Hierarchy of Lifshitz Transitions in the Surface Electronic Structure of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ under Uniaxial Compression

We report the evolution of the electronic structure at the surface of the layered perovskite ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ under large in-plane uniaxial compression, leading to anisotropic $B_{1g}$ strains of ${ϵ}_{xx}-{ϵ}_{yy}=-0.9\pm 0.1\%$. From angle-resolved photoemission, we show how this drives a sequence of Lifshitz transitions, reshaping the low-energy electronic structure and the rich spectrum of van Hove singularities that the surface layer of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ hosts. From comparison to tight-binding modeling, we find that the strain is accommodated predominantly by bond-length changes rather than modifications of octahedral tilt and rotation angles. Our study sheds new light on the nature of structural distortions at oxide surfaces, and how targeted control of these can be used to tune density of state singularities to the Fermi level, in turn paving the way to the possible realization of rich collective states at the ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ surface.

Figure 1

(a) Top view of the ${\mathrm{RuO}}_2$ layer of bulk ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. (b) Bulk Fermi surface measured using ARPES (left, reproduced from Ref. [19]) and calculated from our tight-binding model (right). (c) Calculated electronic structure in the vicinity of the $\overline{\mathrm{M}}$ point, showing the bulk vHS arising from the saddle point (SP) of the $\gamma$ band. (d) Corresponding calculated dispersions along $\overline{\mathrm{\Gamma }}\text{−}\overline{\mathrm{M}}\text{−}\overline{\mathrm{X}}$. (e) Bipartite ${\mathrm{RuO}}_2$ layer of the surface of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. (f) Surface Fermi surface measured with ARPES (left, $h\nu =100\mathrm{eV}$, linear vertical polarisation) and calculated from a tight-binding model including the octahedral rotation (right). (g) and (h) Corresponding calculated electronic structure of the surface bands in the vicinity of the $\overline{\mathrm{M}}$ point. $\xi$ is the bandwidth of the unstrained surface electronic structure (see Supplemental Material, Fig. S4 [29]).

Figure 2

Dispersions ($h\nu =40\mathrm{eV}$, linear horizontal polarisation) close to the $\overline{\mathrm{M}}$ point of unstrained ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ measured along the (a) $\overline{\mathrm{\Gamma }}\text{−}\overline{\mathrm{M}}$ and (b) $\overline{\mathrm{M}}\text{−}\overline{\mathrm{X}}$ directions. (c)–(f) Equivalent dispersions measured along the (c) $\overline{\mathrm{\Gamma }}\text{−}{\overline{\mathrm{M}}}_y$, (d) ${\overline{\mathrm{M}}}_y\text{−}\overline{\mathrm{X}}$, (e) $\overline{\mathrm{\Gamma }}\text{−}{\overline{\mathrm{M}}}_x$, and (f) ${\overline{\mathrm{M}}}_x\text{−}\overline{\mathrm{X}}$ direction for a strained sample (${ϵ}_{xx}-{ϵ}_{yy}=-0.9\pm 0.1\%$).

Figure 3

Evolution of the surface electronic structure with uniaxial compression in the (a) angular and (c) longitudinal limits (see text). The dispersions extracted from our measured ARPES data using linear horizontal (LH) and vertical (LV) polarisation are shown in (b). The calculations employ a $B_{1g}$ strain of ${ϵ}_{xx}-{ϵ}_{yy}=-2.4\%$, overestimating the experimental value as is also the case for bulk calculations [30, 31] (see the Supplemental Material [29]).

Figure 4

Measured dispersions ($h\nu =40\mathrm{eV}$, linear vertical polarisation) centered at the $\overline{\mathrm{\Gamma }}$ point of the second Brillouin zone (${\overline{\mathrm{\Gamma }}}_{(0,1)}$) for (a) unstrained and (b) strained ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, and (c) $\overline{\mathrm{\Gamma }}$-point energy distribution curves. (d) Tight-binding calculations showing the effect of strain within the longitudinal limit on the states near the Brillouin zone center, with projected $d_{xy}$ orbital weight. (e) Magnified view of band dispersions in the vicinity of the new $\delta$ pocket (top), and corresponding $d$-orbital content (bottom).