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The downscaling of nonlinear optical devices is significantly hindered by the inherently weak nonlinearity in regular materials. Here, we report a giant third-harmonic generation discovered in epitaxial thin films of V-VI chalcogenide topological insulators. Using a tailored substrate and capping layer, a single reflection from a 13 nm film can produce a nonlinear conversion efficiency of nearly 0.01%, a performance that rivals micron-scale waveguides made from conventional materials or metasurfaces with far more complex structures. Such strong nonlinear optical emission, absent from the topologically trivial member in the same compound family, is found to be generated by the same bulk band characteristics that are responsible for producing the band inversion and the nontrivial topological ordering. This finding reveals the possibility of obtaining superior optical nonlinearity by examining the large pool of newly discovered topological materials with similar band characteristics.

We investigate the impact of electrostatics on the proximity effect between a magnetic insulator and a semiconductor wire in semiconductor-superconductor-magnetic insulator hybrid structures. By performing self-consistent Schr$\ddot{\rm o}$dinger-Poisson calculations using an effective model of the hybrid system, we find that large effective Zeeman fields consistent with the emergence of topological superconductivity emerge within a large parameter window in wires with overlapping layers of magnetic insulator and superconductor, but not in non-overlapping structures. We show that this behavior is essentially the result of electrostatic effects determining the amplitude of the low-energy wave functions near the semiconductor-magnetic insulator interface., Comment: 8 pages, 5 figures

We propose a semiconductor-superconductor hybrid device for realizing topological superconductivity and Majorana zero modes consisting of a planar Josephson junction structure with periodically modulated junction width. By performing a numerical analysis of the effective model describing the low-energy physics of the hybrid structure, we demonstrate that the modulation of the junction width results in a substantial enhancement of the topological gap and, consequently, of the robustness of the topological superconducting phase and associated Majorana zero modes. This enhancement is due to the formation of minibands with strongly renormalized effective parameters, including stronger spin-orbit coupling, generated by the effective periodic potential induced by the modulated structure. In addition to a larger topological gap, the proposed device supports a topological superconducting phase that covers a significant fraction of the parameter space, including the low Zeeman field regime, in the absence of a superconducting phase difference across the junction. Furthermore, the optimal regime for operating the device can be conveniently accessed by tuning the potential in the junction region using, for example, a top gate., 17 pages, 17 figures

We use the available transport measurements in the literature to develop a dataset for the likely amount of disorder in semiconductor (InAs and InSb) materials which are used in fabricating the superconductor-semiconductor nanowire samples in the experimental search for Majorana zero modes. Using the estimated disorder in direct Majorana simulations, we conclude that the current level of disorder in semiconductor Majorana nanowires is at least an order of magnitude higher than that necessary for the emergence of topological Majorana zero modes. In agreement with existing results, we find that our estimated disorder leads to the occasional emergence of trivial zero modes, which can be post-selected and then further fine-tuned by varying system parameters (e.g., tunnel barrier), leading to trivial zero-bias conductance peaks in tunneling spectroscopy with $ \sim 2e^2/h $ magnitude. Most calculated tunnel spectra in these disordered systems, however, manifest essentially no significant features, which is also consistent with the current experimental status, where zero-bias peaks are found only occasionally in some samples under careful fine-tuning., Comment: 39 pages, 32 figures, 1 table

International audience; The perfomance of hematite and Ti-substituted hematite nanorods as photoanodes for solar water splitting was quantitavely evaluated from photoelectrochemical point of view. The nanostructure, morphology and chemical / electronic structure were characterized using various complementary methods, including X-ray diffraction, electron microscopy, X-ray photoelectron spectroscopy and scanning transmission X-ray microscopy. The presence of both reductive and oxidative surface states was evidenced and their impact on the photoelectrochemical efficiency was characterized. We show that both electronic conduction enhancement provided by the Ti substitution and charge transfer promoted by oxidative surface states improve solar water splitting performance.

The recent experimental observations of decaying energy oscillations with increasing magnetic field in semiconductor-superconductor Majorana nanowires is in contrast with the theoretical expectations based on the presence of Majorana zero modes localized at the ends of the system. These observations have been recently theoretically justified by considering a position-dependent spin-orbit coupling that can emerge due to a tunnel gate. Here, we show that the window in parameter space where this phenomenology occurs is vanishingly small when compared to the parameter region where Majorana oscillations should increase in amplitude with the applied magnetic field. Further, including a position-dependent effective potential that is also induced due to a tunnel gate practically removes this small window. Using extensive numerical calculations, we show that, as expected, increasing amplitude oscillations of the hybridization energy represent a generic property of topological Majorana zero modes, while decreasing amplitude oscillations are a generic property of low-energy trivial Andreev bound states, recently called partially separated Andreev bound states. By averaging over several realistic parameter configurations, we identify robust features of the hybridization energy that can be observed in a typical differential conductance experiment without fine-tuning the control parameters.

