## Abstract

Mott transitions, which are metal-insulator transitions (MITs) driven by electron-electron interactions, are usually accompanied in bulk by structural phase transitions. In the layered perovskite Ca_{1.9}Sr_{0.1}RuO_{4}, such a first-order Mott MIT occurs in the bulk at a temperature of 154 kelvin on cooling. In contrast, at the surface, an unusual inherent Mott MIT is observed at 130 kelvin, also on cooling but without a simultaneous lattice distortion. The broken translational symmetry at the surface causes a compressional stress that results in a 150% increase in the buckling of the Ca/Sr-O surface plane as compared to the bulk. The Ca/Sr ions are pulled toward the bulk, which stabilizes a phase more amenable to a Mott insulator ground state than does the bulk structure and also energetically prohibits the structural transition that accompanies the bulk MIT.

The insulating phase associated with metal-insulator transitions (MITs) (*1*–*4*) can be described as either a band insulator (such as silicon) or a Mott insulator (such as nickel oxide). A band insulator has an even number of electrons per unit cell that can be described adequately by an independent electron theory, where all of the bands are either filled or empty at 0 K. If the number of electrons in the unit cell is odd, then band theory always predicts metallicity, but when the onsite Coulomb interaction (*U*) is comparable in magnitude to the bandwidth (*W*), the material can become a Mott insulator (*1*, *2*). A transition from the Mott insulating phase to the metallic phase can be induced by temperature, pressure, magnetic field, or doping (*4*). Normally, the MIT for a band insulator is accompanied by a structural phase transition that changes or breaks the symmetry (*5*, *6*). The simplest example is a one-dimensional chain of atoms, which, as Peierls showed (*3*), is unstable because of the degeneracy caused by Fermi surface nesting at 2 *k*_{F}, where *k*_{F} is the Fermi wavevector. The lattice reconstructs itself, doubling the periodicity and lowering the electronic energy by creating a gap at the Fermi energy (*E*_{F}).

In contrast, an inherent Mott transition should be purely electronic in origin and not assisted by a structural transition (*1*, *2*, *5*). In practice, almost all of the highly correlated materials with a large enough ratio of *U*/*W* to be Mott insulators exhibit close coupling between charge, spin, and lattice, so that the Mott transition is nearly always accompanied by a structure transition. This situation complicates the understanding of the basic mechanism of a Mott MIT as a transition driven by the electron-electron (*e-e*) correlations. We now show that the surface layer of a Mott insulator can display a MIT independent of a structural transition.

The layered ruthenate Ca_{2-x}Sr_{x}RuO_{4} shows a rich array of ground states that are associated with the intricate couplings between lattice, electron, and spin degrees of freedom (*7*–*9*). Ca^{2+} replacement of Sr^{2+} gradually enhances the rotational and tilt distortion of the RuO_{6} octahedra, starting with a tetragonal *I*4*/mmm* structure for Sr_{2}RuO_{4}, leading to an *I*4_{1}*/acd* structure for Ca_{1.5}Sr_{0.5}RuO_{4}, and ending with an orthorhombic *S-Pbca* structure for Ca_{2}RuO_{4} (*9*). These structural changes lead to an evolution of the ground state, from an unconventional superconducting state in Sr_{2}RuO_{4} (*10*) to a quantum critical point at *x* = *x*_{c} ∼0.5 (where c is critical) and to an antiferromagnetic Mott insulating phase when *x* <0.2 (*7*, *8*).

The layered structure of this material, which plays a key role in the anisotropic transport and magnetic properties (*7*, *8*), also makes the crystal amenable to creating a surface by cleaving and offers a controlled way to investigate the manifestation of broken symmetry on a Mott MIT (*11*). Bulk studies have demonstrated that the Mott transition in the low Sr-doping regime is intimately related to a structural transition (*9*). When the system changes from a metallic to a Mott insulating phase on cooling, a concomitant structural transition to a more distorted ortho-rhombic phase is observed in the bulk. In sharp contrast, we demonstrate here that the Mott transition on a freshly cleaved surface of Ca_{1.9}Sr_{0.1}RuO_{4} occurs without an accompanying lattice distortion. Our observations and theoretical calculations show that the broken symmetry at the surface creates a structure that allows for an inherent, purely electronic Mott transition. Figure 1 shows unambiguous evidence for a shift of the MIT to lower temperature (*T*) at the surface of a Ca_{1.9}Sr_{0.1}RuO_{4} single crystal. The bulk MIT occurs at *T*_{c} = 154 K (c, critical), as shown by the abrupt change of the bulk electrical resistivity, whereas the surface transition occurs at *T*_{c,s} = 130 K (s, surface), as indicated by the opening of the energy gap measured by scanning tunneling spectroscopy (STS).

