Majorana corner modes and tunable patterns in an altermagnet heterostructure

The mutual competition and synergy of magnetism and superconductivity provide us with a very valuable opportunity to access topological superconductivity and Majorana Fermions. Here, we devise a heterostructure consisting of an $s$-wave superconductor, a 2D topological insulator and an altermagnet, which is classified as the third magnet and featured by zero magnetization but spin polarization in both real and reciprocal spaces. We find that the altermagnet can induce mass terms at the edges that compete with electron pairing, and mass domains are formed at the corners of sample, resulting in zero-energy Majorana corner modes (MCMs). The presence or absence of MCMs can be engineered by only changing the direction of the N\'{e}el vector. Moreover, uniaxial strain can effectively manipulate the patterns of the MCMs, such as moving and interchanging MCMs. Experimental realization, remarkable advantages of our proposal and possible braiding are discussed.Comment: Accepted by PRB, 5 pages main text + 13 pages S

Association of tissue lineage and gene expression: conservatively and differentially expressed genes define common and special functions of tissues

<p>Abstract</p> <p>Background</p> <p>Embryogenesis is the process by which the embryo is formed, develops, and establishes developmental hierarchies of tissues. The recent advance in microarray technology made it possible to investigate the tissue specific patterns of gene expression and their relationship with tissue lineages. This study is focused on how tissue specific functions, tissue lineage, and cell differentiation are correlated, which is essential to understand embryonic development and organism complexity.</p> <p>Results</p> <p>We performed individual gene and gene set based analysis on multiple tissue expression data, in association with the classic topology of mammalian fate maps of embryogenesis. For each sub-group of tissues on the fate map, conservatively, differentially and correlatively expressed genes or gene sets were identified. Tissue distance was found to correlate with gene expression divergence. Tissues of the ectoderm or mesoderm origins from the same segments on the fate map shared more similar expression pattern than those from different origins. Conservatively expressed genes or gene sets define common functions in a tissue group and are related to tissue specific diseases, which is supported by results from Gene Ontology and KEGG pathway analysis. Gene expression divergence is larger in certain human tissues than in the mouse homologous tissues.</p> <p>Conclusion</p> <p>The results from tissue lineage and gene expression analysis indicate that common function features of neighbor tissue groups were defined by the conservatively expressed genes and were related to tissue specific diseases, and differentially expressed genes contribute to the functional divergence of tissues. The difference of gene expression divergence in human and mouse homologous tissues reflected the organism complexity, i.e. distinct neural development levels and different body sizes.</p

Finite Field Multiple Access

In the past several decades, various multiple-access (MA) techniques have been developed and used. These MA techniques are carried out in complex-field domain to separate the outputs of the users. It becomes problematic to find new resources from the physical world. It is desirable to find new resources, physical or virtual, to confront the fast development of MA systems. In this paper, an algebraic virtual resource is proposed to support multiuser transmission. For binary transmission systems, the algebraic virtual resource is based on assigning each user an element pair (EP) from a finite field GF($p^m$). The output bit from each user is mapped into an element in its assigned EP, called the output symbol. For a downlink MA system, the output symbols from the users are jointly multiplexed into a unique symbol in the same field GF($p^m$) for further physical-layer transmission. The EPs assigned to the users are said to form a multiuser algebraic uniquely decodable (UD) code. Using EPs over a finite field, a network, a downlink, and an uplink orthogonal/non-orthogonal MA systems are proposed, which are called finite-field MA (FFMA) systems. Methods for constructing algebraic UD codes for FFMA systems are presented. An FFMA system can be designed in conjunction with the classical complex-field MA techniques to provide more flexibility and varieties.Comment: 32 pages, 10 figure

Imaginary-time Quantum Relaxation Critical Dynamics with Semi-ordered Initial States

We explore the imaginary-time relaxation dynamics near quantum critical points with semi-ordered initial states. Different from the case with homogeneous ordered initial state, in which the order parameter $M$ decays homogeneously as $M\propto \tau^{-\beta/\nu z}$, here $M$ depends on the location $x$, showing rich scaling behaviors. Similar to the classical Model A critical dynamics with an initial domain wall, here as the imaginary time evolves, the domain wall expands into an interfacial region with growing size. In the interfacial region, the local order parameter decays as $M\propto \tau^{-\beta_1/\nu z}$, with $\beta_1$ being an additional dynamic critical exponent. Far away from the interfacial region the local order parameter decays as $M\propto \tau^{-\beta/\nu z}$ in the short-time stage, then crosses over to the scaling behavior of $M\propto \tau^{-\beta_1/\nu z}$ when the location $x$ is absorbed in the interfacial region. A full scaling form characterizing these scaling properties is developed. The quantum Ising model in both one and two dimensions are taken as examples to verify the scaling theory. In addition, we find that for the quantum Ising model the scaling function is an analytical function and $\beta_1$ is not an independent exponent.Comment: 8 pages, 5 figure