Structure-property relation in the cuprates: a possible explanation for the pseudogap

Abstract

We propose a structure-property relation that could be key to the pseudogap phenomenology in cuprates. The underlying nonsymmorphic crystal structure in the low-temperature orthogonal phase endows the lattice with a sublattice structure that gives rise to two electronic bands near the Fermi surface. In the presence of spin-orbit coupling, the hybridization of these two bands generates small Fermi pockets and, correspondingly, a change in the number of free carriers. A sublattice structure also leads to angle-resolved photoemission spectroscopy (ARPES) matrix-element interference, naturally explaining the emergence of Fermi arcs and their consistency with closed Fermi pockets. We employ a symmetry analysis to highlight the expected Fermi surface properties, and complement it with density functional theory (DFT) for a quantitative discussion and comparison with recent experiments in doped La$_2$CuO$_4$. The proposed mechanism can consistently account for the most salient features of the pseudogap in the cuprates, namely, the Fermi surface reconstruction with the formation of small Fermi pockets and the corresponding change in carrier density, and the observation of Fermi arcs by ARPES.

Figures (4)

• Figure 1: Structure-property relation in the pseudogap. Center: Schematic phase diagram for cuprate superconductors highlighting the structural origin of the pseudogap (PG). The dotted line marks both the onset of the PG, usually referred to as $T^*$, and the structural transition from the HTT to the LTO phase. In the HTT phase, both Fermi-liquid (FL) and strange-metallic (SM) behaviour are reported. In the LTO phase, PG behavior is observed. The full line schematically marks the onset of superconductivity at the critical temperature $T_c$. Left and Right: 3D view of the crystal structure of the LTO and HTT phases of of La$_2$CuO$_4$, respectively. La atoms are depicted as large green spheres, O as small red spheres, and Cu as medium blue spheres. Note the two shades of blue in the LTO phase, highlighting the two inequivalent Cu sites. The thin line marks the conventional unit cell with four and two Cu atoms, respectively.
• Figure 2: The pseudogap as a 2D Peierls instability. a) Illustration of a monoatomic chain without (top) and with (bottom) dimerization. b) Band structure of a monatomic chain with only nearest-neighbour hopping at half-filling along the 1D Brillouin zone (BZ). c) Same band structure after zone folding (extra dashed blue curve) corresponding to the unit cell doubling and halving of the BZ. The vertical dashed lines mark the new BZ boundary. d) Resulting band structure after dimerization. e) Illustration of the Cu-O octahedra along the Cu-O bonds in the plane without (top) and with (bottom) the octahedra tilt. f) Band structure of the cuprates close to $p^*$. For this schematic picture, we used Eq. \ref{['Eq:TB_HTT']} with nominal parameters and a chemical potential corresponding to $p<p^*$, $\mu=0.28$ eV. g) Same band structure after zone folding (extra dashed blue curve) associated with the doubling of the unit cell in the plane. h) Resulting band structure with oxygen octahedra tilt, with the formation of small Fermi pockets along the $\Gamma-M$ direction and the gapping of the Fermi surface along the $\Gamma-X$ direction. i) Two-dimensional view of the folded band structure of cuprates close to $p^*$. Highlighted are the high-symmetry points (with labels corresponding to the pre-folded BZ) and BZ boundaries before (full line) and after (dashed line) oxygen octahedra tilt. For simplicity, we focus on the $k_xk_y$ plane and neglect orthorhombicity. j), k), and l) display the Fermi surfaces corresponding to panels f), g), and h), respectively.
• Figure 3: The pseudogap as a structural transition for doped La$_2$CuO$_4$. a) Fermi surface of the HTT phase for $p=0.27$ in the $k_z=0$ plane. The full blue line corresponds to our DFT results, and the full gray line corresponds to the results reported in Fang et al. for $p=0.24$Fang2022. The shifted doping provides better agreement between the presented tight-binding model and both experimental results and full DFT calculations (see Supplemental Material). The full black line indicates the BZ. b) 3D view of the Brillouin Zone (BZ) in the LTO phase, with face-centered orthorhombic character. We highlight the $k_z=0$ boundary of the BZ with a thick full line and the pseudotetragonal (PT) BZ with a thick dashed line. c) Fermi surface of the LTO phase for $p=0.23$ in the $k_z=0$ plane with no $k_z$-dependent terms and no SOC. The full orange line corresponds to our DFT results, and the full gray line corresponds to the results reported in Fang et al. Fang2022 for $p=0.21$. The dashed black line marks the PTBZ, and the dashed gray line marks the BZ of the HTT phase rotated by $45^\circ$ to highlight the band folding. d) Same as panel c), but with $k_z$-dependent terms and no SOC. The full black line highlights the BZ of the LTO phase in the $k_z=0$ plane. e) and f) Same as panel d), but with SOC, $s=20$ meV, in the $k_z=0$ and $k_z=\pi/c$ planes, respectively.
• Figure 4: Main features of the pseudogap. a) Bonding (left) and antibonding (right) bands in the LTO phase plotted separately with nominal parameters excluding the $k_z$ dependence for a simpler discussion within the PTBZ (dashed lines) and enhanced SOC for better visualization ($s=0.1 eV$ and $\mu=0.275$ eV). Note that the antibonding band does not cross the Fermi energy (indicated by the light-coloured plane) and the bonding band is associated with small Fermi pockets highlighted by orange lines. b) Band structure in the HTT phase displaying a large Fermi surface highlighted by the blue line. c) Schematic evolution of carrier density $n_H$ with doping $p$, assuming the structural phase transition at $p^*$. d) ARPES spectra (center) corresponding to the Fermi surface in a). The normalized matrix element associated with the bonding (left) and antibonding (right) bands are shown as side panels, with the black regions corresponding to zero and the bright areas to one. e) ARPES spectra corresponding to the Fermi surface in b). A broadening of $\sigma=50$ meV was used for panels d) and e) (see Supplemental Material for more details).