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Topological superconductivity and Majorana states in low-dimensional systems / V. V. Val'kov, M. S. Shustin, S. V. Aksenov [et al.] // Phys.-Usp. - 2022. - Vol. 65, Is. 1. - P. 2-39, DOI 10.3367/UFNe.2021.03.038950. - Cited References: 320. - This review was prepared in the framework of the Russian Foundation for Basic Research (RFBR) grant 19-12-50087. Part of the presented results were obtained in the framework of RFBR projects 19-02-00348, 20-32-70059, and 20-02-00015. S V A expresses his gratitude for support through a grant from the President of the Russian Federation, MK-1641.2020.2. A O Z and M S Sh express their gratitude to the Theoretical Physics and Math ematics Advancement Foundation “BASIS”. M Yu K thanks the Program for Basic Research of the NationalResearch University Higher School of Economics for support . - ISSN 1063-7869
Кл.слова (ненормированные):
low-dimensional system -- Majorana bound state -- spin-orbit coupling -- topological invariant -- Coulomb correlations -- noncollinear magnetism -- topological superconductivity -- quantum transport
Аннотация: We discuss the properties of topologically nontrivial superconducting phases and the conditions for their realization in condensed matter, the criteria for the appearance of elementary Majorana-type excitations in solids, and the corresponding principles and experimental methods for identifying Majorana bound states (MBSs). Along with the well-known Kitaev chain and superconducting nanowire (SW) models with spin-orbit coupling in an external magnetic field, we discuss models of quasi-two-dimensional materials in which MBSs are realized in the presence of noncollinear spin ordering. For finite-length SWs, we demonstrate a cascade of quantum transitions occurring with a change in the magnetic field, accompanied by a change in the fermion parity of the ground state. The corresponding anomalous behavior of the magnetocaloric effect can be used as a tool for identifying MBSs. We devote considerable attention to the analysis of the transport characteristics of devices that contain topologically nontrivial materials. The results of studying the conductance of an Aharonov-Bohm ring whose arms are connected by an SW are discussed in detail. An important feature of this device is the appearance of Fano resonances in the dependence of conductance on the magnetic field when the SW is in a topologically nontrivial phase. We establish a relation between the characteristics of such resonances and the spatial structure of the lowest-energy SW state. The conditions for the occurrence of an MBS in the phase of the coexistence of chiral d+id superconductivity and 120-degree spin ordering are determined in the framework of the t-J-V model on a triangular lattice. We take electron-electron interactions into account in discussing the topological invariants of low-dimensional superconducting materials with noncollinear spin ordering. The formation of Majorana modes in regions with an odd value of a topological ℤ invariant is demonstrated. The spatial structure of these excitations in the Hubbard fermion ensemble is determined.

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Публикация на русском языке Топологическая сверхпроводимость и майорановские состояния в низкоразмерных системах [Текст] : обзор / В. В. Вальков, M. S. Shustin, S. V. Aksenov [и др.] // Успехи физ. наук. - 2022. - Т. 192 № 1. - С. 3-44

Держатели документа:
Kirensky Institute Of Physics, Federal Research Center Krasnoyarsk Scientific Center, Siberian Branch, Russian Academy Of Sciences, Krasnoyarsk, Russian Federation
National Research University Higher School of Economics, ul. Myasnitskaya 20, 101000 Moscow, Russian Federation
Kapitza Institute for Physical Problems, Russian Academy of Sciences, ul. Kosygina 2, 119334 Moscow, Russian Federation

Доп.точки доступа:
Val'kov, V. V.; Вальков, Валерий Владимирович; Shustin, M. S.; Шустин, Максим Сергеевич; Aksenov, S. V.; Аксенов, Сергей Владимирович; Zlotnikov, A. O.; Злотников, Антон Олегович; Fedoseev, A. D.; Федосеев, Александр Дмитриевич; Mitskan, V. A.; Мицкан, Виталий Александрович; Kagan, M. Yu.
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Zlotnikov, A. O.
Aspects of topological superconductivity in 2D systems: Noncollinear magnetism, skyrmions, and higher-order topology / A. O. Zlotnikov, M. S. Shustin, A. D. Fedoseev // J. Supercond. Nov. Magn. - 2021. - Vol. 34, Is. 12. - P. 3053-3088, DOI 10.1007/s10948-021-06029-z. - Cited References: 230. - The study was funded by the Russian Foundation for Basic Research (Project No. 19-02-00348), Government of Krasnoyarsk Territory, Krasnoyarsk Regional Fund of Science (Grants No. 19-42240011, 20-42-243001). A.O.Z. and M.S.S. are grateful to the support of the Foundation for the Advancement of Theoretical Physics and Mathematics "BASIS" . - ISSN 1557-1939. - ISSN 1557-1947

РУБ Physics, Applied + Physics, Condensed Matter
Рубрики:
D-WAVE SUPERCONDUCTIVITY
NON-ABELIAN STATISTICS
CHIRAL SUPERCONDUCTIVITY
Кл.слова (ненормированные):
Topological superconductivity -- Majorana fermions -- Noncollinear magnetism -- Magnetic skyrmion -- Higher-order topology
Аннотация: The review is aimed at highlighting the aspects of topological superconductivity in the absence of spin-orbit interaction in two-dimensional systems with long-range noncollinear spin ordering or magnetic skyrmions. Another purpose is to give a brief introduction to the new concept of topological superconductivity, i.e. higher-order topology in two-dimensional systems including spin-orbit coupled structures. The formation of Majorana modes due to magnetic textures is discussed. The role of effective triplet pairings and odd fermion parity of the ground state wave function in different systems is emphasized. We describe the peculiarities of the magnetic skyrmions, leading to the formation of the Majorana modes and defects on which the modes are localized. The problem of braiding in the two-dimensional systems, especially in higher-order topological superconductors, is considered.

