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# Mott Transition in VO2 Revealed by Infrared Spectroscopy and Nano-Imaging

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Science  14 Dec 2007:
Vol. 318, Issue 5857, pp. 1750-1753
DOI: 10.1126/science.1150124

## Abstract

Electrons in correlated insulators are prevented from conducting by Coulomb repulsion between them. When an insulator-to-metal transition is induced in a correlated insulator by doping or heating, the resulting conducting state can be radically different from that characterized by free electrons in conventional metals. We report on the electronic properties of a prototypical correlated insulator vanadium dioxide in which the metallic state can be induced by increasing temperature. Scanning near-field infrared microscopy allows us to directly image nanoscale metallic puddles that appear at the onset of the insulator-to-metal transition. In combination with far-field infrared spectroscopy, the data reveal the Mott transition with divergent quasi-particle mass in the metallic puddles. The experimental approach used sets the stage for investigations of charge dynamics on the nanoscale in other inhomogeneous correlated electron systems.

One challenge of contemporary condensed matter physics is the understanding of the emergence of metallic transport in correlated insulators or Mott insulators in which, for example, a temperature change or chemical doping induces anomalous conducting phases (1). In such a correlated metal, the mobile charges experience strong competing interactions leading to exotic phases, including the pseudogap state in cuprates and manganites, high-temperature superconductivity, charge stripes in cuprates, and even phase separation in some manganites and cuprates (18). In systems where multiple phases coexist on the nanometer scale, the dynamical properties of these individual electronic phases remain unexplored because methods appropriate to study charge dynamics (transport, infrared/optical, and many other spectroscopies) lack the required spatial resolution. Scanning near-field infrared microscopy can circumvent this limitation (911). Specifically, we probed coexisting phases in the vicinity of the insulator-to-metal transition in vanadium dioxide (VO2) at length scales down to 20 nm. This enabled us to identify an electronic characteristic of the Mott transition, namely divergent quasi-particle mass in the metallic puddles, which would otherwise have remained obscured in macroscopic studies that average over the coexisting phases in the insulator-to-metal transition regime.

One particular advantage of VO2 for the study of electronic correlations is that the transition to the conducting state is initiated by increasing the temperature without the need to modify the stoichiometry. The salient features of the first-order phase transition that occurs at Tc ≈ 340 K are the orders-of-magnitude increase in conductivity accompanied by a change in the lattice structure (1). Compared to the high-temperature rutile metallic (R) phase, the two main features that distinguish the lattice in the low-temperature monoclinic (M1) insulating phase are dimerization (charge-ordering) of the vanadium ions into pairs and the tilting of these pairs with respect to the c axis of the rutile metal. The experiments on VO2 films (12, 13) reported here reveal a strongly correlated conducting state that exists within the insulator-to-metal transition region in the form of nanoscale metallic puddles. Electromagnetic response of these puddles separated by the insulating host displays the signatures of collective effects in the electronic system, including divergent optical effective mass and optical pseudogap. These findings, which were not anticipated by theoretical models, may also help to settle the decades-long debate (1, 1420) on the respective roles played by the lattice and by the electron-electron correlations in the insulator-to-metal transition.

The gross features of the insulator-to-metal transition in VO2 can be readily identified through the evolution of the far-field optical constants (13) obtained with use of spectroscopic ellipsometry and reflectance (Fig. 1). The insulating monoclinic phase (T ≤ 341 K) displays a sizable energy gap of about 4000 cm–1 (≈0.5 eV) in the dissipative part of the optical conductivity, σ1(ω). The T ≥ 360 K rutile metallic phase is characterized by a broad Drude-like feature in the optical conductivity, linear temperature dependence of resistivity, and an extremely short electronic mean free path of the order of the lattice constant, reminiscent of “bad metal” behavior in other transition metal oxides, including the cuprates (2123). The insulator-to-metal transition is evident from the increase of the conductivity with spectral weight “filling up” the energy gap that has to be contrasted with a gradual decrease of the energy gap magnitude. This feature of the transition, along with an isosbestic point at a frequency of 11,500 ± 125 cm–1, is one of several spectroscopic fingerprints of doped Mott insulators (1) identified in this work. The isosbestic point is defined here as the location of equal conductivity for all spectra obtained at different temperatures. Lastly, the divergence of the real part of the dielectric function ϵ1 (Fig. 1 inset) signals the percolative nature of the insulator-to-metal transition. This divergence of ϵ1 is similar to that observed near the percolative insulator-to-metal transition in ultrathin Au and Pb films (24).

