Multiple Andreev reflection and critical current in topological superconducting nanowire junctions

San-José, Pablo; Cayao, Jorge; Prada, Elsa; Aguado, Ramón

doi:10.1088/1367-2630/15/7/075019

Cited by 107 publications

(128 citation statements)

References 46 publications

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“…19. Our results for this junction, calculated using the scattering matrix formalism, are identical to previous results for the same SNS junction calculated using a Green's function method 61 and similar to the results obtained in Ref. 62 for a topological Josephson junction between superconductors connected through the helical edge states of a 2D topological insulator in the presence of a magnetic barrier.…”

Section: Topological-topological Socsw Junctionsupporting

confidence: 89%

Transport in superconductor–normal metal–superconductor tunneling structures: Spinful p -wave and spin-orbit-coupled topological wires

Setiawan

Cole

et al. 2017

Phys. Rev. B

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We theoretically study transport properties of voltage-biased one-dimensional superconductornormal metal-superconductor tunnel junctions with arbitrary junction transparency where the superconductors can have trivial or nontrivial topology. Motivated by recent experimental efforts on Majorana properties of superconductor-semiconductor hybrid systems, we consider two explicit models for topological superconductors: (i) spinful p-wave, and (ii) spin-split spin-orbit-coupled s-wave. We provide a comprehensive analysis of the zero-temperature dc current I and differential conductance dI/dV of voltage-biased junctions with or without Majorana zero modes (MZMs). The presence of an MZM necessarily gives rise to two tunneling conductance peaks at voltages eV = ±∆ lead , i.e., the voltage at which the superconducting gap edge of the lead aligns with the MZM. We find that the MZM conductance peak probed by a superconducting lead without a BCS singularity has a non-universal value which decreases with decreasing junction transparency. This is in contrast to the MZM tunneling conductance measured by a superconducting lead with a BCS singularity, where the conductance peak in the tunneling limit takes the quantized value GM = (4 − π)2e 2 /h independent of the junction transparency. We also discuss the "subharmonic gap structure", a consequence of multiple Andreev reflections, in the presence and absence of MZMs. Finally, we show that for finite-energy Andreev bound states (ABSs), the conductance peaks shift away from the gap bias voltage eV = ±∆ lead to a larger value set by the ABSs energy. Our work should have important implications for the extensive current experimental efforts toward creating topological superconductivity and MZMs in semiconductor nanowires proximity coupled to ordinary s-wave superconductors.

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Section: Topological-topological Socsw Junctionsupporting

confidence: 89%

Transport in superconductor–normal metal–superconductor tunneling structures: Spinful p -wave and spin-orbit-coupled topological wires

Setiawan

Cole

et al. 2017

Phys. Rev. B

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“…As a result, there is no clear consensus yet on whether MBSs have been observed or not in NWs. 3 Thus, the time seems right to move beyond zero-bias anomaly experiments and study more complex geometries such as superconductor-normal-superconductor (SNS) junctions [37][38][39]. This geometry has a number of advantages including the possibility of studying supercurrents [24,[40][41][42][43], or direct spectroscopy of Andreev bound states (ABS) [28,[44][45][46][47][48][49][50][51].…”

Section: Introductionmentioning

confidence: 99%

“…As we shall discuss, this latter technique can be used, in principle, to directly monitor the detailed evolution from the trivial to the nontrivial regime. Previous papers have mostly focused on short junctions [37,[52][53][54][55], while detailed studies of ABS in other relevant geometries, including long-and intermediate-length junctions, remain largely unaddressed. In particular, the role of Fabry-Perot resonances occurring in normal transport as the middle NW finite-length section of the junction is depleted has never been studied to the best of our knowledge.…”

Section: Introductionmentioning

confidence: 99%

SNS junctions in nanowires with spin-orbit coupling: Role of confinement and helicity on the subgap spectrum

et al. 2015

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We study normal transport and the subgap spectrum of superconductor-normal-superconductor (SNS) junctions made of semiconducting nanowires with strong Rashba spin-orbit coupling. We focus, in particular, on the role of confinement effects in long ballistic junctions. In the normal regime, scattering at the two contacts gives rise to two distinct features in conductance: Fabry-Perot resonances and Fano dips. The latter arise in the presence of a strong Zeeman field B that removes a spin sector in the leads (helical leads), but not in the central region. Conversely, a helical central region between nonhelical leads exhibits helical gaps of half-quantum conductance, with superimposed helical Fabry-Perot oscillations. These normal features translate into distinct subgap states when the leads become superconducting. In particular, Fabry-Perot resonances within the helical gap become parity-protected zero-energy states (parity crossings), well below the critical field B c at which the superconducting leads become topological. As a function of Zeeman field or Fermi energy, these zero modes oscillate around zero energy, forming characteristic loops, which evolve continuously into Majorana bound states as B exceeds B c . The relation with the physics of parity crossings of Yu-Shiba-Rusinov bound states is discussed.