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Держатели документа:
Fed Res Ctr KSC SB RAS, Kirensky Inst Phys, Krasnoyarsk 660036, Russia.

Доп.точки доступа:
Shustin, M. S.; Шустин, Максим Сергеевич; Fedoseev, A. D.; Федосеев, Александр Дмитриевич; Злотников, Антон Олегович; Russian Foundation for Basic ResearchRussian Foundation for Basic Research (RFBR) [19-02-00348]; Government of Krasnoyarsk Territory, Krasnoyarsk Regional Fund of Science [19-42240011, 20-42-243001]; Foundation for the Advancement of Theoretical Physics and Mathematics "BASIS"
}
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    Shustin, M. S.
    Stable Majorana modes in spin-polarized wire with strong interactions / M. S. Shustin // J. Supercond. Novel Magn. - 2022. - Vol. 35, Is. 8 : The Kourovka Winter School of Theoretical Physics. - P. 2209-2216, DOI 10.1007/s10948-022-06238-0. - Cited References: 42. - The study was funded by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (Grant No. 20-1-4-25-1); Russian Foundation for Basic Research, Government of Krasnoyarsk Territory, Krasnoyarsk Regional Fund of Science (Project No. 20-42-243001); and Council of the President of the Russian Federation for Support of Young Scientists and Leading Scientific Schools (Grant No. MK-4687.2022.1) . - ISSN 1557-1939
   Перевод заглавия: Устойчивые майорановские моды в спин-поляризованной проволоке с сильными взаимодействиями
Кл.слова (ненормированные):
Majorana modes -- Quantum wires -- Strong electron correlations -- High spin polarization
Аннотация: For the 1D Hubbard model with spin-orbit coupling and proximity-induced s-wave superconductivity, the damping rates of quasiparticles are studied in the framework of density-matrix renormalization group (DMRG) approach. It is shown that low-energy excitations belonging to the Hubbard bands are stable against strong electron interaction at the spin-polarized regime. In order to confirm this result analytically, the low-energy model of the strongly interacting spin-polarized nanowire was derived in the second order of perturbation theory. This model generalizes Kitaev chain, taking into account the hoppings and anomalous pairings in the secondary coordination spheres as well as terms describing charge correlations. The amplitudes of the latter ones are small, and the system can be effectively described by quadratic Hamiltonian supporting stable Majorana excitations, which confirms numerical calculations. The topological phase diagram of effective model is studied in the framework of mean-field approximation. The evolution of topological phase boundaries under increasing of charge correlations is studied, and the important role of the joint realization of different types of interactions is noted. The results obtained can be applied when describing the Al-EuS-InAs hybrid system, recently synthesized and studied in searching for Majorana bound states.

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Держатели документа:
Kirensky Institute of Physics, Federal Research Center KSC SB RAS, Krasnoyarsk, 660036, Russian Federation

Доп.точки доступа:
Шустин, Максим Сергеевич
}
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Aksenov, S. V.
Manifestation of Majorana modes overlap in the Aharonov-Bohm effect / S. V. Aksenov // J. Phys. Condens. Matter. - 2022. - Vol. 34, Is. 25. - Ст. 255301, DOI 10.1088/1361-648X/ac62a7. - Cited References: 52. - We acknowledge fruitful discussions with A D Fedoseev and M S Shustin. The reported study was funded by Russian Foundation for Basic Research (Project No. 20-02-00015), Government of Krasnoyarsk Territory, Krasnoyarsk Regional Fund of Science to the research project ‘Study of edge states in one- and two-dimensional topological superconductors’ (No. 20-42-243005) . - ISSN 1361-648X
Кл.слова (ненормированные):
Aharonov–Bohm effect -- spin–orbit interaction -- topological superconductivity -- Majorana bound state -- Majorana mode -- quantum dot -- Kitaev chain
Аннотация: One of the key features of the Majorana bound states emerging in topological superconducting (SC) wires is increasing oscillations of their energy under the growth of magnetic field or chemical potential due to concomitant enhancement of hybridization of the Majorana mode wave functions initially localized at the opposite edges of the structure. In this study we found that the other consequence of it is a shift of Aharonov–Bohm (AB) oscillations of linear-response conductance in an interference device where two ends of the SC wire connected with a normal contact via non-SC wires (arms). In addition, it is accompanied by an oscillation period doubling. The numerical calculations for the spinful system are supported by the analytical results for different spinless models allowing to track the conductance evolution as the hybridization of the Majorana modes increases. It is shown that since the coupling between the different arms and normal contact is implemented only via the different-type Majoranas the AB oscillations acquire a fundamental π/2 shift in comparison with the effect for an analogous system of zero-energy quantum dots.

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Держатели документа:
Kirensky Institute of Physics, Federal Research Center KSC SB RAS, Akademgorodok street 50/38, Krasnoyarsk, 660036, Russian Federation

Доп.точки доступа:
Аксенов, Сергей Владимирович
}
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Fedoseev, A. D.
Realization conditions and the magnetic field dependence of corner excitations in the topological insulator with superconducting coupling on the triangular lattice / A. D. Fedoseev // J. Exp. Theor. Phys. - 2021. - Vol. 133, Is. 1. - P. 71-76, DOI 10.1134/S1063776121060029. - Cited References: 38. - This work was supported by the Russian Foundation for Basic Research (project no. 19-02-00348), Government of Krasnoyarsk Territory, Krasnoyarsk Regional Fund of Science to the research projects: "Study of edge states in oneand two-dimensional topological superconductors" (no. 20-42-243005), "Coulomb interactions in the problem of Majorana modes in low-dimensional systems with nontrivial topology" (no. 19-42-240011), and Council of the President of the Russian Federation for Support of Young Scientists and Leading Scientific Schools (Project MK1641.2020.2) . - ISSN 1063-7761. - ISSN 1090-6509

