Spin-Orbit Protection of Induced Superconductivity in Majorana Nanowires.

Spin-orbit interaction (SOI) plays a key role in creating Majorana zero modes in semiconductor nanowires proximity coupled to a superconductor. We track the evolution of the induced superconducting gap in InSb nanowires coupled to a NbTiN superconductor in a large range of magnetic field strengths and orientations. Based on realistic simulations of our devices, we reveal SOI with a strength of 0.15-0.35 eV Å. Our approach identifies the direction of the spin-orbit field, which is strongly affected by the superconductor geometry and electrostatic gates.

Ballistic Majorana nanowire devices.

Majorana modes are zero-energy excitations of a topological superconductor that exhibit non-Abelian statistics1-3. Following proposals for their detection in a semiconductor nanowire coupled to an s-wave superconductor4,5, several tunnelling experiments reported characteristic Majorana signatures6-11. Reducing disorder has been a prime challenge for these experiments because disorder can mimic the zero-energy signatures of Majoranas12-16, and renders the topological properties inaccessible17-20. Here, we show characteristic Majorana signatures in InSb nanowire devices exhibiting clear ballistic transport properties. Application of a magnetic field and spatial control of carrier density using local gates generates a zero bias peak that is rigid over a large region in the parameter space of chemical potential, Zeeman energy and tunnel barrier potential. The reduction of disorder allows us to resolve separate regions in the parameter space with and without a zero bias peak, indicating topologically distinct phases. These observations are consistent with the Majorana theory in a ballistic system 21 , and exclude the known alternative explanations that invoke disorder12-16 or a nonuniform chemical potential22,23.

Ballistic superconductivity in semiconductor nanowires.

Semiconductor nanowires have opened new research avenues in quantum transport owing to their confined geometry and electrostatic tunability. They have offered an exceptional testbed for superconductivity, leading to the realization of hybrid systems combining the macroscopic quantum properties of superconductors with the possibility to control charges down to a single electron. These advances brought semiconductor nanowires to the forefront of efforts to realize topological superconductivity and Majorana modes. A prime challenge to benefit from the topological properties of Majoranas is to reduce the disorder in hybrid nanowire devices. Here we show ballistic superconductivity in InSb semiconductor nanowires. Our structural and chemical analyses demonstrate a high-quality interface between the nanowire and a NbTiN superconductor that enables ballistic transport. This is manifested by a quantized conductance for normal carriers, a strongly enhanced conductance for Andreev-reflecting carriers, and an induced hard gap with a significantly reduced density of states. These results pave the way for disorder-free Majorana devices.

Observation of Conductance Quantization in InSb Nanowire Networks.

Majorana zero modes (MZMs) are prime candidates for robust topological quantum bits, holding a great promise for quantum computing. Semiconducting nanowires with strong spin orbit coupling offer a promising platform to harness one-dimensional electron transport for Majorana physics. Demonstrating the topological nature of MZMs relies on braiding, accomplished by moving MZMs around each other in a certain sequence. Most of the proposed Majorana braiding circuits require nanowire networks with minimal disorder. Here, the electronic transport across a junction between two merged InSb nanowires is studied to investigate how disordered these nanowire networks are. Conductance quantization plateaus are observed in most of the contact pairs of the epitaxial InSb nanowire networks: the hallmark of ballistic transport behavior.

Hard Superconducting Gap in InSb Nanowires.

Topological superconductivity is a state of matter that can host Majorana modes, the building blocks of a topological quantum computer. Many experimental platforms predicted to show such a topological state rely on proximity-induced superconductivity. However, accessing the topological properties requires an induced hard superconducting gap, which is challenging to achieve for most material systems. We have systematically studied how the interface between an InSb semiconductor nanowire and a NbTiN superconductor affects the induced superconducting properties. Step by step, we improve the homogeneity of the interface while ensuring a barrier-free electrical contact to the superconductor and obtain a hard gap in the InSb nanowire. The magnetic field stability of NbTiN allows the InSb nanowire to maintain a hard gap and a supercurrent in the presence of magnetic fields (∼0.5 T), a requirement for topological superconductivity in one-dimensional systems. Our study provides a guideline to induce superconductivity in various experimental platforms such as semiconductor nanowires, two-dimensional electron gases, and topological insulators and holds relevance for topological superconductivity and quantum computation.

InSb Nanowires with Built-In GaxIn1-xSb Tunnel Barriers for Majorana Devices.

Majorana zero modes (MZMs), prime candidates for topological quantum bits, are detected as zero bias conductance peaks (ZBPs) in tunneling spectroscopy measurements. Implementation of a narrow and high tunnel barrier in the next generation of Majorana devices can help to achieve the theoretically predicted quantized height of the ZBP. We propose a material-oriented approach to engineer a sharp and narrow tunnel barrier by synthesizing a thin axial segment of GaxIn1-xSb within an InSb nanowire. By varying the precursor molar fraction and the growth time, we accurately control the composition and the length of the barriers. The height and the width of the GaxIn1-xSb tunnel barrier are extracted from the Wentzel-Kramers-Brillouin (WKB) fits to the experimental I-V traces.

Conductance Quantization at Zero Magnetic Field in InSb Nanowires.

Ballistic electron transport is a key requirement for existence of a topological phase transition in proximitized InSb nanowires. However, measurements of quantized conductance as direct evidence of ballistic transport have so far been obscured due to the increased chance of backscattering in one-dimensional nanowires. We show that by improving the nanowire-metal interface as well as the dielectric environment we can consistently achieve conductance quantization at zero magnetic field. Additionally we study the contribution of orbital effects to the sub-band dispersion for different orientation of the magnetic field, observing a near-degeneracy between the second and third sub-bands.

Towards high mobility InSb nanowire devices.

We study the low-temperature electron mobility of InSb nanowires. We extract the mobility at 4.2 K by means of field effect transport measurements using a model consisting of a nanowire-transistor with contact resistances. This model enables an accurate extraction of device parameters, thereby allowing for a systematic study of the nanowire mobility. We identify factors affecting the mobility, and after optimization obtain a field effect mobility of [Formula: see text] cm(2) V(-1) s(-1). We further demonstrate the reproducibility of these mobility values which are among the highest reported for nanowires. Our investigations indicate that the mobility is currently limited by adsorption of molecules to the nanowire surface and/or the substrate.

Osteochondrosis of the primary ossification center of the patella (Köhler's disease of the patella) report of three cases.

Radiography of three boys 5-6 years old with anterior knee pain revealed increased density and irregularity of the patellar ossification centers. A search of the literature suggested that it was osteochondrosis of the primary ossification center of the patella, named after Köhler. Continuing search also revealed that it might be a normal variant instead of an osteochondrosis. A short course of activity modification led to marked improvement in all. The patients were either asymptomatic or experienced minor symptoms 18-34 months after presentation. It was concluded that the process, either physiological or pathological, has a benign course and favorable prognosis.