We studied the growth of epitaxial ferroelectric layers BaTiO3/Pt(001) in the framework of solar water splitting. The stoichiometry, i.e. the Ti/Ba ratio, appears as a crucial parameter not only for the crystallographic structure but also for the photocurrent generation when the sample is used as photoanode. We established an electrochemical poling method using a modulated potential, without altering the sample to control the electric polarization. Importantly, we show that the photoanode efficiency is improved when the polarization of the film is oriented towards the substrate. We demonstrate that this improvement is only due to the electrical field created by screening charges, which allows the separation of photo-generated charges.

We study one dimensional (1D) and quasi-1D periodic structures as possible platforms for the emergence of Majorana bound states with enhanced robustness against disorder and system inhomogeneity. First, using a simple 1D model, we analytically derive the effective parameters characterizing the minibands generated by the periodic potential. We show that, for strong enough periodic potentials, the higher energy minibands hosting Majorana bound states have significant advantages compared to their counterparts in uniform systems, including increased topological gaps, enhanced robustness against disorder, and enlarged parameter space regions consistent with the presence of topological superconductivity. We identify the problem of engineering a strong enough periodic potential as a key roadblock to realizing efficient periodic 1D structures. To address this challenge, we propose an efficient implementation of the periodic potential based on quasi-1D channels realized in 2D semiconductor heterostructures proximity coupled to superconductor strips of periodically modulated width. Our numerical study of the modulated channel device shows excellent agreement with the simple 1D model, reveals a topological phase diagram that is quite insensitive to the details of the confining potential associated with screening by the superconductor, and demonstrates that engineering patterned 2D structures represents a powerful and versatile approach to realizing robust Majorana bound states., 18 pages, 16 figures

Subband occupancy (i.e. the number of occupied subbands or energy levels in the semiconductor) is a key physical parameter characterizing the topological properties of superconductor-semiconductor hybrid systems in the context of the search for non-Abelian Majorana zero modes. We theoretically study the subband occupation of semiconductor nanowire devices as function of the applied gate potential, the semiconductor-superconductor (SM-SC) work function difference, and the surface charge density by solving self-consistently the Schr\"{o}dinger-Poisson equations for the conduction electrons of the semiconductor nanowire. Realistic surface charge densities, which are responsible for band bending, are shown to significantly increase the number of occupied subbands, making it difficult or impossible to reach a regime where only a few subbands are occupied. We also show that the energy separation between subbands is significantly reduced in the regime of many occupied subbands, with highly detrimental consequences for the realization and observation of robust Majorana zero modes. As a consequence, the requirements for the realization of robust topological superconductivity and Majorana zero modes should include a low value of the chemical potential, consistent with the occupation of only a few subbands. Finally, we show that the local density of states on the exposed nanowire facets provides a powerful tool for identifying a regime with many occupied subbands and is capable of providing additional critical information regarding the feasibility of Majorana physics in semiconductor-superconductor devices. In our work, we address both InAs/Al and InSb/Al superconductor-nanowire hybrid systems of current experimental interest., Comment: 11 pages, 8 figures

Evidence for propagating Majorana quasiparticles is found in a topological superconductor

We discuss the feasibility of measurement-based braiding in semiconductor-superconductor (SM-SC) heterostructures in the so-called quasi-Majorana regime $-$ the topologically-trivial regime due to partially-separated Andreev bound states (ps-ABSs). These low energy ABSs consist of component Majorana bound states (quasi-Majorana modes) that are spatially separated by a length scale smaller than the length of the system, in contrast with the Majorana zero modes (MZMs), which are separated by the length of the wire. In the quasi-Majorana regime, the ZBCPs appear to be robust to various perturbations as long as the energy splitting of the ps-ABS is less than the typical width $\e_w$ of the low-energy conductance peaks $\e_w$. However, the feasibility of measurement-based braiding depends on a different energy scale $\e_m$. In this paper we show that it is possible to prepare the SM-SC system in the quasi-Majorana regime with energy splittings below the $\e_m$ threshold, so that measurement-based braiding is possible in principle. Starting with ps-ABSs with energy below $\e_m$, we identify the maximum amplitudes of different types of perturbations that are consistent with perturbation-induced energy splittings not exceeding the $\e_m$ limit. We argue that measurements generating perturbations larger than the threshold amplitudes appropriate for $\e_m$ cannot realize measurement-based braiding in SM-SC heterostructures in the quasi-Majorana regime. We find that, if possible at all, quantum computation using measurement-based braiding in the quasi-Majorana regime would be plagued with errors introduced by the measurement processes themselves, while such errors are significantly less likely in a scheme involving topological MZMs., Comment: 18 pages, 17 figures