РУБ Physics, Multidisciplinary
Рубрики:
EDGE
STATES
ORDER
Аннотация: The studies of the topological properties of systems have recently been extended due to a new concept of higher-order topological insulators and superconductors. Many models were proposed for two-dimensional systems on a square lattice, where corner excitations can appear; however, the problem of existence of such excitations in superconducting systems with a triangular crystal lattice is still poorly understood. Using a topological insulator in the form of a triangle with a chiral superconducting order parameter as an example, we shows that corner excitations can exist in C3-symmetric systems. In spite of a nontopological character, these excitations have energies inside the gap of the first-order edge excitation spectrum over a wide parameter range and are well localized at the corners of the system. Gapless corner excitations are shown to exist in the system at certain parameters. The application of a magnetic field in the system plane removes the triple degeneracy of the corner excitation energy and makes it possible to control the position of the minimum-energy corner excitation using a magnetic field. At the same time the fine adjustment to achieve the gapless excitations at the chosen corner can be made with changing of the magnetic field value.

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Публикация на русском языке Федосеев, Александр Дмитриевич. Условия реализации и магнитополевая зависимость угловых возбуждений в топологическом изоляторе со сверхпроводящим спариванием на треугольной решетке [Текст] / А. Д. Федосеев // Журн. эксперим. и теор. физ. - 2021. - Т. 160 Вып. 1. - С. 88-94

Держатели документа:
Fed Res Ctr KSC SB RAS, Kirensky Inst Phys, Krasnoyarsk 660036, Russia.

Доп.точки доступа:
Федосеев, Александр Дмитриевич; Russian Foundation for Basic Research, Government of Krasnoyarsk Territory [19-02-00348]; Krasnoyarsk Regional Fund of Science [20-42-243005]; "Coulomb interactions in the problem of Majorana modes in low-dimensional systems with nontrivial topology" [19-42-240011]; Council of the President of the Russian Federation for Support of Young Scientists and Leading Scientific SchoolsLeading Scientific Schools Program [MK1641.2020.2]
}
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    Aksenov, S. V.
    Collapse of the Fano resonance caused by the nonlocality of the majorana state / S. V. Aksenov, M. Y. Kagan // JETP Letters. - 2020. - Vol. 111, Is. 5. - P. 286-292, DOI 10.1134/S0021364020050057. - Cited References: 37. - The work was supported by the Presidium of the Russian Academy of Sciences (Program of Basic Research no. 32 "Nanostructures: Physics, Chemistry, Biology, and Fundamentals of Technologies"), by the Russian Foundation for Basic Research (project nos. 19-02-00348, 20-32-70059, and 20-02-00015), and by the Government of the Krasnoyarsk Territory together with the Krasnoyarsk Science Foundation (project no. 19-42-240011 "Coulomb Interactions in the Problem of Majorana Modes in Low-Dimensional Systems with Nontrivial Topology"). S.V. Aksenov acknowledges the support of the Council of the President of the Russian Federation for Support of Young Russian Scientists and Leading Scientific Schools, grant no. MK3722.2018.2. M.Yu. Kagan acknowledges the support of the National Research University Higher School of Economics (program of basic research). . - ISSN 0021-3640. - ISSN 1090-6487
Рубрики:
BOUND-STATES
   QUANTUM TRANSITIONS
   TRANSMISSION
   CONTINUUM
   CASCADE
Аннотация: Owing to the nonlocal character of the Majorana state, the corresponding excitations are of great interest. It is demonstrated that the direct consequence of such nonlocality is the collapse of the Fano resonance manifesting itself in the conductance of an asymmetric interference device, the arms of which are connected by a one-dimensional topological superconductor. In the framework of the spinless model, it is shown that the predicted effect is associated with an increase in the multiplicity of the degeneracy of the zero-energy state of the structure arising at the critical point of the Kitaev model. Such an increase leads to the formation of a bound state in the continuum.

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Публикация на русском языке Аксенов, Сергей Владимирович. Коллапс резонанса Фано вследствие нелокальности майорановского состояния [Текст] / С. В. Аксенов, М. Ю. Каган // Письма в ЖЭТФ. - 2020. - Т. 111 Вып. 5. - С. 321-327

Держатели документа:
Russian Acad Sci, Kirensky Inst Phys, Fed Res Ctr KSC, Siberian Branch, Krasnoyarsk 660036, Russia.
Natl Res Univ Higher Sch Econom, Moscow 101000, Russia.
Russian Acad Sci, Kapitza Inst Phys Problems, Moscow 119334, Russia.