Mid-infrared near-field images directly show that in fact the insulating and metallic phases co-exist in VO2 over a finite temperature range in the transition region (Fig. 2). This determination was made by using a scattering scanning near-field infrared microscope (s-SNIM) operating at the infrared frequencies ω = 930 cm–1 and ω = 1725 cm–1. S-SNIM is capable of registering contrast between electronic phases according to their optical constants with spatial resolution ≈ 20 nm. Specifically, the scattering amplitude signal demodulated at the second harmonic of the tapping frequency of the tip of our s-SNIM apparatus (maps in Fig. 2) is related to the local value of the complex dielectric function $Math$ of the sample. The amplitude of the scattering signal is expected to increase in metallic regions compared with that in the insulating regions: a behavior grasped well by the so-called dipole model of the near-field infrared contrast (9, 10, 13).

The amplitude-contrast near-field images in Fig. 2 show the electronic insulator-to-metal transition in progress. At temperatures between 295 and 341 K in the insulating phase, we observed uniform maps of low scattering (dark blue color in Fig. 2). A small increase of temperature radically changes the near-field images. For example, in the T = 342.4 K image we then observed nanoscale clusters in which the amplitude of the scattering signal was enhanced by a factor of 2 to 5 compared with that of the insulating host, indicating a metallic phase. Representative scans showed that the metallic regions nucleate, then grow with increasing temperature, and eventually connect. We did not observe any obvious correlations between the size and/or shape of the metallic clusters and the features in simultaneously collected topographic images. Although the percolative nature of the insulator-to-metal transition had been proposed previously (25), it is directly revealed by our scanning near-field infrared measurements reported herein. The insulator-to-metal transition is complete by T = 360 K, at which temperature insulating islands are no longer seen.

With the observation of nanostructured phases in Fig. 2, the far-field infrared spectra in Fig. 1 should be analyzed with use of an effective medium theory (EMT) for such phase-separated systems (13, 26). The effective optical constants of a two-phase heterogeneous system are an average of the optical constants of the insulating and metallic regions weighted by the respective volume fractions. Our near-field images enabled us to determine these fractions. However, a simple weighting of optical constants of the insulating phase and of the rutile metallic phase at T = 360 K within the EMT model does not produce a satisfactory description of the far-field infrared data near the onset of the insulator-to-metal transition in VO2. This discrepancy indicates that the infrared properties of the metallic puddles, once they first appear at T ≈ 342 K, may be different from that of the high-temperature rutile metal. We confirmed this hypothesis by extracting the response of the metallic puddles from a combination nation of near-field results and far-field spectra within an EMT analysis described in (13).

The real part of the conductivity spectrum, σ1a(ω), of the metallic puddles is plotted in Fig. 3B as it evolves with temperature. When these puddles appear at the onset of the electronic insulator-to-metal transition at T ≈ 342 K (Fig. 3A), their conductivity spectrum differs markedly from that of the rutile metallic phase at higher temperature, for example, T = 360 K. These metallic regions exhibit a narrow Drude-like peak at low frequencies and then a dip, followed by a prominent mid-infrared band that peaked at ≈1800 cm–1. Uncertainties in the EMT analysis [detailed in (13)] do not exclude the possibility of a nonmonotonic form of σ1a(ω) at the lowest frequencies, a behavior consistent with Drude response modified by localization. These features indicate that the metallic islands are not simply isolated regions of the higher-temperature VO2 rutile metal.

In order to highlight distinctions between the electrodynamics of the metallic clusters and the rutile metallic phase, we performed the extended Drude analysis (13, 27) on the optical constants of the metallic clusters to extract the scattering rate 1/τ(ω) and the mass enhancement factor m*(ω)/mb (mb is the electronic band mass) of the charge carriers (Fig. 3, C and D). In the limit of ω→0, these quantities can be interpreted in terms of lifetime, τ(ω), and effective mass, m*(ω), of quasi-particles (27) in the metallic regions. One can recognize a prominent enhancement of m* (ω→0)/mb at T = 342 K that has to be contrasted with much lighter masses in the rutile phase (T = 360 K) spectrum in Fig. 3D (22). More importantly, the temperature dependence of m* (ω→0)/mb, plotted in the inset of Fig. 3D, shows divergent behavior in the vicinity of the insulator-to-metal transition: an unambiguous attribute of the Mott transition (28). The spectra of 1/τ(ω) reveal a threshold structure followed by an over-shoot at higher energies up to ≈1000 cm–1. This is characteristic of systems with a (pseudo) gap in the electronic density of states (29) that is to be contrasted with the relatively smooth variation of 1/τ(ω) in the rutile phase. We also note that the new electronic state exhibiting an enhanced mass and a gaplike form of the relaxation rate exists only in a narrow temperature range, as shown by the shaded region in Fig. 3A. By T = 343.6 K, the optical constants of the metallic regions already resemble those of the rutile metallic phase.