International audience; Multifunctional materials having the ability to respond to various external fields are tremendously sought; not only for their potential use as sensing components for devices, but also because they provide an elegant way to optimize materials usage. However, multifunctional single-phase materials are scarce and one approach to overcome this problem is to build artificial compounds combining different properties. This is a challenging materials science task, especially when two-dimensional structures are considered. In this paper, we report on the successful realization of multifunctional systems consisting of ferrimagnetic Mn0.7Fe2.3O4 spinel platelets, of controlled sizes and nanometric thicknesses, embedded in an epitaxial ferroelectric BaTiO3 perovskite thin film. The embedded platelets experience a much higher isostatic strain than that obtained for single layers. We successfully achieved nanometer-thick composite layers, with identical composition, having either in plane or out of plane electric polarization orientations. The optimal samples combine several functionalities: (i) the magnetoelectric nature of the full oxide artificial structures is confirmed; (ii) semiconducting diode behaviors are obtained when contacted with a metal electrode and (iii) marked (8 fold) electro-resistance transport properties with respect to the electric polarization orientation are revealed. The embedded platelets configuration enhances significantly interface and two-dimensional effects and is thus believed of high interest to realize functional device structures.

International audience; Ta3N5 belongs to the group of transition metal nitrides with the cation in a high oxidation state. These are typically challenging to synthesize owing to the low reactivity of nitrogen. This applies similarly to Ta3N5 that crystallizes only in the presence of oxygen during synthesis. Typical preparation methods are ammonolysis of oxidized Ta or magnetron sputtering of a Ta target in an atmosphere of Ar, N2 and O2. However, the material typically obtained by either synthesis method is of varying degrees of crystallinity and the key parameter affecting the crystallinity remains elusive. In this study, we examine the role of oxygen for the crystallinity of Ta3N5 samples by studying. Thin film samples prepared by magnetron sputtering reveal that oxygen is indeed the central driver for Ta3N5 crystallinity. While little oxygen in the films yields the metallic δ-TaN phase, excess oxygen results in low crystallinity Ta3N5 or Ta-O-N films. Ta3N5 samples with a high degree of crystallinity are obtained by limiting the oxygen supply to the sample during the deposition. A comparison with other studies suggests a fundamental oxygen incorporation limit above which the crystallinity of Ta3N5 is compromised. The most crystalline sample from this study contains 4.4 at.% of oxygen. It is grown onto a Si(100) substrate, covered with a 30 nm-thick metallic diffusion layer. For this sample, we observe Ta3N5 grains between 80 and 120 nm in size.

Ferroelectric materials hold significant promise for potential applications in a number of fields including spintronics and solar energy harvesting. When integrating them into heterostructures, it ...

We solve analytically the problem of a finite-length Kitaev chain coupled to a quantum dot (QD) which extends the standard Kitaev chain problem to the quantum dot-semiconductor-superconductor (QD-SM-SC) nanowire heterostructure currently under intense investigation for possible occurrence of Majorana zero modes (MZMs). As a first step we obtain the analytical solution of the finite-length Kitaev chain without the quantum dot which to the best of our knowledge has also not appeared before. Our full solution of the Kitaev chain coupled to a quantum dot reveals the emergence of a robust near-zero-energy Andreev bound state (ABSs) localized in the quantum dot region as the generic lowest energy solution in the topologically trivial phase. By contrast in the Kitaev chain without the quantum dot such a solution does not exist. The robustness of the ABS in the topologically trivial phase is due to a partial spatial decoupling of the component Majorana bound states (MBSs) over the length of the dot potential. As a result the signatures of the ABS in measurements that couple locally to the quantum dot e.g. tunneling measurements are identical to the signatures of topologically protected MZMs which arise only in the topological superconducting (TS) phase of the Kitaev chain.

