One-Dimensional Quantum Dot Array Integrated with Charge Sensors in an InAs Nanowire

We report an experimental study of a 1D quintuple-quantum-dot array integrated with two charge sensors in an InAs nanowire. The device is studied by measuring double quantum dots formed consecutively in the array, and corresponding charge stability diagrams are revealed with both direct current measurements and charge sensor signals. The one-dimensional quintuple-quantum-dot array is then tuned up, and its charge configurations are fully mapped out with the two charge sensors. The energy level of each dot in the array can be controlled individually using virtual gates. After that, four dots in the array are selected to form two double quantum dots, and ultrastrong inter-double-dot interaction is obtained. A theoretical simulation confirms the strong coupling strength between the two double quantum dots. The highly controllable one-dimensional quantum dot array is expected to be valuable for employing InAs nanowires to construct advanced quantum hardware in the future.

Versatile Method of Engineering the Band Alignment and the Electron Wavefunction Hybridization of Hybrid Quantum Devices

Hybrid devices that combine superconductors (S) and semiconductors (Sm) have attracted great attention due to the integration of the properties of both materials, which relies on the interface details and the resulting coupling strength and wavefunction hybridization. However, until now, none of the experiments have reported good control of the band alignment of the interface, as well as its tunability to the coupling and hybridization. Here, the interface is modified by inducing specific argon milling while maintaining its high quality, e.g., atomic connection, which results in a large induced superconducting gap and ballistic transport. By comparing with Schrödinger-Poisson calculations, it is proven that this method can vary the band bending/coupling strength and the electronic spatial distribution. In the strong coupling regime, the coexistence and tunability of crossed Andreev reflection and elastic co-tunneling-key ingredients for the Kitaev chain-are confirmed. This method is also generic for other materials and achieves a hard and huge superconducting gap in lead and indium antimonide nanowire (Pb-InSb) devices. Such a versatile method, compatible with the standard fabrication process and accompanied by the well-controlled modification of the interface, will definitely boost the creation of more sophisticated hybrid devices for exploring physics in solid-state systems.

A Deterministic Method to Construct a Common Supercell Between Two Similar Crystalline Surfaces

Here, a deterministic algorithm is proposed, that is capable of constructing a common supercell between two similar crystalline surfaces without scanning all possible cases. Using the complex plane, the 2D lattice is defined as the 2D complex vector. Then, the relationship between two surfaces becomes the eigenvector-eigenvalue relation where an operator corresponds to a transformation matrix. It is shown that this transformation matrix can be directly determined from the lattice parameters and rotation angle of the two given crystalline surfaces with O(log Nmax) time complexity, where Nmax is the maximum index of repetition matrix elements. This process is much faster than the conventional brute force approach (O ( N max 4 ) $O(N_{\mathrm{max}}^4)$ ). By implementing the method in Python code, experimental 2D heterostructures and their moiré patterns and additionally find new moiré patterns that have not yet been reported are successfully generated. According to the density functional theory (DFT) calculations, some of the new moiré patterns are expected to be as stable as experimentally-observed moiré patterns. Taken together, it is believed that the method can be widely applied as a useful tool for designing new heterostructures with interesting properties.

Spin-selective transport in a correlated double quantum dot-Majorana wire system

In this work we investigate the spin-dependent transport through a double quantum dot embedded in a ferromagnetic tunnel junction and side attached to a topological superconducting nanowire hosting Majorana zero-energy modes. We focus on the transport regime when the Majorana mode leaks into the double quantum dot competing with the two-stage Kondo effect and the ferromagnetic-contact-induced exchange field. In particular, we determine the system's spectral properties and analyze the temperature dependence of the spin-resolved linear conductance by means of the numerical renormalization group method. Our study reveals unique signatures of the interplay between the spin-resolved tunneling, the Kondo effect and the Majorana modes, which are visible in the transport characteristics. In particular, we uncover a competing character of the coupling to topological superconductor and that to ferromagnetic leads, which can be observed already for very low spin polarization of the electrodes. This is signaled by an almost complete quenching of the conductance in one of the spin channels which is revealed through perfect conductance spin polarization. Moreover, we show that the conductance spin polarization can change sign depending on the magnitude of spin imbalance in the leads and strength of interaction with topological wire. Thus, our work demonstrates that even minuscule spin polarization of tunneling processes can have large impact on the transport properties of the system.

Manipulating chiral Majorana mode with additional potential in superconductor-Chern insulator heterostructures

We employed the self-consistent Bogoliubov-de Gennes equations to explore the states of chiral Majorana mode in quantum anomalous Hall insulators in proximity to a superconductor, leading to the development of an extensive topological phase diagram. Our investigation focused on how an additional potential affects the separation of chiral Majorana modes across different phase conditions. We substantiated our findings by examining the zero-energy Local Density of States spectrum and the probability distribution of the chiral Majorana modes. We established the universality of chiral Majorana mode separation by applying an additional potential. This finding serves as a vital resource for future endeavors aimed at controlling and detecting these particles, thereby contributing to the advancement of quantum computing and condensed matter physics.

Nonlocal correlations transmitted between quantum dots via short topological superconductor

We study the quasiparticle states and nonlocal correlations of a hybrid structure, comprising two quantum dots interconnected through a short-length topological superconducting nanowire hosting overlaping Majorana modes. We show that the hybridization between different components of this setup gives rise to the emergence of molecular states, which are responsible for nonlocal correlations. We inspect the resulting energy structure, focusing on the inter-dependence between the quasiparticles of individual quantum dots. We predict the existence of nonlocal effects, which could be accessed and probed by crossed Andreev reflection spectroscopy. Our study would be relevant to a recent experimental realization of the minimal Kitaev model [T. Dvir et al., Nature 614, 445 (2023) ], by considering its hybrid structure with side-attached quantum dots.

