Topological phases, topological flat bands, and topological excitations in a one-dimensional dimerized lattice with spin-orbit coupling

The Su-Schrieffer-Heeger (SSH) model describes a one-dimensional $Z_{2}$ topological insulator, which has two topological distinct phases corresponding to two different dimerizations. When spin-orbit coupling is introduced into the SSH model, we find the structure of the Bloch bands can be greatly changed, and most interestingly, a new topological phase with single zero-energy bound state which exhibits non-Abelian statistics at each end emerges, which suggests that a new topological invariant is needed to fully classify all phases. In a comparatively large range of parameters, we find that spin-orbit coupling induces completely flat band with nontrivial topology. For the case with non-uniform dimerizaton, we find that spin-orbit coupling changes the symmetrical structure of topological excitations known as solitons and antisolitons and when spin-orbit coupling is strong enough to induce a topological phase transition, the whole system is topologically nontrivial but with the disappearance of solitons and antisolitons, consequently, the system is a real topological insulator with well-protected end states.Comment: 5 pages, 2 figure

Measuring the Spin Polarization of a Ferromagnet: an Application of Time-Reversal Invariant Topological Superconductor

The spin polarization (SP) of the ferromagnet (FM) is a quantity of fundamental importance in spintronics. In this work, we propose a quasi-one-dimensional junction structure composed of a FM and a time-reversal invariant topological superconductor (TRITS) with un-spin-polarized pairing type to determine the SP of the FM. We find that due to the topological property of the TRITS, the zero-bias conductance (ZBC) of the FM/TRITS junction which is directly related to the SP is a non-quantized but topological quantity. The ZBC only depends on the parameters of the FM, it is independent of the interface scattering potential and the Fermi surface mismatch between the FM and the superconductor, and is robust against to the magnetic proximity effect, therefore, compared to the traditional FM/$s$-wave superconductor junction, the topological property of the ZBC makes this setup a much more direct and simplified way to determine the SP.Comment: 11 pages, 1 figure

Revisiting Entanglement Entropy of Lattice Gauge Theories

Casini et al raise the issue that the entanglement entropy in gauge theories is ambiguous because its definition depends on the choice of the boundary between two regions.; even a small change in the boundary could annihilate the otherwise finite topological entanglement entropy between two regions. In this article, we first show that the topological entanglement entropy in the Kitaev model which is not a true gauge theory, is free of ambiguity. Then, we give a physical interpretation, from the perspectives of what can be measured in an experiement, to the purported ambiguity of true gauge theories, where the topological entanglement arises as redundancy in counting the degrees of freedom along the boundary separating two regions. We generalize these discussions to non-Abelian gauge theories.Comment: 15 pages, 3 figure