Signatures of topological phase transitions in Josephson current-phase discontinuities

Marra, Pasquale; Citro, Roberta; Braggio, Alessandro

doi:10.1103/physrevb.93.220507

Cited by 49 publications

(42 citation statements)

References 61 publications

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“…Results presented here imply that the breaking of the underlying symmetries can be achieved in superconductorquantum dot structures while maintaining coherent transport of Cooper pairs. In this context, our experiment is directly related to the efforts of studying triplet superconductivity and superconducting spintronics 26 as well as in achieving topological superconducting phase in quantum dots coupled to an s-wave superconductor 16,[27][28][29][30][31][32] . Aside from that, a gate-tunable phase offset may open novel possibilities for the realization of electrically controlled flux-and phase-based quantum bits 33 , superconducting computer memory components 34 , as well as superconducting 'phase' batteries and rectifiers 4,35 .…”

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confidence: 99%

Josephson ϕ0-junction in nanowire quantum dots

et al. 2016

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The Josephson e ect describes supercurrent flowing through a junction connecting two superconducting leads by a thin barrier 1 . This current is driven by a superconducting phase di erence ϕ between the leads. In the presence of chiral and time-reversal symmetry of the Cooper pair tunnelling process 2 , the current is strictly zero when ϕ vanishes. Only if these underlying symmetries are broken can the supercurrent for ϕ = 0 be finite [3][4][5] . This corresponds to a ground state of the junction being o set by a phase ϕ 0 , di erent from 0 or π. Here, we report such a Josephson ϕ 0 -junction based on a nanowire quantum dot. We use a quantum interferometer device to investigate phase o sets and demonstrate that ϕ 0 can be controlled by electrostatic gating. Our results may have far-reaching implications for superconducting flux-and phase-defined quantum bits as well as for exploring topological superconductivity in quantum dot systems.The process of Cooper pair tunnelling through a Josephson junction (JJ) is, in general, symmetric with respect to time inversion. This has a profound consequence for the JJ current-phase relation, I (ϕ). In particular it imposes the condition I (−ϕ) = −I (ϕ), which in turn results in I (ϕ = 0) being strictly zero. The I (ϕ = 0) = 0 condition is a consequence of the fact that for each process contributing to current flowing in one direction there is an opposite time-reversed process, in which spin-up and spin-down electrons are reversed, that exactly cancels this current. However, time inversion is not the only symmetry which can protect the I (ϕ = 0) = 0 condition. For example, in JJs based on single-domain ferromagnets, time inversion is broken, but the supercurrent is still zero for ϕ = 0 owing to chiral symmetry-that is, the symmetry between leftward and rightward tunnelling. This symmetry ensures that the tunnelling coefficient describing the electron tunnelling from the left lead to the right lead is exactly the same as the one describing the tunnelling in reverse, from the right lead to the left lead. The two tunnelling processes (leftward and rightward) cancel each other, which again results in I (ϕ = 0) being strictly zero. This is even the case for so-called π-junctions 6 , in which the current flow is reversed compared to usual JJs, but still the underlying symmetries guarantee zero current for ϕ = 0. To create conditions for a non-zero supercurrent to flow at ϕ = 0, both symmetries need to be broken 7 . Various ways have been proposed theoretically to break the underlying symmetries and create ϕ 0 -junctions, including ones based on non-centrosymmetric or multilayer ferromagnets 3,8 , quantum point contacts 4 , topological insulators 9,10 , diffusive systems 11,12 , nanowires 13,14 and quantum dots 5,15,16 . Alternatively, an effective built-in phase offset can be obtained by combining 0-and π-junctions in parallel 17,18 . However, no experimental demonstration of a ϕ 0 -junction has been reported until now.In quantum dots (QDs), breaking of both symmetries can be achiev...

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confidence: 99%

Josephson ϕ0-junction in nanowire quantum dots

et al. 2016

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“…These current switches are the class DIII analogues of the switches in class D systems, discussed in Ref. 16.…”

Section: Subgap Current Without Fermion Parity Conservationmentioning

confidence: 99%

Signatures of time-reversal-invariant topological superconductivity in the Josephson effect

Mellars

Béri

2016

Phys. Rev. B

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For Josephson junctions based on s-wave superconductors, time-reversal symmetry is known to allow for powerful relations between the normal-state junction properties, the excitation spectrum, and the Josephson current. Here we provide analogous relations for Josephson junctions involving one-dimensional time-reversal invariant topological superconductors supporting Majorana-Kramers pairs, considering both topological-topological and s-wave-topological junctions. Working in the regime where the junction is much shorter than the superconducting coherence length, we obtain a number of analytical and numerical results that hold for arbitrary normal-state conductance and the most general forms of spin-orbit coupling. The signatures of topological superconductivity we find include the fractional AC Josephson effect, which arises in topological-topological junctions provided that the energy relaxation is sufficiently slow. We also show, for both junction types, that robust signatures of topological superconductivity arise in the DC Josephson effect in the form of switches in the Josephson current due to zero-energy crossings of Andreev levels. The junction spinorbit coupling enters the Josephson current only in the topological-topological case and in a manner determined by the switch locations, thereby allowing quantitative predictions for experiments with the normal-state conductance, the induced gaps, and the switch locations as inputs.

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“…The usual periodic boundary condition (PBC) and the anti-periodic boundary condition (APBC) are included in the TBC as limiting cases. In practice, such a boundary condition can be realized by magnetic fluxes and Josephson junctions 6,45,[49][50][51][52][53][54][55][56][57][58][59][60][61] . Our work is motivated by the observation that the fermionic parities in the ground states of the Kitaev chain with the PBC and the APBC have opposite signs in the topological phase, hence indicating a level crossing when one continuously changes the parameters so as to connect the PBC with the APBC.…”

Section: Introductionmentioning

confidence: 99%

Exact zero modes in twisted Kitaev chains

Kawabata

Kobayashi

et al. 2017

Phys. Rev. B

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We study the Kitaev chain under generalized twisted boundary conditions, for which both the amplitudes and the phases of the boundary couplings can be tuned at will. We explicitly show the presence of exact zero modes for large chains belonging to the topological phase in the most general case, in spite of the absence of "edges" in the system. For specific values of the phase parameters, we rigorously obtain the condition for the presence of the exact zero modes in finite chains, and show that the zero modes obtained are indeed localized. The full spectrum of the twisted chains with zero chemical potential is analytically presented. Finally, we demonstrate the persistence of zero modes (level crossing) even in the presence of disorder or interactions.

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Signatures of topological phase transitions in Josephson current-phase discontinuities

Cited by 49 publications

References 61 publications

Josephson ϕ0-junction in nanowire quantum dots

Josephson ϕ0-junction in nanowire quantum dots

Signatures of time-reversal-invariant topological superconductivity in the Josephson effect

Exact zero modes in twisted Kitaev chains

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