Ground State Properties of the Doped Kitaev-Heisenberg Chain: Topological Superconducting and Mott Insulating Phases Driven by Magnetic Frustration

Abstract

We study the hole-doped Kitaev-Heisenberg chain using the density-matrix renormalization group. In the Kitaev-only limit, the bond-directional exchange itself promotes pairing, favoring spin-singlet and spin-triplet superconducting tendencies for antiferromagnetic and ferromagnetic Kitaev couplings, respectively, together with finite-size Majorana edge correlations suggestive of topological superconductivity. In the full Kitaev-Heisenberg chain, cooperative $J$ and $K$ exchanges broadly stabilize superconductivity, while competition between $J$ and $K$ induces a strong filling dependence and enables superconductivity even when both $J$ and $K$ are weak. At quarter filling, this competition produces a Mott insulator with spontaneous hopping dimerization. These results identify magnetic frustration as a common mechanism underlying superconducting and interaction-driven insulating phases in doped Kitaev systems.

Figures (5)

• Figure 1: (a) Lattice structure of the KH chain. (b) Schematic picture of two translation-symmetry-breaking Mott insulating states, where each bonding orbital is occupied by one fermion.
• Figure 2: Phase diagram of the $t$--$K$ chain ($J=0$) in the $K/t$--$n$ plane. Contour lines indicate the TLL parameter $K_\rho$, while color maps show the end-to-end Majorana correlator $G_{1L}$ and the pair-binding energy $\Delta_{\rm B}/t$. Owing to the symmetry under $K\!\to\!-K$, only $G_{1L}$ for $K>0$ and $\Delta_{\rm B}$ for $K<0$ are shown (see text). The data for $G_{1L}$ are shown for an open chain with $L=40$, while those for $\Delta_{\rm B}$ are extrapolated to the thermodynamic limit.
• Figure 3: Phase diagram of the $t$--$J$--$K$ chain in the $K/t$--$J/t$ plane at (a) $n=0.1$, (b) $0.5$, and (c) $0.9$. A color map of the charge gap $\Delta_{\rm c}/t$ is shown for the Mott-insulating phase at $n=0.5$.
• Figure 4: Results for an open chain of length $L=200$. (a) Density--density correlation $\langle n_{100} n_i\rangle$ at $K=5$. (b) Connected density--density correlation $D(r)=\langle n_{100} n_{100+r}\rangle-\langle n_{100}\rangle\langle n_{100+r}\rangle$ at $K=5$, shown on a log--log scale as a function of distance $r$. Insets: semi-log plot of $D(r)$ (left) and a schematic picture of the dimerized Mott state (right). (c) Spin--spin correlations $|\langle S^\alpha_{100} S^\alpha_{100+r}\rangle|$ for $\alpha=x,y,z$ at $K=5$ and $J=-0.5$. (d) Real-space profile of the $y$-component correlation $\langle S^y_{100} S^y_i\rangle$ at $K=5$ and $J=-0.5$.
• Figure 5: Pair--pair correlation functions $P_\gamma(r)$ ($\gamma={\rm S, T1, T2}$) and density--density correlation functions $D(r)$, plotted on log--log scales for representative parameter sets in the phase diagram: (a) $K=10.0$, $J=0.0$, $n=0.1$ (SSC, $K_\rho=2.70$); (b) $K=-11.0$, $J=0.0$, $n=0.3$ (TSC1, $K_\rho=1.64$); (c) $K=5.0$, $J=3.0$, $n=0.5$ (SSC, $K_\rho=1.23$); (d) $K=-5.0$, $J=-4.0$, $n=0.5$ (TSC1, $K_\rho=1.13$); (e) $K=10.0$, $J=-5.0$, $n=0.5$ (TSC2, $K_\rho=1.50$); and (f) $K=-10.0$, $J=2.0$, $n=0.9$ (TSC1/TSC2, $K_\rho=1.05$). Panels (a)--(d) are obtained for open chains with $L=400$, while panels (e) and (f) are for $L=200$.