P-wave Superconductor Research Articles

Shot noise and tunneling magnetoresistance in silicene-based ferromagnet/antiferromagnet/ferromagnet/p-wave superconductor junctions

We investigate the transport properties in silicene-based ferromagnet/antiferromagnet/ferromagnet/p-wave superconductor junctions within the Blonder–Tinkham–Klapwijk formalism by solving the Dirac–Bogoliubov-de Gennes equation. The results show that the conductance and the shot noise strongly depend on the p-wave superconducting pair potentials and the magnetic configurations of the ferromagnetic regions. The simultaneous diminution of the conductance and enhancement of the shot noise can be achieved with the increase of the antiferromagnetic exchange field strength. The conductance and the shot noise can be effectively modulated by the external electric field and the ferromagnetic exchange field strength, and the corresponding switch effects are also achieved. The tunneling magnetoresistance (TMR) outside the subgap energy interval is always larger than the one obtained in the subgap energy interval. When the antiferromagnetic exchange field strength is large enough, a larger TMR can be obtained by tuning the external electric field.

Synthesis of Samarium Nitride Thin Films on Magnesium Oxide (001) Substrates Using Molecular Beam Epitaxy

Rare-earth nitrides are an exciting family of materials with a wide variety of properties desirable for new physics and applications in spintronics and superconducting devices. Among them, samarium nitride is an interesting compound reported to have ferromagnetic behavior coupled with the potential existence of p-wave superconductivity. Synthesis of high-quality thin films is essential in order to manifest these behaviors and understand the impact that vacancies, structural distortions, and doping can have on these properties. In this study, we report the synthesis of samarium nitride monocrystalline thin films on magnesium oxide (001) substrates with a chromium nitride capping layer using molecular beam epitaxy (MBE). We observed a high-quality monocrystalline SmN film with matching orientation to the substrate, then optimized the growth temperature. Despite the initial 2 nm of growth showing formation of a potential samarium oxide layer, the subsequent layers showed high-quality SmN, with semiconducting behavior revealed by an increase in resistivity with decreasing temperature. These promising results highlight the importance of studying diverse heteroepitaxial schemes and open the door for integration of rare-earth nitrides and transition metal nitrides for future spintronic devices.

Lifshitz transitions and Weyl semimetals from a topological superconductor with supercurrent flow

A current flowing through a superconductor induces a spatial modulation in its superconducting order parameter, characterized by a wave vector Q related to the total momentum of a Cooper pair. Here we investigate this phenomenon in a p-wave topological superconductor, described by a one-dimensional Kitaev model. We demonstrate that, by treating Q as an extra synthetic dimension, the current-carrying nonequilibrium steady state can be mapped into the ground state of a half-filled two-dimensional Weyl semimetal, whose Fermi surface exhibits Lifshitz transitions when varying the model parameters. Specifically, the transition from type-I to type-II Weyl phases corresponds to the emergence of a gapless p-wave superconductor, where Cooper pairs coexist with unpaired electrons and holes. Such a transition is signaled by the appearance of a sharp cusp in the Q-dependence of the supercurrent, at a critical value Q* that is robust to variations of the chemical potential μ. We determine the maximal current that the system can sustain in the topological phase, and we discuss possible implementations. Published by the American Physical Society 2024

Theory of Majorana Zero Modes in Unconventional Superconductors

Abstract Majorana fermions are spin-1/2 neutral particles that are their own antiparticles; they were initially predicted by Ettore Majorana in particle physics but their observation still remains elusive. The concept of Majorana fermions has been borrowed by condensed matter physics, where, unlike particle physics, Majorana fermions emerge as zero-energy quasiparticles that can be engineered by combining electrons and holes and have therefore been called Majorana zero modes. In this review, we provide a pedagogical explanation of the basic properties of Majorana zero modes in unconventional superconductors and their consequences in experimental observables, putting a special emphasis on the initial theoretical discoveries. In particular, we first show that Majorana zero modes are self-conjugated and emerge as a special type of zero-energy surface Andreev bound states at the boundary of unconventional superconductors. We then explore Majorana zero modes in 1D spin-polarized p-wave superconductors, where we address the formation of topological superconductivity and the physical realization in superconductor–semiconductor hybrids. In this part we highlight that Majorana quasiparticles appear as zero-energy edge states, exhibiting charge neutrality, spin-polarization, and spatial nonlocality as unique properties that can already be seen from their energies and wavefunctions. Next, we discuss the analytically obtained Green’s functions of p-wave superconductors and demonstrate that the emergence of Majorana zero modes is always accompanied by the formation of odd-frequency spin-triplet pairing as a unique result of the self-conjugate nature of Majorana zero modes. We finally address the signatures of Majorana zero modes in tunneling spectroscopy, including the anomalous proximity effect, and the phase-biased Josephson effect.

