Synthetic spin-orbit interaction for Majorana devices

Advancements and Challenges in the Integration of Indium Arsenide and Van der Waals Heterostructures

The strategic integration of low-dimensional InAs-based materials and emerging van der Waals systems is advancing in various scientific fields, including electronics, optics, and magnetics. With their unique properties, these InAs-based van der Waals materials and devices promise further miniaturization of semiconductor devices in line with Moore's Law. However, progress in this area lags behind other 2D materials like graphene and boron nitride. Challenges include synthesizing pure crystalline phase InAs nanostructures and single-atomic-layer 2D InAs films, both vital for advanced van der Waals heterostructures. Also, diverse surface state effects on InAs-based van der Waals devices complicate their performance evaluation. This review discusses the experimental advances in the van der Waals epitaxy of InAs-based materials and the working principles of InAs-based van der Waals devices. Theoretical achievements in understanding and guiding the design of InAs-based van der Waals systems are highlighted. Focusing on advancing novel selective area growth and remote epitaxy, exploring multi-functional applications, and incorporating deep learning into first-principles calculations are proposed. These initiatives aim to overcome existing bottlenecks and accelerate transformative advancements in integrating InAs and van der Waals heterostructures.

Fermi Surface Spin Texture and Topological Superconductivity in Spin-Orbit Free Noncollinear Antiferromagnets

We explore the relationship among the magnetic ordering in real space, the resulting spin texture on the Fermi surface, and the related superconducting gap structure in noncollinear antiferromagnetic metals without spin-orbit coupling. Via a perturbative approach, we show that noncollinear magnetic ordering in a metal can generate momentum-dependent spin texture on its Fermi surface, even in the absence of spin-orbit coupling, if the metal has more than three sublattices in its magnetic unit cell. Thus, our theory naturally extends the idea of altermagnetism to noncollinear spin structures. When superconductivity is developed in a magnetic metal, as the gap-opening condition is strongly constrained by the spin texture, the nodal structure of the superconducting state is also enforced by the magnetism-induced spin texture. Taking the noncollinear antiferromagnet on the kagome lattice as a representative example, we demonstrate how the Fermi surface spin texture induced by noncollinear antiferromagnetism naturally leads to odd-parity spin-triplet superconductivity with nontrivial topological properties.

Topological band inversion and chiral Majorana mode in hcp thallium

The chiral Majorana fermion is an exotic particle that is its own antiparticle. It can arise in a one-dimensional edge of topological materials, and especially that in a topological superconductor can be exploited in non-Abelian quantum computation. While the chiral Majorana mode (CMM) remains elusive, a promising situation is realized when superconductivity coexists with a topologically non-trivial surface state. Here, we perform fully non-empirical calculation for the CMM considering superconductivity and surface relaxation, and show that hexagonal close-packed thallium (Tl) has an ideal electronic state that harbors the CMM. Thekz=0plane of Tl is a mirror plane, realizing a full-gap band inversion corresponding to a topological crystalline insulating phase. Its surface and hinge are stable and easy to make various structures. Another notable feature is that the surface Dirac point is very close to the Fermi level, so that a small Zeeman field can induce a topological transition. Our calculation indicates that Tl will provide a new platform of the Majorana fermion.

Spin cross-correlation experiments in an electron entangler

Correlations are fundamental in describing many-body systems. However, in experiments, correlations are notoriously difficult to assess on a microscopic scale, especially for electron spins. Even though it is firmly established theoretically that the electrons in a Cooper pair¹ of a superconductor form maximally spin-entangled singlet states with opposite spin projections^2-4, no spin correlation experiments have been demonstrated so far. Here we report the direct measurement of the spin cross-correlations between the currents of a Cooper pair splitter^5-13, an electronic device that emits electrons originating from Cooper pairs. We use ferromagnetic split-gates^14,15, compatible with nearby superconducting structures, to individually spin polarize the transmissions of the quantum dots in the two electronic paths, which act as tunable spin filters. The signals are detected in standard transport and in highly sensitive transconductance experiments. We find that the spin cross-correlation is negative, consistent with spin singlet emission, and deviates from the ideal value mostly due to the overlap of the Zeeman split quantum dot states. Our results demonstrate a new route to perform spin correlation experiments in nano-electronic devices, especially suitable for those relying on magnetic field sensitive superconducting elements, like triplet or topologically non-trivial superconductors^16-18, or to perform Bell tests with massive particles^19,20.

