arXiv subjects

Henry F. Legg

Publications and source records attributed to Henry F. Legg.

At least 19 recordsLinked to original sources

arXiv2026

Probing Fermi-surface spin-textures via the nonlinear Shubnikov-de Haas effect

The coupling of spin and electronic degrees of freedom via the spin-orbit interaction (SOI) is an essential ingredient for many proposed future technologies. However, probing the strength and nature of SOI is a significant challenge, especially in heterostructures. Here, we consider the nonlinear Shubnikov-de Haas (NSdH) effect, a quantum oscillatory effect that occurs under conditions similar to those of the well-known SdH effect, but is second order in the applied electric field. We demonstrate that, unlike its linear counterpart, the NSdH effect is highly sensitive to the spin textures that arise from SOI. We show that the relative phases and beating patterns of the nonlinear oscillations provide additional information that discriminates linear- and cubic-Rashba-dominated regimes in the models considered here. Our results establish NSdH as a complementary phase-resolved probe of SOI, offering a new framework for characterizing materials relevant to topology, spintronics, and solid-state quantum information technologies.

cond-mat.mes-hall↗

arXiv2026

Flux-tunable global and local superconductivity in a topological insulator nano-SQUID

Topological systems are defined by global properties that enforce the existence of local boundary modes. Three-dimensional topological insulators (TIs) were among the earliest proposed systems for hosting topological superconductivity, but experimental focus subsequently shifted to other platforms. Here, we revisit bulk-insulating TIs using a columnar nano-superconducting quantum interference device (nano-SQUID) architecture. This geometry optimises the proximity effect on the TI surface and enables simultaneous probing of global superconducting properties - via the critical current through the nano-SQUID - alongside the local states at the ends of the nano-SQUID via tunnel junctions. We observe several global superconducting features that appear to show a flux-driven global phase transition consistent with entering the topological regime, including periodic critical current oscillations and a sign reversal in the superconducting diode effect. Simultaneously, tunnelling spectroscopy reveals spectral jumps in local and nonlocal conductance that align with these global features. However, zero-bias peaks (ZBPs) in local conductance are present both within the predicted topological range of magnetic fields and in theoretically trivial regimes, including at zero magnetic field. Ultimately, the lack of correlation between local ZBP signatures and global signatures emphasises that conclusively identifying Majorana bound states will necessitate a combined approach, integrating the establishment of global topological properties with the use of local and other, more advanced, probes.

cond-mat.mes-hall↗

arXiv2025

Reply to the Comment by Tikhonov and Khrapai on "Long-range crossed Andreev reflection in a topological insulator nanowire proximitized by a superconductor"

The comment (arXiv:2505.23490) fails to identify any scientific errors and its central arguments actually support the main conclusions of our publication [Nat. Phys. 21, 708 (2025)]. Firstly, the whole argument of the comment to try to explain our data explicitly relies on the existence of a large crossed Andreev reflection (CAR) effect. The presence of a sizable CAR transmission probability over a surprisingly long distance is the first conclusion of our publication. Secondly, the comment discusses the complex interplay of CAR and elastic co-tunneling, especially in the presence of local effects. This complex interplay is precisely the second conclusion of our publication. In essence, the comment amounts to merely pointing out that there is a broader sense in the notion of "dominant CAR" when nonlinear effects become relevant.

cond-mat.mes-hall↗

arXiv2025

Tunable superconducting diode effect in a topological nano-SQUID

A Josephson diode passes current with zero resistance in one direction but is resistive in the other direction. While such an effect has been observed in several platforms, a large and tunable Josephson diode effect has been rare. Here we report that a simple device consisting of a topological-insulator (TI) nanowire side-contacted by superconductors to form a lateral Josephson junction presents a large diode effect with the efficiency $η$ reaching 0.3 when a parallel magnetic field $B_{||}$ is applied. Interestingly, the sign and the magnitude of $η$ is tunable not only by $B_{||}$ but also by the back-gate voltage. This diode effect can be understood by modeling the system as a nano-SQUID, in which the top and bottom surfaces of the TI nanowire each form a line junction and $B_{||}$ creates a magnetic flux to thread the SQUID loop. This model further shows that the observed diode effect marks the emergence of topological superconductivity in TI-nanowire-based Josephson junction.