To investigate the surface Mott transition as well as the evolution of surface electronic properties and associated lattice dynamics, we have performed both STS and high-resolution electron energy loss spectroscopy (HREELS) measurements versus temperature on the surface of Ca_{1.9} Sr_{0.1}RuO_{4} (*12*). Both STS and HREELS are surface-sensitive techniques: STS probes the integrated density of electronic states near *E*_{F}, and the spectra from HREELS provide the surface dielectric response through quasi-particle excitations, including phonons and low-energy electron excitations. The low-energy quasi-particle excitations near *E*_{F}, referred to as the Drude weight in energy loss spectra, provide a signature of metallicity. The information obtained from HREELS at the surface is similar to that from optical conductivity spectroscopy for the bulk.

The measured *T* dependence of STS and HREELS spectra shows that both the STS and HREELS spectra display no sign of an energy gap at room temperature (Fig. 2). The HREELS spectra exhibit a sizable Drude weight apparent on the right shoulder of the elastic scattering peak, indicating the metallic character of the surface. The Drude weight decreases gradually with decreasing sample temperature as the elastic peak in the HREELS spectra becomes more and more symmetric. Correspondingly, the density of states near *E*_{F} also decreases with decreasing temperature as shown in the tunneling conductance (the derivative of the tunneling current *dI*/*dV)* close to zero bias. The energy loss peak at *ħ*ω_{s} ∼81 meV is an optical phonon associated with the apical oxygen vibration at the surface (*13*) (*ħ*, Planck's constant; ω_{s}, surface phonon frequency). The corresponding bulk mode is the RuO_{6}-stretching *A*_{1g} mode (Fig. 2B, inset) that appears at a lower energy [*ħ*ω_{b} ∼72 meV (ω_{b}, bulk phonon frequency)] for Ca_{2}RuO_{4} (*14*). This surface phonon peak gradually decreases its intensity while remaining at a constant energy of ∼81 meV with decreasing temperature until around 130 K.

Below 130 K, several abrupt changes occur in these spectroscopic measurements that are indicative of a distinct surface transition. An energy gap up to 0.3 ± 0.1 eV emerges in the STS spectra (Fig. 2A), indicating the establishment of an insulating state at the surface below *T*_{c,s} = 130 K. This value of the energy gap is near that measured from the bulk of Ca_{2}RuO_{4} (*14*–*16*). The gap of Ca_{2}RuO_{4} obtained from the optical conductivity measurement (*14*, *15*) varies with temperature, from 0.2 ± 0.05 eV at *T*_{c} ∼356 K to 0.6 ± 0.03 eV at 11 K. An analysis of the resistivity versus *T* gives a gap of ∼0.39 eV for Ca_{2}RuO_{4} (*16*). Simultaneously, the stretching phonon peak shows a shift to higher energy and a sudden increase in intensity in the HREELS spectra (Fig. 2B). In addition, the linewidth of the phonon abruptly changes from ∼20 meV above 130 K to 7 meV below. This change indicates a coupling between the lattice dynamics and MIT at the surface associated with a change in electron-phonon (*e-p*) interaction. But, as noted below, the change in the *e-p* coupling does not drive a structural phase transition at *T*_{c,s}.

To elucidate the correlation of these changes at the surface of Ca_{1.9}Sr_{0.1}RuO_{4}, we have analyzed the STS and HREELS spectra (*17*) to extract information about the *T* dependence of the energy gap and the Drude weight, as well as the phonon energy, intensity, and linewidth (Fig. 3) from the data taken on cooling. A sudden drop of the Drude weight and the opening of the energy gap are accompanied by an energy shift, a rapid increase in intensity, and an abrupt linewidth reduction of the surface phonon at the temperature *T*_{c,s} = 130 K, all of which are hallmarks of a surface Mott MIT. The surface MIT temperature (*T*_{c,s}) is more than 20 K lower than *T*_{c} (154 K) in the bulk. This finding is counterintuitive, because the conventional picture suggests that *e-e* correlation effects should be stronger at the surface than in the bulk as a result of the reduced atomic coordination, thus stabilizing the Mott insulating phase and pushing the Mott transition to higher temperatures at the surface as compared to the bulk.

