Electronic Origin of Density Wave Orders in a Trilayer Nickelate

Abstract

The discovery of superconductivity in Ruddlesden-Popper nickelates has established a new frontier in the study of high-temperature superconductors. However, the underlying pairing mechanism and its relationship to the material's electronic and magnetic ground states remain elusive. Since unconventional superconductivity often emerges from a complex interplay of magnetic correlations, elucidating the magnetic ground state of the nickelates at ambient pressure is crucial for understanding the emergence of superconductivity under high pressure. Here, we combine high-resolution angle-resolved photoemission spectroscopy with tight-binding model simulation to investigate the electronic structure of the representative trilayer Ruddlesden-Popper nickelate La$_4$Ni$_3$O$_{10}$. We provide the first experimental evidence of band splitting induced by interlayer coupling and further resolve the momentum-dependent density wave gap structures along all the Fermi surfaces. Our findings identify the mirror-selective Fermi surface nesting as the origin of the interlayer antiferromagnetic spin density wave and demonstrate the dominant role of Ni-3d$_{z^2}$ orbitals in the low-energy physics of La$_4$Ni$_3$O$_{10}$. These results provide a fundamental framework for understanding the magnetic interactions and high-temperature superconductivity mechanism in the Ruddlesden-Popper nickelate family.

Figures (5)

