith is much more effective in describing the effective conductivity rather than a conventional EMT models because it can describe effective conductivities of systems where grain boundaries persist even in large conducting fractions 30,43 . The advantage of Drude-Smith over EMT models in this scenario has been discussed by T. L. Cocker et.al 30 .
Simultaneous complex fitting of optical conductivities gives the information about the parameters v P , c and c. Figure 7 summarizes the v P , c parameters obtained from the fitting procedure as well as the dc conductivity s 0 which is given by the equation, s 0ẽ The Drude-Smith parameters v P and c increase with increasing temperatures in the temperature range 343 K-349 K; above 349 K they remain largely temperature-independent. This characteristic is similar to the temperature dependence of Drude parameters in VO 2 (B). In the temperature range 352 K-400 K, the mean value of v P /2p is , (110 6 4) THz. The fitting parameter c lies between 20.88 and 20.75 which indicates significant carrier backscattering -an attribute of carrier localization, resulting in significant suppression of low-frequency conductivities. The temperature dependence of the fitted values of c supports the percolation picture in VO 2 (M1) 43 .
We find that similar to v P and c, s 0 increases with increasing temperatures till 349 K; at higher temperatures, it attains a mean saturating value of (6.5 6 0.3) 3 10 4 (Ohm.m) 21 . Analogous to VO 2 (B), we can define the temperature range of 343 K-349 K as conductivity regime I and 352 K-400 K as conductivity regime II. However in VO 2 (M1), s 0 remains largely temperature independent in conductivity regime II, while in VO 2 (B) there is a weak temperature dependence in this regime. Figure 7(d) shows the linear fitting plot of logarithmic conductivity, ln(s) versus reciprocal temperature, 1000/T. Similar to our previous analysis of VO 2 (B), we can determine the activation energy of VO 2 (M1) from the slope of the linear relation. For VO 2 (M1), in the low-temperature regime I, the activation energy E a 5 (2200 6 500) meV while in the high-temperature state II, E a 5 (20 6 8) meV. The difference between the activation energies in regions I and II is much larger in VO 2 (M1) than in VO 2 (B) which is consistent with our v P and s 0 results where the quantitative growth of these values as the system goes from regime I to II is much larger in VO 2 (M1) compared to VO 2 (B). Also, while the activation  energies in regime II are similar in these VO 2 polymorphs, E a of VO 2 (M1) is an order of magnitude larger than that of VO 2 (B) in regime I. This means that in regime I, the conductivity slope is steeper in VO 2 (M1) and concomitantly we found a sharper rise of v P and c in VO 2 (M1) in regime I.
According to M. M. Qazilbash et. al. 22 , a significant enhancement of the carrier effective mass, m* (as large as 5m e , where m e is mass of an electron) is found in the infrared spectra, especially in the intermediary phase transition state which is analogous to our conductivity regime I. After the transition is completed (at T , 350 K), m* is close to 2m e which is the value reported by other experiments 46 . Considering m* 5 2m e , at temperatures just above the transition (T 5 352 K), we obtain the carrier density to be ,3.  30,31 . Hall effect measurements reported similar values of carrier density at this temperature but the reported mobility is lower, which is probable as THz study does not face the challenges in Hall measurements due to low-mobility 53 . The fundamental difference between these two techniques is that while Hall measurement is meant for DC conductivity measurements THz-TDS is an AC measurement method. Hall measurement being a contact method requires the charge carriers to travel substantial distance across the biased electrodes but on the other hand THz-TDS captures the conductivity traversed in sub-pico second timescales resulting in 'conductivity snap-shots' 42 . As a consequence, THz-TDS can give conductivity information before the carriers are trapped or recombined and as such it is quite reasonable to expect that the THz mobility would be higher than the Hall mobility. We can also compare the carrier density and the mobility parameters of VO 2 (M1) with that of VO 2 (B). By assuming m* 5 2m e at T 5 295 K for VO 2 (B), which is just after the transition, the calculated values are N < 6.4 3 10 19 cm 23 and m < 21.9 cm 2 /(V?s). It has been reported that the first-order phase transition in VO 2 (M1) takes place via percolation where metallic domains embedded in a matrix of insulating phase starts nucleating sporadically as temperature is increased. When the temperature reaches the metalinsulator transition temperature T MI , the domains become well connected to form a percolating path in this inhomogeneous composite medium. The Drude-Smith model has been applied to various percolating systems where inhomogeneity in conductivity contributes of a non-zero backscattering parameter c. On the other hand VO 2 (B) can be described by a simple Drude model, although it is a poor conductor in comparison to VO 2 (R). The fact that VO 2 (R) cannot have an ideal Drude behavior can be explained by its granular origin, intrinsic inhomogeneity. In VO 2 (B) we cannot see evidence of inhomogeneous phase separation or percolating transport from the THz study and thus shows a good Drude fit. The explanation for this difference between the polymorphs is two-fold -first, VO 2 (B) is a more uniform film in the context of epitaxial growth with lesser roughness and hence no backscattering. VO 2 (M1) on the other hand, has a more grainy morphology due to the larger b inter-axial angle ( Supplementary Information). Second, the activation energy is larger in VO 2 (B) in the conducting state and so the number of thermally activated carriers are smaller.
