Topological Proximity Research Articles

Electrically tunable topological superconductivity and Majorana fermions in two dimensions

The external controllability of topological superconductors and Majorana fermions would be important both for fundamental and practical interests. Here we predict the electric-field control of Majorana fermions in two-dimensional topological superconductors utilizing a topological insulator thin film proximity coupled to a conventional $s$-wave superconductor. With ferromagnetic ordering, the tunable structure inversion asymmetry by vertical electric field could induce topological quantum phase transition and realize a chiral topological superconductor state. A zero-energy Majorana bound state appears at the boundary of an applied electric field spot, which can be observed by scanning tunneling microscopy. Furthermore, the structure inversion asymmetry could also enlarge the helical topological superconductor state in the phase diagram, making the realization of such an exotic state more feasible. The electrical control of topological phases could further apply to van der Waals materials such as two-dimensional transition metal dichalcogenides.

Spinon Majorana fermions

A realization of Majorana fermions is proposed in the frustrated magnets via the topological proximity effect. Specifically, we consider a theoretical model, where a topological insulator is coupled to a frustrated magnetic material through the spin exchange interaction. Using the renormalization group-based self-consistent mean-field approach, and calculating the self-energy correction due to the topological insulator, we find that the spin texture and the spin-momentum locking of the Dirac cone will be inherited by the spinons in the nearby frustrated magnets. This leads to a particular topological state of matter that supports the Majorana excitations. Unlike the conventional realization in SC systems, these Majorana fermions are the combination of spinons and anti-spinons, rather than electrons and holes. They can participate in the transport of spinons, leading to nontrivial properties of the spin transport.

Scanning tunneling microscopy of superconducting topological surface states inBi2Se3

In this paper we present scanning tunneling microscopy of a large $\textrm{Bi}_2\textrm{Se}_3$ crystal with superconducting PbBi islands deposited on the surface. Local density of states measurements are consistent with induced superconductivity in the topological surface state with a coherence length of order 540 nm. At energies above the gap the density of states exhibits oscillations due to scattering caused by a nonuniform order parameter. Strikingly, the spectra taken on islands also display similar oscillations along with traces of the Dirac cone, suggesting an inverse topological proximity effect.

Clustering vs. relative location: Measuring spatial interaction between retail outlets

AbstractThis paper presents a new multivariate spatial statistic developed to identify different interaction patterns between competing retail outlets. In order to define when two outlets are located relatively close to each other, a topological proximity criterion is suggested. Asymptotic properties of the new statistic are derived analytically and finite sample properties are obtained through Monte Carlo simulations. Various simulation experiments confirm that the statistic is robust and that it can distinguish pairwise categorical association from clustering in the joint population. To demonstrate its usefulness, the statistic is applied to competing retail chains in two retail sectors.

Bulk Topological Proximity Effect.

Existing proximity effects stem from systems with a local order parameter, such as a local magnetic moment or a local superconducting pairing amplitude. Here, we demonstrate that despite lacking a local order parameter, topological phases also may give rise to a proximity effect of a distinctively inverted nature. We focus on a general construction in which a topological phase is extensively coupled to a second system, and we argue that, in many cases, the inverse topological order will be induced on the second system. To support our arguments, we rigorously establish this "bulk topological proximity effect" for all gapped free-fermion topological phases and representative integrable models of interacting topological phases. We present a terrace construction which illustrates the phenomenological consequences of this proximity effect. Finally, we discuss generalizations beyond our framework, including how intrinsic topological order may also exhibit this effect.

The chronological and topological structural features of the atria vascular system during prenatal period of ontogenesis

Aim of the work was to establish the chronological and regional special features of the atria vascular system development of human fetuses. For this aim there were used the hearts of human fetuses from archive materials of medical department and city hospitals. Methods : Fixation and formation of mounts for further study were carried out according to recommendations [Yurin N.А., Radostin А.I., 1995]. After fixation there were carried out staining of proteins of smoothly muscular α-SMA actin markers and protein of Prox–1transcription factor, Ki-67cells proliferation marker, CD-34 endothelial marker. Using Image-Pro Plus The Proven Solution Version 3.0.00.00 Windows 95/NT program on the microphotographies of atria histological sections there were separated with marker the vascular structures with further calculation of its absolute area that was then presented in percentage terms relative to the general area of histological section. Positively staining cells were calculated using Image-Pro Plus The Proven Solution Version 3.0.00.00 Windows 95/NT program, the separation of vessels was carried out in manual mode then the relative area of vascular component presented in percentage terms was calculated in automatic mode. We also used morphological analysis of corrosive casts of atria vessels by the method of scanning electron microscopy in fetuses 33–40 weeks old. The photography of samples was done in the mode of secondary electron emission. Results : In fetal period of prenatal period of human ontogenesis the development of vascular bed is inseparably linked with morphogenesis of heart in whole and its parts. The general part of vascular component in human fetuses atria varied within 4,9–9,6 % during the considered period. Arterial and lymphatic links of atria vascular bed were determined separately in spite of topological proximity. The part of lymphatic link of atria vascular system had not reliable differences between the right and left atria till the 16 week of fetal period. Conclusions : An asynchronicity of the atria vascularization processes and topological difference of the vascular component in general and on its separate links established during the study are synchronized regularities of formation of definitive construction of the heart coronal vascular system

