Coherent Quasiparticles with a Small Fermi Surface in Lightly Doped ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$

We characterize the electron doping evolution of $({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{)}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ by means of angle-resolved photoemission. Concomitant with the metal insulator transition around $x\approx 0.05$ we find the emergence of coherent quasiparticle states forming a closed small Fermi surface of volume $3x/2$, where $x$ is the independently measured La concentration. The quasiparticle weight $Z$ remains large along the entire Fermi surface, consistent with the moderate renormalization of the low-energy dispersion, and no pseudogap is observed. This indicates a conventional, weakly correlated Fermi liquid state with a momentum independent residue $Z\approx 0.5$ in lightly doped ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$.

Figure 1

Low energy excitations in lightly doped ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. (a) Experimental Fermi surface of $({\mathrm{Sr}}_{0.935}{\mathrm{La}}_{0.065}{)}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ taken with $h\nu =83\mathrm{eV}$ at 8 K. We denote the $(\pi ,0)$ point of the two-dimensional Ir sublattice by $X$ and the $(\pi /2,\pi /2)$ point by $M$. (b),(c) Photoemission intensity along the $\mathrm{\Gamma }M$ and $\mathrm{\Gamma }X$ high symmetry directions, respectively. (d) Stack of energy distribution curves around the Fermi surface extracted from the data shown in panel (b).

Figure 2

Doping evolution of $({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{)}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. (a) Dispersion along the nodal $\mathrm{\Gamma }M$ direction. Coherent quasiparticle states emerge for $x>0.05$. (b) momentum distribution curves (MDCs) at the Fermi energy. The Fermi wave vector increases monotonically with doping, indicative of an increasing density of itinerant carriers.

Figure 3

$\mathrm{LDA}+\mathrm{SO}+U$ calculations of the Fermi surface for $U=3\mathrm{eV}$ and different doping levels treated by the VCA superimposed on ARPES data for $x=0.065$. The inset shows an EDC taken at 8 K at $\approx (0,-0.6\pi )$, demonstrating the absence of a pseudogap in the antinodal direction at the measurement temperature of 8 K.

Figure 4

Luttinger volume and quasiparticle residue. (a) Luttinger volume of the experimental Fermi surface (blue), compared with the nominal Luttinger volume of $3x/2$ arising from the stoichiometry of $({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{)}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ if every lanthanum atom dopes one itinerant electron (red line). The doping evolution of the conduction band minimum is shown in black on the right axis. (b) Band dispersion along $\mathrm{\Gamma }M$ together with a $\mathrm{LDA}+\mathrm{SO}-\mathrm{VCA}$ calculation ($U=0$, $x=0.065$) along (0, 0, $-2\pi /c$) – ($2\pi /a$, 0, $-2\pi /c$) corresponding to the $\mathrm{\Gamma }M\mathrm{\Gamma }$ direction of the 2D surface Brillouin zone. The hole pocket found in this calculation (see the Supplemental Material [38]) has been suppressed for clarity and the electron pocket at $M$ was shifted in energy to match the experimental Fermi wave vectors. (c),(d) Quasiparticle residue $Z$ along the Fermi surfaces at $\pm (\pi /2,\pi /2)$ (circles and triangles, respectively) estimated from the weight of the coherent quasiparticles.