Electron Glass Phase with Resilient Zhang-Rice Singlets in ${\text{LiCu}}_3{\mathrm{O}}_3$

${\text{LiCu}}_3{\mathrm{O}}_3$ is an antiferromagnetic mixed valence cuprate where trilayers of edge-sharing Cu(II)O ($3d^9$) are sandwiched in between planes of Cu(I) ($3d^{10}$) ions, with Li stochastically substituting Cu(II). Angle-resolved photoemission spectroscopy (ARPES) and density functional theory reveal two insulating electronic subsystems that are segregated in spite of sharing common oxygen atoms: a Cu $d_{z^2}/\mathrm{O}$ $p_z$ derived valence band (VB) dispersing on the Cu(I) plane, and a Cu $3d_{x^2-y^2}/\mathrm{O}$ $2p_{x,y}$ derived Zhang-Rice singlet (ZRS) band dispersing on the Cu(II)O planes. First-principle analysis shows the Li substitution to stabilize the insulating ground state, but only if antiferromagnetic correlations are present. Li further induces substitutional disorder and a 2D electron glass behavior in charge transport, reflected in a large 530 meV Coulomb gap and a linear suppression of VB spectral weight at $E_F$ that is observed by ARPES. Surprisingly, the disorder leaves the Cu(II)-derived ZRS largely unaffected. This indicates a local segregation of Li and Cu atoms onto the two separate corner-sharing $\mathrm{Cu}(\mathrm{II}){\mathrm{O}}_2$ sub-lattices of the edge-sharing Cu(II)O planes, and highlights the ubiquitous resilience of the entangled two hole ZRS entity against impurity scattering.

Figure 1

(a) ${\text{LiCu}}_3{\mathrm{O}}_3$ crystal structure, UC and natural cleavage planes. (b) Cu(I) form a square lattice with periodicity $a$ (red square). (c) In a Cu(II) plane, edge-sharing ${\mathrm{CuO}}_4$ plaquettes form a 2D square lattice with the same periodicity. The black square is the non-primitive $c(2\times 2)$ UC. Li stochastically substitutes Cu(II) according to the stoichiometric ratios in (a). (d) In-plane (red) and out-of-plane (blue) DC resistivity of ${\text{LiCu}}_3{\mathrm{O}}_3$. (e) The natural logarithm of the in plane resistivity scales as $T^{-1/2}$ with slope $\sqrt{T_0}$. (f) Li $1s$ spectra of both ${\text{LiCu}}_3{\mathrm{O}}_3$ cleaves ($h\nu =100\mathrm{eV}$). (g) Integrated VB spectra of both ${\text{LiCu}}_3{\mathrm{O}}_3$ cleaves, compared to results from ${\text{LiCu}}_2{\mathrm{O}}_2$ (blue [14]) and T-CuO (red [12]).

Figure 2

(a) ARPES CE map of ${\text{LiCu}}_3{\mathrm{O}}_3$—C20 ($h\nu =150\mathrm{eV}$, $T=150\mathrm{K}$) at $E=-0.7\mathrm{eV}$. Red and black squares are BZs corresponding to the UCs defined in Fig. 1. As at normal photo-electron emission, the ZRS is suppressed [12, 60], we show data centered around $(k_x,k_y)=(0,4\pi /a^{\prime }$). (b) ARPES dispersion along the white triangular path in (a), compared to results from ${\text{LiCu}}_2{\mathrm{O}}_2$ in (f). The latter also exhibits an umklapp band (UB) not present in ${\text{LiCu}}_3{\mathrm{O}}_3$ [14]. (c) and (d) Dispersions along the black dashed lines in (a), and compare directly to the ZRS of T-CuO in (g) and (h) [12]. (e) Artificial sum of ARPES CE cuts of ${\text{LiCu}}_2{\mathrm{O}}_2$ [14] and T-CuO [12].

Figure 3

ARPES CE maps of ${\text{LiCu}}_3{\mathrm{O}}_3$—C40 ($h\nu =150\mathrm{eV}$, $T=300\mathrm{K}$) at (a) $E=-0.4\mathrm{eV}$ and (b) $E=0=E_F$. (c) VB dispersion along the black dotted path in (b). (d) K deposition shifts the VB and recovers a parabolic dispersion. (e) EDC at $k_x=0$ as a function of K deposition. The undoped EDC (red line) exhibits a linear suppression indicative of a Coulomb gap (cf. Fermi edge of poly-crystalline Cu, black). K doping shifts the VB towards higher energies and recovers a Lorentzian, as highlighted by the line shape comparison in (f). (g) The (bad) metal to insulator transition of the VB is accompanied by a suppression of the shoulder in Li $1s$ [59].

Figure 4

(a) Decomposition of the CuO plane into two corner-sharing ${\mathrm{CuO}}_2$ sublattices. The ZRS is formed from Cu $d_{x^2-y^2}$ (blue) and O $p_{x,y}$ (red) orbitals. (b) Energetically most favorable periodic ordering motif of a Cu3 plane (40% Li). Light and dark blue squares represent $\mathrm{Cu}(\mathrm{II}){\mathrm{O}}_2$ plaquettes on different sublattices; green dots represent Li ions. The nonmagnetic UC is drawn in gray. Unfolded $\mathrm{DFT}+U$ band structure of (c) ${\text{Cu}}_4{\mathrm{O}}_3$ without Li, magnetism and Hubbard-$U$; of (d) ${\text{LiCu}}_3{\mathrm{O}}_3$, without magnetism and Hubbard-$U$; of (e) ${\text{Cu}}_4{\mathrm{O}}_3$ with magnetism and Hubbard-$U$; and of (f) ${\text{LiCu}}_3{\mathrm{O}}_3$ with AFM ordering plus Hubbard-$U$ correlations. The color code in panels (c)–(f) was adapted to the one in Figs. 2 and 3, with yellow corresponding to no and blue corresponding to a strong spectral weight.