Zero energy states clustering in an elemental nanowire coupled to a superconductor

Nanoelectronic hybrid devices combining superconductors and a one-dimensional nanowire are promising platforms to realize topological superconductivity and its resulting exotic excitations. The bulk of experimental studies in this context are transport measurements where conductance peaks allow to perform a spectroscopy of the low lying electronic states and potentially to identify signatures of the aforementioned excitations. The complexity of the experimental landscape calls for a benchmark in an elemental situation. The present work tackles such a task using an ultra-clean carbon nanotube circuit. Specifically, we show that the combination of magnetic field, weak disorder and superconductivity can lead to states clustering at low energy, as predicted by the random matrix theory predictions. Such a phenomenology is very general and should apply to most platforms trying to realize topological superconductivity in 1D systems, thus calling for alternative probes to reveal it.

Topological superconductivity (TSC) is predicted to exist in nanowires with strong spin-orbit coupling (SOC) when they are in proximity to superconductors, with a key signature being zero-energy states in conductance measurements. Here, using weak-SOC carbon nanotubes as the nanowires, the authors show that similar looking zero-energy states can appear even in nanowires which cannot, in principle, host TSC.

Precursors of Majorana modes and their length-dependent energy oscillations probed at both ends of atomic Shiba chains

Isolated Majorana modes (MMs) are highly non-local quantum states with non-Abelian exchange statistics, which localize at the two ends of finite-size 1D topological superconductors of sufficient length. Experimental evidence for MMs is so far based on the detection of several key signatures: for example, a conductance peak pinned to the Fermi energy or an oscillatory peak splitting in short 1D systems when the MMs overlap. However, most of these key signatures were probed only on one of the ends of the 1D system, and firm evidence for an MM requires the simultaneous detection of all the key signatures on both ends. Here we construct short atomic spin chains on a superconductor-also known as Shiba chains-up to a chain length of 45 atoms using tip-assisted atom manipulation in scanning tunnelling microscopy experiments. We observe zero-energy conductance peaks localized at both ends of the chain that simultaneously split off from the Fermi energy in an oscillatory fashion after altering the chain length. By fitting the parameters of a low-energy model to the data, we find that the peaks are consistent with precursors of MMs that evolve into isolated MMs protected by an estimated topological gap of 50 μeV in chains of at least 35 nm length, corresponding to 70 atoms.

Fusion of Majorana bound states with mini-gate control in two-dimensional systems

A hallmark of topological superconductivity is the non-Abelian statistics of Majorana bound states (MBS), its chargeless zero-energy emergent quasiparticles. The resulting fractionalization of a single electron, stored nonlocally as a two spatially-separated MBS, provides a powerful platform for implementing fault-tolerant topological quantum computing. However, despite intensive efforts, experimental support for MBS remains indirect and does not probe their non-Abelian statistics. Here we propose how to overcome this obstacle in mini-gate controlled planar Josephson junctions (JJs) and demonstrate non-Abelian statistics through MBS fusion, detected by charge sensing using a quantum point contact, based on dynamical simulations. The feasibility of preparing, manipulating, and fusing MBS in two-dimensional (2D) systems is supported in our experiments which demonstrate the gate control of topological transition and superconducting properties with five mini gates in InAs/Al-based JJs. While we focus on this well-established platform, where the topological superconductivity was already experimentally detected, our proposal to identify elusive non-Abelian statistics motivates also further MBS studies in other gate-controlled 2D systems.

