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Register a new userScaling of Majorana Zero-Bias Conductance Peaks
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We report an experimental study of the scaling of zero-bias conductance peaks compatible with Majorana zero modes as a function of magnetic field, tunnel coupling, and temperature in one-dimensional structures fabricated from an epitaxial semiconductor-superconductor heterostructure. Results are consistent with theory, including a peak conductance that is proportional to tunnel coupling, saturates at $2e^2/h$, decreases as expected with field-dependent gap, and collapses onto a simple scaling function in the dimensionless ratio of temperature and tunnel coupling.
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A one-dimensional semiconductor nanowire proximitized by a nearby superconductor may become a topological superconductor hosting localized Majorana zero modes at the two wire ends in the presence of spin-orbit coupling and Zeeman spin splitting (arising from an external magnetic field). The hallmark of the presence of such Majorana zero modes is the appearance of a zero-temperature quantized zero-bias conductance peak in the tunneling spectroscopy of the Majorana nanowire. We theoretically study the temperature and the tunnel coupling dependence of the tunneling conductance in such nanowires to understand possible intrinsic deviations from the predicted conductance quantization. We find that the full temperature and the tunneling transmission dependence of the tunnel conductance does not obey any simple scaling relation, and estimating the zero-temperature conductance from finite-temperature and finite-tunnel-broadening tunneling data is difficult in general. A scaling relation, however, does hold at the extreme weak-tunneling low-temperature limit where the conductance depends only on the dimensionless ratio of the temperature and tunnel broadening. We also consider the tunneling contributions from nontopological Andreev bound states which may produce almost-zero-bias conductance peaks, which are not easy to distinguish from the Majorana-induced zero-bias peaks, finding that the nontopological almost-zero-modes associated with Andreev bound states manifest similar temperature and transmission dependence as the topological Majorana modes. We comment on the Zeeman splitting dependence of the zero-bias conductance peak for finite temperature and tunnel coupling.
Motivated by a recent experimental report[1] claiming the likely observation of the Majorana mode in a semiconductor-superconductor hybrid structure[2,3,4,5], we study theoretically the dependence of the zero bias conductance peak associated with the zero-energy Majorana mode in the topological superconducting phase as a function of temperature, tunnel barrier potential, and a magnetic field tilted from the direction of the wire for realistic wires of finite lengths. We find that higher temperatures and tunnel barriers as well as a large magnetic field in the direction transverse to the wire length could very strongly suppress the zero-bias conductance peak as observed in Ref.[1]. We also show that a strong magnetic field along the wire could eventually lead to the splitting of the zero bias peak into a doublet with the doublet energy splitting oscillating as a function of increasing magnetic field. Our results based on the standard theory of topological superconductivity in a semiconductor hybrid structure in the presence of proximity-induced superconductivity, spin-orbit coupling, and Zeeman splitting show that the recently reported experimental data are generally consistent with the existing theory that led to the predictions for the existence of the Majorana modes in the semiconductor hybrid structures in spite of some apparent anomalies in the experimental observations at first sight. We also make several concrete new predictions for future observations regarding Majorana splitting in finite wires used in the experiments.
We show that partially separated Andreev bound states (ps-ABSs), comprised of pairs of overlapping Majorana bound states (MBSs) emerging in quantum dot-semiconductor-superconductor heterostructures, produce robust zero bias conductance plateaus in end-of-wire charge tunneling experiments. These plateaus remain quantized at $2e^2/h$ over large ranges of experimental control parameters. In light of recent experiments reporting the observation of robust $2e^2/h$-quantized conductance plateaus in local charge tunneling experiments, we perform extensive numerical calculations to explicitly show that such quantized conductance plateaus, which are obtained by varying control parameters such as the tunnel barrier height, the super gate potential, and the applied magnetic field, can arise as a result of the existence of ps-ABSs. Because ps-ABSs can form rather generically in the topologically trivial regime, even in the absence of disorder, our results suggest that the observation of a robust quantized conductance plateau does not represent sufficient evidence to demonstrate the existence of non-Abelian topologically-protected Majorana zero modes localized at the opposite ends of a wire.
Superconducting proximity effect (SPE) in topological insulator (TI) and superconductor (SC) hybrid structure has attracted intense attention in recent years in an effort to search for mysterious Majorana fermions (MFs) in condensed matter systems. Here we report on the SPE in a Bi2Se3/NbSe2 junction fabricated with an all-dry transfer method. Resulting from the highly transparent interface, two sharp resistance drops are observed at 7 K and 2 K, respectively, corresponding to the superconducting transition of NbSe2 flake and the SPE induced superconductivity in Bi2Se3 flake. Experimentally measured differential conductance spectra exhibit a bias-independent conductance plateau (BICP) in the vicinity of zero bias below 7 K. As temperatures further decrease a zero bias conductance peak (ZBCP) emerges from the plateau and becomes more enhanced and sharpened at lower temperatures. Our numerically simulated differential conductance spectra reproduce the observed BICP and ZBCP and show that the SPE in topological surface states (TSS) is much stronger than that in the bulk states of Bi2Se3. The SPE induced superconducting gap for the TSS of Bi2Se3 is comparable to that of NbSe2 and gives rise to the observed BICP below 7 K. In contrast, the SPE induced superconducting gap for the bulk states of Bi2Se3 is an order of magnitude smaller than that of NbSe2 and superconducting TSS. These weakly paired bulk states in Bi2Se3 give rise to the ZBCP below 2 K. Our study has clearly unveiled the different roles of TSS and bulk stats in SPE, clarified the physical origin of the SPE induced features, and shined light on further investigation of SPE and MF in TI/SC hybrid structures.
A pair of Majorana zero modes (MZMs) constitutes a nonlocal qubit whose entropy is $log 2$. Upon strongly coupling one of the constituent MZMs to a reservoir with a continuous density of states, a universal entropy change of $frac{1}{2}log 2$ is expected to be observed across an intermediate temperature plateau. We adapt the entropy-measurement scheme that was the basis of a recent experiment [Hartman et. al., Nat. Phys. 14, 1083 (2018)] to the case of a proximitized topological system hosting MZMs, and propose a method to measure this $frac{1}{2}log 2$ entropy change --- an unambiguous signature of the nonlocal nature of the topological state. This approach offers an experimental strategy to distinguish MZMs from non-topological states.
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