DIII topological superconductivity with emergent time-reversal symmetry

Abstract

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...

Zero-energy Andreev bound states from quantum dots in proximitized Rashba nanowires

“…Consistent with our analytical model, we find a low-energy ABS by tuning the spin-orbit length to a resonant value with respect to the dot length L, with no topological phase transition occurring due to the strong proximity coupling. Crucially, we find that the presence of this ABS is insensitive to the thickness of the superconducting layer and the details of the proximity effect; as the properties of the proximitized region of the nanowire, and thus the topo- logical phase transition, are highly dependent on these two quantities [23][24][25], this result further demonstrates that the ABS is a property of the dot and unrelated to any properties of the superconducting region. Finally, we show that if the quantum dot is removed, there are no ABSs present in the system at energies far below the superconducting gap [49,53].…”

“…It was found in Refs. [23,24] that a strong proxim-ity coupling causes a significant renormalization of semiconducting material parameters and generally induces a large effective chemical potential shift in the nanowire, which can push the topological phase transition to prohibitively large magnetic field strengths. To capture these features of the proximity effect, we consider an effective one-subband model to describe the system shown in Fig.…”

“…It was shown in Refs. [23,24] that all properties of the region of nanowire coupled to the superconductor are highly dependent on both the thickness d and the tunneling strength t. In particular, the effective chemical potential shift, and therefore the field strength at which a topological phase transition occurs, can vary greatly depending on the precise value of d, while the renormalization of material parameters is weakened as t is made smaller. However, as shown in Fig.…”

“…With the advent of hybrid experimental systems that can be tuned [18,20] to the strong-proximity regime, there has been a recent theoretical emphasis placed on realistic treatments of the proximity effect in this limit while accounting for the small thickness of the superconducting shell. Studies based on an analytical tunneling Hamiltonian approach [23][24][25] have shown that all material parameters (such as effective mass, g-factor, and spin-orbit strength) of the semiconductor get significantly renormalized toward their corresponding values in the superconductor due to the strong proximity coupling (similarly to studies assuming the superconductor to be infinitely large [26][27][28][29][30][31][32][33][34][35]) and that all subbands within the semiconductor experience very large shifts in their effective chemical potentials that are highly dependent on the geometry of the superconducting shell. The combination of these two effects makes it difficult to realize a topological phase in the strong-coupling limit before destroying superconductivity in the shell.…”

Proximity induced time-reversal topological superconductivity in Bi2Se3 films without phase tuning

“…These, in general, require two basic ingredients: a multichannel or multiband electronic structure and a mechanism for inducing opposite pairing amplitudes on these channels [22]. These include Rashba nanowires proximitized by a d-wave [23] or an Iron-based superconductor with s ± pairing symmetry [24]; or two parallel nanowires with interwire pairing [25][26][27] or subject to opposite Zeeman fields [28]. Another scenario is spin orbit and many body interactions in proximity with ordinary superconductivity [29,30].…”