Nanomaterials for Quantum Information Science and Engineering

Quantum information science and engineering (QISE)-which entails the use of quantum mechanical states for information processing, communications, and sensing-and the area of nanoscience and nanotechnology have dominated condensed matter physics and materials science research in the 21st century. Solid-state devices for QISE have, to this point, predominantly been designed with bulk materials as their constituents. This review considers how nanomaterials (i.e., materials with intrinsic quantum confinement) may offer inherent advantages over conventional materials for QISE. The materials challenges for specific types of qubits, along with how emerging nanomaterials may overcome these challenges, are identified. Challenges for and progress toward nanomaterials-based quantum devices are condidered. The overall aim of the review is to help close the gap between the nanotechnology and quantum information communities and inspire research that will lead to next-generation quantum devices for scalable and practical quantum applications.

Evidence for anisotropic spin-triplet Andreev reflection at the 2D van der Waals ferromagnet/superconductor interface

Fundamental symmetry breaking and relativistic spin-orbit coupling give rise to fascinating phenomena in quantum materials. Of particular interest are the interfaces between ferromagnets and common s-wave superconductors, where the emergent spin-orbit fields support elusive spin-triplet superconductivity, crucial for superconducting spintronics and topologically-protected Majorana bound states. Here, we report the observation of large magnetoresistances at the interface between a quasi-two-dimensional van der Waals ferromagnet Fe0.29TaS2 and a conventional s-wave superconductor NbN, which provides the possible experimental evidence for the spin-triplet Andreev reflection and induced spin-triplet superconductivity at ferromagnet/superconductor interface arising from Rashba spin-orbit coupling. The temperature, voltage, and interfacial barrier dependences of the magnetoresistance further support the induced spin-triplet superconductivity and spin-triplet Andreev reflection. This discovery, together with the impressive advances in two-dimensional van der Waals ferromagnets, opens an important opportunity to design and probe superconducting interfaces with exotic properties.

Sub-gap Fano resonances in a topological superconducting wire with on-site Coulomb interactions

We consider theoretically a 1D-semiconducting wire with strong Rashba interaction in proximity withs-wave superconductor, driven into topological phase by external magnetic field. Additionally, we take into account on-site Coulomb interactions inside the wire. The system is modelled by a tight binding Hamiltonian with Rashba hopping term and induceds-wave superconductivity. Calculations are performed utilizing recursive Green's function method, and Coulomb interactions are treated selfconsistently within Hubbard I approximation. For the Hubbard levels residing withinp-wave superconducting gap, particle-hole symmetric four-resonance structure develops in the density of states, apart from Majorana resonance. One pair of particle-hole symmetric resonances is created by the discrete II-Hubbard levels of the particular site, and the second pair of Hubbard sub-bands originates from recursive summation over the sites of the wire. Quantum interference between both types of pairs of states creates in-gap charge-conjugated Fano resonances with opposite asymmetry factors. We demonstrate that when quantum interference is dominated by two-particle tunneling, the Majorana resonance is strongly diminished, while it is not altered when single-particle tunneling dominates in interference process. We also discuss some consequences for experimental distinction of true Majorana states, and show that on-site Coulomb interactions support the appearance of topological phase.

Synthesis, Magnetic Properties, and Electronic Structure of Magnetic Topological Insulator MnBi2Se4

