arXiv subjects

Jorge Cayao

Publications and source records attributed to Jorge Cayao.

At least 37 records · Page 2Linked to original sources

arXiv2025

Anomalous proximity effect under Andreev and Majorana bound states

We theoretically study the anomalous proximity effect in a ballistic normal metal/diffusive normal metal/superconductor junction based on Rashba semiconductor nanowire model. The system hosts two distinct phases: a trivial helical phase with zero-energy Andreev Bound States and a topological phase with Majorana Bound States. We analyze the local density of states and induced pair correlations at the edge of the normal metal region. We investigate their behavior under scalar onsite disorder and changing the Superconductor and diffusive regions lengths in the trivial helical and topological phases. We find that both phases exhibit a zero-energy peak in the local density of states and spin-triplet pair correlations in the clean limit, which we attribute primarily to odd-frequency spin-triplet pairs. Disorder rapidly splits the zero-energy peak in the trivial helical phase regardless of the lengths of the superconductor and diffusive normal regions. The zero-energy peak in the topological phase show similar fragility when the superconductor region is short. However, for long superconductor regions, the zero-energy peak in the topological phase remain robust against disorder. In contrast, spin-singlet correlations are suppressed near zero energy in both phases. Our results highlight that the robustness of the zero-energy peak against scalar disorder, contingent on the Superconductor region length, serves as a key indicator distinguishing trivial Andreev bound states from topological Majorana bound states.

cond-mat.supr-con↗

arXiv2025

Josephson diode effect with Andreev and Majorana bound states

Superconductor-semiconductor hybrids are useful for realizing the Josephson diode effect, where nonreciprocity in the supercurrents occurs due to the interplay of the Josephson effect and applied magnetic fields. These junctions can host Andreev and Majorana states with the same ingredients, though their interplay with the Josephson diode effect is unclear. In this work, we consider short Josephson junctions based on superconductor-semiconductor systems under homogeneous Zeeman fields and investigate the Josephson diode effect in the presence of Andreev and Majorana states. Under generic conditions, the Zeeman field component parallel to the spin-orbit axis promotes an asymmetric low-energy spectrum as a function of the superconducting phase, which persists in the trivial and topological phases hosting Andreev and Majorana bound states, respectively. Interestingly, this asymmetry creates supercurrents that are not odd functions of the phase difference, leading to a nonreciprocal behaviour and the Josephson diode effect. We show that the Josephson diode effect is particularly promoted under the presence of both zero-energy Andreev and Majorana bound states, revealing that Josephson diodes can be realized in the trivial and topological phases of superconductor-semiconductor hybrids. We then demonstrate that the Zeeman field evolution of the diode's efficiencies can map the topological phase transition and the formation of Majorana bound states via an oscillatory behavior that becomes more visible in long superconductors. While Josephson diodes generally exist in the trivial and topological phases of Josephson junctions, we discover that in the tunneling regime only a Josephson diode effect in the topological phase remains due to the finite contribution of Majorana bound states. Our findings clarify the Josephson diode effect and aid in realizing Majorana-only Josephson diodes.

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arXiv2025

Odd-frequency Pairing in Josephson Junctions Coupled by Magnetic Textures

Josephson junctions coupled through magnetic textures provide a controllable platform for odd-frequency superconductivity and Majorana physics. Within a tight-binding Green function framework, induced pair correlations and spectral properties are analyzed under various magnetic and geometric conditions. When the junction is in the topologically trivial regime, even-frequency singlet pairing is dominant, whereas the topological phase is characterized by the coexistence of Majorana bound states and robust odd-frequency equal-spin triplet pairing at the interface edges. The odd-frequency polarized triplets reveal a divergent $1/ω$ behavior when the Majorana states are decoupled, which is intrinsically connected to their self-conjugation property. The zero-frequency divergence evolves into shifted resonances and linear low-frequency behavior once hybridization occurs. A nonmagnetic interruption in the texture separates the topological superconductor into two topological segments and generates additional inner Majorana modes. When the nonmagnetic barrier is comparable to the inner Majorana states localization length, they hybridize and modify their associated odd-frequency triplet pairing, while the outer edge modes preserve their self-conjugated nature. Tuning the superconducting phase difference further controls the onset of the topological regime and the stability of localized Majorana states. The results highlight the central role of odd-frequency triplet correlations as a probe of topological superconductivity in magnetically engineered Josephson junctions.

