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Novel metal-insulator-transition at the SrTiO3/SmTiO3 interface

We report on a metal-insulator transition (MIT) that is observed in an electron system at the SmTiO3/SrTiO3 interface. This MIT is characterized by an abrupt transition at a critical temperature, below which the resistance changes by more than an order of magnitude. The temperature of the transition systematically depends on the carrier density, which is tuned from ~ 1x10^14 cm^-2 to 3x10^14 cm^-2 by changing the SmTiO3 thickness. Analysis of the transport properties shows non-Fermi liquid behavior and mass enhancement as the carrier density is lowered. We compare the MIT characteristics with those of known MITs in other materials systems and show that they are distinctly different in several aspects. We tentatively conclude that both long range Coulomb interactions and the fixed charge at the polar interface are likely to play a role in this MIT. The strong dependence on the carrier density makes this MIT of interest for field-tunable devices.

Metal-to-insulator transitions (MITs) that are caused by strong electron correlations are the source of some of the most interesting phenomena in condensed matter physics [1][2][3][4]. They can occur either at very high carrier densities, where on-site Coulomb interactions are strong ("strongly correlated systems"), or at ultralow densities, where long-range Coulomb interactions remain unscreened. The corresponding insulating states are the Mott insulator and the Wigner crystal, respectively. Real materials are often significantly removed from either one of these ideal states and contain additional, complex interactions. Furthermore, disorder, which even without correlations can cause localization ("Anderson insulator") [5], can play a central role [6,7]. Transition metal oxides with metallic densities (~one electron/primitive unit cell) have been central to the study of Mott insulators [2], whereas low-dimensional, low-density (sheet densities on order of 10 11 cm -2 and below) semiconductors are employed in the search for a Wigner crystal in the solid state [8].
Electron systems at oxide interfaces offer access to a parameter space that is not easily available in the systems mentioned above. Unlike doped or alloyed bulk transition metal oxides, electrostatic doping (for example by a polar discontinuity [9][10][11]) avoids dopant atoms, a source of disorder. Unlike two-dimensional electron gases in semiconductors, electron masses are high, which promotes localization. Spin-orbit coupling via Rashba fields can also be strong, which may enhance interactions [12]. There are, however, significant challenges. In particular, low carrier mobilities result in high sheet resistances. If these exceed the Mott-Ioffe-Regel limit or quantum resistance (h/e ~ 25 kΩ/ ), systems are insulating at most temperatures. This insulating state preempts correlation-induced MITs or other phenomena that may emerge out of an itinerant correlated electron system. MITs near the Mott-Ioffe-Regel limit have been observed in electron systems at LaAlO 3 /SrTiO 3 [13] and SmTiO 3 /SrTiO 3 interfaces [14]. 4 Here, we study SmTiO 3 /SrTiO 3 interfaces that have sheet resistances well below the quantum limit. The polar discontinuity at such interfaces corresponds to a fixed positive charge of 3×10 14 cm -2 at the interface ( Fig. 1), which can be compensated by free (mobile) carriers in the SrTiO 3 [15]. Mobile carrier densities of 3×10 14 cm -2 per interface are observed for a wide range of sample geometries [11,16]. When SmTiO 3 layers are reduced to a few unit cells (u.c.s), the sheet carrier densities are reduced below this value and depend systematically on the SmTiO 3 thickness [14]. Given carrier densities that are not close to either one of the two limiting cases discussed above, conventional wisdom would suggest that a correlation driven MIT is unlikely to occur. Contrary to this expectation, we show that an abrupt MIT occurs in this interfacial Furthermore, all structures that were still metallic at 110 K showed a hump in R s at that temperature. This resistance anomaly is more visible in the derivative, dR s /dT vs. T, shown in antiferrodistortive transition at ~ 110 K and resistance anomalies have been observed to be associated with it [19][20][21], although their precise origin remains to be determined. Figure 3 shows T MIT as a function of the sheet carrier density (n s ), determined at room temperature from the Hall measurements (shown in Fig. 4 respectively, see Fig. 4(a). Here, T MIT was defined as temperature where dR s /dT ~ 0. Figure 3 shows that T MIT systematically and strongly depends on n s . Even samples with different SrTiO 3 thicknesses, which have slightly different mobilities and/or carrier densities than those with 60 nm SrTiO 3 , follow this general trend. Thus, the primary factor in determining T MIT is the carrier density.
6 Figure 4 shows the results from Hall measurements. Figure 4 [22] and is sometimes thought be a signature of proximity to a quantum critical point [23,24], but no definite explanation exists for it yet [25].
