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 Josephson currents in junctions of hybridized multiband superconductors

Puel, T. O.; Sacramento, P. D.; Continentino, M. A.

doi:10.1103/physrevb.95.094509

Cited by 4 publications

(2 citation statements)

References 84 publications

(61 reference statements)

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“…Also the magnitudes of the various order parameters are in complete agreement with the sequence of phases in the sense that the larger order parameter corresponds to the dominant characteristic of each phase. We expect our method can also be applied to other models, for example the multiband hybridized superconductors 23,28 , that has a diagonal representation of the Hamiltonian at specific points of the phase diagram.…”

Section: Discussionmentioning

confidence: 99%

Detection of topological phases by quasilocal operators

Sacramento

et al. 2019

Phys. Rev. B

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It has been proposed recently by some of the authors that the quantum phase transition of a topological insulator like the SSH model may be detected by the eigenvalues and eigenvectors of the reduced density matrix. Here we further extend the scheme of identifying the order parameters by considering the SSH model with the addition of triplet superconductivity. This model has a rich phase diagram due to the competition of the SSH "order" and the Kitaev "order", which requires the introduction of four order parameters to describe the various topological phases. We show how these order parameters can be expressed simply as averages of projection operators on the ground state at certain points deep in each phase and how one can simply obtain the phase boundaries. A scaling analysis in the vicinity of the transition lines is consistent with the quantum Ising universality class. arXiv:1811.05634v1 [cond-mat.str-el]

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Section: Discussionmentioning

confidence: 99%

Detection of topological phases by quasilocal operators

Sacramento

et al. 2019

Phys. Rev. B

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“…Due to higher dimensionality, it is difficult to obtain the Berry phase (as given by the line integral in equation ( 6)) from the corresponding 4 × 1 eigenvectors. It's rather easier, however, to obtain the Winding number (W) by enumerating the number of revolutions of det[H k ] about the origin of complex plane as k is traversed through the BZ [18,[23][24][25]. For θ = π/2, it turns out to be W ̸ = 0 for |t| > |∆| > 0 as we considered in this work [26].…”

Section: D Chainmentioning

confidence: 99%

Edge state behavior in a Su–Schrieffer–Heeger like model with periodically modulated hopping

Kar

2023

J. Phys.: Condens. Matter

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Su-Schrieffer-Heeger (SSH) model is one of the simplest models to show topological end/edgestates and the existence of Majorana fermions. Here we consider a SSH like model both in oneand two dimensions where a nearest neighbor hopping features spatially periodic modulations. Inthe 1D chain, we witness appearance of new in-gap end states apart from a pair of Majorana zeromodes (MZM) when the hopping periodicity go beyond two lattice spacings. The pair of MZMs, thatappear in the topological regime, characterize the end modes each existing in either end of the chain.These, however, crossover to both-end end modes for small hopping modulation strength in a finitechain. Contrarily in a 2D SSH model with symmetric hopping that we consider, both non-zero andzero energy topological states appear in a finite square lattice even with a simple staggered hopping,though the zero energy modes disappear in a ribbon configuration. Apart from edge modes, the 2Dsystem also features corner modes as well as modes with satellite peaks distributed non-randomlywithin the lattice. In both the dimensions, an increase in the periodicity of hopping modulationcauses the zero energy Majorana modes to become available for either sign of the modulation. Butinterestingly with different periodicity for hopping modulations in the two directions, the zero energymodes in a 2D model become rarer and does not appear for all strength and sign of the modulation.

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Machine learning topological phases in real space

Holanda

Griffith

2020

Phys. Rev. B

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We develop a supervised machine learning algorithm that is able to learn topological phases for finite condensed matter systems in real lattice space. The algorithm employs diagonalization in real space together with any supervised learning algorithm to learn topological phases through an eigenvector-ensembling procedure. We combine our algorithm with decision trees to successfully recover topological phase diagrams of Su-Schrieffer-Heeger (SSH) models from lattice data in real space and show how the Gini impurity of ensembles of lattice eigenvectors can be used to retrieve a topological signal detailing how topological information is distributed along the lattice. The discovery of local Gini topological signals from the analysis of data from several thousand SSH systems illustrates how machine learning can advance the research and discovery of new quantum materials with exotic properties that may power future technological applications such as quantum computing.

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4π Josephson currents in junctions of hybridized multiband superconductors

Cited by 4 publications

References 84 publications

Detection of topological phases by quasilocal operators

Detection of topological phases by quasilocal operators

Edge state behavior in a Su–Schrieffer–Heeger like model with periodically modulated hopping

Machine learning topological phases in real space

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