Доп.точки доступа:
Kagan, M. Yu.; Аксенов, Сергей Владимирович; Presidium of the Russian Academy of SciencesRussian Academy of Sciences [32]; Russian Foundation for Basic ResearchRussian Foundation for Basic Research (RFBR) [19-02-00348, 20-32-70059, 20-02-00015]; Krasnoyarsk Science Foundation [19-42-240011]; Government of the Krasnoyarsk Territory; Council of the President of the Russian Federation for Support of Young Russian Scientists and Leading Scientific SchoolsLeading Scientific Schools Program [MK3722.2018.2]; National Research University Higher School of Economics
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Aksenov, S. V.
Strong Coulomb interactions in the problem of Majorana modes in a wire of the nontrivial topological class BDI / S. V. Aksenov, A. O. Zlotnikov, M. S. Shustin // Phys. Rev. B. - 2020. - Vol. 101, Is. 12. - Ст. 125431, DOI 10.1103/PhysRevB.101.125431. - Cited References: 60. - We acknowledge fruitful discussions with V. V. Valkov and V. A. Mitskan. The reported study was funded by the RAS Presidium programs for fundamental research Nos. 12 and 32, Russian Foundation for Basic Research (Projects No. 18-32-00443 and No. 19-02-00348), Government of Krasnoyarsk Territory, Krasnoyarsk Regional Fund of Science to the research project: "Coulomb interactions in the problem of Majorana modes in low-dimensional systems with nontrivial topology" (Grant No. 19-42-240011). S.V.A. and A.O.Z. are grateful to the Council of the President of the Russian Federation for Support of Young Scientists and Leading Scientific Schools, Projects No. MK-1641.2020.2 and No. MK-3594.2018.2. S.V.A. acknowledges the support from the Foundation for the Advancement of Theoretical Physics and Mathematics "BASIS" (Grant No. 18-46-007). . - ISSN 2469-9950. - ISSN 2469-9969

РУБ Materials Science, Multidisciplinary + Physics, Applied + Physics, Condensed Matter
Рубрики:
QUANTUM
   POLARIZATION
   TRANSITION
   FERMIONS
   SPECTRUM
   STATE
Аннотация: In this study, the problem of strong Coulomb interactions in topological superconducting wire is analyzed by means of the density-matrix-renormalization-group (DMRG) approach. To analyze properties of edge states in the BDI-class structure, a quantity called Majorana polarization is used. From its dependence on wire length and an entanglement-spectrum degeneracy, topological phase diagrams are obtained. The DMRG calculations for the Shubin-Vonsovsky-type model of the wire show the transformation of phases with Majorana single and double modes (MSMs and MDMs, respectively) under the increase of onsite and intersite correlations. In particular, we demonstrate different scenarios including the possibilities of both induction and suppression of the MSMs and MDMs. It is shown that in the strongly correlated regime, the contributions of single-particle excitations to the Majorana-type states significantly decrease at low magnetic fxields. Moreover, the t-J*-V model is derived allowing to study the effective interactions and improve the DMRG numerics. It is found out that in the limiting case of the effective Hamiltonian with infinitely strong onsite repulsion, t model, the topological phases are destroyed. Finally, the ways to probe the MSMs and MDMs via the features of caloric functions are discussed.

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Держатели документа:
Fed Res Ctr KSC SB RAS, Kirensky Inst Phys, Krasnoyarsk 660036, Russia.

Доп.точки доступа:
Zlotnikov, A. O.; Злотников, Антон Олегович; Shustin, M. S.; Шустин, Максим Сергеевич; Аксенов, Сергей Владимирович; RAS Presidium programs for fundamental research [32, 12]; Russian Foundation for Basic ResearchRussian Foundation for Basic Research (RFBR) [18-32-00443, 19-02-00348]; Government of Krasnoyarsk Territory, Krasnoyarsk Regional Fund of Science [19-42-240011]; Council of the President of the Russian Federation for Support of Young Scientists and Leading Scientific SchoolsLeading Scientific Schools Program [MK-1641.2020.2, MK-3594.2018.2]; Foundation for the Advancement of Theoretical Physics and Mathematics "BASIS" [18-46-007]
}
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Zlotnikov, A. O.
Spin-orbit coupling-induced effective interactions in superconducting nanowires in the strong correlation regime / A. O. Zlotnikov, S. V. Aksenov, M. S. Shustin // Phys. Solid State. - 2020. - Vol. 62, Is. 9. - P. 1612-1618, DOI 10.1134/S1063783420090371. - Cited References: 24. - This study was supported by the Russian Foundation for Basic Research, projects nos. 19-02-00348 and 20-3270059, the Government of the Krasnoyarsk Territory and the Krasnoyarsk Territorial Foundation for Support of Scientific and R&D Activity, projects nos. 19-42-240011 and 18-42240014 "Single-Orbit Effective Model of an Ensemble of Spin-Polaron Quasiparticles in the Problem of Describing the Intermediate State and Pseudogap Behavior of Cuprate Superconductors,"and the Presidium of the Russian Academy of Sciences, program I.12 "Fundamental Problems of High-Temperature Superconductivity." S.V.A. thanks the Council for Grants of the President of the Russian Federation for Governmental Support of Young Russian Scientists, project no. MK-1641.2020.2 . - ISSN 1063-7834. - ISSN 1090-6460

РУБ Physics, Condensed Matter

Кл.слова (ненормированные):
superconducting nanowire -- spin-orbit coupling -- Majorana modes -- strong electron correlations
Аннотация: In the second order of the operator form of the perturbation theory, the effective interactions in a superconducting nanowire have been obtained at the strong electron correlations, when the spin-orbit coupling parameter is comparable with the hopping integral. Using the exact diagonalization technique, in short nanowires with the open boundary conditions at the strong Coulomb repulsion, the excitations corresponding to the Majorana edge states with the energy below the value of a bulk superconducting gap have been demonstrated.

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Публикация на русском языке Злотников, Антон Олегович. Эффективные взаимодействия, индуцированные спин-орбитальной связью в сверхпроводящих нанопроволоках в режиме сильных корреляций [Текст] / A. O. Злотников, С. В. Аксенов, М. С. Шустин // Физ. тверд. тела. - 2020. - Т. 62 Вып. 9. - С. 1447-1453

Держатели документа:
Russian Acad Sci, Siberian Branch, Krasnoyarsk Sci Ctr, Kirensky Inst Phys, Krasnoyarsk 660036, Russia.

