Non-adiabatic Berry phase for semiconductor heavy holes under the coexistence of Rashba and Dresselhaus spin-orbit interactions
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We formulate the non-Abelian Berry connection (tensor ℝ) and phase (matrix Γ) 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 k·p approach. The strong intersubband interaction in the valence band causes quasi-degenerate points except for point Γ of the Brillouin zone center. These points work as the singularity and change the Abelian Berry phase by the quantization of π under the adiabatic process. To explore the influence by the non-adiabatic process, we perform the contour integral of ℝ faithfully along the equi-energy surface by combining the time-dependent Schrödinger equation with the semi-classical equation-of-motion for cyclotron motion and then calculate the energy dependence of Γ 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 ℝ and Γ, and the simple π-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 Γ.
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