• Figure 1: Measured and simulated Fermi surface of La$_4$Ni$_3$O$_{10}$.a-b Fermi surface mapping (a) and constant energy contour at the binding energy of 30 meV (b) measured at 20 K by using laser-based ARPES with a photon energy of 6.994 eV under the $s$ polarization geometry where the electric field vector E of the incident light is perpendicular to the photoelectron emission plane; its direction is marked by the double arrow near the bottom-left corner. To increase the momentum coverage, a sample bias voltage of -97 volts was applied during the measurementsMiaoTM2025arXiv. c-d Same as (a-b) but measured under $p$ polarization geometry where the electric field vector E is within the photoelectron emission plane. In our case, it consists of both the in-plane component and the out-of-plane component as marked by a double arrow and an out-of-plane arrow near the bottom-left corner. e Fermi surface mapping measured at 20 K by using synchrotron-based ARPES with a photon energy of 85 eV. f Measured Fermi surface of La$_4$Ni$_3$O$_{10}$ obtained from (a), (c), (e) and band structure analysis. g Schematic of trilayer tight-binding model for La$_4$Ni$_3$O$_{10}$. It consists of three Ni-O planes, one inner plane (IP) and two out planes (OP1 and OP2). It involves two orbitals, $d_{x^2-y^2}$ (Red colored) and $d_{z^2}$ (blue colored). The hopping between orbitals is marked by colored double arrows (see details in Supplementary Information). h Simulated Fermi surface from the tight-binding model. The details are described in Supplementary Information.
• Figure 2: Measured and simulated band structures of La$_4$Ni$_3$O$_{10}$.a Band structures along high symmetry directions of $\overline{M}-\overline{\Gamma}-\overline{M}$ (left panel), $\overline{X}-\overline{\Gamma}-\overline{X}$ (middle panel) and $\overline{M}-\overline{X}-\overline{M}$ (right panel) measured at 20 K by synchrotron-based ARPES with a photon energy of 85 eV. The observed bands are marked by arrows with different colors. b Simulated band structures along the corresponding high symmetry directions. To illustrate both the occupied and unoccupied electronic states, these simulated data are not multiplied by the Fermi-Dirac distribution function. c-d Measured Fermi surface mappings by laser-based ARPES with 6.994 eV photon energy in $s$ (c) and $p$ (d) polarization geometries. A sample bias voltage of -30 volts was applied during the measurements. The locations of the momentum cuts are marked by solid grey lines. e Band structures along different momentum cuts crossing M point measured at 20 K with 6.994 eV photon energy under $s$ polarization geometry. The location of the momentum cuts is indicated by solid grey lines in (c). f Corresponding MDC second derivative images from (e). g Simulated band structures along the corresponding momentum cuts. h Band structures along different momentum cuts measured at 20 K with 6.994 eV photon energy under $p$ polarization geometry. The location of the momentum cuts is indicated by solid grey lines in (d). i Corresponding MDC second derivative images from (h). j Simulated band structures along the corresponding momentum cuts.
• Figure 3: Momentum dependent energy gap along different Fermi surface sheets in La$_4$Ni$_3$O$_{10}$. a Symmetrized EDCs along the $\alpha$ Fermi surface measured at 20 K by laser-based ARPES with 6.994 eV photon energy (lower panel). The location of the momentum points is indicated by empty circles in the upper panel. The EDC peak position is marked by ticks. b-e Same as (a) but along the $\beta$ (b), $\beta_f$ (c) and $\beta'$ (d) Fermi surface. e Symmetrized EDCs along the $\gamma$ Fermi surface measured at 20 K by synchrotron-based ARPES with 85 eV photon energy (lower panel). The location of the momentum points is indicated by empty circles in the upper panel. f Extracted energy gap as a function of the Fermi surface angle $\theta$ for the $\alpha$ (black circles), $\beta$ (red circles), $\beta_f$ (red squares), $\beta'$ (green circles) and $\gamma$ (blue circles) Fermi surfaces obtained from (a-e). The Fermi surface angle $\theta$ is defined in the upper panels of (a-e). The solid symbols are derived from the symmetrized EDCs shown in lower panels of (a–e) whereas the open symbols are obtained by symmetrization, taking into account the fourfold symmetry. The uncertainties are marked by error bars. g Three-dimensional plot of the energy gap in La$_4$Ni$_3$O$_{10}$. The corresponding Fermi surface is shown at the bottom.
• Figure 4: Temperature evolution of the energy gap on $\alpha$ and $\gamma$ bands. a Band structure of the $\alpha$ band measured along the momentum cut (Cut1) at different temperatures. The location of the momentum cut (Cut1) is marked by the black solid line in (b). b Schematic Fermi surface of La$_4$Ni$_3$O$_{10}$. The location of two momentum cuts (Cut1 and Cut2) is marked. c EDCs at the Fermi momentum of the $\alpha$ band measured at different temperatures obtained from (a). The momentum location to extract the EDCs is marked by the black arrow in the left-most panel in (b). d Corresponding symmetrized EDCs obtained from (c). The black ticks mark the peak position of the symmetrized EDCs. e Band structure of the $\gamma$ band measured along the momentum cut (Cut2) at different temperatures. The location of the momentum cut (Cut2) is marked by the blue solid line in (b). f EDCs at the Fermi momentum of the $\gamma$ band measured at different temperatures obtained from (e). The momentum location to extract the EDCs is marked by the blue arrow in (e). g Corresponding symmetrized EDCs obtained from (f). The black ticks mark the peak position of the symmetrized EDCs. h Temperature evolution of the energy gap on the $\alpha$ (black circles) and $\gamma$ (blue squares) bands obtained from (d) and (g), respectively. i Temperature dependent resistivity of La$_4$Ni$_3$O$_{10}$ measured in ab-plane. j Temperature dependent magnetic susceptibility ($\chi$) of La$_4$Ni$_3$O$_{10}$ measured with out-of-plane magnetic field.
• Figure 5: Mirror-selective scattering driven interlayer antiferromagnetic SDW in La$_4$Ni$_3$O$_{10}$. a Calculated band structures along high-symmetry directions from the tight-binding model (see Note 1 in Supplementary Information for details and used parameters). These bands are labeled as $\alpha$, $\beta$, $\beta'$ and $\gamma$ with their bonding character (bonding, non-bonding and anti-bonding) and parity (even (+) and odd (-)) marked. The parity is determined by considering the symmetry of the wavefunction of the bands in the three Ni-O layers with respect to the inner mirror plane (see Supplementary Information for details). b Orbital-projected Fermi surface calculated using the tight-binding model. The color scale represents the relative contribution of the $d_{z^2}$ and $d_{x^2-y^2}$ orbitals. The parity of each Fermi surface sheet is labeled as $+$ (even) or $-$ (odd). The arrowed lines denote the nesting vectors. c Calculated odd-channel susceptibility ($\chi_{odd}$) from the tight-binding model (see Supplementary Information for details). The scattering vector $Q_1\approx(0.62\pi, 0.62\pi)$ is indicated by the arrowed line. d Calculated even-channel susceptibility ($\chi_{even}$). The scattering vectors $Q_2$, $Q_3$ and $Q_4$ are indicated by the arrowed lines. e Schematic of real-space wavefunctions of the bonding and nonbonding states of the $d_{z^2}$ orbitals. Horizontal lines denote the three Ni-O layers. With respect to the inner mirror plane, the wave function of the bonding state exhibit even (+) parity while that of the non-bonding state exhibits odd (-) parity. The $Q_1$ nesting occurs between these two states. f Schematic illustration of the interlayer antiferromagnetic SDW with wave vector $Q_1\approx(0.62\pi, 0.62\pi)$ in La$_4$Ni$_3$O$_{10}$. The blue shapes represent the spin density modulation on the Ni-O layers which exhibits a $\pi$ phase shifts between OP1 and OP2.