Robust electronic edge or surface modes play key roles in the fascinating quantized responses exhibited by topological materials. Even in trivial materials, topological bands and edge states can be induced dynamically by a time-periodic drive. Such Floquet topological insulators (FTIs) inherently exist out of equilibrium; the extent to which they can host quantized transport, which depends on the steady-state population of their dynamically induced edge states, remains a crucial question. In this work, we obtain the steady states of two-dimensional FTIs in the presence of the natural dissipation mechanisms present in solid state systems. We give conditions under which the steady-state distribution resembles that of a topological insulator in the Floquet basis. In this state, the distribution in the Floquet edge modes exhibits a sharp feature akin to a Fermi level, while the bulk hosts a small density of excitations. We determine the regimes where topological edge-state transport persists and can be observed in FTIs.

Quantized transport and steady states of Floquet topological insulators

We present findings for the 0.7(2e2/h) feature in the hole quantum conductance staircase that is caused by silicon one-dimensional channels prepared by the split-gate method inside the p-type silicon quantum well (SQW) on the n-type Si(100) surface. Firstly, the interplay of the spin depolarization with the evolution of the 0.7(2e2/h) feature from the e2/h to 3/2 e2/h values as a function of the sheet density of holes is revealed by the quantum point contact connecting two 2D reservoirs in the p-type SQW. The 1D holes are demonstrated to be spin polarized at low sheet density, because the 0.7(2e2/h) feature is close to the value of 0.5(2e2/h) that indicates the spin degeneracy lifting for the first step of the quantum conductance staircase. The 0.7(2e2/h) feature is found to take, however, the value of 0.75(2e2/h) when the sheet density increases, thereby giving rise to the spin depolarization of the 1D holes. Secondly, the amplitude and phase sensitivity of the 0.7(2e2/h) feature are studied by varying the value of the external magnetic field and the top-gate voltage that are applied perpendicularly to the plane of the double-slit ring embedded in the p-type SQW, with the extra quantum point contact inserted in the one of its arms. The Aharonov–Bohm and the Aharonov–Casher conductance oscillations obtained are evidence of the interplay of the spontaneous spin polarization and the Rashba spin–orbit interaction (SOI) in the formation of the 0.7(2e2/h) feature. Finally, the variations of the 0.7(2e2/h) feature caused by the Rashba SOI are found to take in the fractional form with both the plateaus and steps as a function of the top-gate voltage.

Phase and amplitude response of the '0.7?feature' caused by holes in silicon one-dimensional wires and rings

A 40-band k⋅p model is used to compute the standard k⋅p band parameters at Γ, X, and L valleys in direct-band-gap bulk materials for Td group semiconductors. The values of the effective masses for electrons, heavy holes, and light holes in the Γ, X, and L valleys are in good agreement with those reported in other publications. Satisfactory agreement with available experimental data is also obtained by the present model. Finally, our results show that the effective Lande factor g∗, the κ valence band parameter, and the Dresselhauss spin-orbit coupling constant δ conicide well with available experimental data. The k⋅p Hamiltonian parameters, in particular, are adjusted to get g∗(GaAs)=−0.42, which turn out to be in agreement with the experimental value of −0.44.

Band parameters of GaAs, InAs, InP, and InSb in the 40-band k⋅p model

The role of interfaces and higher bands on the electronic structure of embedded semiconductor quantum dots (QDs) was investigated. The term in the multiband k·p Hamiltonian that captures the effect of interface band mixing was derived starting from the microscopic theory. It was shown, analytically and numerically, that, with such a term included, the right symmetry of the QD system can be captured. It leads to splitting of otherwise degenerate energy levels of the order of several meV. The inclusion of additional higher bands beyond the ones from the standard eight-band model also leads to the reduction of symmetry from an artificially high one to the true atomistic symmetry of the system, however their quantitative effect is weaker. These results prove that the multiband k·p Hamiltonians are fully capable of describing the correct symmetry of a QD.

/pdf/symmetry-reduction-in-multiband-hamiltonians-for-2q76he758d.pdf

Symmetry reduction in multiband Hamiltonians for semiconductor quantum dots: The role of interfaces and higher energy bands

The band structure of indirect-band gap semiconductors (AlAs, GaP) as well as indirect-band gap alloys semiconductors (GeSi) is described theoretically by using a 30×30 k×p model including the d far-level contribution. For all materials investigated, the resulting electronic band structure parameters are in good agreement with experimental values. The method also provides a good description of the second conduction band which is useful for transport modeling. Finally, our results show that Luttinger parameters, the κ valence band parameter, and the effective masses in the X and L valleys are in good agreement with available experimental data.

Band structures of AlAs, GaP, and SiGe alloys: A 30 k×p model

A 24-k ⋅ p model is used to compute the principal effective-mass parameters at Γ, X and L valleys in a direct-band-gap semiconductor (GaAs) as well as an indirect-band-gap semiconductor (Si) The values of the effective masses for electrons, heavy holes and light holes in the Γ, X and L valleys are in very good agreement with those reported in other publications Satisfactory agreement with available experimental data is also obtained by this model The Luttinger parameters and interband momentum matrix elements proposed in this work are consistent with the previous publications

http://iopscience.iop.org/article/10.1088/0268-1242/20/9/003/pdf

O Zitouni

Papers

Band parameters for GaAs and Si in the 24-k sdot p model