Strong ties promote the epidemic prevalence in susceptible–infected–susceptible spreading dynamics

We propose a weighted susceptible–infected–susceptible model on complex networks, where the weight of an edge is defined by the topological proximity of the two associated nodes. Each infected individual is allowed to select a limited number of neighbors to contact, and a tunable parameter is introduced to control the preference to contact through high-weight or low-weight edges. Simulation results on six real networks show that the epidemic prevalence can be largely promoted when strong ties are favored. By comparing with two statistical null models, we show that the distribution pattern of weights, rather than the topological structure, mainly contributes to the observations. Further analysis suggests that the weight–weight correlation strongly affects the results: high-weight edges are more significant in keeping high epidemic prevalence when the weight–weight correlation is positive.

Altered Hub Functioning and Compensatory Activations in the Connectome: A Meta-Analysis of Functional Neuroimaging Studies in Schizophrenia.

Background:Functional neuroimaging studies of schizophrenia have identified abnormal activations in many brain regions. In an effort to interpret these findings from a network perspective, we carried out a meta-analysis of this literature, mapping anatomical locations of under- and over-activation to the topology of a normative human functional connectome. Methods:We included 314 task-based functional neuroimaging studies including more than 5000 patients with schizophrenia and over 5000 controls. Coordinates of significant under- or over-activations in patients relative to controls were mapped to nodes of a normative connectome defined by a prior meta-analysis of 1641 functional neuroimaging studies of task-related activation in healthy volunteers. Results:Under-activations and over-activations were reported in a wide diversity of brain regions. Both under- and over-activations were significantly more likely to be located in hub nodes that constitute the “rich club” or core of the normative connectome. In a subset of 121 studies that reported both under- and over-activations in the same patients, we found that, in network terms, these abnormalities were located in close topological proximity to each other. Under-activation in a peripheral node was more frequently associated specifically with over-activation of core nodes than with over-activation of another peripheral node. Conclusions:Although schizophrenia is associated with altered brain functional activation in a wide variety of regions, abnormal responses are concentrated in hubs of the normative connectome. Task-specific under-activation in schizophrenia is accompanied by over-activation of topologically central, less functionally specialized network nodes, which may represent a compensatory response.

Topological proximity effect in a topological insulator hybrid.

It is well known that a topologically protected gapless state appears at an interface between a topological insulator and an ordinary insulator; however, the physics of the interface between a topological insulator and a metal has largely been left unexplored. Here we report a novel phenomenon termed topological proximity effect, which occurs between a metallic ultrathin film and a three-dimensional topological insulator. We study one bilayer of bismuth metal grown on the three-dimensional topological insulator material TlBiSe2, and by using spin- and angle-resolved photoemission spectroscopy, we found evidence that the topological Dirac-cone state migrates from the surface of TlBiSe2 to the attached one-bilayer Bi. We show that such a migration of the topological state occurs as a result of strong spin-dependent hybridization of the wave functions at the interface, which is also supported by our first-principles calculations. This discovery points to a new route to manipulating the topological properties of materials.

Topological Proximity Effect: A Gauge Influence from Distant Fields on Planar Quantum-Coherent Systems

A quantum system that lies nearby a magnetic or time-varying electric field region, and that is under periodic boundary conditions parallel to the interface, is shown to exhibit a “hidden” Aharonov-Bohm effect (magnetic or electric), caused by fluxes that are not enclosed by, but are merely neighboring to our system − its origin being the absence of magnetic monopoles in 3D space (with corresponding spacetime generalizations). Novel possibilities then arise, where a field-free system can be dramatically affected by manipulating fields in an adjacent or even distant land, provided that these nearby fluxes are not quantized (i.e. they are fractional or irrational parts of the flux quantum). Topological effects (such as Quantum Hall types of behaviors) can therefore be induced from outside our system (that is always field-free and can even reside in simply-connected space). Potential novel applications are outlined, and exotic consequences in solid state physics are pointed out (i.e. the possibility of field-free quantum periodic systems that violate Bloch’s theorem), while formal analogies with certain high energy physics phenomena and with some rather under-explored areas in mechanics and thermodynamics are noted.