Доп.точки доступа:
Aksenov, S. V.; Аксенов, Сергей Владимирович; Shustin, M. S.; Шустин, Максим Сергеевич; Злотников, Антон Олегович; Russian Foundation for Basic ResearchRussian Foundation for Basic Research (RFBR) [19-02-00348, 20-3270059]; Krasnoyarsk Territorial Foundation [19-42-240011, 18-42240014]; Government of the Krasnoyarsk Territory; Presidium of the Russian Academy of SciencesRussian Academy of Sciences [I.12]; Council for Grants of the President of the Russian Federation [MK-1641.2020.2]
}
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    Fedoseev, A. D.
    Corner excitations in the 2D triangle-shaped topological insulator with chiral superconductivity on the triangular lattice / A. D. Fedoseev // J. Phys.: Condens. Matter. - 2020. - Vol. 32, Is. 40. - Ст. 405302, DOI 10.1088/1361-648X/ab9e2f. - Cited References: 49. - The author thanks D M Dzebisashvili, M S Shustin, V A Mitskan and M M Korovushkin for the fruitful discussions and valuable remarks. The reported study was funded by the Russian Foundation for Basic Research (Projects Nos. 19-02-00348, 19-42-240011) and the Council of the President of the Russian Federation for Support of Young Scientists and Leading Scientific Schools (Project MK-1641.2020.2) . - ISSN 0953-8984
   Перевод заглавия: Угловые возбуждения в двумерном топологическом изоляторе в форме треугольника с киральной сверхпроводимостью на треугольной решетке
Кл.слова (ненормированные):
Electric insulators -- Topology -- Edge spectra -- Energy value -- First order -- Majorana -- Parameter spaces -- Triangular lattice -- Weak disorder -- Topological insulators
Аннотация: The 2D triangle-shaped C 3-symmetric topological insulator with the chiral superconducting coupling on the triangular lattice is investigated. While such a system cannot provide the topologically protected corner excitations, we report the presence of the nontopological corner excitations with energy value to lie in the first-order edge spectrum gap. Though these excitations are not topologically protected, they appear for a rather wide range of the parameters values and are robust against the boundary defects and weak disorder. We reveal the presence of the Majorana corner states, which appear along the line in the parameter space.

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Держатели документа:
Federal Research Center KSC SB RAS, Kirensky Institute of Physics, Akademgorodok 50/38, Krasnoyarsk, 660036, Russian Federation

Доп.точки доступа:
Федосеев, Александр Дмитриевич
}
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10.

Aksenov, S. V.
Probing Majorana bound states through an inhomogeneous Andreev double dot interferometer / S. V. Aksenov // Phys. Rev. B. - 2023. - Vol. 107, Is. 8. - Ст. 085417, DOI 10.1103/PhysRevB.107.085417. - Cited References: 60. - We thank A. D. Fedoseev and M. S. Shustin for fruitful discussions. The study was supported by Russian Science Foundation, Project No. 19-12-00167 . - ISSN 2469-9950. - ISSN 2469-9969
Аннотация: In modern experiments with hybrid superconducting (SC)/semiconducting nanowires the presence of zero-energy Andreev bound states (ABSs), characterized by a partial overlap of the Majorana wave functions, is a common problem that significantly complicates the detection of a genuine Majorana bound state (MBS). In this article, taking into account spatial inhomogeneity of experimentally investigated nanowire samples, we study interference transport features of a curved heterostructure in which two normal wires (or arms) are separated by a superconducting wire. Since Andreev reflection on the two N/S interfaces with smoothly changing electrostatic and SC pairing potentials results in the emergence of bound states, the low-energy interference transport is described in the framework of the model of two noninteracting Andreev levels or the Andreev double quantum dot. A set of limiting cases is analyzed allowing us to highlight the interference properties that are unique for the different types of ABSs, such as bulk ABS, inhomogeneous ABS, and MBS. In particular, considerable attention is paid to the features of the Aharonov-Bohm (AB) effect. It is shown that the response of each state can be recognized analyzing both AB period and extrema positions of the conductance oscillations which take place without any fine-tuning of the system parameters.

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Держатели документа:
Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036 Krasnoyarsk, Russia

Доп.точки доступа:
Аксенов, Сергей Владимирович
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11.

Effect of local coulomb interaction on majorana corner modes / S. V. Aksenov, A. D. Fedoseev, M. S. Shustin, A. O. Zlotnikov // 8th International conference on supercondactivity and magnetism (ICSM2023) : abstract book. - 2023. - P. 454. - Cited References: 4. - РНФ № 22-22-20076

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Держатели документа:
Kirensky Institute of Physics, FRC KSC SB RAS

Доп.точки доступа:
Aksenov, S. V.; Аксенов, Сергей Владимирович; Fedoseev, A. D.; Федосеев, Александр Дмитриевич; Shustin, M. S.; Шустин, Максим Сергеевич; Zlotnikov, A. O.; Злотников, Антон Олегович; International Conference on Supercondactivity and Magnetism(8 ; 2023 ; May 4-11 ; Ölüdeniz-Fethiye, Turkey)
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12.

Zlotnikov, A. O.
Majorana vortex modes in magnet-superconductor hybrids with a triangular lattice: local density of states study / A. O. Zlotnikov // 8th International conference on supercondactivity and magnetism (ICSM2023) : abstract book. - 2023. - P. 177. - Cited References: 6

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Kirensky Institute of Physics, FRC KSC SB RAS

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Злотников, Антон Олегович; International Conference on Supercondactivity and Magnetism(8 ; 2023 ; May 4-11 ; Ölüdeniz-Fethiye, Turkey)
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13.

