Abstract:A three-dimensional (3D) topological insulator (TI) is a quantum state of matter with a gapped insulating bulk yet a conducting surface hosting topologically-protected gapless surface states. One of the most distinct electronic transport signatures predicted for such topological surface states (TSS) is a well-defined half-integer quantum Hall effect (QHE) in a magnetic field, where the surface Hall conductivities become quantized in units of (1/2)e 2 /h (e being the electron charge, h the Planck constant) concomitant with vanishing resistance. Here, we observe well-developed QHE arising from TSS in an intrinsic TI of BiSbTeSe 2 . Our samples exhibit surface dominated conduction even close to room temperature, while the bulk conduction is negligible. At low temperatures and high magnetic fields perpendicular to the top and bottom surfaces, we observe well-developed integer quantized Hall plateaus, where the two parallel surfaces each contributing a half integer e 2 /h quantized Hall (QH) conductance, accompanied by vanishing longitudinal resistance. When the bottom surface is gated to match the top surface in carrier density, only odd integer QH plateaus are observed, representing a half-integer QHE of two degenerate Dirac gases. This system provides an excellent platform to pursue a plethora of exotic physics and novel device applications predicted for TIs, ranging from magnetic monopoles and Majorana particles to dissipationless electronics and fault-tolerant quantum computers.2

The proximity effect is a central feature of superconducting junctions that plays a key role in many devices and can be exploited in the design of new systems with quantum functionality [1][2][3][4][5][6][7][8][9][10][11][12] . Recently, exotic proximity effects have been observed in various systems, including superconductor-metallic nanowires 5-7 and graphenesuperconductor structures 4 . However, it is still not clear how superconducting order propagates spatially in a heterogeneous superconductor system. Here we report on intriguing junction geometry effects in a heterogeneous system consisting of electronically two-dimensional superconducting islands on a metallic substrate. Depending on the local geometry, the superconducting gap induced at the metallic surface sometimes decays within ∼20 nm of the superconductor, and sometimes survives at distances that are several coherence lengths from a superconductor. We show in particular that the curvature of the junction plays an essential role in the proximity effect.The sample system comprises superconducting two-dimensional (2D) Pb islands on top of a single-atomic-layer surface metal, the striped incommensurate (SIC) phase of the Pb overlayer on Si(111) (refs 13-16). The scanning tunnelling microscopy (STM) image shown in Fig. 1 captures a variety of junction configurations. Figure 1a shows an interesting 'π'-shaped Pb island five monolayers (ML) thick on top of the SIC surface. Previous scanning tunnelling spectroscopy (STS) studies have shown that the SIC phase is superconducting with T C_SIC = ∼1.8 K (ref. 17) and the 2D Pb islands have a T C around 6 K (ref. 18), although the actual T C value also depends on the lateral size as well as its thickness 19 . At 4.3 K, the SIC template is in the normal state. At locations far from the Pb islands, the tunnelling spectrum exhibits no gap (spectrum no. 2 in Fig. 1b), whereas the spectrum acquired at the 2D Pb island shows a clear superconducting gap (spectrum no. 3). In the SIC region near the 2D Pb island, a superconducting gap can also be observed (spectrum no. 1), indicative of a proximity effect. To address the spatial dependence, we performed spectroscopic mapping over the same area, whose differential conductance at zero bias (zero-bias conductance (ZBC)) is shown in Fig. 1c. As the ZBC directly correlates with the size of the tunnelling gap (the smaller the value of ZBC, the larger the tunnelling gap), the landscape of ZBC is a good representation of the landscape of the superconducting gap.The ZBC image reveals a rich landscape. In some regions (for example, region α), the induced superconducting gap decays very quickly within a very short distance from the SIC/superconductor (S) interface, whereas in region β where the SIC wetting layer is surrounded by Pb islands from both sides, the induced Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA. *e-mail: shih@physics.utexas.edu.superconducting gap is quite uniform. Similarly, in region γ where the SIC region is near the 'recess'...

Current and future wireless applications strongly rely on precise real-time localization. A number of applications such as smart cities, Internet of Things (IoT), medical services, automotive industry, underwater exploration, public safety, and military systems require reliable and accurate localization techniques. Generally, the most popular localization/ positioning system is the Global Positioning System (GPS). GPS works well for outdoor environments but fails in indoor and harsh environments. Therefore, a number of other wireless local localization techniques are developed based on terrestrial wireless networks, wireless sensor networks (WSNs) and wireless local area networks (WLANs). Also, there exist localization techniques which fuse two or more technologies to find out the location of the user, also called signal of opportunity based localization. Most of the localization techniques require ranging measurements such as time of arrival (ToA), time difference of arrival (TDoA), direction of arrival (DoA) and received signal strength (RSS). There are also range-free localization techniques which consider the proximity information and do not require the actual ranging measurements. Dimensionality reduction techniques are famous among the range free localization schemes. Multidimensional scaling (MDS) is one of the dimensionality reduction technique which has been used extensively in the recent past for wireless networks localization. In this paper, a comprehensive survey is presented for MDS and MDS based localization techniques in WSNs, Internet of Things (IoT), cognitive radio networks, and 5G networks. 2 MDS is much popular among all these techniques because of its simplicity and many application areas. MDS analysis finds the spatial map for objects given that the similarity or dissimilarity information between the objects is available [16].In the recent past, MDS is widely used for localization and mapping of wireless sensor networks (WSNs) and the internet of things (IoT). In [17] a proximity information based sensor network localization is proposed, where the main idea is to construct a local configuration of sensor nodes by using classical MDS (CMDS). The MDS based localization algorithms in [17] and [18] are centralized with higher computational complexity [7]. Semi-centralized (or clustered) MDS techniques are developed to compute local coordinates of nodes, which then are refined to find the final position of the nodes [19], [20]. In [21], [22] and [23] the authors proposed manifold learning to estimate the sensor nodes position in wireless sensor networks. In [24] the authors proposed Nystrom approximation for the proximity information matrix in MDS to reduce its size for better localization accuracy in sensor networks. Distributed MDS based localization algorithm is proposed in [25] with noisy range measurements, where the authors assume that the distances are corrupted with independent Gaussian random noise. MDS methods with different refinement schemes have also been proposed in the literature t...

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This survey presents multidimensional scaling (MDS) methods and their applications in real world. MDS is an exploratory and multivariate data analysis technique becoming more and more popular. MDS is one of the multivariate data analysis techniques, which tries to represent the higher dimensional data into lower space. The input data for MDS analysis is measured by the dissimilarity or similarity of the objects under observation. Once the MDS technique is applied to the measured dissimilarity or similarity, MDS results in a spatial map. In the spatial map, the dissimilar objects are far apart while objects which are similar are placed close to each other. In this survey paper, MDS is described fairly in comprehensive fashion by explaining the basic notions of classical MDS and how MDS can be helpful to analyze the multidimensional data. Later on various MDS based special models are described in a more mathematical way.