The intrinsic magnetic topological insulators MnBi₂Te₄ and MnBi₂Se₄ support novel topological states related to symmetry breaking by magnetic order. Unlike MnBi₂Te₄, the study of MnBi₂Se₄ has been inhibited by the lack of bulk crystals, as the van der Waals (vdW) crystal is not the thermodynamic equilibrium phase. Here, we report the layer-by-layer synthesis of vdW MnBi₂Se₄ crystals using nonequilibrium molecular beam epitaxy. Atomic-resolution scanning transmission electron microscopy and scanning tunneling microscopy identify a well-ordered vdW crystal with septuple-layer base units. The magnetic properties agree with the predicted layered antiferromagnetic ordering but disagree with its predicted out-of-plane orientation. Instead, our samples exhibit an easy-plane anisotropy, which is explained by including dipole-dipole interactions. Angle-resolved photoemission spectroscopy reveals the gapless Dirac-like surface state, which demonstrates that MnBi₂Se₄ is a topological insulator above the magnetic-ordering temperature. These studies show that MnBi₂Se₄ is a promising candidate for exploring rich topological phases of layered antiferromagnetic topological insulators.

Reversible engineering of spin-orbit splitting in monolayer MoS2via laser irradiation under controlled gas atmospheres

Monolayer transition metal dichalcogenides, manifesting strong spin-orbit coupling combined with broken inversion symmetry, lead to coupling of spin and valley degrees of freedom. These unique features make them highly interesting for potential spintronic and valleytronic applications. However, engineering spin-orbit coupling at room temperature as demanded after device fabrication is still a great challenge for their practical applications. Here we reversibly engineer the spin-orbit coupling of monolayer MoS2 by laser irradiation under controlled gas environments, where the spin-orbit splitting has been effectively regulated within 140 meV to 200 meV. Furthermore, the photoluminescence intensity of the B exciton can be reversibly manipulated over 2 orders of magnitude. We attribute the engineering of spin-orbit splitting to the reduction of binding energy combined with band renormalization, originating from the enhanced absorption coefficient of monolayer MoS2 under inert gases and subsequently the significantly boosted carrier concentrations. Reflectance contrast spectra during the engineering stages provide unambiguous proof to support our interpretation. Our approach offers a new avenue to actively control the spin-orbit splitting in transition metal dichalcogenide materials at room temperature and paves the way for designing innovative spintronic devices.

Phase Signature of Topological Transition in Josephson Junctions

Topological superconductivity holds promise for fault-tolerant quantum computing. While planar Josephson junctions are attractive candidates to realize this exotic state, direct phase measurements as the fingerprint of the topological transition are missing. By embedding two gate-tunable Al/InAs Josephson junctions in a loop geometry, we measure a π jump in the junction phase with an increasing in-plane magnetic field B_{∥}. This jump is accompanied by a minimum of the critical current, indicating a closing and reopening of the superconducting gap, strongly anisotropic in B_{∥}. Our theory confirms that these signatures of a topological transition are compatible with the emergence of Majorana bound states.

Tuning Magnetic Properties of a Carbon Nanotube-Lanthanide Hybrid Molecular Complex through Controlled Functionalization

Molecular magnets attached to carbon nanotubes (CNT) are being studied as potential candidates for developing spintronic and quantum technologies. However, the functionalization routes used to develop these hybrid systems can drastically affect their respective physiochemical properties. Due to the complexity of this systems, little work has been directed at establishing the correlation between the degree of functionalization and the magnetic character. Here, we demonstrate the chemical functionalization degree associated with molecular magnet loading can be utilized for controlled tuning the magnetic properties of a CNT-lanthanide hybrid complex. CNT functionalization degree was evaluated by interpreting minor Raman phonon modes in relation to the controlled reaction conditions. These findings were exploited in attaching a rare-earth-based molecular magnet (Gd-DTPA) to the CNTs. Inductively coupled plasma mass spectrometry, time-of-flight secondary ion mass spectrometry and super conducting quantum interference device (SQUID) measurements were used to elucidate the variation of magnetic character across the samples. This controlled Gd-DTPA loading on the CNT surface has led to a significant change in the nanotube intrinsic diamagnetism, showing antiferromagnetic coupling with increase in the Weiss temperature with respect to increased loading. This indicates that synthesis of a highly correlated spin system for developing novel spintronic technologies can be realized through a carbon-based hybrid material.