Aksenov, S. V.
Majorana modes and Fano resonances in Aharonov–Bohm ring with topologically nontrivial superconducting bridge / S. V. Aksenov, M. Yu. Kagan // J. Low Temp. Phys. - 2024, DOI 10.1007/s10909-024-03171-5. - Cited References: 46. - We were inspired by Andreev’s seminal contribution in the superconducting nanophysics—the field which started in fact from Josephson effect and Andreev reflection. M. Yu. Kagan thanks the Program for basic research of the National Research University Higher School of Economics for support. The work was partially carried out within the state assignment of Kirensky Institute of Physics. S.V.A. thanks the Foundation for the Advancement of Theoretical Physics and Mathematics "BASIS" for support . - Article in press. - ISSN 0022-2291. - ISSN 1573-7357
Кл.слова (ненормированные):
Topological superconductivity -- Majorana modes -- Aharonov–Bohm ring -- Fano resonanse
Аннотация: We study different resonances (first of all of the Fano type) in the interference device formed by the Aharonov–Bohm ring with superconducting (SC) wire in the topologically nontrivial state playing a role of a bridge between top and bottom arms. We analyze Majorana modes on the ends of the SC wire and show that the collapse of the additional Fano resonance, that is initially induced by transport scheme asymmetry, is connected with the increase of the length of the bridge when the binding energy of the Majorana end modes tends to zero. In local transport regime, the Fano resonances are stable against the change of the transport symmetry. The reasons of both collapse and sustainability are analyzed using a spinless toy model including the Kitaev chain.

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Держатели документа:
Kirensky Institute of Physics, Siberian Branch of Russian Academy of Sciences, Akademgorodok 50/38, Krasnoyarsk, Russia, 660036
National Research University Higher School of Economics, Myasnitskaya Street 20, Moscow, Russia, 101000
P.L. Kapitza Institute for Physical Problems, Russian Academy of Sciences, Kosygin Street 2, Moscow, Russia, 119334

Доп.точки доступа:
Kagan, M. Yu.; Аксенов, Сергей Владимирович
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14.

Topological phases induced by charge fluctuations in Majorana wires / M. S. Shustin, S. V. Aksenov, I. S. Burmistrov // Phys. Rev. B. - 2024. - Vol. 109, Is. 7. - Ст. 075435, DOI 10.1103/PhysRevB.109.075435. - Cited References: 71. - We thank D. M. Dzebisashvili, A. O. Zlotnikov, and, especially, Yu. G. Makhlin, for fruitful discussions. S.V.A. is grateful to Landau Institute for Theoretical Physics for hospitality. The reported study was supported by Russian Science Foundation, Project No. 22-42-04416 . - ISSN 2469-9950. - ISSN 2469-9969
Аннотация: The influence of many-body interactions on topological phases is one of the problems that still remains urgent in modern condensed-matter theory. In this study we address this issue within perturbative theory framework by considering topological phase transitions related to charge correlations in the extended Kitaev chain model that belongs to the BDI symmetry class. Obtained corrections to a zero-frequency quasiparticle Green's function allow to separate the mean-field and fluctuation contributions to a total winding number. As a result, the phase transitions caused solely by the latter are unveiled. We thoroughly analyze the mechanism of such transitions in terms of fluctuation-induced nodal points and spectrum renormalization. Additionally, features of other quasiparticle properties such as effective mass and damping are discussed in the context of topological phase transitions.

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Держатели документа:
L. D. Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia
Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036 Krasnoyarsk, Russia
Laboratory for Condensed Matter Physics, HSE University, 101000 Moscow, Russia

Доп.точки доступа:
Shustin, M. S.; Шустин, Максим Сергеевич; Aksenov, S. V.; Аксенов, Сергей Владимирович; Burmistrov, I. S.
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15.

    Gamov, Alexander.
    Fermion parity of phases supporting multiple Majorana modes in a superconducting nanowire / A. Gamov, A. O. Zlotnikov // J. Sib. Fed. Univ. Math. Phys. - 2023. - Vol. 16, Is. 6. - P. 820-829 ; Журн. СФУ. Матем. и физ. - Cited References: 22. - Gamov A. acknowledges the support of the Theoretical Physics and Mathematics Advancement Foundation "BASIS" . - ISSN 1997-1397. - ISSN 2313-6022
   Перевод заглавия: Фермионная четность в фазах с множеством майорановских мод в сверхпроводящей нанопроволоке
Кл.слова (ненормированные):
Fermion parity -- superconducting nanowire -- Majorana modes -- topological invarian -- topological phase diagram -- фермионная четность -- сверхпроводящая нанопроволока -- майорановские моды -- топологический инвариан -- топологическая фазовая диаграмма
Аннотация: The fermion parity of the ground state is determined in various topological phases of the semiconducting nanowire under external magnetic field with proximity-induced superconductivity and strong spin-orbit interaction. Electron hopping as well as spin-flip hopping due to spin-orbit coupling and superconducting pairings in the second coordination sphere are taken into account. The connection between the fermion parity and the parity of the BDI topological invariant is shown. The formation of topological phases with three and four pairs of Majorana modes has been demonstrated.
Для полупроводниковой нанопроволоки, помещенной во внешнее магнитное поле, с наведенной сверхпроводимостью и сильным спин-орбитальным взаимодействием определена фермионная четность основного состояния в различных топологических фазах при учете перескоков электронов, включая перескоки с переворотом спина за счет спин-орбитальной связи, и сверхпроводящих спариваний во второй координационной сфере. Показана связь фермионной четности и четности BDI топологического инварианта. Продемонстрировано формирование топологических фаз с тремя и четырьмя парами майорановских мод.

