Efficient Numerical Self-Consistent Mean-Field Approach for Fermionic Many-Body Systems by Polynomial Expansion on Spectral Density

Nagai, Yuki; Ota, Yuji; Machida, Masahiko

doi:10.1143/jpsj.81.024710

Cited by 41 publications

(43 citation statements)

References 31 publications

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“…Since BdG Hamiltonians have built-in electron-hole symmetry, b = 0 and a ≈ E max . One can expand the retarded Green's function in terms of the T n (H BdG ) as [58][59][60][61]…”

Section: A Chebyshev Expansion Of the Green's Functionmentioning

confidence: 99%

Robust parity-mixed superconductivity in disordered monolayer transition metal dichalcogenides

Möckli

Khodas

2018

Phys. Rev. B

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Monolayer NbSe2 is a nodal topological Ising superconductor at magnetic in-plane fields exceeding the Pauli limit, with nodal points strictly on high symmetry lines in the Brillouin zone. Here, we use a combined numerical and group-theoretical approach in real-space to characterize the unconventional superconducting state in monolayer transition metal dichalcogenides. Even with a conventional pairing interaction, the superconducting state is intrinsically parity-mixed and robust against on-site disorder. The interplay between the Zeeman magnetic field, strong spin-orbit interaction, and electronic orbital content confer the unique superconducting and topological properties. The discussion also extends to strongly hole-doped MoS2 and its relatives.

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“…Since BdG Hamiltonians have built-in electron-hole symmetry, b = 0 and a ≈ E max . One can expand the retarded Green's function in terms of the T n (H BdG ) as [58][59][60][61]…”

Section: A Chebyshev Expansion Of the Green's Functionmentioning

confidence: 99%

Robust parity-mixed superconductivity in disordered monolayer transition metal dichalcogenides

Möckli

Khodas

2018

Phys. Rev. B

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“…Then the Josephson parameter J c /J 0 is represented by the ratio t s /t according to Ambegaokar-Baratoff's equation [35]. Equation (3) was solved self-consistently [36][37][38] to obtain the pair po- is almost cylindrically symmetric for t s /t = 0.8, the former becomes weaker and the latter is elongated along the junction line as t s /t is reduced to 0.4 and 0.1. Accordingly, the characteristics of N (E = 0, r) are changed; its magnitude around the center is decreased as t s /t is reduced, while the spatial distribution becomes strongly elliptic.…”

mentioning

confidence: 99%

Imaging Josephson Vortices on the Surface SuperconductorSi(111)−(7×3)
Yoshizawa
¹
,
Kim
²
,
Kawakami
³

et al. 2014
Phys. Rev. Lett.
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74
3
57
0
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We have studied the superconducting Si(111)-( √ 7 × √ 3)-In surface using a 3 He-based lowtemperature scanning tunneling microscope (STM). Zero-bias conductance (ZBC) images taken over a large surface area reveal that vortices are trapped at atomic steps after magnetic fields are applied. The crossover behavior from Pearl to Josephson vortices is clearly identified from their elongated shapes along the steps and significant recovery of superconductivity within the cores. Our numerical calculations combined with experiments clarify that these characteristic features are determined by the relative strength of the interterrace Josephson coupling at the atomic step.PACS numbers: 74.25. Ha,74.55.+v,74.50.+r The recent discovery of superconductivity in silicon surface reconstructions with metal adatoms was an unexpected surprise, because they are regarded as one of the thinnest two-dimensional (2D) materials ever possible [1][2][3][4][5]. This class of surface 2D materials has now become relevant for extensive superconductor researches in progress [6][7][8][9]. Notably, these new studies have been advanced by surface analytical techniques such as scanning tunneling microscopy (STM) [1,5,7,8] and ultrahigh vacuum (UHV)-compatible transport measurement [2-4, 10, 11].One ubiquitous feature of these surface systems is the presence of atomic steps. Atomic steps are considered to strongly affect electron transport phenomena, because they potentially decouple neighboring surface terraces [12][13][14][15]. This could prevent superconducting currents from running over a long distance. The presence of supercurrents through atomic steps has indeed been demonstrated by direct electron transport measurements [2][3][4], and recent experiments indicated that atomic steps work as Josephson junctions [2,5]. Nevertheless, direct evidence of Josephson coupling has not been obtained yet, and possible local variation of its strength has remained an open issue. This problem is also closely related to Josephson junctions formed at the grain boundaries in thin films of high-T c cuprates, which are of technological importance [16,17].In this Letter, we report on compelling evidence of the Josephson coupling at atomic steps on the surface superconductor Si (111)Zero-bias conductance (ZBC) images taken with a low-temperature (LT) STM reveal that vortices are present at atomic steps after magnetic fields are applied. The crossover behavior from Pearl to Josephson vortices is evident from their characteristic elongated shapes and significant recovery of superconductivity within their cores. This identification is strongly supported by our numerical calculations, which clarify their dependence on the interterrace Josephson coupling at the atomic step.The experiment was performed using a UHV-LT-STM constructed at the Institute of Solid State Physics, University of Tokyo. The STM head was accommodated within a 3 He-based cryostat combined with a solenoid superconducting magnet, where magnetic field was applied in the normal direction to the sampl...

