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While spin-triplet pairing remains elusive in nature, there is a growing effort to realize proximity-induced equal-spin triplet superconductivity in junctions with magnetic regions or an applied magnetic field and common $s$-wave superconductors. To enhance such spin-triplet contribution, it is expected that junctions with a weak interfacial barrier and strong spin-orbit coupling are desirable. Intuitively, a weak interfacial barrier enables a robust proximity-induced superconductivity and strong spin-orbit coupling promotes spin mixing, converting spin-singlet into spin-triplet superconductivity. In contrast, we reveal a nonmonotonic spin-triplet contribution with the strength of the interfacial barrier and spin-orbit coupling. This picture is established by considering different signatures in conductance and superconducting correlations, as well as by performing self-consistent calculations. As a result, we identify a strongly enhanced spin-triplet superconductivity, realized for an intermediate strength of interfacial barrier and spin-orbit coupling. In junctions with magnetic regions, an enhanced spin-triplet superconductivity leads to a large magnetoanisotropy of conductance and superconducting correlations. This picture of an enhanced spin-triplet superconductivity is consistent with experiments demonstrating a huge increase in the conductance magnetoanisotropy, which we predict can be further enhanced at a finite bias.

Planar Josephson junctions provide a platform to host topological superconductivity which, through manipulating Majorana bound states (MBS), could enable fault-tolerant quantum computing. However, what constitutes experimental signatures of topological superconductivity and how MBS can be detected remains strongly debated. In addition to spurious effects that mimic MBS, there is a challenge to discern the inherent topological signals in realistic systems with many topologically-trivial Andreev bound states, determining the transport properties of Josephson junctions. Guided by the advances in microwave spectroscopy, we theoretically study Al/InAs-based planar Josephson junction embedded into a radio-frequency superconducting quantum interference device to identify microwave signatures of topological superconductivity. Remarkably, by exploring the closing and reopening of a topological gap, we show that even in a wide planar Josephson junction with many Andreev bound states, such a topological signature is distinguishable in the resonance frequency shift of a microwave drive and the ``half-slope'' feature of the microwave absorption spectrum. Our findings provide an important step towards experimental detection of non-Abelian statistics and implementing scalable topological quantum computing.

A planar Josephson junction is a versatile platform to realize topological superconductivity over a large parameter space and host Majorana bound states. With a change in Zeeman field, this system undergoes a transition from trivial to topological superconductivity accompanied by a jump in the superconducting phase difference between the two superconductors. A standard model of these Josephson junctions, which can be fabricated to have a nearly perfect interfacial transparency, predicts a simple universal behavior. In that model, at the same value of Zeeman field for the topological transition, there is a $\pi$ phase jump and a minimum in the critical superconducting current, while applying a controllable phase difference yields a diamond-shaped topological region as a function of that phase difference and a Zeeman field. In contrast, even for a perfect interfacial transparency, we find a much richer and nonuniversal behavior as the width of the superconductor is varied or the Dresselhaus spin-orbit coupling is considered. The Zeeman field for the phase jump, not necessarily $\pi$, is different from the value for the minimum critical current, while there is a strong deviation from the diamond-like topological region. These Josephson junctions show a striking example of a nonreciprocal transport and superconducting diode effect, revealing the importance of our findings not only for topological superconductivity and fault-tolerant quantum computing, but also for superconducting spintronics., Comment: Invited to APL Special Topic Issue: "Josephson Junctions and Related Proximity Effects: From Basic Science to Emerging Applications in Advanced Technologies", accepted version

YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) has favorable macroscopic superconducting properties of $T_\mathrm{c}$ up to 93 K and $H_{c2}$ up to 150 T. However, its nanoscale electronic structure remains mysterious because bulk-like electronic properties are not preserved near the surface of cleaved samples for easy access by local or surface-sensitive probes. It has been hypothesized that Ca-doping at the Y site could induce an alternate cleavage plane that mitigates this issue. We use scanning tunneling microscopy (STM) to study both Ca-free and 10% Ca-doped YBCO, and find that the Ca-doped samples do indeed cleave on an alternate plane, yielding a spatially-disordered partial (Y,Ca) layer. Our density functional theory calculations support the increased likelihood of this new cleavage plane in Ca-doped YBCO. On this surface, we image a superconducting gap with average value 24 $\pm$ 3 meV and characteristic length scale 1-2 nm, similar to Bi-based high-$T_\mathrm{c}$ cuprates, but the first map of gap inhomogeneity in the YBCO family., Comment: corrected typo in metadata author name

A fundamental instability in the nonequilibrium conduction band under a electric field bias is proposed via the spontaneous emission of coherent phonons. Analytic theory, supported by numerical calculations, establishes that the quantum avalanche, an abrupt nonequilibrium occupation of excited bands, results from the competition between the collapse of the band minimum via the phonon emission and the dephasing of the electron with the environment. The continuous avalanche transition is a quantum phase transition with the nonequilibrium phase diagram determined by the avalanche parameter $\beta$, with peculiar reentrant avalanche domes close to the phase boundary. We further confirm the nature of the quantum avalanche with the temperature dependence.

We explain how Rashba spin-orbit coupling (SOC) in a two-dimensional electron gas (2DEG), or in a conventional $s$-wave superconductor, can lead to a large magnetoresistance even with one ferromagnet. However, such enhanced magnetoresistance is not generic and can be nonmonotonic and change its sign with Rashba SOC. For an in-plane rotation of magnetization, it is typically negligibly small for a 2DEG and depends on the perfect transmission which emerges from a spin-parity-time symmetry of the scattering states, while this symmetry is generally absent from the Hamiltonian of the system. The key difference from considering the normal-state magnetoresistance is the presence of the spin-dependent Andreev reflection at superconducting interfaces. In the fabricated junctions of quasi-2D van der Waals ferromagnets with conventional $s$-wave superconductors (Fe$_{0.29}$TaS$_2$/NbN) we find another example of enhanced magnetoresistance where the presence of Rashba SOC reduces the effective interfacial strength and is responsible for an equal-spin Andreev reflection. The observed nonmonotonic trend in the out-of-plane magnetoresistance with the interfacial barrier is an evidence for the proximity-induced equal-spin-triplet superconductivity., Comment: This work is submitted to the special issue of Phys. Rev. B dedicated to Professor Emmanuel Rashba

It is well known that the Eisenbud-Goto regularity conjecture is true for arithmetically Cohen-Macaulay varieties, projective curves, smooth surfaces, smooth threefolds in $\mathbb{P}^5$, and toric varieties of codimension two. After J. McCullough and I. Peeva constructed counterexamples in 2018, it has been an interesting question to find the categories such that the Eisenbud-Goto conjecture holds. So far, surface counterexamples have not been found while counterexamples of any dimension greater or equal to 3 are known. In this paper, we construct counterexamples to the Eisenbud-Goto conjecture for projective surfaces in $\mathbb{P}^4$ and investigate projective invariants, cohomological properties, and geometric properties. The counterexamples are constructed via binomial rational maps between projective spaces., Comment: 23 pages, to appear in Trans. Amer. Math. Soc

Motivated by the resistive switchings in transition-metal oxides (TMOs) induced by a voltage bias, we study the far-from-equilibrium dynamics of an electric-field-driven strongly-correlated model featuring a first-order insulator-to-metal transition at equilibrium, namely the dimer-Hubbard model. We use a non-equilibrium implementation of the dynamical cluster approximation to access the steady-state spectral and transport properties. We show that the electric field can drive both metal-to-insulator and insulator-to-metal transitions. While they proceed by quite distinct mechanisms, specifically simple heating of the metal versus non-equilibrium effects in the correlated charge gap, we show that both of these non-equilibrium transitions can be unified in a single framework once the excitations are accounted for in terms of an effective temperature. This conceptual advance brings together the two sides of the long-lasting debate over the origins of the electrically-driven resistive switching in TMOs., Comment: 15 pages, 11 figures. v2: minor changes

