Local marker for interacting topological insulators

Markov, A. A.; Rubtsov, A. N.

doi:10.1103/physrevb.104.l081105

Cited by 9 publications

(9 citation statements)

References 39 publications

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“…In addition, the approximation we use, which is quadratic in terms of fluctuating potential, allows one to obtain analytical expressions for the derivatives of the components of the self-energy part with respect to energy that simplify numerical calculations of the topological index C 1 . Expanding ĤAV (9) and F R(A) (E) (10) in Pauli matrices (see Appendix B), we obtain an explicit expression for C 1 (7) (see Appendix C). Calculations of the topological index C 1 (7) were carried out in the range of concentrations where the superconducting phase of the system under consideration has a d + id type of symmetry (α = 2π/3) (see the phase diagram in Fig.…”

Section: Model and Resultsmentioning

confidence: 99%

“…k 1 and are the main reciprocal lattice vectors. To obtain an explicit expression for TI of a quasi-two-dimensional system, it is necessary to multiply the matrices under the sign tr in (7). To do this, it is convenient to use their expansion in Pauli matrices (see Appendix B).…”

Section: Calculation Of the Topological Index Taking Into Account The...mentioning

confidence: 99%

“…, valid for T → 0, in the limit Ω n → 0 from (2) we get the standard expression for TI (1). In contrast to (1), integration over energy in (7) is carried out along the real axis.…”

Section: Calculation Of the Topological Index Taking Into Account The...mentioning

confidence: 99%

“…Naturally, the question arises as to whether new topological properties can arise in non-Hermitian systems. Considerable attention has been paid to these issues in recent years (see, for example, [4][5][6][7]).…”

Section: Introductionmentioning

confidence: 99%

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Thermal fluctuations in superconducting phases with chiral d + id and s symmetry on a triangular lattice

Groshev

Аржников

2021

J. Phys.: Condens. Matter

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The behavior of thermal fluctuations of a superconducting order parameter with extended s and chiral d + id symmetry is investigated. The study is carried out on a triangular lattice within the framework of the quasi-two-dimensional single-band model with attraction between electrons at neighboring sites. The method of consistent consideration of the order parameter fluctuations and the charge carrier scattering by fluctuations of coupled electron pairs, based on the theory of functional integration is used. The distribution functions of the phase fluctuation probabilities depending on temperature and charge carrier concentration are obtained. The temperature dependences of the amplitudes of the averaged superconducting order parameter are calculated. A phase diagram of superconducting states is constructed for the entire range of variation in the charge carrier concentration 0 < n < 2. Near the boundaries of this range, topologically trivial superconducting states with extended s symmetry are realized, while a superconducting state with topologically nontrivial chiral d + id symmetry is realized between them. The calculated anomalous self-energies are compared with the experimental ones obtained using machine learning techniques

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Section: Model and Resultsmentioning

confidence: 99%

Section: Calculation Of the Topological Index Taking Into Account The...mentioning

confidence: 99%

“…, valid for T → 0, in the limit Ω n → 0 from (2) we get the standard expression for TI (1). In contrast to (1), integration over energy in (7) is carried out along the real axis.…”

Section: Calculation Of the Topological Index Taking Into Account The...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Thermal fluctuations in superconducting phases with chiral d + id and s symmetry on a triangular lattice

Groshev

Аржников

2021

J. Phys.: Condens. Matter

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“…Until recently, local markers were developed in a non-interacting context as a property derived from the projector onto a band of states. In interacting systems, where the ground state does not correspond to a projector onto a set of single-particle states, most existing markers are inapplicable, however early progress has been made in understanding how local topology can be detected in interacting systems [26]. Clearly, in such a system the mathematical formalism presented here does not work, however our physical argument does not depend on the microscopic details of the system.…”

Section: Discussionmentioning

confidence: 99%

Quantised Bulk Conductivity as a Local Chern Marker

d'Ornellas,

Barnett,

Lee

2022

Preprint

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A central property of Chern insulators is the robustness of the topological phase and edge states to impurities in the system. Despite this, Chern number cannot be straightforwardly calculated in the presence of disorder. Recently, work has been done to propose several local analogs of the Chern number, called local markers, that can be used to characterise disordered systems. However, it was unclear whether the proposed markers represented a physically-measurable property of the system. Here we propose a local marker starting from a physical argument, as a local cross-conductivity measured in the bulk of the system. We find the explicit form of the marker for a non-interacting system of electrons on the lattice and show that it corresponds to existing expressions for the Chern number. Examples are calculated for a variety of disordered and amorphous systems, showing that it is precisely quantised to the Chern number and robust against disorder.

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