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“…, an entire mean-field scheme can be developed as shown by Weiße et al [47] and Nagai et al [48]. Historically, the idea of expanding the Green function or the spectral density of the Green function with a set of orthonormal polynomials has been successfully used by a variety of groups studying condensed matter systems [67,68] beginning with Kunishima, Itoh and Tanaka [69].…”

Section: The Chebyshev Polynomial Expansion Methodsmentioning

confidence: 99%

Self-consistent study of Abelian and non-Abelian order in a two-dimensional topological superconductor

Goertzen

2017

Phys. Rev. B

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In the past few years, there has been a burst of theoretical and experimental activity in the field of topological insulators and topological superconductors. These materials represent new states of matter which are classified by an integer invariant and exhibit topologically protected conducting edge states which appear when the material is physically terminated.One of the consequences of topological superconductivity that makes this field significant is the possible existence of Majorana fermions as an elementary excitation. Despite extensive research, however, these exotic particles remain elusive to this day.In spite of the field of topological superconductivity being a hot topic in condensed matter research, there has been a severe lack of microscopic mean-field studies. In this thesis, we adopt a two-dimensional s-wave topological superconductivity model and perform selfconsistent mean-field studies in the Bogoliubov-de Gennes (BdG) formalism. As the BdG equations for topological superconductivity have high numerical demand, we implement the method of Chebyshev polynomial expansion, allowing self-consistent determination of the mean fields with high parallel efficiency and without any diagonalization of the Hamiltonian.Furthermore, we apply the recently developed Sakurai-Sugiura method to efficiently obtain the eigenpairs of the converged mean-field Hamiltonian.We first demonstrate the differences between Abelian, non-Abelian and trivial topological order by computing the Thouless, Kohmoto, Nightingale, and den Nijs (TKNN) number and investigating the bulk-boundary correspondence. We then shift our focus to self-consistent studies, illustrating how the electron-phonon coupling strength should be chosen for several different parameter sets. Adding boundaries in the system, we are then able to confirm the appearance of Majorana fermions in the non-Abelian topological phase and discuss under which circumstances they appear. We also examine the dependence of the critical temperature of the system on the TKNN number and compare results with a recent momentum-space study on impurity effects in an s-wave topological superconductor [1]. The effects of depositing a single non-magnetic impurity in the center of the sample are also investigated. In particular, we find that in the case of odd TKNN number, the order parameter is extremely sensitive to even weak non-magnetic impurities signifying unconventional p-wave-like behaviour.ii Finally, we investigate the possible interplay of charge density waves and topological superconductivity. We show that within our model, topological superconductivity and topological charge density waves can coexist in the Abelian topological phase. Studying separately the pure superconducting state, the pure density wave state and the mixed state, we find that these three states are degenerate with the same ground-state energy just as in the conventional s-wave case. Upon introducing open surfaces in the system, zero-energy bound states are also found within all three states. Fin...

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Efficient Numerical Self-Consistent Mean-Field Approach for Fermionic Many-Body Systems by Polynomial Expansion on Spectral Density

Cited by 41 publications

References 31 publications

Robust parity-mixed superconductivity in disordered monolayer transition metal dichalcogenides

Robust parity-mixed superconductivity in disordered monolayer transition metal dichalcogenides

Imaging Josephson Vortices on the Surface SuperconductorSi(111)−(7×3)
Yoshizawa
¹
,
Kim
²
,
Kawakami
³

et al. 2014
Phys. Rev. Lett.
Self Cite
74
3
57
0
View full text Add to dashboard Cite

Self-consistent study of Abelian and non-Abelian order in a two-dimensional topological superconductor

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Efficient Numerical Self-Consistent Mean-Field Approach for Fermionic Many-Body Systems by Polynomial Expansion on Spectral Density

Cited by 41 publications

References 31 publications

Robust parity-mixed superconductivity in disordered monolayer transition metal dichalcogenides

Robust parity-mixed superconductivity in disordered monolayer transition metal dichalcogenides

Imaging Josephson Vortices on the Surface SuperconductorSi(111)−(7×3)Yoshizawa1, Kim2, Kawakami3 et al. 2014Phys. Rev. Lett.Self Cite743570View full textAdd to dashboardCite

Self-consistent study of Abelian and non-Abelian order in a two-dimensional topological superconductor

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Imaging Josephson Vortices on the Surface SuperconductorSi(111)−(7×3)
Yoshizawa
¹
,
Kim
²
,
Kawakami
³

et al. 2014
Phys. Rev. Lett.
Self Cite
74
3
57
0
View full text Add to dashboard Cite