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arXiv2025

Superconducting phenomena in systems with unconventional magnets

In this work we review the recent advances on superconducting phenomena in junctions formed by superconductors and unconventional magnets. Conventional magnets, such as ferromagnets and antiferromagnets, are characterized by broken time-reversal symmetry but only ferromagnets produce a finite net magnetization due to parallel spin alignment and spin-split bands in momentum. Very recently, a new type of magnets has been reported and here we refer to them as unconventional magnets because they exhibit special properties of both ferromagnets and antiferromagnets: they exhibit zero net magnetization (like antiferromagnets) and a nonrelativistic spin splitting of energy bands (like ferromagnets), both leading to anisotropic spin-polarized Fermi surfaces. An interesting property of unconventional magnets is that their magnetic order can be even or odd with respect to momentum, where $d$-wave altermagnets and $p$-wave magnets are the most representative examples. In this regard, $d$-wave altermagnets and $p$-wave magnets are seen as counterparts in magnetism of the unconventional $d$- and $p$-wave superconducting states, respectively. While the impact of conventional magnetism on superconductivity has been largely studied, the combination of unconventional magnets and superconductivity has only lately attracted considerably attention. This work provides a comprehensive review of the recent progress on the interplay between superconductivity and unconventional magnets. In particular, we focus on the fundamental emerging superconducting phenomena and also discuss the potential implications towards quantum applications.

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arXiv2025

The Josephson effect in Fibonacci superconductors

We theoretically investigate the Josephson effect between two proximized Fibonacci quasicrystals. A quasiperiodic modulation of the chemical potential on a superconducting substrate induces topological gaps and edge modes with energies above the superconducting gap. We reveal that these edge modes develop superconducting correlations which significantly impact the Josephson current, and we term them Fibonacci-Andreev bound states. Notably, the contribution from these edge modes can be controlled by the Fibonacci sequence arrangement, known as phason angle, and can dominate the Josephson effect over the conventional subgap Andreev bound states in short junctions. The interplay between the Josephson effect and nontrivial edge modes in quasiperiodic systems presents new opportunities for exploring exotic superconducting phenomena in quasicrystals.

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arXiv2025

Odd-frequency pairing due to Majorana and trivial Andreev bound states

Majorana and trivial Andreev bound states are predicted to appear in superconductor-semiconductor hybrid systems, but their identification is still a challenging task. Here we consider superconducting junctions with Rashba spin-orbit coupling and explore the signatures of Majorana and trivial Andreev bound states in the emergent superconducting correlations when the systems are subjected to an external Zeeman field. We first show that robust zero-energy Andreev bound states naturally appear due to confinement and helicity when the normal sector of the junction becomes helical. These Andreev states can evolve into Majorana states, developing alike oscillations around zero energy as a function of Zeeman field. Unlike Majorana states located at both ends, helical Andreev states are located at the interface. We then demonstrate that the emergent superconducting correlations are locally composed of even-frequency spin-singlet even-parity and odd-frequency spin-triplet even-parity pair amplitudes, which coexist due to the interplay of spin-orbit coupling, Zeeman field, and spatial translation invariance breaking. In the helical regime, trivial Andreev states enhance odd-frequency spin-triplet pairing, which decays in the superconductor and has a homogeneous long-range profile in the normal region. At zero frequency, however, odd-frequency spin-triplet pairing vanishes in the helical regime. In the topological phase, Majorana states enhance odd-frequency spin-triplet pairing, producing a long-range homogeneous leakage into the normal region. Interestingly, we discover that when Majorana states are truly zero-energy modes, odd-frequency pairing develops a divergent low-frequency profile, which we interpret as the unambiguous self-conjugated Majorana signature. Our results help understand Majorana and trivial Andreev states from a superconducting correlations perspective in Majorana devices.

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arXiv2025

Non-Hermitian minimal Kitaev chains

Starting from a double quantum dot realization of a minimal Kitaev chain, we demonstrate that non-Hermicity stabilizes the so-called poor man's Majorana zero modes in a region of parameter space that is much broader than in the Hermitian regime. In particular, we consider the simplest non-Hermitian mechanism which naturally appears due to coupling to normal reservoirs and is commonly present in all transport experiments. Specifically, such couplings induce exceptional points which connect stable and highly tunable zero energy real lines that are well separated from the quasicontinuum. Such zero-energy lines reflect spectral degeneracies protected by topology and represent the non-Hermitian generalization of the Hermitian poor mans Majorana modes occurring at single points in parameter space. Our findings pave the way for realizing robust non-Hermitian effects by combining unconventional superconductors and non-Hermitian topology.

cond-mat.mes-hall↗

arXiv2025

Orientation-dependent transport in junctions formed by $d$-wave altermagnets and $d$-wave superconductors

