Topological insulators (TIs) are a new quantum state of matter discovered recently, which are characterized by unconventional bulk topological invariants. Proposals for practical applications of the TIs are mostly based upon their metallic surface or edge states. Here, we report the theoretical discovery of a bulk quantum pumping effect in a two-dimensional TI electrically modulated in adiabatic cycles. In each cycle, an amount of spin proportional to the sample width can be pumped into a nonmagnetic electrode, which is attributed to nonzero spin Chern numbers C±. Moreover, by using a half-metallic electrode, universal quantized charge pumping conductivities −C±e 2 /h can be measured. This discovery paves the way for direct investigation of the robust topological properties of the TIs.

We investigate the effect of introducing nearest-neighbor p-wave superconducting pairing to both the static and kicked extended Harper model with two periodic phase parameters acting as artificial dimensions to simulate three-dimensional systems. It is found that in both the static model and the kicked model, by varying the p-wave pairing order parameter, the system can switch between a fully gapped phase and a gapless phase with point nodes or line nodes. The topological property of both the static and kicked model is revealed by calculating corresponding topological invariants defined in the one-dimensional lattice dimension. Under open boundary conditions along the physical dimension, Majorana flat bands at energy zero (quasienergy zero and π) emerge in the static (kicked) model at the two-dimensional surface Brillouin zone. For certain values of pairing order parameter, (Floquet) Su-Schrieffer-Heeger-like edge modes appear in the form of arcs connecting different (Floquet) Majorana flat bands. Finally, we find that in the kicked model, it is possible to generate two controllable Floquet Majorana modes, one at quasienergy zero and the other at quasienergy π, at the same parameter values.

We numerically study the effect of the edge states on the conductance and thermopower in zigzag phosphorene nanoribbons (ZPNRs) based on the tight-binding model and the scattering-matrix method. It is interesting to find that the band dispersion, conductance, and thermopower can be modulated by applying a bias voltage and boundary potentials to the two layers of the ZPNRs. Under the certain bias voltage, the two-fold degenerate quasi-flat edge bands split perfectly. The conductance can be switched off, and the thermopower around zero energy increases. In addition, when only the boundary potential of the top layer or bottom layer is adjusted, only one edge band bends and merges into the bulk band. The first conductance plateau is strongly decreased to e 2 /h around zero energy. Particularly, when the two boundary potentials are adjusted, all the edge bands bend and fully merge into the bulk band, and the bulk energy gap is maximized. More interestingly, a pronounced conductance plateau with G = 0 is found around zero energy, which is attributable to the opening of the bulk energy gap between the valence and conduction bands. Meanwhile, the thermopower can be enhanced more than twice, compared to that of the perfect ZPNRs. The large magnitude of thermopower is ascribed to the appearance of the bulk energy gap around zero energy. Our results show that the modulated ZPNRs are more reliable in thermoelectric application.

No abstract