Search

We theoretically discuss the emergence of fractional Shapiro steps in a Josephson junction created by confining a two-dimensional electron gas at an oxide interface. This phenomenon is induced by an alternating current of proper amplitude and frequency and can be tuned by a magnetic field applied perpendicular to the Rashba spin-orbit axis. The presence of fractional Shapiro steps can be associated with the creation of Majorana bound states at the boundaries of the superconducting leads. Our findings represent a route for the identification of topological superconductivity in non-centrosymmetric materials and confined systems in the presence of spin--orbit interaction, offering also new insights into recently explored frameworks., Comment: 7 pages, 4 figures

We propose a novel neutron interferometry setup to explore the potential existence of mirror neutrons, a candidate for dark matter. Our work demonstrates that if mirror neutrons exist, neutrons will acquire an observable geometric phase due to mixing with these mirror counterparts. This geometric phase, detectable through our interferometric setup, could serve as a direct probe for the presence of mirror matter particles. Additionally, this investigation could shed light on unresolved issues in particle physics, such as the neutron lifetime puzzle. We discuss the setup's versatility and limitations, showing its capability to explore a wide range of parameters in neutron interferometry and potentially uncover new physics., Comment: 5 pages, 5 figures

The superconducting diode effect, reminiscent of the unidirectional charge transport in semiconductor diodes, is characterized by a nonreciprocal, dissipationless flow of Cooper pairs. This remarkable phenomenon arises from the interplay between symmetry constraints and the inherent quantum behavior of superconductors. Here, we explore the geometric control of the diode effect in a kinked nanostrip Josephson junction based on a two-dimensional electron gas (2DEGs) with Rashba spin-orbit interaction. We provide a comprehensive analysis of the diode effect as a function of the kink angle and the out-of-plane magnetic field. Our analysis reveals a rich phase diagram, showcasing a geometry and field-controlled diode effect. The phase diagram also reveals the presence of an anomalous Josephson effect related to the emergence of trivial zero-energy Andreev bound states, which can evolve into Majorana bound states. Our findings indicate that the exceptional synergy between geometric control of the diode effect and topological phases can be effectively leveraged to design and optimize superconducting devices with tailored transport properties., Comment: 10 pages, 6 figures

We prove that cycles, wheels and block graphs have sequentially Cohen-Macaulay binomial edge ideals. Moreover, we provide a construction of new families of sequentially Cohen-Macaulay graphs by cones., Comment: In this version we have made a substantial correction of the Introduction. We also improved the overall notation. Moreover, to improve the readability and comprehension, we added Example 2.4, 3.2, 4.3, 4.4 and Remark 4.2

In this paper, we present OliVier a new Public Key Exchange cryptosystem that is based on a multivariate quadratic polynomial system: Oil & Vinegar polynomials together with fully quadratic ones. We describe its designing process, usage, complexity

We demonstrate that the well-known $(k\uparrow, -k\downarrow)$ Bardeen-Cooper-Schrieffer interaction, when considered in real space, is equivalent to an infinite-range Penson-Kolb pairing mechanism coexisting with an attractive Hubbard term. Driven by this discovery and aiming at exploring the conduction properties, we investigate the dynamics of fermionic particles confined in a ring-shaped lattice. We assume that fermions are simultaneously influenced by the pairing interaction and by an Aharonov-Bohm electromagnetic phase, which is incorporated into the model in a highly non-trivial manner. Remarkably, the aforementioned model shows Richardson integrability for both integer and half-integer values of the applied magnetic flux $\Phi/\Phi_0$, thus permitting the exact solution of a genuine many-body problem. We discuss the ground state properties of both two-particle and many-particle systems, drawing comparisons with results from the attractive Hubbard model. Our approach combines exact diagonalization, density matrix renormalization group techniques, and numerical solution of the Richardson equations. This comprehensive analysis allows us to study various key metrics, including the system's conductivity as a function of the interaction strength. In this way, the BCS-BEC transition is investigated in a continuous manner, thus permitting to shed light on fundamental aspects of superconducting pairing. Our findings can be experimentally tested in a condensed matter context or, with greater level of control, using atomtronics platforms., Comment: 21 pages, 9 figures; Updated version enhanced with comprehensive new appendices, minor changes and corrections of residual typos

In this paper, we analyze the algebraic invariants for two classes of multivariate quadratic systems: systems made by OV quadratic polynomials and systems made by both OV polynomials and fully quadratic ones. For such systems, we explicitly compute the Hilbert series, and we give bounds on the degree of regularity, solving degree and first fall degree that are useful in cryptographic applications.