The Hall angle, Hcot(θ H ) is shown in Fig. 4(b). We note that Hcot(θ H ) = µ -1 , where µ is the Hall mobility. The Hall angle follows a well-defined T 2 behavior to room temperature as described by: where C is the residual and α is the Hall scattering amplitude. Hα increases from 1.2×10 -6 Vs/cm 2 /K 2 for the 20 u.c. SmTiO 3 /60 nm SrTiO 3 sample to 2×10 -6 Vs/cm 2 /K 2 for the 3 u.c. SmTiO 3 /60 nm SrTiO 3 sample. The 3 u.c. SmTiO 3 /60 nm SrTiO 3 sample displays slight deviations from T 2 behavior, in particular, in the proximity of the MIT. 7 We next discuss the results. First and foremost, we note that the MIT is very different from the MITs that observed near the Mott-Ioffe-Regel limit (or quantum resistance) in a wide range of materials, such as two-dimensional electron gases in semiconductors [26] or oxide thin films [13,27]. In these cases, the MIT occurs near R s ~ 25 kΩ/ , when the mean free path length is on order of the lattice spacing [28][29][30] Fig. 3. All other samples show an abrupt MIT even though R s is an order of magnitude below the Mott-Ioffe-Regel limit. The insulator emerges from a state that is metallic -note the T 2 behavior of the Hall angle -and the insulator very quickly becomes highly resistive. Thus, the origin of the MIT observed here must lie in more unconventional physics.
The MIT is reminiscent of that in correlated materials, such as VO 2 [31] or the rare earth nickelates [32]. These materials also show an abrupt MIT as the temperature is lowered.
However, the MIT in these materials is accompanied by a reduction of the lattice symmetry and they exhibit a pronounced hysteresis indicative of a first order transition. Here we do not observe a hysteresis, suggesting an electronic origin. The strongly insulating state is also striking.
The Hall effect can still be measured well below T MIT in charge ordered systems such as the rare earth nickelates (though it may be non-trivial to interpret) [33].
Carrier densities in the samples here are low compared to strongly correlated materials.
A significant portion of the carriers spread over the entire SrTiO 3 thickness [11,34,35]. This 8 renders the carrier density at a fraction of the 1 electron/u.c. required of a Mott insulator. Even more crucially, T MIT increases as we reduce the carrier density; this is opposite of what would be expected for physics driven by on-site Coulomb interactions, which should become more pronounced as the carrier density is increased towards half-filling. Thus, it is unlikely that shortrange Coulomb interactions are at the origin of the MIT in this system.
The key observation is that T MIT increases with decreasing n s . Moreover, the scattering amplitude, α, also increases with decreasing n s . This indicates an increase in effective mass, m*, since , where is a temperature-dependent scattering rate and e the elementary charge. A higher effective mass indicates stronger correlations in samples with lower n s . Given the systematic dependence of these two independent quantities on n s , long range Coulomb interactions should be considered. To first order, their importance is determined by the ratio of the interaction energy (E e-e ) and the kinetic energy (Fermi energy, E F ). This ratio often expressed in terms of the Wigner-Seitz radius, r s , which for a two-dimensional electron system is given as: , where the reduced Planck's constant, and ε the dielectric constant. Using m* = 10, which is not unrealistic for electrons in the d yz,xz -derived bands [36], ε = 300 (undoped SrTiO 3 at room temperature [37]), and n s = 1×10 14 cm -2 , we obtain r s ~ 5, which is not high. Typically, electron systems are considered to be strongly correlated for r s ~ 10, with a value of 37 believed to be needed for the Wigner crystal in two dimensions [38]. However, several factors could increase r s substantially. First, multiple subbands are occupied in this system [34,[39][40][41]. This will increase r s by factors corresponding to the subband degeneracy. Secondly, a substantial portion of the fixed charge at the interface remains unscreened if the mobile carrier density is less than 3×10 14 cm -2 . We believe the fixed charge at the polar interface is a key ingredient in the microscopic origins of this MIT, as no abrupt MITs with change in temperature are observed either in bulk doped SrTiO 3 [42] or in other interfacial systems involving SrTiO 3 , such as LaAlO 3 /SrTiO 3 , at comparable (or even lower) carrier densities. One consequence of the polar fixed charge are very large, asymmetric electric fields, and thus Rashba-type of spin-orbit coupling, which is believed to aid in the localization [12]. Finally, we note that the samples are certainly not free of disorder, which may promote unconventional metallic and insulating states even at small r s [7].
In conclusion, the observed mass enhancement, non-Fermi liquid behavior, MITs at resistances much below the quantum resistance, and, most of all, the systematic scaling of T MIT with the carrier density all point to an unconventional insulator in which long-range electron correlations play a key role. Future studies, though experimentally challenging, should be directed at determining the nature of insulating state, in particular with regards to magnetic order, or absence thereof, and the spatial distribution of carriers. The results highlight the potential for new discoveries in MITs in materials systems that are substantially different from the wellstudied strongly correlated Mott insulators and dilute semiconductor systems. They also have implications for practical applications. The fact that T MIT is highly sensitive to the carrier density makes this system of substantial interest for electric field gating of MITs. The relatively low (in comparison to strongly correlated materials) carrier densities promise an MIT that can be gated with conventional solid-state gate dielectrics, which has been a long-sought-after goal [43]. nonstoichiometry,…) [15]. For thick SmTiO 3 , interfaces have the full 3×10 14 cm -2 mobile charge density, but for thin SmTiO 3 , the carrier density is reduced. It is likely that this is due to the proximity to the polar surface. A significant fraction of the mobile electrons, specifically those that are located in d xz,yz orbitals, spread out far into the SrTiO 3 [34,35]. The degree to which the electron gas spreads is determined by a number of boundary conditions, including the carrier density and field-dependent permittivity of SrTiO 3 . The SrTiO 3 thickness thus affects the spatial distribution.