The analysis and discussion above suggest that the classic temperature-induced insulator-to-metal transition in VO2 occurs from the monoclinic insulator to an incipient strongly correlated metal (SCM) in the form of nanoscale puddles. These metallic puddles exhibit mass divergence, which is a clear signature of electronic correlations due to many-body Coulomb interactions (28). The pseudogap and mid-infrared band are consequences of optically induced electronic excitations across a gap on some parts of the Fermi surface. The energy scale of the pseudogap in the SCM state in VO2 can be determined by the overshoot in 1/τ(ω) spectra that occurs at ≈1000 cm–1 (or ≈4kBTc). We note that the pseudogap is a common property of doped Mott insulators (1, 27). The pseudogap features in the optical conductivity and 1/τ(ω) spectra also bear resemblance to those found in metallic systems with a partial charge density wave (CDW) gap (30). The pseudogap in VO2 may result from a complex interplay between electronic correlations and charge ordering.

The Mott transition commonly leads to an anti-ferromagnetically ordered insulator as in closely related V2O3 (1). Vanadium dioxide avoids this magnetic ordering via dimerization of vanadium ions in the monoclinic insulating phase (14) because of competing effects of charge ordering (Peierls instability) that is likely caused by electron-phonon interactions. Thus, the insulating monoclinic (M1) phase of VO2 should be classified as a Mott insulator with charge ordering. It remains an open question whether or not the insulator-to-metal transition occurs at a slightly different temperature from the structural transformation associated with charge ordering (18, 19, 31), and this raises the issue about the precise lattice structure of the metallic nanopuddles we have observed. This issue does not affect our observation of divergent optical mass and can only be resolved by x-ray diffraction measurements on the nanoscale. We also note that the images of phase coexistence and percolation reported here (Fig. 2) are consistent with the thermodynamic evidence of the first-order nature of the phase transition in VO2 (21). Moreover, our experiments show that the collapse of a large ≈0.5 eV energy gap and the formation of heavy quasi-particles in the emergent metallic nanopuddles at the onset of the insulator-to-metal transition are due to Mott physics (1, 28) and that percolation occurs at a later stage when these metallic puddles grow and connect (Fig. 2).

A transformation from an insulator to a metal in many correlated electron systems, including high-Tc cuprates, colossal magnetoresistive manganites, and others, occurs through an intermediate pseudogap regime (1, 5, 27, 29). At least in the case of cuprates, optical signatures of the pseudogap state are similar to the results in the SCM state of VO2 (27). Furthermore, in many correlated systems, the pseudogap state is in the vicinity of the regime of the bad metal in which resistivity shows a peculiar linear dependence with temperature, whereas the absolute values of the resistivity are so large that the notion of quasi-particles becomes inapplicable (2123). Often a crossover from pseudogapped metal to bad metal occupies an extended region of the phase diagram. In VO2, the boundary between the two electronic regimes is relatively abrupt, and the emergence of bad metal transport in the rutile phase may be linked to the loss of long-range charge order that does not extend into the rutile metal. Then the poor conductivity of rutile VO2 and other bad metals appears to arise from the collapse of electronically and/or magnetically ordered states in the vicinity of a Mott insulator, thereby causing the resistivity to exceed the Ioffe-Regel-Mott limit of metallic transport (2123). Lastly, we note that, in the cuprates, in contrast to VO2, the effective mass of doped carriers inferred from infrared spectroscopy data (32) shows no divergence. However, if electronic phase separation exists in doped cuprates, as suggested by recent scanning probe studies (6, 8), then infrared analysis of the effective quasi-particle mass needs to be revisited with the help of nano-imaging tools used in this work.

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