We investigate de Gennes-Saint-James states and Josephson effect in hybrid junctions based on $d$-wave altermagnet and $d$-wave superconductor. Even though these states are associated to long junctions, we find that the $d_{x^{2}-y^{2}}$-altermagnet in a normal metal/altermagnet/$d$-wave superconductor junction forms de Gennes-Saint-James states in a short junction due to an enhanced mismatch between electron and hole wave vectors. As a result, the zero-bias conductance peak vanishes and pronounced resonance spikes emerge in the subgap conductance spectra. By contrast, the $d_{xy}$-altermagnet only features de Gennes-Saint-James states in the long junction. Moreover, the well-known features such as V-shape conductance for $d_{x^2-y^2}$ pairings and zero-biased conductance peak for $d_{xy}$ pairings are not affected by the strength of $d_{xy}$-altermagnetism in the short junction. We also study the Josephson current-phase relation $I(φ)$ of $d$-wave superconductor/altermagnet/$d$-wave superconductor hybrids, where $φ$ is the macroscopic phase difference between two $d$-wave superconductors. In symmetric junctions, we obtain anomalous current phase relation such as a $0$-$π$ transition by changing either the orientation or the magnitude of the altermagnetic order parameter and dominant higher Josephson harmonics. Interestingly, we find the first-order Josephson coupling in an asymmetric $d_{x^{2}-y^{2}}$-superconductor/altermagnet/$d_{xy}$-superconductor junction when the symmetry of altermagnetic order parameter is neither $d_{x^{2}-y^{2}}$- nor $d_{xy}$-wave. We present the symmetry analysis and conclude that the anomalous orientation-dependent current-phase relations are ascribed to the peculiar feature of the altermagnetic spin-splitting field.

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arXiv2025

Classification of pair symmetries in superconductors with unconventional magnetism

We consider unconventional magnets with proximity-induced superconductivity and investigate the emergence of superconducting correlations by carrying out a full classification of allowed Cooper pair symmetries. In particular, we focus on $d$-wave altermagnets and $p$-wave magnets under the influence of spin-singlet and spin-triplet superconductivity induced by proximity effect. Under generic conditions, we find that unconventional magnets not only drive a spin-singlet to spin-triplet conversion but also they transfer their parity symmetry that induces superconducting correlations with higher angular momentum. For instance, a conventional spin-singlet $s$-wave superconductor with $d$-wave altermagnetism is able to host odd-frequency mixed spin-triplet $d$-wave superconducting pair amplitudes, while when combining with $p$-wave magnetism the emerging superconducting pairing acquires an even-frequency mixed spin-triplet $p$-wave symmetry. We further demonstrate that unconventional magnetism produces even more exotic superconducting correlations in spin-singlet $d$-wave superconductors, where odd-frequency mixed spin-triplet $g$-wave and even-frequency mixed spin-triplet $f$-wave pair symmetries are possible in altermagnets and $p$-wave magnets, respectively. We also discuss how these ideas generalize to spin-triplet $p$-wave superconductors and also show how our results can be applied to unconventional magnets with higher angular momentum, such as with $f$-, $g$-, and $i$-wave symmetries. Our results can help understand the emergent superconducting correlations due to the interplay of unconventional magnetism and superconductivity.

cond-mat.supr-con↗

arXiv2025

Josephson effect and odd-frequency pairing in superconducting junctions with unconventional magnets

We consider Josephson junctions formed by coupling two conventional superconductors via an unconventional magnet and investigate the formation of Andreev bound states, their impact on the Josephson effect, and the emergent superconducting correlations. We focus on unconventional magnets known as $d$-wave altermagnets and $p$-wave magnets. We find that the Andreev bound states in $d$-wave altermagnet and $p_y$-wave magnet Josephson junctions strongly depend on the transverse momentum, with a spin splitting and low-energy minima as a function of the superconducting phase difference $φ$. In contrast, the Andreev bound states for $p_{x}$-wave magnets are insensitive to the transverse momentum. We show that the Andreev bound states can be probed by the local density of states in the middle of the junction, which also reveals that $d_{x^{2}-y^{2}}$- and $p$-wave magnet junctions are prone to host zero energy peaks. While the zero-energy peak in $d_{x^{2}-y^{2}}$-wave altermagnet junctions tends to oscillate with the magnetic order, it remains robust in $p$-wave magnet junctions. We also demonstrate that the critical currents in $d$-wave altermagnet Josephson junctions exhibit an oscillatory decay with the increase of the magnetic order, while the oscillations are absent in $p$-wave magnet junctions albeit the currents exhibit a slow decay. Furthermore, we also demonstrate that the interplay of the Josephson effect and unconventional magnetic order of $d$-wave altermagnets and $p$-wave magnets originates from odd-frequency spin-triplet $s$-wave superconducting correlations that are otherwise absent. Our results can serve as a guide to pursue the new functionality of Josephson junctions based on unconventional magnets.

