Direct Observation of Unidirectional Density Wave and Band splitting in a Single-Domain Trilayer Nickelate Pr$_4$Ni$_3$O$_{10}$

TL;DR

This study uses micro-focused ARPES on a single-domain Pr4Ni3O10 to disentangle intrinsic electronic structure from density-wave folding in a trilayer nickelate. It identifies inter-orbital nesting between alpha and beta bands as the dominant driver of the SDW, quantifies an isotropic ~$44$ meV gap on the alpha pocket, and resolves a genuine intrinsic beta-band splitting arising from interlayer hopping between outer NiO2 layers with magnitude near $50$ meV. Additionally, it reveals strong orbital-selective mass renormalization, especially for the dz2-derived gamma band, and maps back-folded bands associated with CDW/SDW vectors. Collectively, these findings provide a coherent microscopic fingerprint of the interplay between density waves, orbital physics, and trilayer coupling in Pr4Ni3O10, informing models of superconductivity in nickelate RP phases.

Abstract

Unraveling the interplay between density-wave (DW) instabilities and multi-orbital physics is critical for understanding superconductivity in Ruddlesden-Popper nickelates, yet intrinsic electronic features have been persistently obscured by material inhomogeneity and thus the multi-domain averaging effect. Here, we employ micro-focused angle-resolved photoemission spectroscopy ($μ$-ARPES) on single-domain Pr$_4$Ni$_3$O$_{10}$ to disentangle the complex hierarchy of intrinsic and back-folded bands, explicitly identifying the electronic states driving the DW phase transition. We provide decisive spectroscopic evidence that the low-energy reconstruction is governed by inter-orbital nesting between the $α$ and $β$ bands. Specifically, we resolve a orbital-dependent gap of $\sim44$ meV on the $α$ pocket, a value quantitatively consistent with prior measurements, unifying previously conflicting experimental reports regarding the locus and magnitude of the DW gap. Furthermore, we reveal strong orbital-selective mass renormalization in the $d_{z^2}$ states and successfully resolve the long-sought intrinsic trilayer $β$-band splitting, establishing a critical lower bound for the outer-layer hopping. These results define a coherent microscopic fingerprint for the trilayer nickelates, identifying the specific nesting channels and correlation effects that underpin the phase diagram.

Figures (5)