Using topological insulator proximity to generate perfectly conducting channels in materials without topological protection

We show that hybrid structures of topological insulators (TI) and materials without topological protection can be employed to create perfectly conducting channels (PCCs) hosted in the non-topological part. These states inherit the topological protection from the proximity of the TI but are more fragile to time-reversal symmetry breaking because of their extended character. We explore their formation in the band structure of model hybrid systems as well as realistic heterostructures involving HgTe/CdTe-based two-dimensional TIs and show how their appearance can be understood in terms of an effective boundary condition. Using numerical quantum transport calculations for the HgTe/CdTe material system we propose two experimental settings which allow for the detection of the induced PCCs, both in the localized and diffusive regime, by means of magneto conductance and shot noise.

Quasiclassical Eilenberger theory of the topological proximity effect in a superconducting nanowire

We use the quasiclassical Eilenberger theory to study the topological superconducting proximity effects between a segment of a nanowire with a p-wave order parameter and a metallic segment. This model faithfully represents key qualitative features of an experimental setup, where only a part of a nanowire is in immediate contact with a bulk superconductor, inducing topological superconductivity. It is shown that the Eilenberger equations represent a viable alternative to the Bogoliubov-de Gennes theory of the topological superconducting heterostructures and provide a much simpler quantitative description of some observables. For our setup, we obtain exact analytical solutions for the quasiclassical Green's functions and the density of states as a function of position and energy. The correlations induced by the boundary involve terms associated with both p-wave and odd-frequency pairing, which are intertwined and contribute to observables on an equal footing. We recover the signatures of the standard Majorana mode near the end of the superconducting segment, but find no such localized mode induced in the metallic segment. Instead, the zero-bias feature is spread out across the entire metallic part in accordance with the previous works. In shorter wires, the Majorana mode and delocalized peak split up away from zero energy. For long metallic segments, non-topological Andreev bound states appear and eventually merge together, giving rise to a gapless superconductor.

Quantum phase transitions and topological proximity effects in graphene nanoribbon heterostructures

Topological insulators are bulk insulators that possess robust chiral conducting states along their interfaces with normal insulators. A tremendous research effort has recently been devoted to topological insulator-based heterostructures, in which conventional proximity effects give rise to a series of exotic physical phenomena. Here we establish the potential existence of topological proximity effects at the interface between a topological insulator and a normal insulator, using graphene-based heterostructures as prototypical systems. Unlike conventional proximity effects in topological insulator based heterostructures, which refer to various phase transitions associated with the symmetry breaking of specific local order parameters, topological proximity effects describe the rich variety of quantum phase transitions associated with the global properties of the system measured by the location of the topological edge states. Specifically, we show that the location of the topological edge states exhibits a versatile tunability as a function of the interface orientation, the strength of the interface tunnel coupling between a topological graphene nanoribbon and a normal graphene nanoribbon, the spin-orbit coupling strength in the normal graphene nanoribbon, and the width of the system. For zigzag and bearded graphene nanoribbons, the topological edge states can be tuned to be either at the interface or outer edge of the normal ribbon. For armchair graphene nanoribbons, the potential location of the topological edge state can be further shifted to the edge of or within the normal ribbon, to the interface, or diving into the topological graphene nanoribbon. We further show that the topological phase diagram established for the prototypical graphene heterostructures can also explain the intriguing quantum phase transition reported recently in other topological-insulator heterostructures. We also discuss potential experimental realizations of the predicted topological proximity effects, which may pave the way for integrating the salient functionality of topological insulators and graphene in future device applications.

Effects of access to public open spaces on walking: Is proximity enough?

Public open spaces (POSs) are important destinations and settings for walking in neighborhoods and different aspects of POSs can influence walking. Proximity to POSs is a key urban design issue that should be considered in distributing such resources within neighborhoods and it is worthwhile to examine how POS proximity may influence residents’ walking. However, little research has explored how different measures of proximity to POSs might influence POS-related walking.This study examined both metric and topological proximity measures to examine associations with amount of walking to and within POSs. Residents (n=320) of three neighborhoods in Melbourne, Australia completed a questionnaire reporting their level of walking to and within POS and perceptions of their neighborhoods. GIS and space syntax were used to extract four proximity measures: distance to the closest POS, number of POSs, total area of POSs within 1km, and POS integration.None of the proximity measures were associated with walking (versus not walking) to or within POSs. Distance to the nearest POS and the number of POSs within 1km was negatively associated with the absolute amount of walking to POSs. Residents who lived in areas in which POSs were located on less integrated streets reported more walking to and within POSs. Future landscape and urban design research should consider not only proximity to POSs, but also how factors such as characteristics of the routes that people traverse to reach POS influence use of, and the likelihood of walking to and within, these important neighborhood destinations.