Recent tunneling conductance measurements of Majorana nanowires show a strong variation in the magnetic field dependence of the superconducting gap among different devices. Here, we theoretically study the magnetic field dependence of the gap closing feature and establish that the degree of convexity (or concavity) of the gap closing as a function of Zeeman field can provide critical constraints on the underlying microscopic parameters of the semiconductor-superconductor hybrid system model. Specifically, we show that the gap closing feature is entirely concave only for strong spin-orbit coupling strength relative to the chemical potential. Additionally, the non-linearity (i.e. concavity or convexity) of the gap closing as a function of magnetic field complicates the simple assignment of a constant effective $ g $-factor to the states in the Majorana nanowire. We develop a procedure to estimate the effective $ g $-factor from recent experimental data that accounts for the non-linear gap closing resulting from the interplay between chemical potential and spin-orbit coupling. Thus, measurements of the magnetic field dependence of the gap closure on the trivial side of the topological quantum phase transition can provide useful information on parameters that are critical to the theoretical modeling of Majorana nanowires., Comment: 12 pages, 5 figures

International audience; Photocatalysis and photoelectrochemical (PEC) activities not only strongly depend on the chemical formulae of the electrode materials, but also on the local ionic environment that deserves to be addressed in detail for a given compound. Specifically, within the framework of PEC water splitting, we studied the growth, crystal and electronic structures, and the PEC properties of thin epitaxial films of TiO2 deposited on Pt(111), Pt(001), and Nb:SrTiO3(001) substrates. We found that the crystallographic structure is respectively rutile (100), anatase (001) on interfacial TiO2–B(001), and anatase (001). We studied in detail the relevant electronic properties such as band gap, position of valence and conduction bands, flat-band potential, and charge carrier density. We demonstrate that the largest photocurrent is obtained for rutile (100) deposited on Pt(111) owing to a higher position of the conduction band, whereas the lowest photocurrent is obtained for anatase (001) deposited on Nb:SrTiO3(001) due to a detrimental larger band gap. This study shows that for pure phase epitaxial layers, rutile (100) is much more efficient than anatase (001) for solar water splitting. Our results suggest that biphase heterojunctions may be a fruitful route to tune the properties allowing for PEC photoanode improvement.

Higher order topological superconductors hosting Majorana-Kramers pairs (MKPs) as corner modes have recently been proposed in a two-dimensional (2D) quantum spin Hall insulator (QSHI) proximity-coupled to unconventional cuprate or iron-based superconductors. Here, we show that such MKPs can be realized using a conventional s-wave superfluid with a soliton in cold atom systems governed by the Hubbard-Hofstadter model. The MKPs emerge in the presence of interaction at the "corners" defined by the intersections of line solitons and the one-dimensional edges of the system. Our scheme is based on the recently realized cold atom Hubbard-Hofstadter lattice and will pave the way for observing Majorana corner modes and possible higher order topological superfluidity with conventional s-wave superfluids/superconductors., Comment: 5+ pages and 4 figures; Version accepted for publication in PRL

Recent tunneling conductance measurements on semiconductor-superconductor nanowires find zero-bias peaks to be ubiquitous across wide ranges of chemical potential and Zeeman energy. Motivated by this, we demonstrate that topologically-trivial Andreev abound states (ABSs) pinned near zero energy are produced rather generically in inhomogeneous systems with multi-band occupancy in the presence of inter-band coupling. We first investigate the inter-band coupling mechanism responsible for the pinning within a multi-band 1D toy model, then we confirm the findings using a 3D Schr\"{o}dinger-Poisson approach that incorporates the geometric and electrostatic details of the actual device. Our analysis shows that level-repulsion generated by inter-band coupling can lead to a rather spectacular pinning of the lowest-energy mode near zero energy in systems (or regions) characterized by very-short length scales ($\sim100~$nm).We show that level repulsion between the lowest energy levels can mimic the gap opening feature (simultaneous with the emergence of a near-zero energy mode) predicted to occur in Majorana hybrid systems. We also demonstrate that nearly-zero bias differential conductance features exhibiting particle-hole asymmetry are due to the presence of (topologically-trivial) ABSs pinned near zero-energy by level repulsion, not to Majorana zero modes, quasi-Majoranas, or any other low-energy mode that involves (partially) separated Majorana bound states. Our findings demonstrate the importance of understanding in detail multi-band physics and electrostatic effects in the context of the ongoing search for Majorana modes in semiconductor-superconductor heterostructures., Comment: 16 pages, 14 figures