We present a detailed study concerning a new physics scenario involving four fermion operators of the Nambu-Jona-Lasinio type characterized by a strong-coupling ultraviolet fixed point where composite particles are formed as bound states of elementary fermions at the scale $\Lambda ={\cal O}(\text{TeV})$. After implementing the model in the Universal FeynRules Output format, we focus on the phenomenology of the scalar leptoquarks at the LHC and the High-Luminosity option. Leptoquark particles have undergone extensive scrutiny in the literature and experimental searches, primarily relying on pair production and, more recently, incorporating single, t-channel, and lepton-induced processes. This study marks, for the first time, the examination of these production modes at varying jet multiplicities. Novel mechanisms emerge, enhancing the total production cross-section, especially for leptoquarks couplings to higher fermion generations. A global strategy is devised to capture all final state particles produced in association with leptoquarks or originating from their decay, which we termed ``exclusive'', in an analogy to the nomenclature used in nuclear reactions. The assessment of the significance in current and future LHC runs, focusing on the case of leptoquark coupling to a muon - $\textit{c}$ quark pair, reveals superior sensitivity compared to ongoing searches. Given this heightened discovery potential, we advocate the incorporation of exclusive leptoquark searches in future investigations at the LHC.

In this paper, by using a combinatorial approach, we establish a new upper bound for the F-threshold $c^\mm(\mm)$ of determinantal rings generated by maximal minors. We prove that $c^\mm(\mm)$ coincides with the $a$-invariant in the case of $3\times n$ and $4\times n$ matrices and we conjecture such equality holds for all matrices., Comment: 18 pages

We classify path polyominoes which are level and pseudo-Gorenstein. Moreover, we compute all level and pseudo-Gorenstein simple thin polyominoes with rank less than or equal to 10. We also compute the regularity of the pseudo-Gorenstein simple thin polyominoes in relation to their rank.

Deep learning approaches for jet tagging in high-energy physics are characterized as black boxes that process a large amount of information from which it is difficult to extract key distinctive observables. In this proceeding, we present an alternative to deep learning approaches, Boost Invariant Polynomials, which enables direct analysis of simple analytic expressions representing the most important features in a given task. Further, we show how this approach provides an extremely low dimensional classifier with a minimum set of features representing %effective discriminating physically relevant observables and how it consequently speeds up the algorithm execution, with relatively close performance to the algorithm using the full information.

A tight binding supercell approach is used for the calculation of the electronic structure of the (111) LaAlO$_3$/SrTiO$_3$ interface. The confinement potential at the interface is evaluated solving a discrete Poisson equation by means of an iterative method. In addition to the effect of the confinement, local Hubbard electron-electron terms are included at mean-field level within a fully self-consistent procedure. The calculation carefully describes how the two-dimensional electron gas arises from the quantum confinement of electrons near the interface due to band bending potential. The resulting electronic sub-bands and Fermi surfaces show full agreement with the electronic structure determined by angle-resolved photoelectron spectroscopy experiments. In particular, it is analyzed how the effect of local Hubbard interactions changes the density distribution over the layers from the interface to the bulk. Interestingly, the two-dimensional electron gas at interface is not depleted by local Hubbard interactions which indeed induce an enhancement of the electron density between the first layers and the bulk., Comment: 14 pages, 9 figures

We investigate the robustness of topological superconductors under the perturbing influence of a finite charge current. To this aim, we introduce a modified Kitaev Hamiltonian parametrically dependent on the quasiparticle momentum induced by the current. Using different quantifiers of the topological phase, such as the Majorana polarization and the edge state quantum conditional mutual information, we prove the existence of a finite critical value of the quasiparticle momentum below which edge modes and topological superconductivity survive. We also discuss how a finite current breaks time reversal symmetry and changes the topological class in the Altland-Zirnbauer classification scheme compared to the case of isolated systems. Our findings provide a nontrivial example of the interplay between topology and the nonequilibrium physics of open quantum systems, a relation of crucial importance in the quest to a viable topological quantum electronics., Comment: 8 pages, 3 figures, regular paper