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arXiv2025

Collective modes in Fulde-Ferrell-Larkin-Ovchinnikov superconductors: The role of long-range Coulomb interaction and signatures in density response

We theoretically investigate collective excitations in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states of Pauli-limited superconducting films. When the long-range Coulomb interaction is absent, excitation spectra consist of two gapless and three gapped modes. The gapless modes are the Nambu-Goldstone modes associated with the spontaneous breaking of the ${\rm U}(1)$ symmetry and the translational symmetry. The gapped modes include the Higgs mode and the twofold degenerate modes that cause the oscillation of the domain width and grayness of FFLO nodal planes. We find that the long-range Coulomb interaction only gaps out the gapless phase mode through the Anderson-Higgs mechanism, while the other modes remain unaffected. Furthermore, the field evolution of the dispersion of the gapless elastic mode, the Nambu-Goldstone mode associated with the translational symmetry breaking, is associated with that of the bandwidth of the mid-gap Andreev bound states. We demonstrate that the signature of the elastic mode can be detected by measuring the density-density response function.

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arXiv2025

Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors

Majorana zero modes have been shown to be the simplest quasiparticles exhibiting pure odd-frequency pairing, an effect that has so far been theoretically established in the static regime. In this work, we investigate the formation of Majorana modes and odd-frequency pairing in $p$-wave spin-polarized superconductors under a time-dependent drive. We first show that the driven system hosts multiple Majorana modes emerging at zero and $π$, whose formation can be controlled by an appropriate tuning of the drive frequency and chemical potential, in agreement with previous studies. Then we explore the induced pair correlations and find that odd-frequency spin-polarized $s$-wave pairing is broadly induced, acquiring large values in the presence of Majorana modes. We discover that, while odd-frequency pairing is proportional to $\sim1/ω$ in the presence of Majorana zero modes, it is proportional to $\sim 1/(ω-π\hbar/T)$ in the presence of Majorana $π$ modes, where $T$ is the periodicity of the drive. Furthermore, we find that the amount of odd-frequency pairing becomes larger when multiple Majorana modes appear but the overall divergent profile as a function of frequency remains. We also show that the divergent odd-frequency pairing is robust against scalar disorder. Notably, we establish a spectral bulk-boundary correspondence between the amount of boundary odd-$ω$ pairing and the bulk topological invariants in driven chiral systems, which we show to be protected by chiral symmetry and is thus robust against disorder. Our work thus paves the way for understanding the emergent pair correlations in driven topological superconductors

cond-mat.supr-con↗

arXiv2024

Non-Hermitian multiterminal phase-biased Josephson junctions

We study non-Hermitian Josephson junctions formed by multiple superconductors and discover the emergence of exceptional points entirely determined by the interplay of the distinct superconducting phases and non-Hermiticity due to normal reservoirs. In particular, in Josephson junctions with three and four superconductors, we find stable lines and surfaces of exceptional points protected by non-Hermitian topology and highly tuneable by the superconducting phases. We also discover that, in Josephson junctions formed by laterally coupled superconductors, exceptional points can result from hybridized Andreev bound states and lead to the enhancement of supercurrents controlled by dissipation. Our work unveils the potential of multi-terminal Josephson junctions for realizing higher dimensional topological non-Hermitian superconducting phenomena.

cond-mat.mes-hall↗

arXiv2024

Entanglement measures of Majorana bound states

Majorana bound states emerge in topological superconductors as zero-energy edge states exhibiting spatial nonlocality. Despite the enormous advances, the detection of Majorana bound states is still challenging mainly because topologically trivial Andreev bound states produce similar signatures. In this work we consider a topological superconductor with Majorana bound states coupled to quantum dots and investigate the dynamics of their quantum correlations with the aim to explore their entanglement properties. In particular, we characterize entanglement by using concurrence and discord, which are also complemented by the entanglement dynamics and return probability. We find that Majorana bound states at truly zero energy can transform an initially entangled system into its classical state, while they can create maximally entangled states at a finite energy overlap. Interestingly, we show that the system can generate a maximally entangled state between MBSs and a quantum dot by simply controlling the Majorana nonlocality. We demonstrate that these results hold in the scenarios when the initial state is either maximally entangled or separable, albeit in the latter maximally entangled states are achieved in the long time dynamics. Furthermore, we contrast our findings with those produced by a regular fermion and obtain very distinct entanglement signatures. Our work offers an alternative approach to characterize Majorana bound states, which can be also useful towards their utilization for quantum information tasks.

