Electronic structure, magnetic properties and pairing tendencies of the copper-based honeycomb lattice Na$_2$Cu$_2$TeO$_6$

TL;DR

This study uses computational methods to analyze the electronic, magnetic, and pairing properties of Na$_2$Cu$_2$TeO$_6$, revealing it as a Mott insulator with complex magnetic interactions and potential pairing tendencies.

Contribution

It provides a comprehensive theoretical analysis of Na$_2$Cu$_2$TeO$_6$, including electronic structure, magnetic exchange, and pairing tendencies, which advances understanding of this dimerized copper-based chain system.

Findings

Na$_2$Cu$_2$TeO$_6$ is a Mott insulator with strong electronic correlations.

The system exhibits both antiferromagnetic and ferromagnetic couplings.

Hole doping leads to tight pairs, indicating possible pairing tendencies.

Abstract

Spin-$1/2$ chains with alternating antiferromagnetic and ferromagnetic couplings have attracted considerable interest due to the topological character of their spin excitations. Here, using density functional theory and density matrix renormalization group methods, we have systematically studied the dimerized chain system Na$_2$Cu$_2$TeO$_6$. Near the Fermi level, the dominant states are mainly contributed by the Cu $3d_{x^2-y^2}$ orbitals highly hybridized with the O $2p$ orbitals in the nonmagnetic phase, leading to an "effective" single-orbital low-energy model. Furthermore, the bandwidth of the Cu $3d_{x^2-y^2}$ states is small ($\sim 0.8$ eV), suggesting that electronic correlations will strongly affect this system. By introducing such electronic correlations, we found this system is a Mott insulator. Moreover, by calculating the magnetic exchange interactions ($J_1$, $J_2$ and $J_3$), we explained the size and sign of the exchange interactions in Na$_2$Cu$_2$TeO$_6$, in agreement with neutron experiments. In addition, we constructed a single-orbital Hubbard model for this dimerized chain system, where the quantum fluctuations are taken into account. Both AFM and FM coupling ($\uparrow$-$\downarrow$-$\downarrow$-$\uparrow$) along the chain were found in our DMRG and Lanczos calculations, in agreement with DFT and neutron results. We also calculated the hole pairing binding energy $\Delta E$ which becomes negative at Hubbard $U \sim 11$ eV, indicating incipient pairing tendencies. Finally, we also looked at various cases of hole doping that always exhibit tight pairs. Thus, we believe our results for Na$_2$Cu$_2$TeO$_6$ could provide guidance to experimentalists and theorists working on this dimerized chain system, such as short-range magnetic coupling, doping effects, and possible pairing tendencies.