Topological superfluid in a fermionic bilayer optical lattice

In this paper, a topological superfluid phase with Chern number C=1 possessing gapless edge states and non-Abelian anyons is designed in a C=1 topological insulator proximity to an s-wave superfluid on an optical lattice with the effective gauge field and layer-dependent Zeeman field coupled to ultracold fermionic atoms pseudo spin. We also study its topological properties and calculate the phase stiffness by using the random-phase-approximation approach. Finally we derive the temperature of the Kosterlitz-Thouless transition by means of renormalized group theory. Owning to the existence of non-Abelian anyons, this C=1 topological superfluid may be a possible candidate for topological quantum computation.

Odd-frequency superconducting pairing in topological insulators

We discuss the appearance of odd-frequency spin-triplet $s$-wave superconductivity, first proposed by Berezinskii [J. Exp. Theor. Phys. 20, 287 (1974)], on the surface of a topological insulator proximity coupled to a conventional spin-singlet $s$-wave superconductor. Using both analytical and numerical methods, we show that this disorder robust odd-frequency state is present whenever there is an in-surface gradient in the proximity induced gap, including superconductor-normal state junctions. The time-independent order parameter for the odd-frequency superconductor is proportional to the in-surface gap gradient. The induced odd-frequency component does not produce any low-energy states.

Predicting errors from reconfiguration patterns in human brain networks

Task preparation is a complex cognitive process that implements anticipatory adjustments to facilitate future task performance. Little is known about quantitative network parameters governing this process in humans. Using functional magnetic resonance imaging (fMRI) and functional connectivity measurements, we show that the large-scale topology of the brain network involved in task preparation shows a pattern of dynamic reconfigurations that guides optimal behavior. This network could be decomposed into two distinct topological structures, an error-resilient core acting as a major hub that integrates most of the network's communication and a predominantly sensory periphery showing more flexible network adaptations. During task preparation, core-periphery interactions were dynamically adjusted. Task-relevant visual areas showed a higher topological proximity to the network core and an enhancement in their local centrality and interconnectivity. Failure to reconfigure the network topology was predictive for errors, indicating that anticipatory network reconfigurations are crucial for successful task performance. On the basis of a unique network decoding approach, we also develop a general framework for the identification of characteristic patterns in complex networks, which is applicable to other fields in neuroscience that relate dynamic network properties to behavior.

Viral Perturbations of Host Networks Reflect Disease Etiology

Many human diseases, arising from mutations of disease susceptibility genes (genetic diseases), are also associated with viral infections (virally implicated diseases), either in a directly causal manner or by indirect associations. Here we examine whether viral perturbations of host interactome may underlie such virally implicated disease relationships. Using as models two different human viruses, Epstein-Barr virus (EBV) and human papillomavirus (HPV), we find that host targets of viral proteins reside in network proximity to products of disease susceptibility genes. Expression changes in virally implicated disease tissues and comorbidity patterns cluster significantly in the network vicinity of viral targets. The topological proximity found between cellular targets of viral proteins and disease genes was exploited to uncover a novel pathway linking HPV to Fanconi anemia.

Functional clustering of time series gene expression data by Granger causality

BackgroundA common approach for time series gene expression data analysis includes the clustering of genes with similar expression patterns throughout time. Clustered gene expression profiles point to the joint contribution of groups of genes to a particular cellular process. However, since genes belong to intricate networks, other features, besides comparable expression patterns, should provide additional information for the identification of functionally similar genes.ResultsIn this study we perform gene clustering through the identification of Granger causality between and within sets of time series gene expression data. Granger causality is based on the idea that the cause of an event cannot come after its consequence.ConclusionsThis kind of analysis can be used as a complementary approach for functional clustering, wherein genes would be clustered not solely based on their expression similarity but on their topological proximity built according to the intensity of Granger causality among them.

A cloud-based data-sharing and analysis cyberinfrastructure for neuroinformatics

A cloud-based data-sharing and analysis cyberinfrastructure for neuroinformatics