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Держатели документа:
Siberian Federal University, Krasnoyarsk, Russian Federation
Kirensky Institute of Physics Federal Research Center KSC SB RAS, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Zlotnikov, A. O.; Злотников, Антон Олегович

}
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16.

Shustin, M. S.
Effect of strong intersite Coulomb interaction on the topological properties of a superconducting nanowire / M. S. Shustin, S. V. Aksenov // Phys. Solid State. - 2022. - Vol. 64, Is. 13. - P. 2047-2053, DOI 10.21883/PSS.2022.13.53972.23s. - Cited References: 55. - This study was supported by the Russian Foundation for Basic Research, the Government of the Krasnoyarsk Territory and the Krasnoyarsk Regional Fund of Science, projects nos. 20-42-243001 and 20-42-243005. M.S.S. thanks the Foundation for the Advancement of Theoretical Physics and Mathematics ”BASIS“. S.V.A. is grateful to the Council of the President of the Russian Federation for Support of Young Scientists and Leading Scientific Schools, project No. MK-1641.2020.2 . - ISSN 1063-7834. - ISSN 1090-6460
Кл.слова (ненормированные):
superconducting nanowires -- Majorana zero modes -- strong electron correlations
Аннотация: For superconducting nanowire with the pairing of extended s-type symmetry, Rashba spin-orbit interaction in a magnetic field, the influence of strong intersite charge correlations on single-particle Majorana excitations is analyzed. This problem is investigated on the basis of the density matrix renormalization group numerical method. It is shown that with an increase in the repulsion intensity of electrons located at the neighboring sites, two subbands emerge in the lower Hubbard band of the open system. Based on calculations of the Majorana polarization and degeneracy of the entanglement spectrum, it was found that a topologically nontrivial phase with one edge state survives at the edge of each of the subbands where the concentration of electrons or holes is minimal.

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Публикация на русском языке Шустин, Максим Сергеевич. Влияние сильного межузельного кулоновского взаимодействия на топологические свойства сверхпроводящей нанопроволоки [Текст] / М. С. Шустин, С. В. Аксенов // Физ. тверд. тела. - 2021. - Т. 63 Вып. 11. - С. 1758-1765

17.

Effect of local Coulomb interaction on Majorana corner modes: Weak and strong correlation limits / S. V. Aksenov, A. D. Fedoseev, M. S. Shustin, A. O. Zlotnikov // Phys. Rev. B. - 2023. - Vol. 107, Is. 12. - Ст. 125401, DOI 10.1103/PhysRevB.107.125401. - Cited References: 63. - We acknowledge fruitful discussions with D. M. Dzebisashvili and V. A. Mitskan. The reported study was supported by Russian Science Foundation Project No. 22-22-20076, and Krasnoyarsk Regional Fund of Science . - ISSN 2469-9950. - ISSN 2469-9969
Аннотация: Here we present an analysis of the evolution of Majorana corner modes realizing in a two-dimensional higher-order topological superconductor (HOTSC) on a square lattice under the influence of local Coulomb repulsion. Both weak- and strong-interaction regimes are studied. It is shown that in the homogeneous system, the weak repulsion widens the region of the topologically nontrivial phase on the phase diagram. The open-boundary effect, resulting in spatial inhomogeneity of the system, leads to the appearance of the ground-state crossover as the repulsion intensity increases. Before the crossover, concentration correlators are C4 symmetric and spin independent, and the corner states have energies that are determined by the overlap of the excitation wave functions localized at the different corners. After the crossover, the concentration correlators are spin dependent and possess the spontaneously broken symmetry. In turn, the corner excitation energy is size independent and defined by the Coulomb repulsion intensity with a quadratic law. In the strong-repulsion regime we derive the effective HOTSC Hamiltonian in the atomic representation and found a rich variety of interactions induced by virtual processes between the lower and upper Hubbard subbands. It is shown that Majorana corner modes still can be realized in the limit of the infinite repulsion, although the boundaries of the topologically nontrivial phase are strongly renormalized by Hubbard corrections.

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Держатели документа:
Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036 Krasnoyarsk, Russia

Доп.точки доступа:
Aksenov, S. V.; Аксенов, Сергей Владимирович; Fedoseev, A. D.; Федосеев, Александр Дмитриевич; Shustin, M. S.; Шустин, Максим Сергеевич; Zlotnikov, A. O.; Злотников, Антон Олегович
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18.

On the Dirac mass of Hubbard fermions in strongly correlated higher-order topological superconductor / S. V. Aksenov, A. D. Fedoseev, M. S. Shustin, A. O. Zlotnikov // Phys. Solid State. - 2023. - Vol. 65, Is. 7. - P1063-1070, DOI 10.61011/PSS.2023.07.56391.31H. - Cited References: 28. - The study was supported by the Russian Science Foundation (project No. 22-22-20076), and Krasnoyarsk Regional Fund of Science . - ISSN 1063-7834. - ISSN 1090-6460
Кл.слова (ненормированные):
topological phases -- Dirac fermions -- Coulomb interaction -- strong correlations -- Majorana modes
Аннотация: Majorana corner modes have a number of advantages over the conventional Majorana states in terms of performing topologically protected quantum computations. However, the problem of the influence of Coulomb repulsion on higher-order phases, which inevitably arises when trying to implement such systems in practice, has been poorly studied. In this article, we analyze the features of a topological invariant describing the nontrivial phase with the corner modes for a two-dimensional two-orbital model of a hybrid structure in the regime of extremely strong electron correlations. For this purpose, approximate wave functions of the edge states with a linear dispersion law and the associated Dirac masses, which arise when superconducting pairing in the system is taken into account, are obtained.