cond-mat.supr-con↗

arXiv2025

Topological Insulator nano-SQUID: Flux-tunable platform for topological superconductivity

Many efforts have been made in the past decade to realize topological superconductivity using superconducting proximity effect, but an ideal platform is still lacking. A 3D topological insulator (TI) is promising for this purpose due to the spin-momentum-locked surface state. Here we propose a novel yet simple TI platform which gives rise to a topological phase that is robust against disorder. It consists of a bulk-insulating rectangular TI nanowire laterally sandwiched by two superconductors. In this structure, the top and bottom surfaces individually work as SNS line junctions, forming a nanometer-scale columnar SQUID in which the nanowire cross-section defines the threading magnetic flux $Φ$ in axial magnetic fields. We theoretically show that, when the two junctions are asymmetric, a robust topological phase occurs periodically for a wide range of $Φ$, independently of the chemical potential. Our experiment found that a TI device of this structure indeed behaves as a columnar nano-SQUID where the supercurrent flows only through the top and bottom surfaces with vanishing bulk contribution. Furthermore, the top/bottom asymmetry can be tuned by a back gate, a key ingredient for the topological phase.

cond-mat.mes-hall↗

arXiv2025

Anomalous Josephson effect in hybrid superconductor-hole systems

We consider hybrid systems consisting of a hole-doped semiconductor coupled to electronic states of finite-size superconductors, where the opposite sign of the masses in the two subsystems give rise to insulating gaps at subband anticrossings. Consequently, increasing the coupling strength to the superconductor can paradoxically suppress the proximity-induced superconductivity in the semiconductor by enhancing these insulating gaps. We demonstrate that the presence of such induced insulating gaps leads to a characteristic anomalous behavior of the critical supercurrent in Josephson junctions based on these hybrid structures. Our findings provide important insights for the design of robust quantum computing platforms utilizing hybrid superconductor-hole systems.

cond-mat.mes-hall↗

arXiv2025

Properties and prevalence of false poor man's Majoranas in two- and three-site artificial Kitaev chains

It was predicted that a minimal chain of two quantum dots (QDs) connected via a superconductor can host perfectly localized zero-energy states, known as poor man's Majoranas (PMMs). It is expected that these states are related to Majorana bound states (MBSs) in longer chains and that the tunable nature of this setup makes it a promising platform to study MBSs. However, realistic systems can only host highly, but not perfectly, localized near-zero-energy states, called imperfect PMMs. It has been shown that these imperfect PMMs can evolve into trivial states unrelated to MBSs when the chain is extended. Such states are called false PMMs, whereas PMMs that evolve into MBSs in long chains are called true PMMs. Here, using a microscopic model of QD-superconductor arrays, we consider properties of false PMMs and the circumstances under which they appear. In two-site systems, we find that the origin of many false PMMs can be related to zero-energy states occurring in the absence of superconductivity and we use this analytic understanding to characterize the false PMMs that are typical for different regions of parameter space. In three-site systems, we show that false PMMs can occur via the same mechanism as for two-site systems, but we also find them in regions of parameter space where they are not predicted to exist, thus hinting that the physics of false PMMs can be richer in longer chains. Finally, we demonstrate that the PMMs most stable to perturbations in chemical potential and with the largest excitation gaps appear in a region of parameter space that also has a large ratio of false to true PMMs.

cond-mat.mes-hall↗

arXiv2025

Fate of poor man's Majoranas in the long Kitaev chain limit

A minimal Kitaev chain, consisting of two quantum dots connected via a superconductor, can host highly localized near-zero-energy states, known as poor man's Majoranas (PMMs). These states have been proposed as promising candidates to study Majorana bound states (MBSs) in a highly tunable setup. However, it is unclear whether and how PMMs observed in real systems are actually connected to the topological phase of the full Kitaev chain. Here, we study PMMs using a microscopic model and show that, in the long chain limit, not all PMMs are related to topological states. Rather, in long chains, some PMMs evolve into trivial highly localized low-energy states. We provide an explanation for the occurrence of these states and show that there is no clear conductance signature that is able to distinguish PMMs that evolve into true topological states from PMMs that evolve into trivial states.

