Time-reversal invariant topological superconductivity in planar Josephson bijunction

Volpez, Yanick; Loss, Daniel; Klinovaja, Jelena

doi:10.1103/physrevresearch.2.023415

Cited by 8 publications

(4 citation statements)

References 89 publications

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“…Since TRS is preserved, it belongs to Class DIII according to the ten-fold classification. On the boundary of the interface, there exist a pair of helical Majorana edge states [58][59][60][61][62][63][64][65][66][67].…”

Section: Helical Superconductivitymentioning

confidence: 99%

Spin-orbit-coupled superconductivity with spin-singlet non-unitary pairing

Zeng¹,

Xu²,

Wang³

et al. 2022

Preprint

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An unconventional superconductor is distinguished with two types of gap functions: unitary and non-unitary. This core subject has been concentrated on purely spin-triplet or singlet-triplet mixed superconductors. However, the generalization to a purely spin-singlet superconductor has remained primarily of theoretical interest, which requires at least a multi-orbital correlated electronic systems. In this work, we present a possible establishment of both unitary and non-unitary pairings for spin-singlet superconductors with two atomic orbitals. Then we investigate the effects of atomic spin-orbit coupling and find a new spin-orbit-coupled non-unitary superconductor that supports exotic phenomena. Remarkably, there are mainly three features. Firstly, the atomic spin-orbit coupling locks the electron spins to be out-of-plane, which could give birth to the Type II Ising superconductivity with a large in-plane upper critical field compared to the Pauli limit. Secondly, topological chiral or helical Majorana edge state could be realized even in the absence of external magnetic fields or Zeeman fields. In addition, a spin-polarized superconducting state could even be generated by spin-singlet non-unitary pairings with spontaneous time-reversal breaking, which severs as a smoking gun to detect this exotic state by measuring the spin-resolved density of states. Therefore, our work might pave a new avenue to spin-orbit-coupled superconductors with spin-singlet non-unitary pairing symmetries.

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Section: Helical Superconductivitymentioning

confidence: 99%

Spin-orbit-coupled superconductivity with spin-singlet non-unitary pairing

Zeng¹,

Xu²,

Wang³

et al. 2022

Preprint

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“…However, since intrinsic p-wave superconductors turn out to be rare, the main experimental focus has been on engineering hybrid platforms based on proximity effect that can become topological superconductors. A wide variety of engineered systems have been proposed to host MBSs or chiral Majorana modes [5,[7][8][9][10][11][12][13][14] such as edge or surface states of topological insulators (TIs) [15], semiconductor nanowires [16][17][18][19][20][21][22], planar Josephson junctions [23][24][25], TI nanowires [26,27], graphene-based systems [28,[28][29][30][31][32][33][34][35][36][37], and many more.…”

Section: Introductionmentioning

confidence: 99%

Prevalence of trivial zero-energy subgap states in nonuniform helical spin chains on the surface of superconductors

et al. 2022

Self Cite

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Helical spin chains, consisting of magnetic (ad)atoms, on the surface of bulk superconductors are predicted to host Majorana bound states (MBSs) at the ends of the chain. Here, we investigate the prevalence of trivial zero-energy bound states in these helical spin-chain systems. The existence of trivial zero-energy bound states can prevent the conclusive identification of MBSs and, given the limited tunability of atomic spin-chain systems, could present a major experimental roadblock. First, we show that the Hamiltonian of a helical spin chain with varying nonuniform rotation rate between neighboring magnetic moments on a superconductor can be mapped to an effective Hamiltonian reminiscent of a ferromagnetic chain with strong Rashba spin-orbit coupling and with smooth nonuniform chemical potential, reminding a Rashba nanowire setups. Previously it has been found that trivial zero-energy states are abundant in nanowire systems with smoothly changing potentials. Therefore, we perform an extensive search for zero-energy bound states in helical spin-chain systems with varying rotation rates. Although bound states with near zero energy do exist for certain dimensionalities and rotation profiles, we find that zero-energy bound states are far less prevalent than in semiconductor nanowire systems with equivalent nonuniformities. In particular, utilizing varying rotation rates, we do not find zero-energy bound states in the most experimentally relevant setup consisting of a one-dimensional helical spin chain on the surface of a threedimensional superconductor, even for profiles that produce near zero-energy states in equivalent one-and twodimensional systems. Although our findings do not rule them out, the much reduced prevalence of zero-energy bound states in long nonuniform helical spin chains compared with equivalent semiconductor nanowires, as well as the ability to measure states locally via scanning tunneling microscopy, should reduce the experimental barrier to identifying MBSs in such systems.

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“…More recently, there has been experimental research as well as theoretical studies in similar models, including those for time-reversal invariant topological superconductors, 12,13 of the effects of MZMs in Josephson junctions, in particular because the dependence on the applied magnetic flux introduces an additional control knob. [13][14][15][16][17][18][19][20] In particular, it has been recently proposed that the current-phase relation measured in Josephson junctions may be used to find the parameters that define the MZMs. 20 A possible difficulty in these experiments is the slow thermalization to the ground state in the presence of a gap.…”

Section: Introductionmentioning

confidence: 99%

Phase diagram of a model for topological superconducting wires

Daroca

Aligia

2021

Phys. Rev. B

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We calculate the phase diagram of a model for topological superconducting wires with local swave pairing, spin-orbit coupling λ and magnetic field B with arbitrary orientations. This model is a generalized lattice version of the one proposed by Lutchyn et al. [Phys. Rev. Lett. 105 077001 (2010)] and Oreg et al. [Phys. Rev. Lett. 105 177002 (2010)], who considered λ perpendicular to B. The model has a topological gapped phase with Majorana zero modes localized at the ends of the wires. We determine analytically the boundary of this phase. When the directions of the spin-orbit coupling and magnetic field are not perpendicular, in addition to the topological phase and the gapped non-topological phase, a gapless superconducting phase appear.

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Time-reversal invariant topological superconductivity in planar Josephson bijunction

Cited by 8 publications

References 89 publications

Spin-orbit-coupled superconductivity with spin-singlet non-unitary pairing

Spin-orbit-coupled superconductivity with spin-singlet non-unitary pairing

Prevalence of trivial zero-energy subgap states in nonuniform helical spin chains on the surface of superconductors

Phase diagram of a model for topological superconducting wires

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