Nanowires: Exponential speedup in quantum computing

This review paper examines the crucial role of nanowires in the field of quantum computing, highlighting their importance as versatile platforms for qubits and vital building blocks for creating fault-tolerant and scalable quantum information processing systems. Researchers are studying many categories of nanowires, including semiconductor, superconducting, and topological nanowires, to explore their distinct quantum features that play a role in creating various qubit designs. The paper explores the interdisciplinary character of quantum computing, combining the fields of quantum physics and materials science. This text highlights the significance of quantum gate operations in manipulating qubits for computation, thus creating the toolbox of quantum algorithms. The paper emphasizes the key research areas in quantum technology, such as entanglement engineering, quantum error correction, and a wide range of applications spanning from encryption to climate change modeling. The research highlights the importance of tackling difficulties related to decoding mitigation, error correction, and hardware scalability to fully utilize the transformative potential of quantum computing in scientific, technical, and computational fields.

Cross-correlations between currents and tunnel magnetoresistance in interacting double quantum dot-Majorana wire system

We theoretically investigate the spin and charge transport properties of a double quantum dot coupled to distinct edges of the nanowire hosting Majorana zero-energy modes. The focus is on the analysis of the currents flowing through the left and right junctions and their cross-correlations. We show that the system reveals very different transport properties depending on the detuning protocol of the quantum dot energy levels. For the symmetric detuning, the current dependencies reveal only two maxima associated with resonant tunneling, and currents in the left and right arms of the system reveal weak positive cross-correlations. On the other hand, for antisymmetric detuning, the flow of electrons into drains is maximized and strongly correlated in one bias voltage direction, while for the opposite bias direction a spin blockade is predicted. Furthermore, we observe a suppression of the current cross-correlations at a highly symmetric detuning point, indicating the involvement of the Majorana zero-energy modes in the transport processes. To gain insight into the role of the spin polarization of the Majorana edge states, we analyze the spin-dependent transport characteristics by considering the relationship between the spin canting angle, which describes the coupling of the Majorana modes to the spin of the quantum dots, and the magnetic configurations of the ferromagnetic drains. Moreover, we examine the non-local zero bias anomaly in the differential conductance, detailed analysis of which revealed a specific operational mode of the device that can facilitate the identification of the Majorana presence in the quantum dot-Majorana wire system. Finally, we also consider the transport properties in different magnetic configurations of the system and discuss the behavior of the associated tunnel magnetoresistance.

Robust topological superconductivity in spin-orbit coupled systems at higher-order van Hove filling

Van Hove singularities in proximity to the Fermi level promote electronic interactions and generate diverse competing instabilities. It is also known that a nontrivial Berry phase derived from spin-orbit coupling can introduce an intriguing decoration into the interactions and thus alter correlated phenomena. However, it is unclear how and what type of new physics can emerge in a system featured by the interplay between van Hove singularities (VHSs) and the Berry phase. Here, based on a general Rashba model on the square lattice, we comprehensively explore such an interplay and its significant influence on the competing electronic instabilities by performing a parquet renormalization group analysis. Despite the existence of a variety of comparable fluctuations in the particle-particle and particle-hole channels associated with higher-order VHSs, we find that the chiral p±ip pairings emerge as two stable fixed trajectories within the generic interaction parameter space, namely the system becomes a robust topological superconductor. The chiral pairings stem from the hopping interaction induced by the nontrivial Berry phase. The possible experimental realization and implications are discussed. Our work sheds new light on the correlated states in quantum materials with strong spin-orbit coupling (SOC) and offers fresh insights into the exploration of topological superconductivity.

Non-Abelian Holonomy of Majorana Zero Modes Coupled to a Chaotic Quantum Dot

If a quantum dot is coupled to a topological superconductor via tunneling contacts, each contact hosts a Majorana zero mode in the limit of zero transmission. Close to a resonance and at a finite contact transparency, the resonant level in the quantum dot couples the Majorana modes, but a ground-state degeneracy per fermion parity subspace remains if the number of Majorana modes coupled to the dot is five or larger. Upon varying shape-defining gate voltages while remaining close to resonance, a nontrivial evolution within the degenerate ground-state manifold is achieved. We characterize the corresponding non-Abelian holonomy for a quantum dot with chaotic classical dynamics using random matrix theory and discuss measurable signatures of the non-Abelian time evolution.

Selective area growth of in-plane InAs nanowires and nanowire networks on Si substrates by molecular-beam epitaxy

In-plane InAs nanowires and nanowire networks show great potential to be used as building blocks for electronic, optoelectronic and topological quantum devices, and all these applications are keen to grow the InAs materials directly on Si substrates since it may enable nanowire electronic and quantum devices with seamless integration with Si platform. However, almost all the in-plane InAs nanowires and nanowire networks have been realized on substrates of III-V semiconductors. Here, we demonstrate the selective area epitaxial growth of in-plane InAs nanowires and nanowire networks on Si substrates. We find that the selectivity of InAs growth on Si substrates is mainly dependent on the growth temperature, while the morphology of InAs nanowires is closely related to the V/III flux ratio. We examine the cross-sectional shapes and facets of the InAs nanowires grown along the 〈110〉, 〈100〉 and 〈112〉 orientations. Thanks to the non-polar characteristics of Si substrates, the InAs nanowires and nanowire networks exhibit superior symmetry compared to that grown on III-V substrates. The InAs nanowires and nanowire networks are zinc-blende (ZB) crystals, but there are many defects in the nanowires, such as stacking faults, twins and grain boundaries. The crystal quality of InAs nanowires and nanowire networks can be improved by increasing the growth temperature within the growth temperature window. Our work demonstrates the feasibility of selective area epitaxial growth of in-plane InAs nanowires and nanowire networks on Si substrates.