We propose a microscopic mechanism to resolve the long-standing puzzle of the insulator-to-metal transition in correlated electronic systems, most notably charge-density-wave (CDW) materials and Mott insulators, driven far-from-equilibrium by a DC electric field. By introducing a generic model of electrons coupled to an inelastic medium of phonons, we demonstrate that an electron avalanche can occur in the bulk limit of such insulators at arbitrarily small electric field. The quantum avalanche arises by the generation of a ladder of in-gap states, created by a multi-phonon emission process. Hot-phonons in the avalanche trigger a premature and partial collapse of the correlated gap. The details of the phonon spectrum dictate two-stage versus single-stage mechanisms which we associate with CDW and Mott resistive transitions, respectively. The electron and phonon temperatures, as well as the temperature dependence of the threshold fields, point to the quantum nature of this nonequilibrium phase transition.

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., Comment: 10 pages, 7 figures; Accepted in Nature Communications

We reveal that the interplay between Rashba spin-orbit coupling and proximity-induced magnetization in a two-dimensional electron gas leads to peculiar transport properties and large anisotropy of magnetoresistance. While the related tunneling anisotropic magnetoresistance (TAMR) has been extensively studied before, we predict an effect with a different origin arising from the evolution of a resonant condition with the in-plane rotation of magnetization and having a much larger magnitude. The resonances in the tunneling emerge from a spin-parity-time symmetry of the scattering states. However, such a symmetry is generally absent from the system itself and only appears for certain parameter values. Without resonant behavior in the topological surface states of a proximitized three-dimensional topological insulator (TI), TAMR measurements can readily distinguish them from often misinterpreted trivial Rashba-like states inherent to many TIs.

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 the main efforts to realize MBS have 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 experimental advances 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., Comment: 6 pages, 4 figures, accepted in PRL

A common path to superconducting spintronics, Majorana fermions, and topologically-protected quantum computing relies on spin-triplet superconductivity. While naturally occurring spin-triplet pairing is elusive and even common spin-triplet candidates, such as Sr$_2$RuO$_4$, support alternative explanations, proximity effects in heterostructures can overcome these limitations. It is expected that robust spin-triplet superconductivity in magnetic junctions should rely on highly spin-polarized magnets or complex magnetic multilayers. Instead, we predict that the interplay of interfacial spin-orbit coupling and the barrier strength in simple magnetic junctions, with only a small spin polarization and s-wave superconductors, can lead to nearly complete spin-triplet superconducting proximity effects. This peculiar behavior arises from an effective perfect transparency: interfacial spin-orbit coupling counteracts the native potential barrier for states of a given spin and wave vector. We show that the enhanced spin-triplet regime is characterized by a huge increase in conductance magnetoanisotropy, orders of magnitude larger than in the normal state.

A hybrid semiconductor-superconductor nanowire on the top of a magnetic film in the stripe phase experiences a magnetic texture from the underlying fringing fields. The Zeeman interaction with the highly inhomogeneous magnetic textures generates a large synthetic spin-orbit coupling. We show that this platform can support the formation of Majorana bound states (MBS) localized at the ends of the nanowire. The transition to the topological superconducting phase not only depends on the nanowire parameters and stripe size but also on the relative orientation of the stripes with respect to the nanowire axis. Topological phase transitions with the corresponding emergence or destruction of MBS can be induced by reorienting the stripes or shifting their position, which can be achieved by passing a charge current through the magnetic film or by applying electrically-controlled strain to it. The proposed platform removes the need for external magnetic fields and offers a non-invasive electrical tuning of MBS with the perturbation (current or strain) acting only on thee magnetic film., Comment: 9 pages, 6 figures