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 onedimensional 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.Recent years have seen rapid progress in the study of Majorana zero modes (MZMs) in condensed matter. Following initial reports of zero-bias peaks (ZBPs) in conductance of nanowire-superconductor hybrids appearing at moderate magnetic fields [1], improvements in materials [2-4] resulted in harder induced gaps and the emergence of zero-bias peaks from coalescing Andreev bound states (ABSs) [5,6], as well as the observation of exponential suppression of Coulomb peak oscillations with nanowire length [7]. Recently, indications of MZMs were also identified in wires lithographically patterned on hybrid two-dimensional heterostructures [8,9]. In many respects, experimentally observed ZBPs are consistent with theoretical expectations for MZMs, but important questions remain, particularly concerning theoretical models that show ZBPs arising from nontopological ABSs in localized states at the wire ends [10,11]. Furthermore, the fact that observed zero-bias peaks [1,5,6,12] were considerably smaller than the theoretically expected value of 2e 2 /h [13-18] has raised concern. Speculations about the origin of this discrepancy included effects of dissipation [19] as well as nontopological ZBPs induced by disorder [20][21][22] or a spin-orbit-induced precursor [10].In this Letter, we investigate ZBPs in lithographically defined wires as a function of temperature, tunnel coupling to a metallic lead (parametrized by the normal state conductance G N ), and magnetic field. For weak coupling to the lead (G N e 2 /h), a small ZBP with strong temperature dependence is observed over an extended range of magnetic fields. For strong coupling (G N ∼ e 2 /h), the dependence of the ZBP on G N and temperature weakens, with a low-temperature saturation at ∼ 2e 2 /h. Experimental results are well described by a theoretical model of resonant transport through a zero-energy state that includes both broadening due to coupling to a normal lead and temperature.Fitting ZBP heights as a function of temperature, T , and G N yields values for the energy broadening, Γ, which we find obey the linear relationship Γ ∝ G N . The fit results for Γ are found to be in excellent agreement with a scaling function that depends only on the dimensionless ratio Γ/k B T . The observed magnetic field dependence of the ZBP is quantitatively consistent with a picture in which field reduces the induced superconducting gap, ∆ * , which in turn reduces the ZBP height through the dependence of Γ on ∆ * .Overall, the...

No abstract

Thermal diodes [1,2], i.e., devices allowing heat to flow preferentially in one direction, constitute one of the key tools for the implementation of solid-state thermal circuits. These would find application in many fields of nanoscience, e.g., cooling, energy harvesting, thermal isolation, radiation detection [3], quantum information [4], or emerging fields such as phononics [5][6][7] and coherent caloritronics [8][9][10]. Yet, both in terms of phononic [11][12][13] or electronic heat conduction [14], which is the scope of this work, their experimental realization remains still very challenging [15]. A highly-efficient thermal diode should provide differences of at least one order of magnitude between the heat current transmitted in the forward temperature (T )-bias configuration, J f w , and that generated upon T -bias reversal, J rev , leading to R = J f w /J rev 1 or 1. So far, R ∼ 1.07 − 1.4 has been reported in phononic devices [16][17][18] whereas R ∼ 1.1 was obtained with a quantum-dot electronic thermal rectifier at cryogenic temperatures [19]. Here we show that unprecedented ratios reaching R ∼ 140 can be attained in a hybrid device combining normal metals tunnel-coupled to superconductors [20][21][22]. Our approach provides with a high-performance realization of a thermal diode for the electronic heat current that could be successfully implemented in true low-temperature solidstate thermal circuits.As recently proposed, substantial rectification of the electronic heat current can be achieved in metallic microcircuits based on tunnel junctions at low temperatures [20][21][22]. These simple elements, based on widespread fabrication technology and well-known physics, should indeed allow the realization of efficient electronic thermal diodes and have still to be realized experimentally. Two kinds of devices have been analyzed theoretically so far. One consisted of a NIS junction -where N stands for a normal metal, I for a thin insulating layer and S denotes a superconducting electrode -in which thermal symmetry is broken by the T -dependence of the energy gap (∆) in the superconducting density of states (DOS). R up to ∼ 0.8 was predicted to occur at temperatures close to the critical temperature (T c ) of S [20,21]. Strongly improved results were foreseen for a N L ININ R chain -where subscripts L and R refer to the left and right leads, respectively -subjected to the following two conditions: first, the thermal coupling between the normal metal electrodes in the left junction (∝ 1/R L , R L being the normal-state resistance of the N L IN contact) must differ largely from that in the right (∝ 1/R R ); second, electrons in the central lead have to be coupled to the phonon bath. Experimentally, this latter condition can be realized through a thermalizing cold finger tunnel-coupled to the * f.giazotto@sns.it N electrode. Under these circumstances, R up to ∼ 2000 can be theoretically achieved [22].Here we experimentally demonstrate a thermal diode design which joins the two aforementioned strategies. In our d...