Ballistic PbTe Nanowire Devices

Disorder is the primary obstacle in the current Majorana nanowire experiments. Reducing disorder or achieving ballistic transport is thus of paramount importance. In clean and ballistic nanowire devices, quantized conductance is expected, with plateau quality serving as a benchmark for disorder assessment. Here, we introduce ballistic PbTe nanowire devices grown by using the selective-area-growth (SAG) technique. Quantized conductance plateaus in units of 2e2/h are observed at zero magnetic field. This observation represents an advancement in diminishing disorder within SAG nanowires as most of the previously studied SAG nanowires (InSb or InAs) have not exhibited zero-field ballistic transport. Notably, the plateau values indicate that the ubiquitous valley degeneracy in PbTe is lifted in nanowire devices. This degeneracy lifting addresses an additional concern in the pursuit of Majorana realization. Moreover, these ballistic PbTe nanowires may enable the search for clean signatures of the spin-orbit helical gap in future devices.

Parity-Time Symmetric Holographic Principle

Originating from the Hamiltonian of a single qubit system, the phenomenon of the avoided level crossing is ubiquitous in multiple branches of physics, including the Landau-Zener transition in atomic, molecular, and optical physics, the band structure of condensed matter physics and the dispersion relation of relativistic quantum physics. We revisit this fundamental phenomenon in the simple example of a spinless relativistic quantum particle traveling in (1+1)-dimensional space-time and establish its relation to a spin-1/2 system evolving under a PT-symmetric Hamiltonian. This relation allows us to simulate 1-dimensional eigenvalue problems with a single qubit. Generalizing this relation to the eigenenergy problem of a bulk system with N spatial dimensions reveals that its eigenvalue problem can be mapped onto the time evolution of the edge state with (N-1) spatial dimensions governed by a non-Hermitian Hamiltonian. In other words, the bulk eigenenergy state is encoded in the edge state as a hologram, which can be decoded by the propagation of the edge state in the temporal dimension. We argue that the evolution will be PT-symmetric as long as the bulk system admits parity symmetry. Our work finds the application of PT-symmetric and non-Hermitian physics in quantum simulation and provides insights into the fundamental symmetries.

Honing in on a topological zero-bias conductance peak

A popular signature of Majorana bound states in topological superconductors is the quantized zero-energy conductance peak. However, a similar zero energy conductance peak can also arise due to non-topological reasons. Here we show that these trivial and topological zero energy conductance peaks can be distinguished via the zero energy local density of states (LDOSs) and local magnetization density of states (LMDOSs). We find that the zero-energy LDOSs and the LMDOSs exhibit periodic oscillations for a trivial zero-bias conductance peak (ZBCP). In contrast, these oscillations disappear for the topological ZBCP because of perfect Andreev reflection at zero energy in topological superconductor junctions. Our results suggest that the zero-energy LDOSs and the LMDOSs can be used as an experimental probe to distinguish a trivial zero-energy conductance peak from a topological zero-energy conductance peak.

Spin effects on transport and zero-bias anomaly in a hybrid Majorana wire-quantum dot system

We examine the impact of spin effects on the nonequilibrium transport properties of a nanowire hosting Majorana zero-energy modes at its ends, coupled to a quantum dot junction with ferromagnetic leads. Using the real-time diagrammatic technique, we determine the current, differential conductance and current cross-correlations in the nonlinear response regime. We also explore transport in different magnetic configurations of the system, which can be quantified by the tunnel magnetoresistance. We show that the presence of Majorana quasiparticles gives rise to unique features in all spin-resolved transport characteristics, in particular, to zero-bias anomaly, negative differential conductance, negative tunnel magnetoresistance, and it is also reflected in the current cross-correlations. Moreover, we study the dependence of the zero-bias anomaly on various system parameters and demonstrate its dependence on the magnetic configuration of the system as well as on the degree of spin polarization in the leads. A highly nontrivial behavior is also found for the tunnel magnetoresistance, which exhibits regions of enhanced or negative values-new features resulting from the coupling to Majorana wire.

Topological Superconductors from a Materials Perspective

Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (nonuniversal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this Perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and synthetic material systems. We further introduce various experimental techniques to probe TSCs, focusing on how a system is identified as a TSC candidate and why a conclusive answer is often challenging to draw. We conclude by calling for new experimental signatures and stronger computational support to accelerate the search for new TSC candidates.

Phonon-Assisted Tunneling through Quantum Dot Systems Connected to Majorana Bound States

We theoretically analyze phonon-assisted tunneling transport in a quantum dot side connected to a Majorana bound state in a topological superconducting nanowire. We investigate the behavior of the current through the dot, for a range of experimentally relevant parameters, in the presence of one long-wave optical phonon mode. We consider the current-gate voltage, the current-bias voltage and the current-dot-Majorana coupling characteristics under the influence of the electron-phonon coupling. In the absence of electron-phonon interaction, the Majorana bound states suppress the current when the gate voltage matches the Fermi level, but the increase in the bias voltage counteracts this effect. In the presence of electron-phonon coupling, the current behaves similarly as a function of the renormalized gate voltage. As an added feature at large bias voltages, it presents a dip or a plateau, depending on the size of the dot-Majorana coupling. Lastly, we show that the currents are most sensitive to, and depend non-trivially on the parameters of the Majorana circuit element, in the regime of low temperatures combined with low voltages. Our results provide insights into the complex physics of quantum dot devices used to probe Majorana bound states.

Improving the intrinsic conductance of selective area grown in-plane InAs nanowires with a GaSb shell

The nanoscale intrinsic electrical properties of in-plane InAs nanowires grown by selective area epitaxy are investigated using a process-free method involving a multi-probe scanning tunneling microscope. The resistance of oxide-free InAs nanowires grown on an InP(111)_Bsubstrate and the resistance of InAs/GaSb core-shell nanowires grown on an InP(001) substrate are measured using a collinear four-point probe arrangement in ultrahigh vacuum. They are compared with the resistance of two-dimensional electron gas reference samples measured using the same method and with the Van der Pauw geometry for validation. A significant improvement of the conductance is achieved when the InAs nanowires are fully embedded in GaSb, exhibiting an intrinsic sheet conductance close to the one of the quantum well counterpart.