cond-mat.mes-hall↗

arXiv2025

Comment on "Interferometric single-shot parity measurement in InAs-Al hybrid devices", Microsoft Quantum, Nature 638, 651-655 (2025)

We consider the 'parity readout' of a (topological) superconductor claimed in Nature 638, 651-655 (2025). A prerequisite for this claim is the existence of a superconducting gap in the nanowire device. However, to determine the presence of a gap, Nature 638, 651-655 (2025) relied on the so-called topological gap protocol (TGP). Here, we show that the TGP can report the regions where the 'parity readout' occurred as either gapped or gapless, depending on data parameters such as magnetic field range and cutter pair (junction transparency). Compounding these issues are inaccuracies in the presented TGP outcomes, which limited investigation of reproducibility. Since these inconsistent outcomes demonstrate that the TGP is not a reliable diagnostic tool for the presence of a superconducting gap, we instead investigate the conductance data for the studied regions -- data that were not presented in Nature 638, 651-655 (2025), but are in the public data repository. These conductance data show that the regions where 'parity readout' occurred are in fact highly disordered and present no clear gap in the nanowire, i.e., the underlying conductance data show that these regions are indeed gapless. That these regions are gapless contradicts the claim that the reported measurements are of the parity of a superconducting nanowire, let alone the parity of a topological superconducting nanowire. Taken together, these issues mean that the core findings in Nature 638, 651-655 (2025) are not reliable and should be revisited.

cond-mat.mes-hall↗

arXiv2025

Comment on "InAs-Al hybrid devices passing the topological gap protocol", Microsoft Quantum, Phys. Rev. B 107, 245423 (2023)

The topological gap protocol (TGP) is presented as "a series of stringent experimental tests" for the presence of topological superconductivity and associated Majorana bound states. Here, we show that the TGP, 'passed' by Microsoft Quantum [PRB 107, 245423 (2023)], lacks a consistent definition of 'gap' or 'topological', and even utilises different parameters when applied to theoretical simulations compared to experimental data. Furthermore, the TGP's outcome is sensitive to the choice of magnetic field range, bias voltage range, data resolution, and number of cutter voltage pairs - data parameters that, in PRB 107, 245423 (2023), vary significantly, even for measurements of the same device. As a result, the core claims of PRB 107, 245423 (2023) are primarily based on unexplained measurement choices and inconsistent definitions, rather than on intrinsic properties of the studied devices. As such, Microsoft Quantum's claim in PRB 107, 245423 (2023) that their devices have a "high probability of being in the topological phase" is not reliable and must be revisited. Our findings also suggest that subsequent studies, e.g. Nature 638, 651-655 (2025), that are based on tuning up devices via the TGP are built on a flawed protocol and should also be revisited.

cond-mat.mes-hall↗

arXiv2024

From perfect to imperfect poor man's Majoranas in minimal Kitaev chains

Poor man's Majoranas (PMMs) hold the promise to engineer Majorana bound states in a highly tunable setup consisting of a chain of quantum dots that are connected via superconductors. Due to recent progress in controlling the amplitudes of elastic cotunneling (ECT) and crossed Andreev reflection (CAR), two vital ingredients for PMMs, experimental investigations of PMMs have gained significant interest. Previously, analytic conditions for the "sweet spots" that result in PMMs have focused on systems with infinite Zeeman energy. Here, we derive analytically a sweet spot condition for PMMs in a system with finite Zeeman energy in the absence of Coulomb interaction. We then consider two numerical models, one in which ECT and CAR are transmitted via superconducting bulk states and one in which they are transmitted via an Andreev bound state. We demonstrate that the analytical sweet spot conditions can only be approximated in these more realistic models, but they cannot be satisfied exactly. As a consequence, we do not find perfect PMMs in these systems, but instead near-zero-energy states that are highly, but not perfectly, localized. These states can be considered as imperfect PMMs and their classification relies on threshold values, which adds some arbitrariness to the concept of PMMs.