• Figure 1: (a) Side view of the crystal structure of Pr$_4$Ni$_3$O$_{10}$, dark frame indicates the unit cell (consisting of two Pr$_4$Ni$_3$O$_{10}$ formula units); (b) Top view of the crystal structure with a two-dimensional lattice of O and Ni atoms. The dash dark line frame represent the original unit cell without considering the tilted Ni-O octahedra and the solid line frame represents the real structural unit cell by considering the tilting of the Ni-O octahedra; (c) Calculated Fermi surface of Pr$_4$Ni$_3$O$_{10}$ obtained from the DFT calculations, appended red arrow represent the scattering $\textbf{q*}$ is the unit scattering vector. To note, the anisotropy lattice parameter generate 0.01 Å$^{-1}$ difference on $k_x$/$k_y$ direction of the Brillouin zone. Therefore the magnitude of unit scattering vector $\textbf{q*}$ can be denoted as $q*~=~\frac{2\pi}{(a+b)/2}$. (d) In-plane resistivity ($\rho_{ab}$) of Pr$_4$Ni$_3$O$_{10}$; (e) Schematic SDW and CDW alien with Ni lattice model, the SDW/CDW propagates unidirectionally along the a/b-axis of the crystal lattice. (f) The two domains with orthogonal electronic structures measured in the Pr$_4$Ni$_3$O$_{10}$.
• Figure 2: (a) Photon energies-$k_{//}$ mapping along the (0, 0)-($\pi$, $\pi$) direction. It is obtained by integrating the spectral intensity within 50 meV with respect to the Fermi level; (b) Fermi surface mapping measured at 8 K by using synchrotron-based ARPES with a photon energy of 75 eV. It is obtained by integrating the spectral intensity within 50 meV with respect to the Fermi level. Brillouin zones are appended, with the dark solid lines represent the BZ of pristine lattice, and dark dash lines represent the BZ of octahedral lattice. (c) Measured Fermi surface of Pr$_4$Ni$_3$O$_{10}$ obtained form (b), appended with momentum cuts marks. It consists of two main Fermi surface sheets, $\alpha$ and $\beta$, and their octahedral back-folded bands $\alpha_{oct}$ and $\beta_{oct}$. (d-e) Band dispersions measured along momentum cuts Cut1 and Cut2, respectively. The location of the momentum cuts is shown in (c). The observed bands are labeled by their corresponding Fermi surface sheets; (f) DFT calculated band dispersion of Pr$_4$Ni$_3$O$_{10}$ without considering U. Red lines represent the contribution of Ni 3$d_{x^2-y^2}$ orbitals and blue lines represent the contribution of Ni 3$d_{z^2}$ orbitals. (g-j) Measured band dipsersions (empty circles) and the corresponding calculated bands (solid lines). The direction of the corresponding momentum cut is shown in the inset at the bottom-right corner of each figure. The gray curve in the figure is the quadratic curve obtained by fitting the original DFT calculation results, while the black curve is the result after being scaled by the corresponding mass enhancement values to match the experimental data.
• Figure 3: (a) A 3D intensity plot of the ARPES spectra along orthogonal directions $\overline{\Gamma}$-$\overline{X}/\overline{Y}$, with red arrows label the anisotropic features. (b) Fermi surface mapping measured at 8 K by using 75 eV photons, appended with $\beta$ and $\beta_{oct}$ pockets. It is obtained by integrating the spectral intensity within 10 meV with respect to the Fermi level. The a* = (a+b)/2. The red arrows with label "1" mark the crossed extra features circled by $\beta$ and $\beta_{oct}$ pockets, and those labeled by "2" mark those extra features parallel to $\beta_{oct}$ pockets. (c) Fermi surface mapping taken with 75 eV appended with $\beta$ (dark solid frame) and $\beta_{CDW}$ (green solid frame). (d) Fermi surface mapping measured at 8 K by using 49 eV photons, appended with $\beta$ (dark solid frame) and $\beta_{SDW}$ pockets (orange solid frame); (e) Band dispersions extracted from the 75 eV mapping along momentum cuts along $k_y$ = 0.775 Å$^{-1}$ [cut (i), the inset of (e)]; (f) Band dispersions extracted from the 75 eV mapping along momentum cuts along $k_y$ = 0.205 Å$^{-1}$ [cut (ii), the inset of (e)]; In (e-f) The MDC (red curve) extracted at Fermi level is appended on the top empty region above the $E_F$. The double-head arrows indicate the scattering vector; (g) Band dispersions extracted from the 49 eV mapping along momentum cuts along $k_y$ = -0.21 Å$^{-1}$ (labeled by red dash line in the inset); (h) Schematic Fermi surface combined with all the pristine $\beta$ (dark solid) and back-folded $\beta$ result from octahedral tilting superlattice (dark dash lines), SDW (origin solid lines) and CDW (green solid lines).
• Figure 4: (a) Fermi surface intensity map at $E_F$ measured with 75 eV photons; (b) Constant energy map at $E_F$ - 30 meV; black arrows indicate the $\alpha$ pocket. (c) The $E_F$ - 30 meV map overlaid with the extracted $\alpha$-band counter (hollow red circles) and the $\beta$-band counter (blue lines). The dashed red lines mark the momentum cut (i) and (ii) used in (d,e); the orange arrow highlights the nesting relation between the $\alpha$ and $\beta$ pockets. (d,e) Energy-momentum dispersions along cut (i) and (ii), respectively. (f) The EDCs extracted from the shaded momentum windows in (e), taken at the $\alpha$-band top (red) and at $k_F$ of the $\beta$ band (blue).
• Figure 5: (a) Schematic Fermi surface including all relevant bands. The red (blue) dashed box marks region I (II), corresponding to the zoomed Fermi-surface maps in (b) [(f)]. Colored dots indicate representative momenta $k_{\beta}$ used for the splitting analysis in (e) and (g,h). (b) Zoomed Fermi-surface intensity map measured at 8 K with 75 eV photons. (c) Tight-binding Fermi surface calculated with an outer--outer NiO$_2$-plane hopping $t_{\perp}^{x_{oo}}=50$ meV. (d,e) Energy--momentum dispersions from the 75 eV dataset along the cuts $k_y=0$ and $k_y$=-0.38 Å$^{-1}$, respectively, as indicated by the yellow dashed lines (i) and (ii) in (b); the corresponding MDC stacks are shown on the right. (f) Zoomed Fermi-surface intensity map measured at 8 K with 49 eV photons; arrows highlight the resolved $\beta/\beta'$ splitting. (g,h) Energy-momentum dispersions from the 49 eV dataset along the cuts $k_x=0$ and $k_x$ = 0.13 Å$^{-1}$, respectively, as indicated by the yellow dashed lines (iii) and (iv) in (f). The accompanying MDCs (bottom panels) are integrated over the energy window from $E_F$ to $E_F-50$ meV. Inverted triangles mark the extracted band splittings.