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Публикация на русском языке О дираковской массе хаббардовских фермионов в сильно коррелированном топологическом сверхпроводнике высокого порядка [Текст] / С. В. Аксенов, А. Д. Федосеев, М. С. Шустин, А. О. Злотников. - 9 с. // Физ. твердого тела. - 2023. - Т. 65 Вып. 7. - С. 1109-1117

Держатели документа:
Kirensky Institute of Physics, Federal Research Center KSC SB, Russian Academy of Sciences, Krasnoyarsk, Russia

Доп.точки доступа:
Aksenov, S. V.; Аксенов, Сергей Владимирович; Fedoseev, A. D.; Федосеев, Александр Дмитриевич; Shustin, M. S.; Шустин, Максим Сергеевич; Zlotnikov, A. O.; Злотников, Антон Олегович; Nanophysics and Nanoelectronics, International Symposium(XXVII ; 13-16 March 2023 ; Nizhny Novgorod, Russia)
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19.

Zlotnikov, A. O.
Majorana vortex modes in spin-singlet chiral superconductors with noncollinear spin ordering: Local density of states study / A. O. Zlotnikov // Phys. Rev. B. - 2023. - Vol. 107, Is. 14. - Ст. 144513, DOI 10.1103/PhysRevB.107.144513. - Cited References: 71. - I am grateful for fruitful discussions with participants of the seminar of Laboratory of Theoretical Physics in Kirensky Institute of Physics, especially with V. V. Val'kov, S. V. Aksenov, A. D. Fedoseev, and M. S. Shustin. The reported study was funded by the Theoretical Physics and Mathematics Advancement Foundation “BASIS” . - ISSN 2469-9950. - ISSN 2469-9969
Аннотация: In this study, topologically nontrivial edge and vortex bound states are described in the coexistence phase of chiral spin-singlet superconductivity and noncollinear spin ordering on a triangular lattice in the presence of few (up to four) vortices. We consider the topological phase transition induced by the magnetic order between the phase hosting Majorana modes and the initial phase of the chiral d-wave superconductivity supporting non-Majorana modes which is also topologically nontrivial. The change of the excitation spectrum at the critical point is obtained in both cases of open and periodic boundary conditions in the presence of vortices. It is proved that zero-energy Majorana modes localized at vortex cores are caused by noncollinear long-range magnetic ordering. Even though nearby excitation energies of subgap states including the edge-localized and vortex-localized states are very close to each other, the energy difference between different vortex bound states is an order of magnitude higher. This difference determines the energy gap for Majorana vortex modes separating them from other vortex bound states. It is found that even in the presence of noncollinear spin ordering its value can be estimated from the excitation energy of vortex bound states in the pure chiral d-wave state for the nonmagnetic case. By studying local density of states near the vortex cores the possibility to experimentally detect the described Majorana vortex modes by scanning tunneling microscopy is discussed. It is demonstrated that Majorana vortex modes and Majorana antivortex modes induced by noncollinear magnetism have different features in energy and spatially resolved density of states due to the chiral symmetry on the superconducting order parameter.

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Держатели документа:
Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036 Krasnoyarsk, Russia

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Злотников, Антон Олегович
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20.

    Aksenov, S. V.
    Majorana modes in BDI-class wire with strong Coulomb correlations / S. V. Aksenov, A. O. Zlotnikov, M. S. Shustin. - Electronic text data // ArXiv. - 2019. - Ст. 1911.01035. - Cited References: 55. - We acknowledge fruitful discussions with V.V. Valkov and V.A. Mitskan. The reported study was funded by the RAS Presidium programs for fundamental research Nos. 12 and 32, Russian Foundation for Basic Research (projects Nos. 18-32-00443, 19-02-00348), Government of Krasnoyarsk Territory, Krasnoyarsk Regional Fund of Science to the research projects: ”The manifestation of Coulomb interactions and effects of bounded geometry in the properties of topological edge states of nanostructures with spin-orbit interaction” (No. 18-42-243017), ”Coulomb interactions in the problem of Majorana modes in low-dimensional systems with nontrivial topology” (No. 19-42-240011). S.A. and A.Z. are grateful to the Council of the President of the Russian Federation for Support of Young Scientists and Leading Scientific Schools, projects Nos. MK-3722.2018.2, MK-3594.2018.2.
Рубрики:
Mesoscale and Nanoscale Physics
   Strongly Correlated Electrons
   Superconductivity
Аннотация: In this study the problem of strong Coulomb interactions in topological superconducting wire is analyzed by means of the density-matrix-renormalization-group (DMRG) approach. To obtain the topological phase diagrams and analyze properties of edge states in the BDI-class structure the quantity called Majorana polarization is used. Its behavior agrees with the entanglement-spectrum degeneracy which has topological nature. The DMRG calculations for the Shubin-Vonsovsky-type model of the wire show the transformation of phases with Majorana single and double modes (MSMs and MDMs, respectively) under the increase of on- and inter-site correlations. In particular, the effects of MSM and MDM robustness as well as their induction are observed. It is shown that in the strongly correlated regime the contributions of single-particle excitations to the Majorana-type states significantly decrease if averaged on-site spin-dependent concentrations have comparable values. Moreover, the t−J∗−V-model is derived allowing to study the effective interactions and improve the DMRG numerics. In order to demonstrate the key role of spin and charge fluctuations in the revealed effects we analytically consider the limiting case of the effective Hamiltonian with infinitely strong on-site repulsion using the Hubbard-I approximation. Finally, the ways to probe the MSMs and MDMs via the features of caloric functions are discussed.

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Держатели документа:
Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036 Krasnoyarsk, Russia

Доп.точки доступа:
Zlotnikov, A. O.; Злотников, Антон Олегович; Shustin, M. S.; Шустин, Максим Сергеевич; Аксенов, Сергей Владимирович
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