cond-mat.mes-hall↗

arXiv2024

Long-range crossed Andreev reflection in topological insulator nanowires proximitized by a superconductor

Crossed Andreev reflection (CAR) is a nonlocal transport phenomenon that creates/detects Cooper-pair correlations between distant places. It is also the basis of Cooper-pair splitting to generate remote entanglement. Although CAR has been extensively studied in semiconductors proximity-coupled to a superconductor, it has been very difficult to observe it in a topological insulator (TI). Here we report the first observation of CAR in a proximitized TI nanowire (TINW). We performed local and nonlocal conductance spectroscopy on mesoscopic TINW devices in which superconducting (Nb) and metallic (Pt/Au) contacts are made on a bulk-insulating TINW. The local conductance detected a hard gap, accompanied by the appearance of Andreev bound states that can reach zero-bias, while a negative nonlocal conductance was occasionally observed upon sweeping the chemical potential, giving evidence for CAR. Surprisingly, the CAR signal was detected even over 1.5 $μ$m, which implies that pair correlations extend over a length scale much longer than the expected superconducting coherence length of either Nb or the proximitised TINW. Such a long-range CAR effect is possibly due to an intricate role of disorder in proximitized nanowires. Also, our 0.9-$μ$m device presented a decent Cooper-pair splitting efficiency of up to 0.5.

cond-mat.mes-hall↗

arXiv2024

Interband contributions to nonlinear transport in semiconductor nanostructures

Spin-orbit interaction (SOI) is a crucial ingredient for many potential applications of quantum devices, such as the use of semiconductor nanostructures for quantum computing. It is known that nonlinear conductivities are sensitive to the strength and type of SOI, however, many calculations of nonlinear transport coefficients are based on the semiclassical Boltzmann theory and make simplifying assumptions about scattering effects due to disorder. In this paper we develop and employ a microscopic theory based on the Keldysh formalism that goes beyond simple semiclassical approximations. This approach, for instance, naturally takes into account the effects of interband transitions, Berry curvature, and allows for a more precise treatment of impurity scattering. As a test of this formalism, we consider the nonlinear transport properties in an effective two-band model of one-dimensional nanowires (1DNWs) and two-dimensional hole gases (2DHGs) in the presence of a magnetic field causing Zeeman splittings of the spin states. We find that the small energy scales in nanostructures mean that interband contributions can be relevant, especially in the dirty limit, and therefore could modify qualitative features found using a purely semiclassical approach. Nonetheless, we find that different types of SOI (linear or cubic) still result in remarkably pronounced different in-plane field angle dependences, which survive even when interband effects are relevant. Our results provide a detailed understanding of when interband effects become important for nonlinear transport and can serve as the basis for a microscopic description to predict other nonlinear transport effects in materials and devices.

cond-mat.mes-hall↗

arXiv2024

Reply to Antipov et al., Microsoft Quantum: "Comment on Hess et al. Phys. Rev. Lett. 130, 207001 (2023)"

In this Reply we respond to the comment by Antipov et al. from Microsoft Quantum on Hess et al., PRL 130, 207001 (2023). Antipov et al. reported only a single simulation and claimed it did not pass the Microsoft Quantum topological gap protocol (TGP). They have provided no parameters or data for this simulation (despite request). Regardless, in this reply we demonstrate that the trivial bulk gap reopening mechanism outlined in Hess et al., in combination with trivial ZBPs, passes the TGP and therefore can result in TGP false positives.

cond-mat.mes-hall↗

arXiv2024

Relations between normal state nonreciprocal transport and the superconducting diode effect in the trivial and topological phases

