Interaction-driven topological superconductivity in one dimension

Haim, Arbel; Wölms, Konrad; Berg, Erez; Oreg, Yuval; Flensberg, Karsten

doi:10.1103/physrevb.94.115124

Cited by 40 publications

(51 citation statements)

References 79 publications

(136 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was also shown in Ref. [50] that z k is always a positive semidefinite matrix, and by extension it is straightforward to show that 0 k is also always positive semidefinite. Consequently, it is only possible for the DIII topological invariant to take a nontrivial value if both z k and 0 k are nonzero, as the anomalous self-energy is not restricted to be either positive or negative semidefinite in this case.…”

mentioning

confidence: 66%

“…It has also been proposed to realize class DIII topological superconductivity in a system of two Rashba nanowires [43][44][45] or two topological insulators [46] coupled to a single conventional superconductor, but repulsive interactions are also necessary to reach the topological phase in these setups, which require a strength of induced crossed Andreev (interwire) pairing exceeding that of the direct (intrawire) pairing [47][48][49]. While it would be beneficial to engineer a DIII topological superconductor in a noninteracting 1D system coupled to a single conventional superconductor, as such a setup could avoid relying on unconventional superconductivity or interactions that are difficult to control experimentally, it has been shown that this is not possible in a fully time-reversal invariant system [38,50].In this paper, we show that such a 1D topological superconductor in class DIII can be realized when time-reversal …”

mentioning

confidence: 99%

“…It has been well demonstrated that the class DIII topological invariant can take a nontrivial value only if there exist at least two bands with opposite sign of the pairing potential [38,40,41,50,61], or, equivalently, that the anomalous component of the self-energy has both positive and negative eigenvalues. It was also shown in Ref.…”

mentioning

confidence: 99%

“…Note that it was concluded in Ref. [50] that the DIII invariant always takes a trivial value because it was assumed that the full tunneling Hamiltonian [Eq. (6)] is time-reversal symmetric, and hence T 0 k = 0 k = 0.…”

mentioning

confidence: 99%

See 3 more Smart Citations

DIII topological superconductivity with emergent time-reversal symmetry

et al. 2017

View full text Add to dashboard Cite

We find a class of topological superconductors which possess an emergent time-reversal symmetry that is present only after projecting to an effective low-dimensional model. We show that a topological phase in symmetry class DIII can be realized in a noninteracting system coupled to an s-wave superconductor only if the physical time-reversal symmetry of the system is broken, and we provide three general criteria that must be satisfied in order to have such a phase. We also provide an explicit model which realizes the class DIII topological superconductor in 1D. We show that, just as in time-reversal invariant topological superconductors, the topological phase is characterized by a Kramers pair of Majorana fermions that are protected by the emergent time-reversal symmetry. DOI: 10.1103/PhysRevB.96.161407 Introduction. Topological superconductors have been intensively pursued in recent years [1][2][3] because the Majorana fermions which are localized to their boundaries have potential applications in the development of a topological quantum computer [4,5]. The most promising proposals to date for engineering topological superconductivity involve coupling a conventional superconductor either to a nanowire with Rashba spin-orbit interaction that is subjected to an external magnetic field or to a ferromagnetic atomic chain [27][28][29][30][31][32][33][34].Additionally, there have been several proposals to engineer topological superconductors in symmetry class DIII. Such systems possess both particle-hole symmetry and time-reversal symmetry [35], with the presence of time-reversal symmetry ensuring that the Majorana fermions existing at the boundaries of class DIII topological superconductors come in Kramers pairs. In one dimension (1D), where superconductivity is required to be induced by the proximity effect, it has been shown that a nontrivial topological phase in class DIII can be realized by proximity coupling a noninteracting multichannel Rashba nanowire to an unconventional superconductor [36][37][38][39] or to two conventional superconductors forming a Josephson junction with a phase difference of π [40]. Alternatively, an effective π -phase difference can be induced in a multichannel Rashba nanowire with repulsive electron-electron interactions [41] or in a system of two topological insulators coupled to a conventional superconductor via a magnetic insulator [42]. It has also been proposed to realize class DIII topological superconductivity in a system of two Rashba nanowires [43][44][45] or two topological insulators [46] coupled to a single conventional superconductor, but repulsive interactions are also necessary to reach the topological phase in these setups, which require a strength of induced crossed Andreev (interwire) pairing exceeding that of the direct (intrawire) pairing [47][48][49]. While it would be beneficial to engineer a DIII topological superconductor in a noninteracting 1D system coupled to a single conventional superconductor, as such a setup could avoid relying on unconventional superc...

show abstract

mentioning

confidence: 66%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

DIII topological superconductivity with emergent time-reversal symmetry

et al. 2017

View full text Add to dashboard Cite

show abstract

“…More importantly, d-wave superconductors can induce an extended s-wave superconductivity, and this can be the main ingredient for the production of TRI MDs 29,32 . On the other way around, Majorana quasiparticles on the wire may couple to the nodal fermions in d-wave superconductors, and leaking of Majorana states in the substrate has been theoretically predicted 33 .…”

Section: Introductionmentioning

confidence: 99%

High critical temperature nodal superconductors as building block for time-reversal invariant topological superconductivity

Trani¹,

Campagnano²,

Tagliacozzo³

et al. 2016

Phys. Rev. B

View full text Add to dashboard Cite

We study possible applications of high critical temperature nodal superconductors for the search for Majorana bound states in the DIII class. We propose a microscopic analysis of the proximity effect induced by d-wave superconductors on a semiconductor wire with strong spin-orbit coupling. We characterize the induced superconductivity on the wire employing a numerical self-consistent tight-binding Bogoliubov-De-Gennes approach, and analytical considerations on the Green's funtion. The order parameter induced on the wire, the pair correlation function and the renormalization of the Fermi points are analyzed in detail, as well as the topological phase diagram in the case of weak coupling. We highlight optimal Hamiltonian parameters to access the non trivial topological phase which could display time-reversal invariant Majorana doublets at the boundaries of the wire.

show abstract