We introduce a real-space version of the Bardeen-Cooper-Schrieffer interaction allowing the investigation of the non-trivial interplay between many-body physics and particles confinement on a quantum graph. When the two-body problem is considered, we find that the two-particle wavefunction is solution of an integro-differential Schr\"{o}dinger equation. The solution of the two-body eigenproblem shows the presence of a two-particle bound state whose stability is enhanced in quantum graphs with peculiar network topology. We demonstrate that the enhancement effect is robust against many-body effects, which can be studied by means of the Richardson exact solution of the many-body problem. These findings suggest that the effective pairing interaction can be enhanced in quantum graphs with peculiar connectivity. Experimental evidences in Josephson junctions arrays are also discussed in connection with the microscopic mechanism described in the present work., Comment: 15 pages, 9 figures

We investigate the topological properties of a Josephson junction obtained by constraining a two-dimensional electron gas at oxide interface to form a quasi-1D conductor. We reveal an anomalous critical current behaviour with a magnetic field applied perpendicular to the Rashba spin-orbit one. We relate the observed critical current enhancement at small magnetic fields with a non-trivial topology, accompanied by Majorana bound states (MBSs) pinned at the edges of the superconducting leads. Signatures of MBSs also include a sawtooth profile in the current-phase relation. Our findings allow to recognize fingerprints of topological superconductivity in non-centrosymmetric materials and confined systems with Rashba spin-orbit interaction, and to explain recent experimental observations for which a microscopic description is still lacking., Comment: 10 pages, 8 figures, paper

We study the properties of the rook complex $\mathcal{R}$ of a polyomino $\mathcal{P}$ seen as independence complex of a graph $G$, and the associated Stanley--Reisner ideal $I_\mathcal{R}$. In particular, we characterize the polyominoes $\mathcal{P}$ having a pure rook complex, and the ones whose Stanley--Reisner ideal has linear resolution. Furthermore, we prove that for a class of polyominoes the Castelnuovo-Mumford regularity of $I_\mathcal{R}$ coincides with the induced matching number of $G$.

The production of heavy mass resonances has been widely studied theoretically and experimentally. Several extensions of the standard model (SM) of particle physics, naturally give rise to a new resonance, with neutral electric charge, commonly referred to as the $\textrm{Z}^{\prime}$ boson. The nature, mass, couplings, and associated quantum numbers of this hypothetical particle are yet to be determined. We present a feasibility study on the production of a vector like $\textrm{Z}^{\prime}$ boson at the LHC, with preferential couplings to third generation fermions, considering proton-proton collisions at $\sqrt{s} = 13$ $\mathrm{TeV}$ and 14 TeV. We work under two simplified phenomenological frameworks where the $\mathrm{Z}^{\prime}$ masses and couplings to the SM particles are free parameters, and consider final states of the $\textrm{Z}^{\prime}$ decaying to a pair of $\mathrm{b}$ quarks. The analysis is performed using machine learning techniques in order to maximize the experimental sensitivity. The proposed search methodology can be a key mode for discovery, complementary to the existing search strategies considered in literature, and extends the LHC sensitivity to the $\mathrm{Z}^{\prime}$ parameter space., Comment: 13 pages, 15 figures

Squashed entanglement and its universal upper bound, the quantum conditional mutual information, are faithful measures of bipartite quantum correlations defined in terms of multipartitions. As such, they are sensitive to the fine-grain structure of quantum systems. Building on this observation, we introduce the concept of quantum conditional mutual information between the edges of quantum many-body systems. We show that this quantity characterizes unambiguously one-dimensional topological insulators and superconductors, being equal to Bell-state entanglement in the former and to half Bell-state entanglement in the latter, mirroring the different statistics of the edge modes in the two systems. The edge-to-edge quantum conditional mutual information is robust in the presence of disorder or local perturbations, converges exponentially with the system size to a quantized topological invariant, even in the presence of interactions, and vanishes in the trivial phase. We thus conjecture that it coincides with the edge-to-edge squashed entanglement in the entire ground-state phase diagram of symmetry-protected topological systems, and we provide some analytical evidence supporting the claim. By comparing them with the entanglement negativity, we collect further indications that the quantum conditional mutual information and the squashed entanglement provide a very accurate characterization of nonlocal correlation patterns in one-dimensional quantum matter., Comment: 13 pages, 8 figures, revised and expanded version

