Tomography of Majorana fermions with STM tips

We study the conductance of a junction between the normal and superconducting segments of a nanowire, both of which are subject to spin-orbit coupling and an external magnetic field. We directly compare the transport properties of the nanowire assuming two different models for the superconducting segment: one where we put superconductivity by hand into the wire, and one where superconductivity is induced through a tunneling junction with a bulk s-wave superconductor. While these two models are equivalent at low energies and at weak coupling between the nanowire and the superconductor, we show that there are several interesting qualitative differences away from these two limits. In particular, the tunneling model introduces an additional conductance peak at the energy corresponding to the bulk gap of the parent superconductor. By employing a combination of analytical methods at zero temperature and numerical methods at finite temperature, we show that the tunneling model of the proximity effect reproduces many more of the qualitative features that are seen experimentally in such a nanowire system.

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“…57). Therefore, the temperatures at which one achieves the expected universal zero-bias conductance 2e…”

Section: Finite Temperaturementioning

confidence: 99%

Transport signatures of topological superconductivity in a proximity-coupled nanowire

Reeg

Maslov

2017

Phys. Rev. B

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“…Two types of experiments could be carried out to detect the spin or charge reversal at the topological phase transition point. The first one is based on spin-polarized STM spectroscopy which allows one to inject a current in the lowest bands [32][33][34]47]. Depending on the polarization of the STM probe, a current will flow or not in the trivial phase and the opposite situation will occur in the topological phase.…”

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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“…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.…”

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confidence: 99%

“…We calculate the conductance (G = dI/dV ) for the SNS junction using the scattering matrix formalism as detailed in Ref. [32], in complement to the Green's function approach commonly employed in the literature to study the TS junctions [28,[33][34][35]. In this formalism, the scattering processes are partitioned into scattering processes at the left NS interface, tunnel barrier and right NS interface.…”

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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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Tomography of Majorana fermions with STM tips

Cited by 48 publications

References 58 publications

Transport signatures of topological superconductivity in a proximity-coupled nanowire

Transport signatures of topological superconductivity in a proximity-coupled nanowire

Spin and charge signatures of topological superconductivity in Rashba nanowires

Conductance spectroscopy of nontopological-topological superconductor junctions

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