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Effect of electron-electron interactions on Rashba-like and spin-split systems

机译：电子-电子相互作用对Rashba样和自旋分裂系统的影响

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摘要

The role of electron-electron interactions is analyzed for Rashba-like and spin-split systems within a tight-binding single-band Hubbard model with on-site and all nearest-neighbor matrix elements of the Coulomb interaction. By Rashba-like systems we refer to the Dresselhaus and Rashba spin-orbit-coupled phases while spin-split systems have spin-up and spin-down Fermi surfaces shifted relative to each other. Both systems break parity but preserve time-reversal symmetry. They belong to a class of symmetry-breaking ground states that satisfy: (i) electron crystal momentum is a good quantum number, (ii) these states have no net magnetic moment, and (iii) their distribution of "polarized spin" in momentum space breaks the lattice symmetry. For all members of this class, the relevant Coulomb matrix elements are found to be nearest-neighbor exchange J, pair hopping J', and nearest-neighbor repulsion V. These ground states lower their energy most effectively through J, hence we name them class J states. The competing effects of V-J' on the direct and exchange energies determine the relative stability of class J states. We show that the spin-split and Rashba-like phases are the most favored ground states within class J because they have the minimum anisotropy in polarized spin. We analyze these two states on a square lattice and find that the spin-split phase is always favored for near-empty bands; above a critical filling, we predict a transition from the paramagnetic to the Rashba-like phase at a critical J(J_(c1)) and a second transition from the Rashba-like to the spin-split state at J_(c2)>J_(c1)- An energetic comparison with ferromagnetism highlights the importance of the role of V in the stability of class J states. We discuss the relevance of our results to (i) the α and β phases proposed by Wu and Zhang in the Fermi-liquid formalism and (ii) experimental observations of spin-orbit splitting in Au(111) surface states.
机译：在具有库仑相互作用的现场和所有最近邻矩阵元素的紧密结合的单带Hubbard模型中，分析了Rashba型和自旋分裂系统的电子-电子相互作用的作用。在类似Rashba的系统中，我们指的是Dresselhaus和Rashba自旋轨道耦合的相，而自旋分裂系统的自旋向上和向下旋转的费米表面彼此相对偏移。两个系统都打破了奇偶性，但保留了时间反转对称性。它们属于满足以下条件的一类对称破坏基态：（i）电子晶体动量是一个好的量子数，（ii）这些状态没有净磁矩，并且（iii）它们在动量中的“极化自旋”分布空间破坏了晶格对称性。对于此类的所有成员，相关的库仑矩阵元素被发现为最近邻居交换J，成对跳跃J'和最近邻居排斥V。这些基态通过J最有效地降低其能量，因此我们将它们命名为Class J状态。 V-J'对直接和交换能量的竞争作用决定了J类状态的相对稳定性。我们证明自旋分裂相和Rashba样相是J类中最受青睐的基态，因为它们在极化自旋中具有最小的各向异性。我们在一个方格上分析这两个状态，发现自旋分裂相始终适合于近空频带。在临界填充以上，我们预测在临界J（J_（c1））下从顺磁相到Rashba样相的转变，并且在J_（c2）> J_处从Rashba样到自旋分裂状态的第二个转变。 （c1）-与铁磁性的能量比较突显了V在J类状态的稳定性中的重要性。我们讨论了我们的结果与（i）Wu和Zhang在费米-液形式学中提出的α和β相以及（ii）Au（111）表面态自旋轨道分裂的实验观察的相关性。

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  • 来源
    《Physical review》 |2010年第19期|p.195131.1-195131.19|共19页
  • 作者

    A. Alexandradinata; J. E. Hirsch;

  • 作者单位

    Department of Physics, University of California-San Diego, La Jolla, California 92093-0319, USA;

    Department of Physics, University of California-San Diego, La Jolla, California 92093-0319, USA;

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  • 关键词

    band and itinerant models;

    机译：带和巡回模型;

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