Signatures of Topological Superconductors

Topological superconductors are particularly interesting in light of the active ongoing experimental efforts for realizing exotic physics such as Majorana zero modes. These systems have excitations with non-Abelian exchange statistics, which provides a path towards topological quantum information processing. Intrinsic topological superconductors are quite rare in nature. However, one can engineer topological superconductivity by inducing effective p-wave pairing in materials which can be grown in the laboratory. One possibility is to induce the proximity effect in topological insulators; another is to use hybrid structures of superconductors and semiconductors.

The proposal of interfacing s-wave superconductors with quantum spin Hall systems provides a promising route to engineered topological superconductivity. Given the exciting recent progress on the fabrication side, identifying experiments that definitively expose the topological superconducting phase (and clearly distinguish it from a trivial state) raises an increasingly important problem. With this goal in mind, we proposed a detection scheme to get an unambiguous signature of topological superconductivity, even in the presence of ordinarily detrimental effects such as thermal fluctuations and quasiparticle poisoning. We considered a Josephson junction built on top of a quantum spin Hall material. This system allows the proximity effect to turn edge states in effective topological superconductors. Such a setup is promising because experimentalists have demonstrated that supercurrents indeed flow through quantum spin Hall edges. To demonstrate the topological nature of the superconducting quantum spin Hall edges, theorists have proposed examining the periodicity of Josephson currents respect to the phase across a Josephson junction. The periodicity of tunneling currents of ground states in a topological superconductor Josephson junction is double that of a conventional Josephson junction. In practice, this modification of periodicity is extremely difficult to observe because noise sources, such as quasiparticle poisoning, wash out the signature of topological superconductors. For this reason, We propose a new, relatively simple DC measurement that can compellingly reveal topological superconductivity in such quantum spin Hall/superconductor heterostructures. More specifically, We develop a general framework for capturing the junction's current-voltage characteristics as a function of applied magnetic flux. Our analysis reveals sharp signatures of topological superconductivity in the field-dependent critical current. These signatures include the presence of multiple critical currents and a non-vanishing critical current for all magnetic field strengths as a reliable identification scheme for topological superconductivity.

This system becomes more interesting as interactions between electrons are involved. By modeling edge states as a Luttinger liquid, we find conductance provides universal signatures to distinguish between normal and topological superconductors. More specifically, we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as a lead. Interestingly, arbitrarily weak interactions induce qualitative changes in the behavior relative to the free-fermion limit, leading to a sharp dichotomy in conductance for the trivial (narrow superconductor) and topological (wide superconductor) cases. Furthermore, we find that strong interactions can in principle induce parafermion excitations at a superconductor/quantum spin Hall junction.

As we identify the existence of topological superconductor, we can take a step further. One can use topological superconductor for realizing Majorana modes by breaking time reversal symmetry. An advantage of 2D topological insulator is that networks required for braiding Majoranas along the edge channels can be obtained by adjoining 2D topological insulator to form corner junctions. Physically cutting quantum wells for this purpose, however, presents technical challenges. For this reason, I propose a more accessible means of forming networks that rely on dynamically manipulating the location of edge states inside of a single 2D topological insulator sheet. In particular, I show that edge states can effectively be dragged into the system's interior by gating a region near the edge into a metallic regime and then removing the resulting gapless carriers via proximity-induced superconductivity. This method allows one to construct rather general quasi-1D networks along which Majorana modes can be exchanged by electrostatic means.

Apart from 2D topological insulators, Majorana fermions can also be generated in other more accessible materials such as semiconductors. Following up on a suggestion by experimentalist Charlie Marcus, I proposed a novel geometry to create Majorana fermions by placing a 2D electron gas in proximity to an interdigitated superconductor-ferromagnet structure. This architecture evades several manufacturing challenges by allowing single-side fabrication and widening the class of 2D electron gas that may be used, such as the surface states of bulk semiconductors. Furthermore, it naturally allows one to trap and manipulate Majorana fermions through the application of currents. Thus, this structure may lead to the development of a circuit that enables fully electrical manipulation of topologically-protected quantum memory. To reveal these exotic Majorana zero modes, I also proposed an interference scheme to detect Majorana fermions that is broadly applicable to any 2D topological superconductor platform.