In a recent high-quality experimental work on normal metal--superconducting nanowire junctions arXiv:1807.01940 (2018), strong anisotropic suppression of induced superconductivity has been observed in tunnel conductance measurements in the presence of applied magnetic field with variable orientation. Following this finding, we investigate theoretically the dependence of tunnel conductance on the direction of the Zeeman field in order to understand the operational mechanisms and to extract effective system parameters. Second, motivated by a generic discrepancy between experiment and theory, i.e., many in-gap and above-gap conductance features predicted by theory are barely observed in experiments, we study several mechanisms possibly responsible for the suppression of the theoretically predicted conductance features (e.g., length of the nanowire, self-energy effect due to the proximity effect, finite temperature, finite dissipation, and multiband effect). One essential finding in the current work is that only by a combined understanding of both suppression mechanisms can we extract effective system parameters from the experimental data (e.g., the effective nanowire-superconductor coupling, the effective Land\'e $g$ factor, and the chemical potential of the semiconducting nanowire). In addition, we consider topologically trivial Andreev bound states in hybrid nanowires in the presence of potential inhomogeneities, such as external quantum dots or potential inhomogeneities inside the nanowire. We compare the anisotropic, field-dependent features induced by these nontopological Andreev bound states with the corresponding features produced by topological Majorana zero modes in pristine nanostructures, so that we can provide guidance to differentiate between the topologically trivial and nontrivial cases., Comment: 19 pages, 15 figures

We perform tunneling measurements on indium antimonide nanowire/superconductor hybrid devices fabricated for the studies of Majorana bound states. At finite magnetic field, resonances that strongly resemble Majorana bound states, including zero-bias pinning, become common to the point of ubiquity. Since Majorana bound states are predicted in only a limited parameter range in nanowire devices, we seek an alternative explanation for the observed zero-bias peaks. With the help of a self-consistent Poission-Schr\"odinger multiband model developed in parallel, we identify several families of trivial subgap states which overlap and interact, giving rise to a crowded spectrum near zero energy and zero-bias conductance peaks in experiments. These findings advance the search for Majorana bound states through improved understanding of broader phenomena found in superconductor-semiconductor systems., Comment: 14 pages, 4 figures in main text and 8 figures in supplemental materials. All raw data can be found under directory \anc

We study the electronic structure of full-shell superconductor-semiconductor nanowires, which have recently been proposed for creating Majorana zero modes, using an eight-band $\vec{k} \cdot \vec{p}$ model within a fully self-consistent Schr\"{o}dinger-Poisson scheme. We find that the spin-orbit coupling induced by the intrinsic radial electric field is generically weak for sub-bands with their minimum near the Fermi energy. Furthermore, we show that the chemical potential windows consistent with the emergence of a topological phase are small and sparse and can only be reached by fine tunning the diameter of the wire. These findings suggest that the parameter space consistent with the realization of a topological phase in full-shell InAs/Al nanowires is, at best, very narrow., Comment: 5 pages, 4 figures + Supplemental Material

We theoretically study a spin-orbit-coupled nanowire proximitized by a superconductor in the presence of an externally applied Zeeman field ("Majorana nanowire") with zero-energy Majorana bound states localized at the two ends of the wire when the Zeeman spin splitting is large enough for the system to enter the topological phase. The specific physics of interest in the current work is the effect of having several tunnel probes attached to the wire along its length. Such tunnel probes should allow, as a matter of principle, one to observe both the predicted bulk superconducting gap closing and opening associated with the topological quantum phase transition as well as the Majorana bound states at the wire ends showing up as zero-bias conductance peaks, depending on which probes are used for the tunneling spectroscopy measurement. Because of the possible invasive nature of the tunnel probes, producing local potential fluctuations in the nanowire, we find the physical situation to be quite complex. In particular, depending on the details of the tunnel barrier operational at the probes, the Majorana nanowire could manifest additional low-energy Andreev bound states which will manifest their own almost-zero-bias peaks, complicating the interpretation of the tunneling data in multiprobe Majorana nanowires. We use two complementary microscopic models to simulate the probes, finding that the tunneling conductance spectrum depends rather sensitively on the details of the tunnel barriers at the probes. We apply our general analysis to simulate a recent multiprobe nanowire experiment commenting on the nature of the quasiparticle gaps likely controlling the experimental observations., 11 pages, 8 figures, published version