Nonreciprocal transport effects can occur in the normal state of conductors and in superconductors when both inversion and time-reversal symmetry are broken. Here, we consider systems where magnetochiral anisotropy (MCA) of the energy spectrum due to an externally applied magnetic field results in a rectification effect in the normal state and a superconducting (SC) diode effect when the system is proximitised by a superconductor. Focussing on nanowire systems, we obtain analytic expressions for both normal state rectification and SC diode effects that reveal the commonalities - as well as differences - between these two phenomena. Furthermore, we consider the nanowire brought into an (almost) helical state in the normal phase or a topological superconducting phase when proximitised. In both cases this reveals that the topology of the system considerably modifies its nonreciprocal transport properties. Our results provide new insights into how to determine the origin of nonreciprocal effects and further evince the strong connection of nonreciprocal transport with the topological properties of a system.

cond-mat.mes-hall↗

arXiv2023

Majorana bound states in germanium Josephson junctions via phase control

We consider superconductor-normal-superconductor-normal-superconductor (SNSNS) planar Josephson junctions in hole systems with spin-orbit interaction that is cubic in momentum (CSOI). Using only the superconducting phase difference, we find parameter regimes where junctions of experimentally achievable transparency can enter a topological superconducting phase with Majorana bound states (MBSs) at the junction ends. In planar germanium heterostructures CSOI can be the dominant form of SOI and extremely strong. We show analytically and numerically that, within experimental regimes, our results provide an achievable roadmap for a new MBS platform with low disorder, minimal magnetic fields, and very strong spin-orbit interaction, overcoming many of the key deficiencies that have so far prevented the conclusive observation of MBSs.

cond-mat.mes-hall↗

arXiv2023

Microscopic analysis of proximity-induced superconductivity and metallization effects in superconductor-germanium hole nanowires

Low-dimensional germanium hole devices are promising systems with many potential applications such as hole spin qubits, Andreev spin qubits, and Josephson junctions, and can serve as a basis for the realization of topological superconductivity. This vast array of potential uses for Ge largely stems from the exceptionally strong and controllable spin-orbit interaction (SOI), ultralong mean free paths, long coherence times, and compatibility with complementary metal-oxide-semiconductor (CMOS) technology. However, when brought into proximity with a superconductor (SC), metallization normally diminishes many useful properties of a semiconductor, for instance, typically reducing the g factor and SOI energy, as well as renormalizing the effective mass. In this paper, we consider metallization of a Ge nanowire (NW) in proximity to a SC, explicitly taking into account the three-dimensional (3D) geometry of the NW. We find that proximitized Ge exhibits a unique phenomenology of metallization effects, where the 3D cross section plays a crucial role. For instance, in contrast to expectations, we find that SOI can be enhanced by strong coupling to the superconductor. We also show that the thickness of the NW plays a critical role in determining both the size of the proximity-induced pairing potential and metallization effects, since the coupling between the NW and SC strongly depends on the distance of the NW wave function from the interface with the SC. In the absence of electrostatic effects, we find that a sizable gap opens only in thin NWs ($d \lesssim 3$ nm). In thicker NWs, the wave function must be pushed closer to the SC by electrostatic effects in order to achieve a sizable proximity gap such that the required electrostatic field strength can simultaneously induce a strong SOI.

cond-mat.mes-hall↗

arXiv2023

Nonlinear transport due to magnetic-field-induced flat bands in the nodal-line semimetal ZrTe5

The Dirac material ZrTe$_5$ at very low carrier density was recently found to be a nodal-line semimetal, where ultra-flat bands are expected to emerge in magnetic fields parallel to the nodal-line plane. Here we report that in very low carrier-density samples of ZrTe$_5$, when the current and the magnetic field are both along the crystallographic $a$ axis, the current-voltage characteristics presents a pronounced nonlinearity which tends to saturate in the ultra quantum limit. The magnetic-field dependence of the nonlinear coefficient is well explained by the Boltzmann theory for flat-band transport, and we argue that this nonlinear transport is likely due to the combined effect of flat bands and charge puddles, the latter appear due to very low carrier densities.

cond-mat.mtrl-sci↗