Local and Nonlocal Transport Spectroscopy in Planar Josephson Junctions

We report simultaneously acquired local and nonlocal transport spectroscopy in a phase-biased planar Josephson junction based on an epitaxial InAs-Al hybrid two-dimensional heterostructure. Quantum point contacts at the junction ends allow measurement of the 2×2 matrix of local and nonlocal tunneling conductances as a function of magnetic field along the junction, phase difference across the junction, and carrier density. A closing and reopening of a gap was observed in both the local and nonlocal tunneling spectra as a function of magnetic field. For particular tunings of junction density, gap reopenings were accompanied by zero-bias conductance peaks (ZBCPs) in local conductances. End-to-end correlation of gap reopening was strong, while correlation of local ZBCPs was weak. A model of the device, with disorder treated phenomenologically, shows comparable conductance matrix behavior associated with a topological phase transition. Phase dependence helps distinguish possible origins of the ZBCPs.

Extreme enhancement of superconductivity in epitaxial aluminum near the monolayer limit

BCS theory has been widely successful at describing elemental bulk superconductors. Yet, as the length scales of such superconductors approach the atomic limit, dimensionality as well as the environment of the superconductor can lead to drastically different and unpredictable superconducting behavior. Here, we report a threefold enhancement of the superconducting critical temperature and gap size in ultrathin epitaxial Al films on Si(111), when approaching the 2D limit, based on high-resolution scanning tunneling microscopy/spectroscopy (STM/STS) measurements. Using spatially resolved spectroscopy, we characterize the vortex structure in the presence of a strong Zeeman field and find evidence of a paramagnetic Meissner effect originating from odd-frequency pairing contributions. These results illustrate two notable influences of reduced dimensionality on a BCS superconductor and present a platform to study BCS superconductivity in large magnetic fields.

Realization of a minimal Kitaev chain in coupled quantum dots

Majorana bound states constitute one of the simplest examples of emergent non-Abelian excitations in condensed matter physics. A toy model proposed by Kitaev shows that such states can arise at the ends of a spinless p-wave superconducting chain¹. Practical proposals for its realization^2,3 require coupling neighbouring quantum dots (QDs) in a chain through both electron tunnelling and crossed Andreev reflection⁴. Although both processes have been observed in semiconducting nanowires and carbon nanotubes^5-8, crossed-Andreev interaction was neither easily tunable nor strong enough to induce coherent hybridization of dot states. Here we demonstrate the simultaneous presence of all necessary ingredients for an artificial Kitaev chain: two spin-polarized QDs in an InSb nanowire strongly coupled by both elastic co-tunnelling (ECT) and crossed Andreev reflection (CAR). We fine-tune this system to a sweet spot where a pair of poor man's Majorana states is predicted to appear. At this sweet spot, the transport characteristics satisfy the theoretical predictions for such a system, including pairwise correlation, zero charge and stability against local perturbations. Although the simple system presented here can be scaled to simulate a full Kitaev chain with an emergent topological order, it can also be used imminently to explore relevant physics related to non-Abelian anyons.

Energy dynamics, heat production and heat-work conversion with qubits: toward the development of quantum machines

We present an overview of recent advances in the study of energy dynamics and mechanisms for energy conversion in qubit systems with special focus on realizations in superconducting quantum circuits. We briefly introduce the relevant theoretical framework to analyze heat generation, energy transport and energy conversion in these systems with and without time-dependent driving considering the effect of equilibrium and non-equilibrium environments. We analyze specific problems and mechanisms under current investigation in the context of qubit systems. These include the problem of energy dissipation and possible routes for its control, energy pumping between driving sources and heat pumping between reservoirs, implementation of thermal machines and mechanisms for energy storage. We highlight the underlying fundamental phenomena related to geometrical and topological properties, as well as many-body correlations. We also present an overview of recent experimental activity in this field.

Competing Vortex Topologies in Iron-Based Superconductors

In this Letter, we establish a new theoretical paradigm for vortex Majorana physics in the recently discovered topological iron-based superconductors (TFeSCs). While TFeSCs are widely accepted as an exemplar of topological insulators (TIs) with intrinsic s-wave superconductivity, our theory implies that such a common belief could be oversimplified. Our main finding is that the normal-state bulk Dirac nodes, usually ignored in TI-based vortex Majorana theories for TFeSCs, will play a key role of determining the vortex state topology. In particular, the interplay between TI and Dirac nodal bands will lead to multiple competing topological phases for a superconducting vortex line in TFeSCs, including an unprecedented hybrid topological vortex state that carries both Majorana bound states and a gapless dispersion. Remarkably, this exotic hybrid vortex phase generally exists in the vortex phase diagram for our minimal model for TFeSCs and is directly relevant to TFeSC candidates such as LiFeAs. When the fourfold rotation symmetry is broken by vortex-line tilting or curving, the hybrid vortex gets topologically trivialized and becomes Majorana free, which could explain the puzzle of ubiquitous trivial vortices observed in LiFeAs. The origin of the Majorana signal in other TFeSC candidates such as FeTe_{x}Se_{1-x} and CaKFe_{4}As_{4} is also interpreted within our theory framework. Our theory sheds new light on theoretically understanding and experimentally engineering Majorana physics in high-temperature iron-based systems.

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.

Majorana-like Coulomb spectroscopy in the absence of zero-bias peaks

Hybrid semiconductor-superconductor devices hold great promise for realizing topological quantum computing with Majorana zero modes^1-5. However, multiple claims of Majorana detection, based on either tunnelling^6-10 or Coulomb blockade (CB) spectroscopy^11,12, remain disputed. Here we devise an experimental protocol that allows us to perform both types of measurement on the same hybrid island by adjusting its charging energy via tunable junctions to the normal leads. This method reduces ambiguities of Majorana detections by checking the consistency between CB spectroscopy and zero-bias peaks in non-blockaded transport. Specifically, we observe junction-dependent, even-odd modulated, single-electron CB peaks in InAs/Al hybrid nanowires without concomitant low-bias peaks in tunnelling spectroscopy. We provide a theoretical interpretation of the experimental observations in terms of low-energy, longitudinally confined island states rather than overlapping Majorana modes. Our results highlight the importance of combined measurements on the same device for the identification of topological Majorana zero modes.