Converting charge current into spin current is one of the main mechanisms exploited in spintronics. One prominent example is the Edelstein effect, namely the generation of a magnetization in response to an external electric field, which can be realized in systems with lack of inversion symmetry. If a system has electrons with an orbital angular momentum character, an orbital magnetization can be generated by the applied electric field giving rise to the so-called orbital Edelstein effect. Oxide heterostructures are the ideal platform for these effects due to the strong spin-orbit coupling and the lack of inversion symmetries. Beyond a gate-tunable spin Edelstein effect, we predict an orbital Edelstein effect an order of magnitude larger then the spin one at the (111) LaAlO$_3$/SrTiO$_3$ interface. We model the material as a bilayer of $t_{2g}$ orbitals using a tight-binding approach, while transport properties are obtained in the Boltzmann approach. We give an effective model at low filling which explains the non-trivial behaviour of the Edelstein response, showing that the hybridization between the electronic bands crucially impacts the Edelstein susceptibility., Comment: 12 pages, 7 figures

Measurements indicating that planar networks of superconductive islands connected by Josephson junctions display long range quantum coherence are reported. The networks consist of superconducting islands connected by Josephson junctions and have a tree-like topological structure containing no loops. Enhancements of superconductive gap over specific branches of the networks and sharp increases of pair currents are the main signatures of the coherent states and, in order to unambiguously attribute the observed effects to branches being embedded in the networks, comparisons with geometrically equivalent, but isolated, counterparts are reported. Tuning the Josephson coupling energy by an external magnetic field generates increases of the Josephson currents, along the above mentioned specific branches, which follow a functional dependence typical of phase transitions. Results are presented for double comb and star geometry networks and in both cases the observed effects provide positive quantitative evidence of the predictions of existing theoretical models.

We present the theoretical prediction of a gate tunable anomalous Hall effect (AHE) in an oxide interface as a hallmark of spin-orbit coupling. The observed AHE at low-temperatures in the presence of an external magnetic field emerges from a complex structure of the Berry curvature of the electrons on the Fermi surface and strongly depends on the orbital character of the occupied bands. A detailed picture of the results comes from a multiband low-energy model with a generalized Rashba interaction that supports characteristic out-of-plane spin and orbital textures. We discuss strategies for optimizing the intrinsic AHE in (111) SrTiO$_3$ heterostructure interfaces., Comment: 16 pages, 11 figures, submitted

We present a conjecture about the reduced Hilbert series of the coordinate ring of a simple polyomino in terms of particular arrangements of non-attacking rooks that can be placed on the polyomino. By using a computational approach, we prove that the above conjecture holds for all simple polyominoes up to rank $11$. In addition, we prove that the conjecture holds true for the class of parallelogram polyominoes, by looking at those as simple planar distributive lattices. Finally, we give a combinatorial interpretation of the Gorensteinnes of parallelogram polyominoes.

We describe the simplicial complex $\Delta$ such that the initial ideal of $J_G$ is the Stanley-Reisner ideal of $\Delta$. By $\Delta$ we show that if $J_G$ is $(S_2)$ then $G$ is accessible. We also characterize all accessible blocks with whiskers of cycle rank 3 and we define a new infinite class of accessible blocks with whiskers for any cycle rank. Finally, by using a computational approach, we show that the graphs with at most 12 vertices whose binomial edge ideal is Cohen-Macaulay are all and only the accessible ones., Comment: In this new version we added the case n=12 in Theorem 5.1

We study the transport properties of a hybrid junction made of a ferromagnetic lead in electrical connection with the helical edge modes of a two-dimensional topological insulator. In this system, the time reversal symmetry, which characterizes the ballistic edge modes of the topological insulator, is explicitly broken inside the ferromagnetic region. This conflict situation generates unusual transport phenomena at the interface which are the manifestation of the interplay between the spin polarization of the injected current and the spin-momentum locking mechanism operating inside the topological insulator. We show that the spin polarized current originated in the ferromagnetic region is asymmetrically divided in spatially separated branch currents sustained by edge channels with different helicity inside the topological insulator. The above findings provide the working principle of a topological current divider in which the relative intensity of the branch currents is determined by the polarization of the incoming current. We discuss the relevance of this effect in spintronics where, for instance, it offers an alternative way to measure the current polarization generated by a ferromagnetic electrode., Comment: 11 pages, 5 figures

A generalization of the de Gennes-Alexander micronetworks theory is presented. In this framework, the phase transition of synthetic networks of superconducting islands is described by means of a Ginzburg-Landau approach adapted to the case of granular systems. The general implications of the theory are carefully explained. As a specific example, we demonstrate that star networks support the exponential localization of the order parameter accompanied by an enhancement of the critical temperature of the system. These findings contribute to clarify the physics of the phase transitions in synthetic networks of Josephson-coupled superconducting islands., Comment: 8 pages, 6 figures

Let P be a simple thin polyomino, roughly speaking a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert series $h(t)/(1-t)^d$ of K[P] by proving that $h(t)$ is the rook polynomial of P. As an application, we characterize the Gorenstein simple thin polyominoes.