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., Comment: 8 pages, 8 figures

International audience; Multiferroic biphase systems with robust ferromagnetic and ferroelectric response at room temperature would be ideally suitable for voltage-controlled nonvolatile memories. Understanding the role of strain and charges at interfaces is central for an accurate control of the ferroelectricity as well as of the ferromagnetism. In this paper, we probe the relationship between the strain and the ferromagnetic/ferroelectric properties in the layered CoFe2O4/BaTiO3 (CFO/BTO) model system. For this purpose, ultrathin epitaxial bilayers, ranging from highly strained to fully relaxed, were grown by molecular beam epitaxy on Nb:SrTiO3(001). The lattice characteristics, determined by X-ray diffraction, evidence a non-intuitive cross-correlation: the strain in the bottom BTO layer depends on the thickness of the top CFO layer and vice versa. Plastic deformation participates in the relaxation process through dislocations at both interfaces, revealed by electron microscopy. Importantly, the switching of the BTO ferroelectric polarization, probed by piezoresponse force microscopy, is found dependent on the CFO thickness: the larger is the latter, the easiest is the BTO switching. In the thinnest thickness regime, the tetragonality of BTO and CFO has a strong impact on the 3d electronic levels of the different cations, which were probed by X-ray linear dichroism. The quantitative determination of the nature and repartition of the magnetic ions in CFO, as well as of their magnetic moments, has been carried out by X-ray magnetic circular dichroism, with the support of multiplet calculations. While bulklike ferrimagnetism is found for 5-15 nm thick CFO layers with a magnetization resulting as expected from the Co2+ ions alone, important changes occur at the interface with BTO over a thickness of 2-3 nm because of the formation of Fe2+ and Co3+ ions. This oxidoreduction process at the interface has strong implications concerning the mechanisms of polarity compensation and coupling in multiferroic heterostructures.

We show theoretically that in the generic finite chemical potential situation, the clean superconducting spin-orbit-coupled nanowire has two distinct nontopological regimes as a function of Zeeman splitting (below the topological quantum phase transition): one is characterized by finite-energy in-gap Andreev bound states, while the other has only extended bulk states. The Andreev bound state regime is characterized by strong features in the tunneling spectra creating a "gap closure" signature, but no "gap reopening" signature should be apparent above the topological quantum phase transition, in agreement with most recent experimental observations. The gap closure feature is actually the coming together of the Andreev bound states at high chemical potential rather than a simple trivial gap of extended bulk states closing at the transition. Our theoretical finding establishes the generic intrinsic Andreev bound states on the trivial side of the topological quantum phase transition as the main contributors to the tunneling conductance spectra, providing a generic interpretation of existing experiments in clean Majorana nanowires. Our work also explains why experimental tunnel conductance spectra generically have gap closing features below the topological quantum phase transition, but no gap opening features above it., 28 pages, 29 figures, accepted version

We propose a method for solving the Schrodinger-Poisson problem that can be efficiently implemented in realistic 3D tight-binding models of semiconductor-based Majorana devices. The method is based on two key ideas: i) For a given geometry, the Poisson problem is only solved once (for each local orbital) and the results are stored as an interaction tensor; using this Green's function scheme, the Poisson component of the iteration procedure is reduced to a few simple summations. ii) The 3D problem is mapped into an effective multi-orbital 1D problem with molecular orbitals calculated self-consistently as the transverse modes of an infinite wire with the same electrostatic potential as the local electrostatic potential of the finite 3D device. To demonstrate the capabilities of our approach, we calculate the response of the system to an external magnetic field, the dependence of the effective chemical potential on the work function difference, and the dependence of the effective semiconductor-superconductor coupling on the applied gate potential. We find that different low-energy bands are characterized by similar effective couplings, which results in induced gap features characterized by a single energy scale. We also find that electrostatic effects are responsible for a partial suppression of the Majorana energy splitting oscillations. Finally, we show that a position-dependent work function difference can produce a non-homogeneous effective potential that is not affected by the screening due to the superconductor and is only partially suppressed by the charge inside the wire. In turn, this potential can induce trivial low-energy states that mimic the phenomenology of Majorana zero modes. Thus, any position-dependent work function difference (even at the 1% level) along the nanowire must be avoided through carefully engineered semiconductor-superconductor interfaces., 28 pages, 25 figures