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“…Our formalism can be used for any sSC topo non-topo SOCSW kind of SNS junctions requiring only NS scattering matrices which can be easily computed using Kwant [37]. Our formalism thus complements the Green's function method which is used to treat the topological superconductor junctions [28,[33][34][35]; (2) our theory shows that the conductance in such topological junctions could be quite complex depending on the system parameters and any signature for Majorana zero modes are inherently subtle requiring a careful interpretation of the conductance using our theory; and (3) a necessary corollary of the last item is that the conductance quantization found earlier in the weak-tunneling limit of topological superconductor junctions [28] is unlikely to be present in the generic experimental situation where the constraints of weak tunneling and/or number of Andreev bound states cannot be a priori guaranteed. Our theory should serve as the benchmark for future SNS conductance experiments and simulations where at least one of the superconductors is a topological superconductor.…”

mentioning

confidence: 99%

Conductance spectroscopy of nontopological-topological superconductor junctions

Setiawan

Cole

et al. 2017

Phys. Rev. B

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We calculate the zero-temperature differential conductance dI/dV of a voltage-biased onedimensional junction between a nontopological and a topological superconductor for arbitrary junction transparency using the scattering matrix formalism. We consider two representative models for the topological superconductors: (i) spinful p-wave and (ii) s-wave with spin-orbit coupling and spin splitting. We verify that in the tunneling limit (small junction transparencies) where only single Andreev reflections contribute to the current, the conductance for voltages below the nontopological superconductor gap ∆s is zero and there are two symmetric conductance peaks appearing at eV = ±∆s with the quantized value (4 − π)2e 2 /h due to resonant Andreev reflection from the Majorana zero mode. However, when the junction transparency is not small, there is a finite conductance for e|V | < ∆s arising from multiple Andreev reflections. The conductance at eV = ±∆s in this case is no longer quantized. In general, the conductance is particle-hole asymmetric except for sufficiently small transparencies. We further show that, for certain values of parameters, the tunneling conductance from a zero-energy conventional Andreev bound state can be made to mimic the conductance from a true Majorana mode.Topological superconductors (TSs), which host localized Majorana zero modes (MZMs) at their boundaries or in defects, have drawn a considerable amount of interest as the most promising platform for topological quantum computation [1][2][3][4][5][6][7]. One straightforward experimental signature of the MZM is the zero-bias conductance peak [8][9][10][11][12][13][14][15] (robustly quantized at a value 2e 2 /h) of a normal metal-superconductor (NS) junction. This quantized conductance arises from perfect Andreev reflection facilitated by the MZM at the edge of the TS [11][12][13][14][15]. A recent group of proposals for realizing TS in realistic solid state systems [10,[16][17][18][19] led quickly to several suggestive experimental observations of zero-bias conductance peaks [20][21][22][23][24][25][26][27]. While such features have been carefully shown to correspond to the topological regime, the observed zero-bias conductance is still far below the expected quantized value. This deviation can be attributed at least in part to thermal broadening in the normal metal lead which in turn broadens the zero-bias peak and reduces its maximum conductance value.Since the effect of thermal broadening in a superconductor is exponentially suppressed by the superconducting gap ∆ s , Peng et al. [28] have proposed to use a conventional superconducting lead as the "probe" in an MZM tunneling experiment. They found that, in the tunneling limit (or small junction transparency), the MZM manifests as two symmetric conductance peaks quantized at G M = (4 − π)2e 2 /h appearing at the threshold voltages eV = ±∆ s , i.e., when the BCS singularity of the probe lead aligns with the MZM. The result was derived using the nonequilibrium Green's function approach in the per...

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Multiple Andreev reflection and critical current in topological superconducting nanowire junctions

Cited by 107 publications

References 46 publications

Transport in superconductor–normal metal–superconductor tunneling structures: Spinful p -wave and spin-orbit-coupled topological wires

Transport in superconductor–normal metal–superconductor tunneling structures: Spinful p -wave and spin-orbit-coupled topological wires

SNS junctions in nanowires with spin-orbit coupling: Role of confinement and helicity on the subgap spectrum

Conductance spectroscopy of nontopological-topological superconductor junctions

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