Polaron-Driven Surface Reconstructions

Geometric and electronic surface reconstructions determine the physical and chemical properties of surfaces and, consequently, their functionality in applications. The reconstruction of a surface minimizes its surface free energy in otherwise thermodynamically unstable situations, typically caused by dangling bonds, lattice stress, or a divergent surface potential, and it is achieved by a cooperative modification of the atomic and electronic structure. Here, we combined first-principles calculations and surface techniques (scanning tunneling microscopy, non-contact atomic force microscopy, scanning tunneling spectroscopy) to report that the repulsion between negatively charged polaronic quasiparticles, formed by the interaction between excess electrons and the lattice phonon field, plays a key role in surface reconstructions. As a paradigmatic example, we explain the ($1\times 1$) to ($1\times 2$) transition in rutile ${\mathrm{TiO}}_2(110)$.

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When a crystal is cleaved, a new surface forms that interrupts the regular distribution of ions within the material. The breaking of surface bonds and the alteration of interatomic forces increase the surface stress and reduce the stability of the fresh surface. To overcome this instability, the majority of surfaces undergo a spontaneous geometrical reconstruction, which is generally associated with charge transfer between surface atoms. Unraveling the mechanism responsible for such reconstructions is essential to understanding properties of surfaces, and it helps optimize materials performance in applications such as microelectronics and fuel cells. By combining calculations and experiments, we have found an alternative and radically different mechanism for surface reconstructions based on charge trapping.

Polarons play a pivotal role in this process. These quasiparticles, which form via the coupling between excess charges and the lattice phonon field, are ubiquitous in polar semiconductors such as oxides. We studied an archetypal polaron material, rutile titanium dioxide, and varied the polaron density at the surface by introducing an increasing number of surface oxygen vacancies. Owing to the repulsive interaction between the polarons, the surface free energy increases until, at a critical amount, the surface transforms.

This polaron-mediated mechanism is likely to be a pervasive phenomenon that could explain structural, electronic, and magnetic reconstructions at surfaces and interfaces of ionic materials. Besides the fundamental interest, surface polarons could be employed to tune surface properties, control surface geometries, and provide a way to facilitate charge transfer in catalytic processes.

Figure 1

The ($1\times 1$) and ($1\times 2$) surface phases of ${\mathrm{TiO}}_2(110)$. (a) Large-area STM image of a reduced rutile (110) single crystal. Unreconstructed ($1\times 1$) regions with single oxygen vacancies $V_{\mathrm{O}}$ appear together with reconstructed ($1\times 2$) ${\mathrm{Ti}}_2{\mathrm{O}}_3$ stripes. (b,c) Structural models of the ($1\times 1$) and ($1\times 2$) phases, respectively. (d,e) STS spectra (line) taken above ($1\times 1$) and ($1\times 2$), together with calculated polaronic gap states (filled area), shifted upwards by $\approx 0.25\mathrm{eV}$ to align the center of mass of the ${\mathrm{Ti}}^{3+}$ (polaronic) peaks with the experiment (in this way, the DFT peak positions are also in better agreement with the calculated vertical excitation energy $E_{\mathrm{EL}}$ [46]). (f)–(k) High-resolution images of the ($1\times 1$) and ($1\times 2$) regions marked in panel (a), overlaid with the respective structural models. AFM images (i,f) show the highest O atoms (${\mathrm{O}}_{2c}$ and ${\mathrm{O}}_{\mathrm{rec}}$) on the surface, and STM images show the empty (g,j) and filled (h,k) states.

Figure 2

Polaron distribution in ${\mathrm{TiO}}_2(110)$. (a)–(d), Most stable polaron configurations obtained by FPMD and subsequent relaxations at the various $V_{\mathrm{O}}$ concentrations specified in each panel. The histograms illustrate how often the polarons are found in $S0$ (orange) and $S1$ (green) Ti sites during the FPMD runs.

Figure 3

Polaron distribution along the ${\mathrm{Ti}}_{S1}^{\mathrm{A}}$ row. (a) Simulated filled-states STM (at 2 Å from the surface) of an isolated polaron around a ${\mathrm{Ti}}_{S1}^A$ site. (b) The corresponding charge density isosurface shows the high-density $d_{z^2}$-like orbital localized at ${\mathrm{Ti}}_{S1}^A$ (yellow) and the large, low-density cloud extending across the nearby ${\mathrm{Ti}}_{S1}^A$ and ${\mathrm{Ti}}_{S0}^A$ sites. (c)–(e) Calculated polaron-polaron autocorrelation functions along ${\mathrm{Ti}}_{S1}^A$ and ${\mathrm{Ti}}_{S0}^A$ rows extracted from FPMD runs at $c_{V_{\mathrm{O}}}=5.6\%$, 16.7%, and 22.2%. (f) Experimental filled-states STM image at $c_{V_{\mathrm{O}}}=16.7\%$, and (g) corresponding polaron-polaron autocorrelation function along the [001] rows. (h) Sketch of the $3\times 1$ periodicity in the ${\mathrm{Ti}}_{S1}^A$ row.

Figure 4

${\mathrm{TiO}}_2(110)$ surface phase diagram. Surface free energy ($\mathrm{\Delta }G$) for the most stable configurations obtained from the MD for the reduced ($1\times 1$) structures at different $V_{\mathrm{O}}$ concentrations (all lines except pink) and for the ($1\times 2$) ${\mathrm{Ti}}_2{\mathrm{O}}_3$ reconstruction (pink line) as a function of the chemical potential $\mathrm{\Delta }{\mu }_{\mathrm{O}}$ with respect to the stoichiometric ($1\times 1$) phase. (a) Delocalized solution: Excess electrons are spread across all lattice sites and delocalized at the bottom of the conduction band. At $c_{V_{\mathrm{O}}}=50.0\%$, the ($1\times 1$) structure is degenerate with the ($1\times 2$) ${\mathrm{Ti}}_2{\mathrm{O}}_3$ reconstruction (${\mathrm{Ti}}_2{\mathrm{O}}_4$ with 50% of $V_{\mathrm{O}}$). (b) Localized solution: The excess electrons are trapped in distinct Ti sites, mostly located in $S0$. The insets show the distribution of excess electrons in the ($1\times 2$) structure. The localized polaron picture is capable of predicting the ($1\times 1$) to ($1\times 2$) transition, manifested by the increased stability of the reconstructed ${\mathrm{Ti}}_2{\mathrm{O}}_3$ phase at low oxygen chemical potential compared to the highly reduced ($1\times 1$) phases.

Figure 5

Polaron energies (meV/polaron) as a function of $c_{V_{\mathrm{O}}}$. (a) Polaron formation energy $E_{\mathrm{POL}}$, computed as the difference between the ground states of the localized and delocalized solutions. (b) Strain energy $E_{\mathrm{ST}}$, i.e., energy cost to locally distort the lattice in order to accommodate polarons. (c) Electronic energy $E_{\mathrm{EL}}$, i.e., energy gained by localizing the electron in the distorted lattice.