Composite Majorana fermion wave functions in nanowires

Klinovaja, Jelena; Loss, Daniel

doi:10.1103/physrevb.86.085408

Cited by 215 publications

(253 citation statements)

References 46 publications

(92 reference statements)

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“…This is because our systems hosts 4 instead of 2 MBS and thus hybridization of these levels lifts the crossing at E = 0 (see the SM for the full spectrum). As shown previously [1], the overlap of the γ 1 and γ 2 MBS scales as ∼ exp (−l 12 /ξ), with ξ the coherence length that, in the regime discussed in the work scales as ξ ∝ V z [39]. Second, the signal evolves from a double-peak structure for Zeeman fields near the topological phase transition (V z ∼ ∆ w s ), dominated by χ D (φ, ω), becoming a single peak around φ = π for larger Zeeman fields (V z ∼ 2∆ w s ), where it is dominated by χ N D (φ, ω) (for a comparison of the two contributions see SM).…”

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confidence: 76%

Dynamic current susceptibility as a probe of Majorana bound states in nanowire-based Josephson junctions

et al. 2018

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We theoretically study a Josephson junction based on a semiconducting nanowire subject to a time-dependent flux bias. We establish a general density matrix approach for the dynamical response of the Majorana junction and calculate the resulting flux-dependent susceptibility using both microscopic and effective low-energy descriptions for the nanowire. We find that the diagonal component of the susceptibility, associated with the dynamics of the Majorana states populations, dominates over the standard Kubo contribution for a wide range of experimentally relevant parameters. The diagonal term, thus far unexplored in the context of Majorana physics, allows to probe accurately the presence of Majorana bound states in the junction.

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confidence: 76%

Dynamic current susceptibility as a probe of Majorana bound states in nanowire-based Josephson junctions

et al. 2018

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“…37 The condition L≫ξ M cannot be fulfilled as the Zeeman field exceeds the critical value above the topological transition. If, on the other hand, we assume stronger SO couplings, ξ M saturates to ξ M ∼α/Δ, 16,36 which, for typical values of Δ, is still much larger than the SO length. For example, assuming a SO coupling ten times larger than before, α∼2 eVÅ, and a proximity gap Δ = 0.5 meV (of the order of the experimental one in ref.…”

Section: Resultsmentioning

confidence: 99%

“…The incompressible regions are contours of constant ε eff F , 36 so that s = −gκ eff /g eff is a ratio between system's μ-compressibility κ eff ¼ @ε eff F =@μ, and the V Z -compressibility g eff =g ¼ @ε eff F =@V Z discussed above. While both are equal for μ < 0, κ eff becomes suppressed for μ > 0, so that s ≈ −1/(1 + (v/μ) 1/2 ) for a constant v∝V b 2 related to the interaction strength (see Supplementary Information).…”

Section: Resultsmentioning

confidence: 99%

Zero-energy pinning from interactions in Majorana nanowires

et al. 2017

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Majorana zero modes at the boundaries of topological superconductors are charge-neutral, an equal superposition of electrons and holes. This ideal situation is, however, hard to achieve in physical implementations, such as proximitized semiconducting nanowires of realistic length. In such systems Majorana overlaps are unavoidable and lead to their hybridization into charged Bogoliubov quasiparticles of finite energy, which, unlike true zero modes, are affected by electronic interactions. We here demonstrate that these interactions, particularly with bound charges in the dielectric surroundings, drastically change the non-interacting paradigm. Remarkably, interactions may completely suppress Majorana hybridization around parity crossings, where the total charge in the nanowire changes. This effect, dubbed zero-energy pinning, stabilizes Majoranas back to zero energy and charge, and leads to electronically incompressible parameter regions wherein Majoranas remain insensitive to local perturbations, despite their overlap.

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“…The sign reversal of spin and charge does not depend on boundaries of the system, and is thus independent of the presence of MFs. This provides an advantage over detecting the topological phase via the presence of MFs, which could either leak into the lead [45] or be masked by disorder effects [37][38][39][40]. To show that our results are robust against disorder, we add random on-site fluctuations to μ, 1 meV), N = 1200, and m = 0.015m e , with m e being the bare electron mass, for InSb nanowires (t = 10 meV, a = 15 nm).…”

Section: Figmentioning

confidence: 99%

Spin and charge signatures of topological superconductivity in Rashba nanowires

Szumniak¹,

Chevallier²,

Loss³

et al. 2017

Phys. Rev. B

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We consider a Rashba nanowire with a proximity gap which can be brought into the topological phase by tuning external magnetic field or chemical potential. We study spin and charge of the bulk quasiparticle states when passing through the topological transition for open and closed systems. We show, analytically and numerically, that the spin of bulk states around the topological gap reverses its sign when crossing the transition due to band inversion, independent of the presence of Majorana fermions in the system. This spin reversal can be considered as a bulk signature of topological superconductivity that can be accessed experimentally. We find a similar behavior for the charge of the bulk quasiparticle states, also exhibiting a sign reversal at the transition. We show that these signatures are robust against random static disorder. DOI: 10.1103/PhysRevB.96.041401Introduction. Topological phases of condensed matter systems [1,2] have attracted a lot of attention over many years due to their high promise for applications such as topological quantum computation [3,4]. One of the hallmarks of such phases, in particular of topological superconductivity, are zero-energy modes such as Majorana fermions (MF) that emerge at the edges of the system. Various candidate materials can host such topological states [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] but one of the most promising platforms are semiconducting nanowires of InAs or InSb material, with strong Rashba spin orbit interaction (SOI), subjected to an external magnetic field and in proximity to an s-wave superconductor [22,23]. Experimental evidence has been reported for topological phases in such wires [24][25][26][27][28][29][30][31] as well as in magnetic atomic chains on superconducting substrates [32][33][34]. However, most of the work so far has focused on the detection of the MFs in these nanowires and not on their bulk properties. This is quite surprising given the fact that the unambiguous identification of MFs from transport data alone can be challenging [35][36][37][38][39][40][41][42][43]. It is thus of great interest to look for alternative signatures of topological phases and to address the question how the bulk states change when passing from trivial to topological phase and if these changes appear in physically observable quantities.In this work, we show that the phase of a topological superconductor can be monitored by bulk states, in particular by certain spin and charge degrees of freedom. Quite remarkably, we find that the sign of the spin component along the magnetic field reverses for low-momentum states close to the Fermi level when the system passes through the phase transition, and similarly for the charge of such bulk states. This sign reversal is a direct consequence of the band inversion at the transition point and is directly accessible by spin-and energy resolved measurements. Another remarkable feature is that this signature is independent of boundary effects and thus unrelated to the presence of MFs. To demons...

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Composite Majorana fermion wave functions in nanowires

Cited by 215 publications

References 46 publications

Dynamic current susceptibility as a probe of Majorana bound states in nanowire-based Josephson junctions

Dynamic current susceptibility as a probe of Majorana bound states in nanowire-based Josephson junctions

Zero-energy pinning from interactions in Majorana nanowires

Spin and charge signatures of topological superconductivity in Rashba nanowires

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