Non-adiabatic Berry phase for semiconductor heavy holes under the coexistence of Rashba and Dresselhaus spin-orbit interactions

Abstract

We formulate the non-Abelian Berry connection (tensor $\mathbb{R}$) and phase (matrix $\mathbf{\Gamma }$) 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 $\mathbf{k}\cdot \mathbf{p}$ 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 Schrödinger equation with the semi-classical equation-of-motion for cyclotron motion and then calculate the energy dependence of $\mathbf{\Gamma }$ 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 $\mathbf{\Gamma }$, 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 $\mathbf{\Gamma }$.

21 pages, 9 figures

References in corpus (13)

• Electric Field Effect in Atomically Thin Carbon Films
• Experimental Realization of Universal Geometric Quantum Gates with Solid-State Spins
• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Phase analysis of quantum oscillations in graphite
• Spin states and persistent currents in mesoscopic rings: spin-orbit interactions
• The Two-flux Composite Fermion Series of Fractional Quantum Hall States in Strained Si
• Spin Orientation of Holes in Quantum Wells
• Second Chern Number and Non-Abelian Berry Phase in Topological Superconducting Systems
• Role of linear and cubic terms for the drift-induced Dresselhaus spin-orbit splitting in a two-dimensional electron gas
• Spin precession and alternating spin polarization in spin-3/2 hole systems
• Valley splitting of Si/SiGe heterostructures in tilted magnetic fields
• Spin-dependent edge-channel transport in a Si/SiGe quantum Hall system
• Berry-phase induced entanglement of hole-spin qubits in a microwave cavity