We study the topological phase transitions of a Kitaev chain in the presence of geometric frustration caused by the addition of a single long-range hopping. The latter condition defines a legged-ring geometry (Kitaev tie) lacking of translational invariance. In order to study the topological properties of the system, we generalize the transfer matrix approach through which the emergence of Majorana modes is studied. We find that geometric frustration gives rise to a topological phase diagram in which non-trivial phases alternate with trivial ones at varying the range of the extra hopping and the chemical potential. Frustration effects are also studied in a translational invariant model consisting of multiple-ties. In the latter system, the translational invariance permits to use the topological bulk invariant to determine the phase diagram and bulk-edge correspondence is recovered. It has been demonstrated that geometric frustration effects persist even when translational invariance is restored. These findings are relevant in studying the topological phases of looped ballistic conductors., Comment: 9 pages, 9 figures

In this work, we provide a necessary and sufficient condition on a polyomino ideal for having the set of inner 2-minors as degree reverse lexicographic Gr\"obner basis, due to combinatorial properties of the polyomino itself. Moreover, we prove that when the latter holds the ideal coincides with the lattice ideal associated to the polyomino, that is the ideal is prime. As an application, we describe two new infinite families of prime polyominoes., Comment: arXiv admin note: text overlap with arXiv:1907.08438

A new high order accurate staggered semi-implicit space-time discontinuous Galerkin (DG) method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions. The staggered DG scheme defines the discrete pressure on the primal triangular mesh, while the discrete velocity is defined on a staggered edge-based dual quadrilateral mesh. In this paper, a new pair of equal-order-interpolation velocity-pressure finite elements is proposed. On the primary triangular mesh (the pressure elements) the basis functions are piecewise polynomials of degree $N$ and are allowed to jump on the boundaries of each triangle. On the dual mesh instead (the velocity elements), the basis functions consist in the union of piecewise polynomials of degree $N$ on the two subtriangles that compose each quadrilateral and are allowed to jump only on the dual element boundaries, while they are continuous inside. In other words, the basis functions on the dual mesh are built by continuous finite elements on the subtriangles. This choice allows the construction of an efficient, quadrature-free and memory saving algorithm. In our coupled space-time pressure correction formulation for the incompressible Navier-Stokes equations, arbitrary high order of accuracy in time is achieved through the use of time-dependent test and basis functions, in combination with simple and efficient Picard iterations. Several numerical tests on classical benchmarks confirm that the proposed method outperforms existing staggered semi-implicit space-time DG schemes, not only from a computer memory point of view, but also concerning the computational time., Comment: 42 pages, 22 figures. Submitted to "Communications on Applied Mathematics and Computation"

A new high order accurate semi-implicit space-time Discontinuous Galerkin method on staggered grids, for the simulation of viscous incompressible flows on two-dimensional domains is presented. The designed scheme is of the Arbitrary Lagrangian Eulerian type, which is suitable to work on fixed as well as on moving meshes. In our space-time formulation, by expressing the numerical solution in terms of piecewise space-time polynomials, an arbitrary high order of accuracy in time is achieved through a simple and efficient method of Picard iterations. For the dual mesh, the basis functions consist in the union of continuous piecewise polynomials on the two subtriangles within the quadrilaterals: this allows the construction of a quadrature-free scheme, resulting in a very efficient algorithm. Some numerical examples confirm that the proposed method outperforms existing ones., Comment: 4 pages, 2 figures. To be published in the AIP Conference Proceedings of ICNAAM 2019

We study the coordinate ring of an $L$-convex polyomino, determine its regularity in terms of the maximal number of rooks that can be placed in the polyomino. We also characterize the Gorenstein $L$-convex polyominoes and those which are Gorenstein on the punctured spectrum, and compute the Cohen--Macaulay type of any $L$-convex polyomino in terms of the maximal rectangles covering it.