Sr₂IrO₄中d波赝自旋电流序的微观模型实现
Microscopic model realization of $\boldsymbol{d}$-wave pseudospin current order in Sr$_{\boldsymbol{2}}$IrO$_{\boldsymbol{4}}$
AI总结：
该研究构建了包含库仑排斥与面内各向异性的Sr₂IrO₄有效单轨道模型，在平均场层面实现了d波赝自旋电流序，揭示其与反铁磁性的竞争共存关系及衍生的自旋键向列性，并证明载流子掺杂可调控共存态与手性。
摘要：
具有交错环流赝自旋电流的d波赝自旋电流序（dPSCO）被提出作为一种隐藏电子序，用于解释化学计量比Sr₂IrO₄中出人意料的空间对称性破缺，以及电子掺杂Sr₂IrO₄中的非常规赝能隙现象。然而，目前仍缺乏能够解释dPSCO产生机制的微观模型。由于Ir的5d轨道空间延展范围较大，最近邻库仑排斥作用V在Sr₂IrO₄中被认为具有显著强度，它能够在平均场层面驱动dPSCO的形成，不过此时dPSCO与带有环流电荷电流的交错通量相在能量上是简并的。我们发现，源于Ir 5d电子的洪特规则耦合与自旋轨道耦合协同相互作用的、J_eff=1/2赝自旋之间有效超交换相互作用的面内各向异性Γ₂，能够解除这种简并并稳定赝自旋电流。随后我们研究了包含在位库仑排斥U、最近邻库仑排斥V以及面内各向异性Γ₂的J_eff=1/2电子有效单轨道模型。我们得到了平均场基态，分析了其性质，并确定了在固定Γ₂时、以U和V为坐标轴的平面内化学计量比Sr₂IrO₄的相图。我们证明了dPSCO的实现，以及它与反铁磁性的竞争和共存关系。值得注意的是，我们发现dPSCO与反铁磁性的共存会自然产生自旋键向列性，且这三种有序态的自旋方向会形成非平庸的手性。此外，我们还表明共存态的出现及其手性可以通过载流子掺杂进行调控。
英文摘要：
The $d$-wave pseudospin current order ($d$PSCO) with staggered circulating pseudospin current has been proposed as the hidden electronic order to describe the unexpected breaking of spatial symmetries in stoichiometric Sr$_{2}$IrO$_{4}$ and the unconventional pseudogap phenomena in electron doped Sr$_{2}$IrO$_{4}$. However, a microscopic model for the emergence of $d$PSCO is still lacking. The nearest neighbor Coulomb repulsion $V$, which is expected to be significant in Sr$_{2}$IrO$_{4}$ due to the large spatial extension of the Ir $5d$ orbitals, is capable of driving $d$PSCO on the mean-field level, albeit the latter is energetically degenerate to the staggered flux phase with circulating charge current. We find the in-plane anisotropy $Γ_2$ in the effective superexchange interaction between $J_\text{eff}={1\over 2}$ pseudospins, originating from the cooperative interplay between Hund's rule coupling and spin-orbit coupling of Ir $5d$ electrons, is able to lift the degeneracy and stabilize the pseudospin currents. The effective single-orbital model of $J_\text{eff}={1\over 2}$ electrons, including onsite Coulomb repulsion $U$, nearest neighbor Coulomb repulsion $V$, and the in-plane anisotropy $Γ_2$, is then studied. We obtain the mean-field ground states, analyze their properties, and determine the phase diagram of stoichiometric Sr$_{2}$IrO$_{4}$ in the plane spanned by $U$ and $V$ at a fixed $Γ_2$. We demonstrate the realization of $d$PSCO, and its competition and coexistence with antiferromagnetism. Remarkably, we find the coexistence of $d$PSCO and antiferromagnetism naturally leads to spin bond nematicity, with the spin directions of these three orders forming nontrivial chirality. Furthermore, we show that the emergence of the coexistent state and its chirality can be tuned by carrier doping.
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