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

Study on the tunneling spectroscopy of N−pSN-pS junction and N−hSN-hS junction

We study the complete tunneling spectroscopy of a normal metal/$p$-wave superconductor junction ($N-pS$) and normal metal/heterostructure superconductor junction ($N-hS$) by Blonder-Tinkham-Klapwijk (BTK) method. We find that, for $p$-wave superconductor with non-trivial topology, there exists a quantized zero-bias conductance peak stably, for heterostructure superconductor with non-trivial topology, the emerging zero-bias conductance peak is non-quantized and usually has a considerable gap to the quantized value. Furthermore, it is sensitive to parameters, especially to spin-orbit coupling and the $s$-wave pairing potential. Results obtained suggest that the observation of a small zero-bias conductance peak, instead of a quantized zero-bias conductance peak, in current tunneling experiments can be a natural result if the spin-orbit coupling turns out to be several times smaller than the reported one. Results obtained also suggest that both a stronger spin-orbit coupling and proximity $s$-wave superconductor with relative weaker pairing potential can produce a much more striking zero-bias conductance peak (compared to the experiments), even an almost quantized one. As $s$-wave superconductors are common in nature, the prediction can be verified within current experiment ability.Comment: 9 pages, 6 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

Condensate Fraction and Pair Coherence Lengths of Two-Dimension Fermi Gases with Spin-Orbit Coupling

The effects of Rashba spin-orbit coupling on BCS-BEC crossover, the condensate fraction and pair coherence lengths for a two-component attractive Fermi gas in two dimension are studied. The results at $T=0K$ indicate that (1) when the strength of SOC is beyond a critical value, BCS-BEC crossover does not happen in a conventional sense; (2) SOC enhances the condensate fraction, but suppresses pair coherence lengths