{
  "id": "2302.07436",
  "version": "v1",
  "published": "2023-02-15T02:57:55.000Z",
  "updated": "2023-02-15T02:57:55.000Z",
  "title": "Non-adiabatic Berry phase for semiconductor heavy holes under the coexistence of Rashba and Dresselhaus spin-orbit interactions",
  "authors": [
    "Tatsuki Tojo",
    "Kyozaburo Takeda"
  ],
  "comment": "21 pages, 9 figures",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.mtrl-sci",
    "cs.CE",
    "physics.comp-ph",
    "quant-ph"
  ],
  "abstract": "We formulate the non-Abelian Berry connection (tensor $\\mathbb R$) and phase (matrix $\\boldsymbol \\Gamma$) for a multiband system and apply them to semiconductor holes under the coexistence of Rashba and Dresselhaus spin-orbit interactions. For this purpose, we focus on the heavy-mass holes confined in a SiGe two-dimensional quantum well, whose electronic structure and spin texture are explored by the extended $\\boldsymbol{k}\\cdot\\boldsymbol{p}$ approach. The strong intersubband interaction in the valence band causes quasi-degenerate points except for point $\\Gamma$ of the Brillouin zone center. These points work as the singularity and change the Abelian Berry phase by the quantization of $\\pi$ under the adiabatic process. To explore the influence by the non-adiabatic process, we perform the contour integral of $\\mathbb R$ faithfully along the equi-energy surface by combining the time-dependent Schr\\\"{o}dinger equation with the semi-classical equation-of-motion for cyclotron motion and then calculate the energy dependence of $\\boldsymbol \\Gamma$ computationally. In addition to the function as a Dirac-like singularity, the quasi-degenerate point functions in enhancing the intersubband transition via the non-adiabatic process. Consequently, the off-diagonal components generate both in $\\mathbb R$ and $\\boldsymbol \\Gamma$, and the simple $\\pi$-quantization found in the Abelian Berry phase is violated. More interestingly, these off-diagonal terms cause \"resonant repulsion\" at the quasi-degenerate energy and result in the discontinuity in the energy profile of $\\boldsymbol \\Gamma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-15T02:57:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dresselhaus spin-orbit interactions",
      "semiconductor heavy holes",
      "non-adiabatic berry phase",
      "abelian berry phase",
      "coexistence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}