Coherent and incoherent bands in La and Rh doped ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$

In ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ and ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$, correlations, magnetism, and spin-orbit coupling compete on similar energy scales, creating a new context to study metal-insulator transitions (MIT). We use here angle-resolved photoemission to investigate the MIT as a function of hole and electron doping in ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$, obtained respectively by Ir/Rh and Sr/La substitutions. We show that there is a clear reduction as a function of doping of the gap between a lower and upper band on both sides of the Fermi level, from 0.2 to 0.05 eV. Although these two bands have a counterpart in band structure calculations, they are characterized by a very different degree of coherence. The upper band exhibits clear quasiparticle peaks, while the lower band is very broad and loses weight as a function of doping. Moreover, their ARPES spectral weights obey different periodicities, reinforcing the idea of their different nature. We argue that a very similar situation occurs in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ and conclude that the physics of the two families is essentially the same.

Figure 1

(a) Sketch of the band structure expected for ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ in DFT calculations (thick lines, see Appendix for full calculation). Two bands cross the Fermi level that we call lower and upper band, forming respectively hole pockets at $X$ and electron pockets at M. They can be viewed as originating from the thin lines with a gap (see arrow) opening at their crossings. The thin lines are similar to the $J=1/2$ band of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ (see Appendix), doubled because of the bilayer. The colors refer to the two bands of the bilayer and the solid/dotted lines to the direct/folded bands due to the 2 Ir in-plane (see Appendix). (b) Simplified version of the semi-metallic structure described in (a). (c): Same as (b) with a larger gap between lower and upper bands. The two bands could be viewed as DFT bands split by a large magnetic gap, as obtained, for example, in a magnetic LDA+$U$ calculation. They could also be viewed as incoherent Hubbard bands of a DMFT calculation. They are shown here shifted in k to recall the initial semimetallic situation, but this is not an important point. The larger width of the lines is meant to symbolize the incoherent nature. (d) Scenario expected for electron doping of a Mott insulator: the Hubbard bands do not shift significantly, but transfer weight (their lower weight is symbolized by the grey color) to a QP band (solid lines) forming at the bottom of the upper Hubbard band. This QP band is typically strongly renormalized with respect to DFT bands. (e) What we observe in ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ seems an intermediate situation, where the upper band behaves as a DFT or weakly renormalized QP band and the lower band as a shifted Hubbard band.

Figure 2

Energy-momentum plots of the dispersion along $\mathrm{\Gamma }M$ (a) and $\mathrm{\Gamma }X$ (b) in ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. (c) Dispersions extracted from (a) and (b). (d) EDC peaks at $\mathrm{\Gamma }$ and $X$. (e) Map of the spectral weight integrated at $-200$ meV in a 20 meV window. The thick black square delimits the 1 Ir BZ and the dotted thinner black square the 2 Ir BZ.

Figure 3

(a)–(c) Energy-momentum plots of the dispersion along $\mathrm{\Gamma }M$ and around X in ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ doped with 3% Rh (a), 1.6% La (b), and 6% La (c). The black dotted line indicates the position of the $J=3/2$ band in ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. (d)–(f) Extracted dispersion, compared with that of the pure ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ (Fig. 2), shifted as indicated. (g) EDC at $\mathrm{\Gamma }$ compared between selected samples. (h) EDC at $M$, $X$, and $X^{\prime }$ $[X^{\prime }$ is defined in (c)].

Figure 4

[(a), (d), and (g)] Energy-momentum plots of the dispersion along ${\mathrm{\Gamma }}^{\prime }M$ in a sample with 6% La, at photon energies of (a) 80, (d) 54, and (g) 36 eV, corresponding respectively to $k_z=1$, 0, 0.5. [(b), (e), and (h)] Zoom on the dispersion around $M$ ($k=0.707$) of the image above. Thick lines: sketch of the $J=1/2$ bands expected around $M$. The different colors correspond to bilayer splitting and the solid (dotted) line to the direct (folded) character. [(c), (f), and (i)] MDC spectra at $E_F$ (top) and $-250$ meV (bottom), showing the oscillation of weight between the different bands. The vertical markers indicate the positions expected for the four different bands.

Figure 5

Resistivity of the four samples used in this study. (Inset) Image of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ sample by electron microscope.

Figure 6

(a) Sketch of the Fermi surface expected for the $J=1/2$ band of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. The black square is the 1 Ir BZ and the dotted square the 2 Ir BZ. We call “direct” the bands of the 1 Ir BZ (solid lines) and “folded” those obtained by folding in the 2 Ir BZ (dotted lines). (b) Dispersion along $X\mathrm{\Gamma }M\mathrm{\Gamma }$ of the $J=1/2$ band (thin blue line) and its folded band (dotted blue line). Bold curves simulate the opening of a gap for an interaction at $\mathrm{q}=(\pi ,\pi )$, such as the AF order. The size of the line is proportional to the expected ARPES intensity. The top of the $J=3/2$ band at $\mathrm{\Gamma }$ is shown by red lines. (c) ARPES Energy-momentum plots of the band structure along $\mathrm{\Gamma }M$ in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$.

Figure 7

(a) Black lines: band structure calculation for ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. The bands of dominant $J=1/2$ ($J=3/2$) character are emphasized by blue (red) lines. The folded bands are shown as dotted lines. (b) Calculation for the same compound, but with magnetism stabilized by $U=2.7$ eV.