Response of the topological surface state to surface disorder in TlBiSe2

Through a combination of experimental techniques we show that the topmost layer of the topological insulator TlBiSe2 as prepared by cleavage is formed by irregularly shaped Tl islands at cryogenic temperatures and by mobile Tl atoms at room temperature. No trivial surface states are observed in photoemission at low temperatures, which suggests that these islands cannot be regarded as a clear surface termination. The topological surface state is, however, clearly resolved in photoemission experiments. This is interpreted as direct evidence of its topological self-protection and shows the robust nature of the Dirac cone-like surface state. Our results can also help explain the apparent mass acquisition in S-doped TlBiSe2.

The topological configuration and conformational analysis of mRNA in translation

The theoretical model construction of mRNA hairpin structure and single-stranded structure as well as the simulation studies on RNA structure determined by the X-ray crystal diffraction and nuclear magnetic resonance revealed that in translation, after mRNA being unfolded into single-stranded structure, its topological configuration was closely correlative with the original hairpin structure. The conformational features of single-stranded mRNA appeared as helical regions alternating with curly regions to different extents, which might exert the influence on the folding of nascent polypeptide by various regulating effects including different translational rates.

Magnetic quantum oscillations for the surface states of topological insulator Bi2Se3

We study quantum oscillations of the magnetization in Bi2Se3 (111) surface system in the presence of a perpendicular magnetic field. The combined spin-chiral Dirac cone and Landau quantization produce profound effects on the magnetization properties that are fundamentally different from those in the conventional semiconductor two-dimensional electron gas. In particular, we show that the oscillating center in the magnetization chooses to pick up positive or negative values depending on whether the zero-mode Landau level is occupied or empty. An intuitive analysis of these features is given and the subsequent effects on the magnetic susceptibility and Hall conductance are also discussed.

Electric field driven quantum phase transition between band insulator and topological insulator

We demonstrate theoretically that electric field can drive a quantum phase transition between band insulator to topological insulator in CdTe/HgCdTe/CdTe quantum wells. The numerical results suggest that the electric field could be used as a switch to turn on or off the topological insulator phase, and temperature can affect significantly the phase diagram for different gate voltage and compositions. Our theoretical results provide us an efficient way to manipulate the quantum phase of HgTe quantum wells.

Electron tunneling through double magnetic barriers on the surface of a topological insulator

We study electron tunneling through a planar magnetic and electric barrier on the surface of a three-dimensional topological insulator. For the double barrier structures, we find (i) a directional-dependent tunneling which is sensitive to the magnetic field configuration and the electric gate voltage, (ii) a spin rotation controlled by the magnetic field and the gate voltage, (iii) many Fabry-Perot resonances in the transmission determined by the distance between the two barriers, and (iv) the electrostatic potential can enhance the difference in the transmission between the two magnetization configurations, and consequently lead to a giant magnetoresistance. Points (i), (iii), and (iv) are alike with that in graphene stemming from the same linear-dispersion relations.

Biomimetic (topological) pattern recognition - A new model of pattern recognition theory and its application

A new theoretical model of Pattern Recognition principles was proposed, which is based on "matter cognition" instead of "matter classification" in traditional statistical Pattern Recognition. This new model is closer to the function of human being, rather than traditional statistical Pattern Recognition using "optimal separating" as its main principle. So the new model of Pattern Recognition is called the Biomimetic Pattern Recognition (BPR)(1). Its mathematical basis is placed on topological analysis of the sample set in the high dimensional feature space. Therefore, it is also called the Topological Pattern Recognition (TPR). The fundamental idea of this model is based on the fact of the continuity in the feature space of any one of the certain kinds of samples. We experimented with the Biomimetic Pattern Recognition (BPR) by using artificial neural networks, which act through covering the high dimensional geometrical distribution of the sample set in the feature space. Onmidirectionally cognitive tests were done on various kinds of animal and vehicle models of rather similar shapes. For the total 8800 tests, the correct recognition rate is 99.87%. The rejection rate is 0.13% and on the condition of zero error rates, the correct rate of BPR was much better than that of RBF-SVM.