The bulk first-order Mott MIT in Ca_{1.9}Sr_{0.1}RuO_{4} is accompanied by an abrupt lattice distortion (*9*). The bulk structure above and below the bulk MIT, as well as the difference between them, are presented in Table 1. We have determined the surface lattice structure by quantitatively analyzing the low-energy electron diffraction (LEED) *I*-*V* (intensity as a function of voltage) spectra (*18*) at both room temperature (RT) metallic and low-temperature (LT) insulating phases. In order to precisely determine the complex surface structure of this oxide compound, we have used a new self-consistent procedure (*19*) developed for LEED *I*-*V* structural determinations of oxide surfaces. The *I*-*V* of 16 nonequivalent beams was measured and compared with calculated intensities for surface model structures. The total *I*-*V* energy range (summation of energy ranges for the 16 non-equivalent beams) varied from 3982 to 4469 eV for four sets of data. A good fit with the Pendry reliability factor (*20*) *R*_{P} = 0.22 to experimental spectra was achieved, yielding the structure listed in Table 1.

A typical LEED image, which does not change with temperature from 300 to 90 K, is shown in Fig. 4A. The symmetry and the existence of a single glide line in the image pattern indicate a *p*(1 × 1) [001] surface of a bulk-terminated orthorhombic structure. This ortho-rhombic structure (with *Pbca* space group symmetry) is characterized by a static tilt and rotational distortions of RuO_{6} octahedra from the simple cubic perovskite phase. However, the analysis of the LEED *I*-*V* data shows that surface structure remains static across both the bulk and surface MIT (Table 1) except for a very gradual thermal relaxation. The comparison of the 90 and 300 K structures reveals no measurable difference (within the error bars). The error bars associated with a change in structure can be reduced by comparing the experimental data below and above the transition. *R*_{P} for such a comparison is ∼0.1, which allows us to conclude that both the octahedral tilt and the surface buckling remain unchanged within the error bars (0 ± 0.4° for tilt and 0 ± 0.02 Å for surface buckling).

Structural distortion is important to create and stabilize a Mott insulating state in the bulk of Ca_{2-x}Sr_{x}RuO_{4} (*7*–*9*). While keeping the same symmetry, the bulk crystal undergoes a distinct structural transition at *T*_{c} that is intimately linked to the MIT (*9*). This spontaneous structural transition (Table 1) is characterized by a substantial increase in the RuO_{6} tilt angle (∼5°), accompanied by a reduction in the Ru–apical oxygen ion O(2) distances (∼0.05 Å) and by a considerable increase of the in-plane Ru-O(1) bond lengths (∼0.04 Å). Similar structural distortions were not observed on the surface; therefore, we were observing a MIT that was solely driven by *e*-*e* interactions. All of our structural and spectroscopic data indicate that the surface MIT is of the same nature as the bulk; that is, a Mott MIT. Thus, despite its lower transition temperature (20 K lower), the inherent Mott insulating phase at the surface may be more stable than the inherent Mott insulating phase in bulk, if the bulk structural distortion can be eliminated.

Although in the metallic phase the surface has a slightly larger RuO_{6} rotation and tilt than the metallic bulk at room temperature, the observed tilts on the surface never reach the values observed in the bulk insulating phase. As shown schematically in Fig. 4B, the largest surface relaxation is the inward motion of the top Ca/Sr ions (which remains the same at both high and low temperature). This results in a static buckling in the surface Ca/Sr-O(2) layer of 0.23 Å. The explanation for this compression of the surface layer is straightforward and quite general. When the oxygen above the top Ca/Sr is removed, so is the attractive ionic force that allows the Sr to be pulled inward by the attractive forces from the oxygen below. This type of relaxation has been documented for surfaces of perovskites such as SrTiO_{3} (*21*), BaTiO_{3}, and PbTiO_{3} (*22*). This buckling of the surface Ca/Sr-O layer impedes the structural transition that occurs in the bulk at *T*_{c}.