Spin Transport in Ferromagnet-InSb Nanowire Quantum Devices

Signatures of Majorana zero modes (MZMs) have been observed in semiconductor nanowires (NWs) with a strong spin-orbital interaction (SOI) with proximity-induced superconductivity. Realizing topological superconductivity and MZMs in this platform requires eliminating spin degeneracy by applying a magnetic field. However, the field can adversely impact the induced superconductivity and places geometric restrictions on the device. These challenges could be circumvented by integrating magnetic elements with the NWs. Here, we report the first experimental investigation of spin transport across InSb NWs with ferromagnetic (FM) contacts. We observe signatures of spin polarization and spin-dependent transport in the quasi-one-dimensional ballistic regime. Moreover, we show that electrostatic gating tunes the observed magnetic signal and reveals a regime where the device acts as a spin filter. These results open an avenue toward developing MZM devices with spin degeneracy lifted locally without external fields. They could also enable spin-based devices that leverage spin-orbital states in quantum wires.

Signature of a pair of Majorana zero modes in superconducting gold surface states

Under certain conditions, a fermion in a superconductor can separate in space into two parts known as Majorana zero modes, which are immune to decoherence from local noise sources and are attractive building blocks for quantum computers. Promising experimental progress has been made to demonstrate Majorana zero modes in materials with strong spin-orbit coupling proximity coupled to superconductors. Here we report signatures of Majorana zero modes in a material platform utilizing the surface states of gold. Using scanning tunneling microscope to probe EuS islands grown on top of gold nanowires, we observe two well-separated zero-bias tunneling conductance peaks aligned along the direction of the applied magnetic field, as expected for a pair of Majorana zero modes. This platform has the advantage of having a robust energy scale and the possibility of realizing complex designs using lithographic methods.

Phase Control of Majorana Bound States in a Topological X Junction

Topological superconductivity supports exotic Majorana bound states (MBS) which are chargeless zero-energy emergent quasiparticles. With their non-Abelian exchange statistics and fractionalization of a single electron stored nonlocally as a spatially separated MBS, they are particularly suitable for implementing fault-tolerant topological quantum computing. While realizing MBS has focused on one-dimensional systems, the onset of topological superconductivity requires delicate parameter tuning and geometric constraints pose significant challenges for their control and demonstration of non-Abelian statistics. To overcome these challenges, building on recent experiments in planar Josephson junctions (JJs), we propose a MBS platform of X-shaped JJs. This versatile implementation reveals how external flux control of the superconducting phase difference can generate and manipulate multiple MBS pairs to probe non-Abelian statistics. The underlying topological superconductivity exists over a large parameter space, consistent with materials used in our fabrication of such X junctions, as an important step towards scalable topological quantum computing.

Semiconductor-Ferromagnetic Insulator-Superconductor Nanowires: Stray Field and Exchange Field

Nanowires can serve as flexible substrates for hybrid epitaxial growth on selected facets, allowing for the design of heterostructures with complex material combinations and geometries. In this work we report on hybrid epitaxy of freestanding vapor-liquid-solid grown and in-plane selective area grown semiconductor-ferromagnetic insulator-superconductor (InAs/EuS/Al) nanowire heterostructures. We study the crystal growth and complex epitaxial matching of wurtzite and zinc-blende InAs/rock-salt EuS interfaces as well as rock-salt EuS/face-centered cubic Al interfaces. Because of the magnetic anisotropy originating from the nanowire shape, the magnetic structure of the EuS phase is easily tuned into single magnetic domains. This effect efficiently ejects the stray field lines along the nanowires. With tunnel spectroscopy measurements of the density of states, we show that the material has a hard induced superconducting gap, and magnetic hysteretic evolution which indicates that the magnetic exchange fields are not negligible. These hybrid nanowires fulfill key material requirements for serving as a platform for spin-based quantum applications, such as scalable topological quantum computing.