Proposal for Detection of the 0^{'} and π^{'} Phases in Quantum-Dot Josephson Junctions

The competition between the Kondo correlation and superconductivity in quantum-dot Josephson junctions (QDJJs) has been known to drive a quantum phase transition between 0 and π junctions. Theoretical studies so far have predicted that under strong Coulomb correlations the 0-π transition should go through intermediate states, 0^{'} and π^{'} phases. By combining a nonperturbative numerical method and the resistively shunted junction model, we investigated the magnetic-field-driven phase transition of the QDJJs in the Kondo regime and found that the low-field magnetotransport exhibits a unique feature which can be used to distinguish the intermediate phases. In particular, the magnetic-field driven π^{'}-π transition is found to lead to the enhancement of the supercurrent which is strongly related to the Kondo effect.

Anomalous universal conductance as a hallmark of non-locality in a Majorana-hosted superconducting island

The non-local feature of topological states of matter is the key for the topological protection of quantum information and enables robust non-local manipulation in quantum information. Here we propose to manifest the non-local feature of a Majorana-hosted superconducting island by measuring the temperature dependence of Coulomb blockade peak conductance in different regimes. In the low-temperature regime, we discover a coherent double Majorana-assisted teleportation (MT) process, where any independent tunneling process always involves two coherent non-local MTs; and we also find an anomalous universal scaling behavior, i.e., a crossover from a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${[\max (T,eV)]}^{6}$$\end{document}[max(T,eV)]6 power-law to a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${[\max (T,eV)]}^{3}$$\end{document}[max(T,eV)]3 power-law conductance behavior when energy scale increases — in stark contrast to the usual exponential suppression due to certain local transport. In the high-temperature regime, the conductance is instead proportional to the temperature inverse, indicating a non-monotonic temperature-dependence of the conductance. Both the anomalous power law and non-monotonic temperature-dependence of the conductance can be distinguished from the conductance peak in the traditional Coulomb block, and therefore, together serve as a hallmark for the non-local feature in the Majorana-hosted superconducting island.

The ability to detect the non-local nature of topological states in electron transport is highly desirable for topological quantum computation. Hao et al. propose a two-terminal transport scheme to detect the non-locality of a topological superconducting island via anomalous scaling of the tunnelling conductance.

Plateau Regions for Zero-Bias Peaks within 5% of the Quantized Conductance Value 2e^{2}/h

Probing an isolated Majorana zero mode is predicted to reveal a tunneling conductance quantized at 2e^{2}/h at zero temperature. Experimentally, a zero-bias peak (ZBP) is expected and its height should remain robust against relevant parameter tuning, forming a quantized plateau. Here, we report the observation of large ZBPs in a thin InAs-Al hybrid nanowire device. The ZBP height can stick close to 2e^{2}/h, mostly within 5% tolerance, by sweeping gate voltages and magnetic field. We further map out the phase diagram and identify two plateau regions in the phase space. Despite the presence of disorder and quantum dots, our result constitutes a step forward toward establishing Majorana zero modes.

Photon-Assisted Tunneling of High-Order Multiple Andreev Reflections in Epitaxial Nanowire Josephson Junctions

Semiconductor/superconductor hybrids exhibit a range of phenomena that can be exploited for the study of novel physics and the development of new technologies. Understanding the origin of the energy spectrum of such hybrids is therefore a crucial goal. Here, we study Josephson junctions defined by shadow epitaxy on InAsSb/Al nanowires. The devices exhibit gate-tunable supercurrents at low temperatures and multiple Andreev reflections (MARs) at finite voltage bias. Under microwave irradiation, photon-assisted tunneling (PAT) of MARs produces characteristic oscillating sidebands at quantized energies, which depend on MAR order, n, in agreement with a recently suggested modification of the classical Tien-Gordon equation. The scaling of the quantized energy spacings with microwave frequency provides independent confirmation of the effective charge, ne, transferred by the nth-order tunneling process. The measurements suggest PAT as a powerful method for assigning the origin of low-energy spectral features in hybrid Josephson devices.

Tuning lower dimensional superconductivity with hybridization at a superconducting-semiconducting interface

The influence of interface electronic structure is vital to control lower dimensional superconductivity and its applications to gated superconducting electronics, and superconducting layered heterostructures. Lower dimensional superconductors are typically synthesized on insulating substrates to reduce interfacial driven effects that destroy superconductivity and delocalize the confined wavefunction. Here, we demonstrate that the hybrid electronic structure formed at the interface between a lead film and a semiconducting and highly anisotropic black phosphorus substrate significantly renormalizes the superconductivity in the lead film. Using ultra-low temperature scanning tunneling microscopy and spectroscopy, we characterize the renormalization of lead’s quantum well states, its superconducting gap, and its vortex structure which show strong anisotropic characteristics. Density functional theory calculations confirm that the renormalization of superconductivity is driven by hybridization at the interface which modifies the confinement potential and imprints the anisotropic characteristics of the semiconductor substrate on selected regions of the Fermi surface of lead. Using an analytical model, we link the modulated superconductivity to an anisotropy that selectively tunes the superconducting order parameter in reciprocal space. These results illustrate that interfacial hybridization can be used to tune superconductivity in quantum technologies based on lower dimensional superconducting electronics.

Lower-dimensional superconductors are typically synthesized on insulating substrates. Here, the authors find that the hybrid electronic structure formed at the interface between a lead film and a semiconducting black phosphorus substrate significantly renormalizes the superconductivity in the lead film.