Furthermore, the narrow intermediate state of VO 2 (M1), which falls in our conductivity regime I, is a strongly correlated phase marked by enhanced mass and an optical pseudo-gap before crossing over to a rutile metallic state as indicated by several optical measurements including infrared spectroscopy, ellipsometry and femtosecond pump-probe measurements 22,23,49,54 . It is also possible that in the intermediate state of VO 2 (B), electronic correlations may play a significant role in this intermediate transition state. The rich electronic phase diagram of these vanadium dioxide polymorphs can be summarized from our THz transmission spectra as illustrated in Figure 8.

Discussion
In conclusion, we have used THz spectroscopy to measure the temperature-dependent complex optical conductivity of vanadium dioxide polymorphs. In our operational frequency range (0.3-2.3) THz, VO 2 (B) exhibits no phonon modes and the onset of Drude conductivity behaviour arrives for temperatures higher than 240 K. On the other hand, in VO 2 (M1) the THz conductivity can be better described by the Drude-Smith model. Key parameters of carrier dynamics (i) plasma frequency (v P ) and (ii) scattering rate (c) are obtained by fitting to the Drude (in VO 2 (B)) and Drude-Smith in (VO 2 (M1)) models. Interestingly, our THz analysis revealed that like in VO 2 (M1), VO 2 (B) also transforms from an insulating system to a conducting system but is mediated by a much broader intermediate state with the transition onset much closer to room temperature making it more suitable than the widely studied VO 2 (M1) for optoelectronic devices operating at room temperature. Our study also demonstrates that these polymorphs can also be used as temperature-controlled THz frequency modulators. While the sharp phase  transition in VO 2 (M1) is suitable for digital-like THz modulation, the broad phase transition in VO 2 (B) offers analog-like continuous modulation of THz spectra very similar to W-doped VO 2 (M1) 55 . THz conductivity study is a fascinating subject of research from viewpoints of phase transitions in these systems. We show that THz spectroscopy is an excellent method of studying polymorphism in materials.

Methods
Sample growth. Pulsed Laser Deposition is used to fabricate the various VO 2 polymorph thin films by ablating a commercial Vanadium single crystal (100) orientated target on the SLAO (001) substrate. The growth temperature is 500uC and the oxygen pressure is varied from 5 3 10 23 to 7 3 10 23 Torr. By systematic control of oxygen growth pressure and pulse laser frequency, the various phases of VO 2 are stabilized. Detailed growth conditions study has been reported in a previous study 56 .
XRD and AFM. The h-2h diffraction data measurements are done on a Bruker D8 Discover diffractometer CuK a1 (l 5 1.54 Å ). Temperature-dependent electrical transport measurements are carried out in Physical Property Measurement system (Quantum Design) utilizing a four probe geometry. The surface morphology analysis of the various films are characterized on an atomic force microscope (AFM, Dimension V, Veeco).
THz-TDS. THz transmission spectra measurements of the VO 2 films are carried out using the TeraView Spectra 3000 THz-TDS system, incorporated with a Janis ST-100-FTIR cryostat. The operational temperature range of the cryostat is 10 K to 450 K. In this system low temperature-grown GaAs films is used for the generation and detection of THz waves. THz time-domain data of VO 2 films are taken with respect to the signal transmitted through the bare substrate as a reference. Optical properties of the bare SLAO substrate are determined by THz-TDS, with vacuum as the reference signal. The complex refractive index,ñ sub of SLAO substrate is obtained to beñ sub <4:1{0:004i and almost temperature and frequency-independent, and thus is a very suitable THz transparent material in our operational temperature and frequency range. The cryostat is equipped with a vertical motorized stage with a resolution of 2.5 mm which is used to control the back and forth motion between the sample and reference positions.
The aperture diameter used is 7 mm which allowed for an accurate measurement of the THz signal for frequencies as low as 0.3 THz. For each sample and reference run, 900 THz traces are taken in 3 minutes. The thickness difference between the film substrate and the bare substrate (reference), must be taken into account in our subsequent analysis 57 . The sample is kept in a high vacuum (,10 26 mbar) for all our experiments.