Majorana zero modes in the coexistence phase of chiral superconductivity and 120°-type magnetic order on the triangular lattice

Вальков, В. В.; Zlotnikov, A. O.; Fedoseev, A. D.; Шустин, М. С.

doi:10.1016/j.jmmm.2016.12.093

Cited by 12 publications

(8 citation statements)

References 14 publications

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“…It is sufficient that all of the zero modes shown in Figure 1 are the edge ones. This is an important difference from the case ∆ 21 = 0 considered in [17] where the continual region with the bulk gapless excitations is appeared in the space of the parameters h and µ. As the result the zero energy modes of the system with the cylinder topology which are found in this region are not the edge ones and represent the bulk excitations modified due to the boundary effects.…”

Section: Hamiltonian Symmetry and Z 2 Topological Invariantmentioning

confidence: 73%

“…I f m is the parameter of the exchange interaction, being considered within the two coordination spheres. An important difference of the system (1) from the model studied in [17] is the consideration of superconducting pairings between nearest neighbors. Hereinafter, the model is considered both in the case of periodic boundary conditions along the direction a 2 (the cylinder topology), and in the case of periodic boundary conditions in two spatial directions (the torus topology).…”

Section: Model and Methodsmentioning

confidence: 99%

“…In Ref. [17], as well as in Ref. [8], the superconducting pairings in the second coordination sphere were only considered.…”

Section: Introductionmentioning

confidence: 99%

“…In [16] on the basis of the self-consistent integral equations in the coexistence phase for the t − J − V model it has been shown that in the presence of stripe magnetic ordering the superconducting order parameter does not have the chiral structure. Thus, the conditions for the realizations of the Majorana zero modes on the triangular lattice have been analyzed for the coexistence phase of chiral superconductivity and 120 • magnetic ordering [17]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

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The nontrivial ground state topology in the coexistence phase of chiral d-wave superconductivity and 120-degree magnetic order on a triangular lattice

Вальков

Zlotnikov

Шустин

2018

Journal of Magnetism and Magnetic Materials

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The Z 2 topological invariant is defined in the chiral d-wave superconductor having a triangular lattice in the presence of the 120 degrees magnetic ordering. By analyzing the Z 2 invariant, we determine the conditions of implementing nontrivial phases in the model with regard to superconducting pairings between nearest and next nearest neighbors. It is often supposed in such system that the pairing parameter between nearest neighbors should be equal to zero due to influence of the intersite Coulomb interaction. We show that taking into account even weak pairings in the first coordination sphere leads to the disappearance of the gapless excitations of the bulk spectrum in the wide region of the parameter space. Thus topological invariants can be defined in such region. Solving the problem of open edges it is shown that the zero energy modes are realized basically in the topologically nontrivial phases. Such zero modes are topologically protected Majorana modes. A connection between the Z 2 invariant calculated at the symmetric points of the Brillouin zone with respect to the electron-hole symmetry and the integer topological invariant of the ground state of the 2D lattice expressed in terms of the Green functions is established in the presence of noncollinear magnetic ordering.

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Section: Hamiltonian Symmetry and Z 2 Topological Invariantmentioning

confidence: 73%

Section: Model and Methodsmentioning

confidence: 99%

“…In Ref. [17], as well as in Ref. [8], the superconducting pairings in the second coordination sphere were only considered.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The nontrivial ground state topology in the coexistence phase of chiral d-wave superconductivity and 120-degree magnetic order on a triangular lattice

Вальков

Zlotnikov

Шустин

2018

Journal of Magnetism and Magnetic Materials

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“…Впоследствии для такой фазы в рамках квадратичного гамильтониана были най-дены условия реализации майорановских мод [8].…”

Section: Introductionunclassified

Влияние Межузельного Кулоновского Взаимодействия На Киральную Сверхпроводимость При Наличии Неколлинеарного Спинового Упорядочения

Вальков¹,

Злотников²

2017

Физика Твердого Тела

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Исследовано влияние межузельного кулоновского взаимодействия в планарной системе с треугольной решеткой на структуру кирального параметра порядка Delta( p) в фазе сосуществования сверхпроводимости и неколлинеарного 120o магнитного упорядочения. Установлено, что кулоновские корреляции в отмеченной фазе инициируют состояние, в котором квазиимпульсная зависимость Delta( p) представима в виде суперпозиции киральных инвариантов, соответствующих dx2-y2+idxy- и px+ipy-типам симметрии. Показано, что включение кулоновского взаимодействия смещает положение нодальных точек Delta( p), изменяя тем самым условия реализации квантового топологического перехода.03k Работа выполнена при поддержке фонда РФФИ, правительства Красноярского края и Краевого фонда науки (проекты N 16-02-00073-а, 16-42-243057-р-мол-а) и Комплексной программы СО РАН II.2П (проект 0358-2015-002). А.О. Злотников благодарит за поддержку в рамках стипендии президента РФ СП-1370.2015.5. DOI: 10.21883/FTT.2017.11.45044.03k

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Aspects of Topological Superconductivity in 2D Systems: Noncollinear Magnetism, Skyrmions, and Higher-order Topology

Zlotnikov

Шустин

Fedoseev

2021

J Supercond Nov Magn

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Majorana zero modes in the coexistence phase of chiral superconductivity and 120°-type magnetic order on the triangular lattice

Cited by 12 publications

References 14 publications

The nontrivial ground state topology in the coexistence phase of chiral d-wave superconductivity and 120-degree magnetic order on a triangular lattice

The nontrivial ground state topology in the coexistence phase of chiral d-wave superconductivity and 120-degree magnetic order on a triangular lattice

Влияние Межузельного Кулоновского Взаимодействия На Киральную Сверхпроводимость При Наличии Неколлинеарного Спинового Упорядочения

Aspects of Topological Superconductivity in 2D Systems: Noncollinear Magnetism, Skyrmions, and Higher-order Topology

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