Current through a hybrid four-terminal Josephson junction with Majorana nanowires

We investigate the current through a hybrid four-terminal Josephson junction with semiconductor nanowires, in which the junction is connected with two superconducting electrodes and two normal electrodes. The semiconductor nanowire, which is subject to an external magnetic field with Rashba spin-orbit coupling and proximity-induced superconductivity, can host Majorana bound states. When all the nanowires lie in topological nontrivial region, a 4π-periodic current can be observed through the normal terminal and a 2π-periodic current through the superconducting terminal. When a rotating magnetic field is applied to the junction, the supercurrent through different terminals varies with the variation of the magnetic field direction. Only when the magnetic field is applied at certain angles, we find that the 4π-periodic current will appear through the normal terminal.

Readout of Parafermionic States by Transport Measurements

Recent experiments have demonstrated the possibility of inducing superconducting pairing into counterpropagating fractional quantum Hall edge modes. This paves the way for the realization of localized parafermionic modes, non-Abelian anyons that share fractional charges in a nonlocal way. We show that, for a pair of isolated parafermions, this joint degree of freedom can be read by conductance measurements across standard metallic electrodes. We propose two complementary setups. We investigate first the transport through a grounded superconductor hosting two interacting parafermions. In the low-energy limit, its conductance peaks reveal their shared fractional charge yielding a three-state telegraph noise for weak quasiparticle poisoning. We then examine the two-terminal electron conductance of a blockaded fractional topological superconductor, which displays a characteristic e/3 periodicity of its zero-bias peaks in the deep topological regime, thus signaling the presence of parafermionic modes.

Ordered and tunable Majorana-zero-mode lattice in naturally strained LiFeAs

Majorana zero modes (MZMs) obey non-Abelian statistics and are considered building blocks for constructing topological qubits^1,2. Iron-based superconductors with topological bandstructures have emerged as promising hosting materials, because isolated candidate MZMs in the quantum limit have been observed inside the topological vortex cores^3-9. However, these materials suffer from issues related to alloying induced disorder, uncontrolled vortex lattices^10-13 and a low yield of topological vortices^5-8. Here we report the formation of an ordered and tunable MZM lattice in naturally strained stoichiometric LiFeAs by scanning tunnelling microscopy/spectroscopy. We observe biaxial charge density wave (CDW) stripes along the Fe-Fe and As-As directions in the strained regions. The vortices are pinned on the CDW stripes in the As-As direction and form an ordered lattice. We detect that more than 90 per cent of the vortices are topological and possess the characteristics of isolated MZMs at the vortex centre, forming an ordered MZM lattice with the density and the geometry tunable by an external magnetic field. Notably, with decreasing the spacing of neighbouring vortices, the MZMs start to couple with each other. Our findings provide a pathway towards tunable and ordered MZM lattices as a platform for future topological quantum computation.

Heat-Mode Excitation in a Proximity Superconductor

Mesoscopic superconductivity deals with various quasiparticle excitation modes, only one of them-the charge-mode-being directly accessible for conductance measurements due to the imbalance in populations of quasi-electron and quasihole excitation branches. Other modes carrying heat or even spin, valley etc. currents populate the branches equally and are charge-neutral, which makes them much harder to control. This noticeable gap in the experimental studies of mesoscopic non-equilibrium superconductivity can be filled by going beyond the conventional DC transport measurements and exploiting spontaneous current fluctuations. Here, we perform such an experiment and investigate the transport of heat in an open hybrid device based on a superconductor proximitized InAs nanowire. Using shot noise measurements, we investigate sub-gap Andreev heat guiding along the superconducting interface and fully characterize it in terms of the thermal conductance on the order of Gth∼e2/h, tunable by a back gate voltage. Understanding of the heat-mode also uncovers its implicit signatures in the non-local charge transport. Our experiments open a direct pathway to probe generic charge-neutral excitations in superconducting hybrids.

Electronic Structure and Epitaxy of CdTe Shells on InSb Nanowires

Indium antimonide (InSb) nanowires are used as building blocks for quantum devices because of their unique properties, that is, strong spin-orbit interaction and large Landé g-factor. Integrating InSb nanowires with other materials could potentially unfold novel devices with distinctive functionality. A prominent example is the combination of InSb nanowires with superconductors for the emerging topological particles research. Here, the combination of the II-VI cadmium telluride (CdTe) with the III-V InSb in the form of core-shell (InSb-CdTe) nanowires is investigated and potential applications based on the electronic structure of the InSb-CdTe interface and the epitaxy of CdTe on the InSb nanowires are explored. The electronic structure of the InSb-CdTe interface using density functional theory is determined and a type-I band alignment is extracted with a small conduction band offset ( ⩽0.3 eV). These results indicate the potential application of these shells for surface passivation or as tunnel barriers in combination with superconductors. In terms of structural quality, it is demonstrated that the lattice-matched CdTe can be grown epitaxially on the InSb nanowires without interfacial strain or defects. These shells do not introduce disorder to the InSb nanowires as indicated by the comparable field-effect mobility measured for both uncapped and CdTe-capped nanowires.

High-T c superconductor Fe(Se,Te) monolayer: an intrinsic, scalable and electrically tunable Majorana platform

Iron-based superconductors have been identified as a novel platform for realizing Majorana zero modes (MZMs) without heterostructures, due to their intrinsic topological properties and high-T c superconductivity. In the two-dimensional limit, the FeTe1-x Se x monolayer, a topological band inversion has recently been experimentally observed. Here, we propose to create MZMs by applying an in-plane magnetic field to the FeTe1-x Se x monolayer and tuning the local chemical potential via electric gating. Owing to the anisotropic magnetic couplings on edges, an in-plane magnetic field drives the system into an intrinsic high-order topological superconductor phase with Majorana corner modes. Furthermore, MZMs can occur at the domain wall of chemical potentials at either one edge or certain type of tri-junction in the two-dimensional bulk. Our study not only reveals the FeTe1-x Se x monolayer as a promising Majorana platform with scalability and electrical tunability and within reach of contemporary experimental capability, but also provides a general principle to search for realistic realization of high-order topological superconductivity.