cond-mat.mes-hall↗

arXiv2024

Non-Hermitian phase-biased Josephson junctions

We study non-Hermitian Josephson junctions formed by superconductors with a finite phase difference under non-Hermiticity, which naturally appears due to coupling to normal reservoirs. Depending on the structure of non-Hermiticity, captured in terms of retarded self-energies, the low-energy spectrum hosts topologically stable exceptional points either at zero or finite real energies as a function of the superconducting phase difference. Interestingly, the corresponding phase-biased supercurrents may acquire divergent profiles at such exceptional points. This instance is a natural and unique non-Hermitian effect that signals a possible way to enhance the sensitivity of Josephson junctions. Our work opens a way for realizing unique non-Hermitian phenomena due to the interplay between non-Hermitian topology and the Josephson effect.

cond-mat.supr-con↗

arXiv2024

Identifying trivial and Majorana zero-energy modes using the Majorana polarization

In this work we consider superconductor-semiconductor hybrids containing both trivial and Majorana zero modes and explore their signatures in the Majorana polarization. In particular, we consider trivial zero energy states due to confinement and disorder, which seem to be very likely experimental scenarios. We show that the Majorana polarization is able to characterize the topological phase transition as well as the emergence of Majorana zero modes even when trivial zero-energy states proliferate. Notably, the Majorana polarization inherits direct information about spatial correlations which are then the key for distinguishing Majorana and trivial zero-modes. We demonstrate the utility of the Majorana polarization in normal-superconductor junctions and superconductor-normal-superconductor Josephson junctions. Our results support the interpretation of the Majorana polarization as a real space topological indicator.

cond-mat.mes-hall↗

arXiv2024

Emergent pair symmetries in systems with poor man's Majorana modes

Few-site Kitaev chains are promising for realizing Majorana zero modes without topological protection but fully nonlocal, which are known as poor man's Majorana modes. While several signatures have already been reported both theoretically and experimentally, it still remains unknown what is the nature of superconducting correlations in the presence of poor man's Majorana modes. In this work, we study few-site Kitaev chains and demonstrate that they host pair correlations with distinct symmetries, entirely determined by the underlying quantum numbers. In particular, we find that a two-site Kitaev chain hosts local (odd-frequency) and nonlocal (odd- and even-frequency) pair correlations, both spin polarized and highly tunable by the system parameters. Interestingly, the odd-frequency pair correlations exhibit a divergent behaviour around zero frequency when the nonlocal $p$-wave pair potential and electron tunneling are of the same order, an effect that can be controlled by the onsite energies. Since a divergent odd-frequency pairing is directly connected to the intrinsic spatial nonlocality of Majorana zero modes in topological superconductors, the divergent odd-frequency pairing here reflects the intrinsic Majorana nonlocality of poor man's Majorana modes but without any relation to topology. Our findings could help understanding the emergent pair correlations in few-site Kitaev chains.

cond-mat.mes-hall↗

arXiv2024

Non-Hermitian zero-energy pinning of Andreev and Majorana bound states in superconductor-semiconductor systems

The emergence of Majorana bound states in finite length superconductor-semiconductor hybrid systems has been predicted to occur in the form of oscillatory energy levels with parity crossings around zero energy. Each zero-energy crossing is expected to produce a quantized zero-bias conductance peak but several studies have reported conductance peaks pinned at zero energy over a range of Zeeman fields, whose origin, however, is not clear. In this work we consider superconducting systems with spin-orbit coupling under a Zeeman field and demonstrate that non-Hermitian effects, due to coupling to ferromagnet leads, induce zero-energy pinning of Majorana and trivial Andreev bound states. We find that this zero-energy pinning effect occurs due to the formation of non-Hermitian spectral degeneracies known as exceptional points, whose emergence can be controlled by the interplay of non-Hermiticity, the applied Zeeman field, and chemical potentials. Moreover, depending on the non-Hermitian spatial profile, we find that non-Hermiticity changes the single point Hermitian topological phase transition into a flattened zero energy line bounded by exceptional points from multiple low energy levels. This seemingly innocent change notably enables a gap closing well below the Hermitian topological phase transition, which can be in principle simpler to achieve. Furthermore, we reveal that the energy gap separating Majorana and trivial Andreev bound states from the quasicontinuum remains robust for the values that give rise to the zero-energy pinning effect. While reasonable values of non-Hermiticity can be indeed beneficial, very strong non-Hermitian effects can be detrimental as it might destroy superconductivity. Our findings can be therefore useful for understanding the zero-energy pinning of trivial and topological states in Majorana devices.

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