The above scenario is confirmed by our first-principles calculations using a plane-wave pseudo-potential method and local density approximation [see (*23*, *24*) for technique details]. We calculate the total energy as a function of structural distortions, namely RuO_{6} rotation and tilting, while fixing the lattice parameters to the experimental ones (neutron diffraction data for the bulk (*9*) and the LEED results for the surface shown in Table 1). With the bulk structural parameters, our theoretical calculations reproduce the two stable bulk lattice structures (Fig. 4C); one with a tilt angle of ∼6.5° for the metallic phase and the other with a tilt angle of ∼10° for the insulating phase. To simulate the situation of the surface, we include the enhanced buckling of the Ca/Sr-O plane in a bulk calculation. As shown in Fig. 4C, this enhanced buckling pins the tilt angle at ∼7°, making the increased tilt energetically unfavorable and inhibiting the structural transition. The calculated tilt angle (∼7°) is in excellent agreement with LEED *I-V*–determined results, even though this is not a surface calculation. Although our calculations do not directly account for the broken symmetry of the surface, the search for total energy minima using a bulk calculation including the observed surface structural distortions reveals the influence of the surface enhanced buckling on the ground state structure.

With no structural transition involved in the surface Mott MIT, we can ask what drives the observed inherent Mott MIT at the surface of Ca_{1.9}Sr_{0.1}RuO_{4}. In Ca_{2-x}Sr_{x}RuO_{4}, three *t*_{2g} orbitals (4*d*_{xy}, 4*d*_{yz}, and 4*d*_{zx}) contribute to the electronic states near *E*_{F}. In the bulk crystal, both tilt and flattening of the RuO_{6} octahedra favor an antiferromagnetic ground state, whereas both tilt and rotational distortion stabilize the insulating phase by narrowing the *t*_{2g} bandwidth (*23*, *24*). Although never reaching the bulk insulating phase values (∼10° on average), the surface tilt angle (∼8° on average) is slightly greater than the bulk metallic phase values (∼6° on average). In addition, the surface RuO_{6} rotational distortion is greater than that in the bulk. All of these factors, plus the reduced coordination at the surface (*25*–*27*), which presumably enhances surface correlations, point in the direction of increasing the ratio of correlation to bandwidth (*U/W*). It is this enhanced ratio that is strong enough to drive the surface Mott MIT without the necessity of a structural transition.

A recent finite-temperature (250 K) multi-band dynamical mean field theory calculation for the Mott MIT in Ca_{2-x}Sr_{x}RuO_{4} (*28*) presents a model that lets us test these assertions. The occupancy of the in-plane *d*_{xy} band (*n*_{xy}) is critical for creating the Mott insulating state. We have used density functional theory (DFT) to calculate *n*_{xy} for the three relevant structures: (i) the RT bulk (RTB) metallic phase, (ii) the LT bulk (LTB) insulating phase, and (iii) the surface (s), with *n*_{xy}(s) calculated for a bulk with this structure. The DFT calculation yields *n*_{xy}(RTB) = 0.71, *n*_{xy}(LTB) = 0.75, and *n*_{xy}(s) = 0.73. The *n*_{xy} value for the pure Sr compound is 0.64. This calculation clearly shows the tendency, without any correlation of the three different structures, toward Mott insulator formation. The surface is more susceptible to an inherent Mott MIT than the room-temperature bulk.

The identification of the appropriate microscopic order parameter for a finite temperature MIT has and continues to be actively discussed (*29*–*31*). The order parameter associated with an inherent Mott MIT is masked by complications arising from coupled transitions (*31*). Figure 3 shows that, for the surface inherent Mott MIT, there are several experimental observables that can be configured as order parameters. The normalized gap seen with STS is an appropriate order parameter, as is the gap seen in optical conductivity measurements (*29*, *30*). The Drude weight can be configured to be another order parameter and, because of the strong *e*-*p* interaction, the energy and intensity of the optical phonon offer two other physical observables that can be defined appropriately to serve as order parameters. The data in Fig. 3 show how these observables all give the same *T*_{c,s}. Comparison to the first-order structural transition that occurs in the bulk at the MIT temperature indicates that the surface transition may be more gradual. Whether the surface Mott MIT is a second-order phase transition awaits a much more detailed investigation. What is required is a detailed study of the thermal hysteresis of the STS energy gap. However, the bulk first-order character of the Ca-rich single crystals in the Ca_{2-x}Sr_{x}RuO_{4} family complicates these measurements. Further experiments are also needed to elucidate the nature of the surface transition. A decisive experiment would be an angle-resolved photoemission study of the evolution of the coherent quasi-particle band as *T* approaches *T*_{c,s}, especially for *T* < *T*_{c}.

**Supporting Online Material**

www.sciencemag.org/cgi/content/full/318/5850/615/DC1

Materials and Methods

Figs. S1 to S4

References