Diagnosing topological phase transitions in 1D superconductors using Berry singularity markers

In this work I demonstrate how to characterize topological phase transitions in BDI symmetry class superconductors (SCs) in 1D, using the recently introduced approach of Berry singularity markers (BSMs). In particular, I apply the BSM method to the celebrated Kitaev chain model, as well as to a variant of it, which contains both nearest and next nearest neighbor equal spin pairings. Depending on the situation, I identify pairs of external fields which can detect the topological charges of the Berry singularities which are responsible for the various topological phase transitions. These pairs of fields consist of either a flux knob which controls the supercurrent flow through the SC, or, strain, combined with a field which can tune the chemical potential of the system. Employing the present BSM approach appears to be within experimental reach for topological nanowire hybrids.

Suppressing Andreev Bound State Zero Bias Peaks Using a Strongly Dissipative Lead

Hybrid semiconductor-superconductor nanowires are predicted to host Majorana zero modes that induce zero-bias peaks (ZBPs) in tunneling conductance. ZBPs alone, however, are not sufficient evidence due to the ubiquitous presence of Andreev bound states. Here, we implement a strongly resistive normal lead in InAs-Al nanowire devices and show that most of the expected Andreev bound state-induced ZBPs can be suppressed, a phenomenon known as environmental Coulomb blockade. Our result is the first experimental demonstration of this dissipative interaction effect on Andreev bound states and can serve as a possible filter to narrow down the ZBP phase diagram in future Majorana searches.

Universal Conductance Scaling of Andreev Reflections Using a Dissipative Probe

The Majorana search is caught up in an extensive debate about the false-positive signals from nontopological Andreev bound states. We introduce a remedy using the dissipative probe to generate electron-boson interaction. We theoretically show that the interaction-induced renormalization leads to significantly distinct universal zero-bias conductance behaviors, i.e., distinct characteristic power law in temperature, for different types of Andreev reflections, that show a sharp contrast to that of a Majorana zero mode. Various specific cases have been studied, including the cases in which two charges involved in an Andreev reflection process maintain or lose coherence, and the cases for multiple Andreev bound states with or without a Majorana. A transparent list of conductance features in each case is provided to help distinguish the observed subgap states in experiments, which also promotes the identification of Majorana zero modes.

Topological Superconducting Transition Characterized by a Modified Real-Space-Pfaffian Method and Mobility Edges in a One-Dimensional Quasiperiodic Lattice

A modified real-space-Pfaffian method is applied to characterize the topological superconducting transition of a one-dimensional p-wave superconductor with quasiperiodic potentials. We found that the Majorana zero-energy mode exists in the topological non-trivial phase, and its spatial distribution is localized at ends of the system, whereas in the topological trivial phase, there is no Majorana zero mode. Furthermore, we numerically found that due to the competition between the localized quasi-disorder and the extended p-wave pairing, there are mobility edges in the energy spectra. Our theoretical work enriches the research on the quasiperiodic p-wave superconducting models.

Accessing the degree of Majorana nonlocality in a quantum dot-optical microcavity system

We explore the tunneling transport properties of a quantum dot embedded in an optical microcavity and coupled to a semiconductor-superconductor one-dimensional nanowire (Majorana nanowire) hosting Majorana zero modes (MZMs) at their edges. Conductance profiles reveal that strong light-matter coupling can be employed to distinguish between the cases of highly nonlocal MZMs, overlapped MZMs and MZMs with less degree of nonlocal feature. Moreover, we show that it is possible to access the degree of Majorana nonlocality (topological quality factor) by changing the dot spectrum through photon-induced transitions tuned by an external pump applied to the microcavity.

Signatures of Andreev Blockade in a Double Quantum Dot Coupled to a Superconductor

We investigate an electron transport blockade regime in which a spin triplet localized in the path of current is forbidden from entering a spin-singlet superconductor. To stabilize the triplet, a double quantum dot is created electrostatically near a superconducting Al lead in an InAs nanowire. The quantum dot closest to the normal lead exhibits Coulomb diamonds, and the dot closest to the superconducting lead exhibits Andreev bound states and an induced gap. The experimental observations compare favorably to a theoretical model of Andreev blockade, named so because the triplet double dot configuration suppresses Andreev reflections. Observed leakage currents can be accounted for by finite temperature. We observe the predicted quadruple level degeneracy points of high current and a periodic conductance pattern controlled by the occupation of the normal dot. Even-odd transport asymmetry is lifted with increased temperature and magnetic field. This blockade phenomenon can be used to study spin structure of superconductors. It may also find utility in quantum computing devices that use Andreev or Majorana states.

Manipulation of Majorana bound states in proximity to a quantum ring with Rashba coupling

The quest for Majorana zero modes in the laboratory is an active field of research in condensed matter physics. In this regard, there have been many theoretical proposals; however, their experimental detection remains elusive. In this article, we present a realistic setting by considering a quantum ring with Rashba spin-orbit coupling and threaded by a magnetic flux, in contact with a topological superconducting nanowire. We focus on spin-polarized persistent currents to assess the existence of Majorana zero modes. We find that the Rashba spin-orbit coupling allows for tuning the position of the zero energy crossings in the flux parameter space and has sizable effects on spin-polarized persistent currents. We believe that our results will contribute towards probing the existence of Majorana zero modes.

Moiré-Enabled Topological Superconductivity

The search for artificial topological superconductivity has been limited by the stringent conditions required for its emergence. As exemplified by the recent discoveries of various correlated electronic states in twisted van der Waals materials, moiré patterns can act as a powerful knob to create artificial electronic structures. Here, we demonstrate that a moiré pattern between a van der Waals superconductor and a monolayer ferromagnet creates a periodic potential modulation that enables the realization of a topological superconducting state that would not be accessible in the absence of the moiré. The magnetic moiré pattern gives rise to Yu-Shiba-Rusinov minibands and periodic modulation of the Majorana edge modes that we detect using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS). Moiré patterns and, more broadly, periodic potential modulations are powerful tools to overcome the conventional constraints for realizing and controlling topological superconductivity.

Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires

Majorana bound states (MBS) and Andreev bound states (ABS) in realistic Majorana nanowires setups have similar experimental signatures which make them hard to distinguishing one from the other. Here, we characterize the continuous Majorana/Andreev crossover interpolating between fully-separated, partially-separated, and fully-overlapping Majorana modes, in terms of global and local topological invariants, fermion parity, quasiparticle densities, Majorana pseudospin and spin polarizations, density overlaps and transition probabilities between opposite Majorana components. We found that in inhomogeneous wires, the transition between fully-overlapping trivial ABS and nontrivial MBS does not necessarily mandate the closing of the bulk gap of quasiparticle excitations, but a simple parity crossing of partially-separated Majorana modes (ps-MM) from trivial to nontrivial regimes. We demonstrate that fully-separated and fully-overlapping Majorana modes correspond to the two limiting cases at the opposite sides of a continuous crossover: the only distinction between the two can be obtained by estimating the degree of separations of the Majorana components. This result does not contradict the bulk-edge correspondence: indeed, the field inhomogeneities driving the Majorana/Andreev crossover have a length scale comparable with the nanowire length, and therefore correspond to a nonlocal perturbation which breaks the topological protection of the MBS.

Nanoresonator Enhancement of Majorana-Fermion-Induced Slow Light in Superconducting Iron Chains

We theoretically investigate Fano resonance in the absorption spectrum of a quantum dot (QD) based on a hybrid QD-nanomechanical resonator (QD-NR) system mediated by Majorana fermions (MFs) in superconducting iron (Fe) chains. The absorption spectra exhibit a series of asymmetric Fano line shapes, which are accompanied by the rapid normal phase dispersion and induce the optical propagation properties such as the slow light effect under suitable parametric regimes. The results indicated that the slow light induced by MFs can be obtained under different coupling regimes and different detuning regimes. Moreover, we also investigated the role of the NR, and the NR behaving as a phonon cavity enhances the slow light effect.

Supercurrent and Phase Slips in a Ballistic Carbon Nanotube Bundle Embedded into a van der Waals Heterostructure

We demonstrate long-range superconducting correlations in a several-micrometers-long carbon nanotube bundle encapsulated in a van der Waals stack between hBN and NbSe₂. We show that a substantial supercurrent flows through the nanotube section beneath the NbSe₂ crystal as well as through the 2 μm long section not in contact with it. The large in-plane critical magnetic field of this supercurrent is an indication that even inside the carbon nanotube Cooper pairs enjoy a degree of paramagnetic protection typical of the parent Ising superconductor. As expected for superconductors of nanoscopic cross section, the current-induced breakdown of superconductivity is characterized by resistance steps due to the nucleation of phase slip centers. All elements of our hybrid device are active building blocks of several recently proposed setups for realization of Majorana fermions in carbon nanotubes.

Andreev Molecule in Parallel InAs Nanowires

Coupling individual atoms fundamentally changes the state of matter: electrons bound to atomic cores become delocalized turning an insulating state to a metallic one. A chain of atoms could lead to more exotic states if the tunneling takes place via the superconducting vacuum and can induce topologically protected excitations like Majorana or parafermions. Although coupling a single atom to a superconductor is well studied, the hybridization of two sites with individual tunability was not reported yet. The peculiar vacuum of the Bardeen-Cooper-Schrieffer (BCS) condensate opens the way to annihilate or generate two electrons from the bulk resulting in a so-called Andreev molecular state. By employing parallel nanowires with an Al shell, two artificial atoms were created at a minimal distance with an epitaxial superconducting link between. Hybridization via the BCS vacuum was observed and the spectrum of an Andreev molecule as a function of level positions was explored for the first time.

Probing Time Reversal Symmetry Breaking Topological Superconductivity in Twisted Double Layer Copper Oxides with Polar Kerr Effect

Recent theoretical work predicted the emergence of a chiral topological superconducting phase with spontaneously broken time reversal symmetry in a twisted bilayer composed of two high-T_{c} cuprate monolayers such as Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}. Here, we identify a large intrinsic Hall response that can be probed through the polar Kerr effect measurement as a convenient signature of the T-broken phase. Our modeling predicts the Kerr angle θ_{K} to be in the range of 10-100  μrad, which is a factor of 10^{3} to 10^{4} times larger than what is expected for the leading chiral superconductor candidate Sr_{2}RuO_{4}. In addition, we show that the optical Hall conductivity σ_{H}(ω) can be used to distinguish between the topological d_{x^{2}-y^{2}}±id_{xy} phase and the d_{x^{2}-y^{2}}±is phase, which is also expected to be present in the phase diagram but is topologically trivial.

Transparent qubit manipulations with spin-orbit coupled two-electron nanowire quantum dot

We report on the first set of exact orthonormalized states to an ac driven one-dimensional (1D) two-electron nanowire quantum dot with the Rashba-Dresselhaus coexisted spin-orbit coupling (SOC) and the controlled magnetic field orientation and trapping frequency. In the ground state case, it is shown that the spatiotemporal evolutions of probability densities occupying internal spin states and the transfer rates between different spin states can be adjusted by the ac electric field and the intensities of SOC and magnetic field. Effects of the system parameters and initial-state-dependent constants on the mean entanglement are revealed, where the approximately maximal entanglement associated with the stronger SOC and its insensitivity to the initial and parametric perturbations are demonstrated numerically. A novel resonance transition mechanism is found, in which the ladder-like time-evolution process of expected energy and the transition time between two arbitrary exact states are controlled by the ac field strength. Using such maximally entangled exact states to encode qubits can render the qubit control more transparent and robust. The results could be extended to 2D case and to an array of two-electron quantum dots with weak neighboring coupling for quantum information processing.