Unconventional superconductivity in Cr-based compound Pr3Cr10−xN11

We report results of specific heat and muon spin relaxation (μSR) measurements on a polycrystalline sample of Pr3Cr10−xN11, which shows superconducting state below Tc = 5.25 K, a large upper critical field Hc2 ~ 20 T and a residual Sommerfeld coefficient γ0. The field dependence of γ0(H) resembles γ of the U-based superconductors UTe2 and URhGe at low temperatures. The temperature-dependent superfluid density measured by transverse-field μSR experiments is consistent with a p-wave pairing symmetry. ZF-μSR experiment suggests a time-reversal symmetry broken superconducting transition, and temperature-independent spin fluctuations at low temperatures are revealed by LF-μSR experiments. These results indicate that Pr3Cr10−xN11 is a candidate of p-wave superconductor which breaks time-reversal symmetry.

Superconducting state generated dynamically from distant pair source and drain

It has been well established that the origin of p-wave superconductivity is the balance between pair creation and annihilation, described by the spin-less fermionic Kitaev chain model. In this work, we study the dynamics of a composite system where the pair source and drain are spatially separated by a long distance. We show that this non-Hermitian system possesses a high-order exceptional point (EP) when only a source or drain is considered. The EP dynamics provide a clear picture: A pair source can fully fill the system with pairs, while a drain can completely empty the system. When the two coexist simultaneously, the dynamics depend on the distance and the relative phase between the pair creation and annihilation terms. Analytical analysis and numerical simulation results show that the superconducting state can be dynamically established at the resonant pair source and drain: from an initial empty state to a stationary state with the maximal pair order parameter. It provides an alternative way of understanding the mechanism of the nonequilibrium superconducting state.

Spin and charge fluctuation induced pairing in ABCB tetralayer graphene

Motivated by the recent experimental realization of ABCB stacked tetralayer graphene [Wirth , ], we study correlated phenomena in moiré-less graphene tetralayers for realistic interaction profiles using an orbital resolved random phase approximation approach. We demonstrate that magnetic fluctuations originating from local interactions are crucial close to the van Hove singularities on the electron- and hole-doped side promoting layer selective ferrimagnetic states. Spin fluctuations around these magnetic states enhance unconventional spin-triplet, valley-singlet superconductivity with f-wave symmetry due to intervalley scattering. Charge fluctuations arising from long range Coulomb interactions promote doubly degenerate p-wave superconductivity close to the van Hove singularities. At the conduction band edge of ABCB graphene, we find that both spin and charge fluctuations drive f-wave superconductivity. Our analysis suggests a strong competition between superconducting states emerging from long- and short-ranged Coulomb interactions and thus stresses the importance of microscopically derived interaction profiles to make reliable predictions for the origin of superconductivity in graphene-based heterostructures. Published by the American Physical Society 2024

Intrinsic surface p-wave superconductivity in layered AuSn4

The search for topological superconductivity (TSC) is currently an exciting pursuit, since non-trivial topological superconducting phases could host exotic Majorana modes. However, the difficulty in fabricating proximity-induced TSC heterostructures, the sensitivity to disorder and stringent topological restrictions of intrinsic TSC place serious limitations and formidable challenges on the materials and related applications. Here, we report a new type of intrinsic TSC, namely intrinsic surface topological superconductivity (IS-TSC) and demonstrate it in layered AuSn4 with Tc of 2.4 K. Different in-plane and out-of-plane upper critical fields reflect a two-dimensional (2D) character of superconductivity. The two-fold symmetric angular dependences of both magneto-transport and the zero-bias conductance peak (ZBCP) in point-contact spectroscopy (PCS) in the superconducting regime indicate an unconventional pairing symmetry of AuSn4. The superconducting gap and surface multi-bands with Rashba splitting at the Fermi level (EF), in conjunction with first-principle calculations, strongly suggest that 2D unconventional SC in AuSn4 originates from the mixture of p-wave surface and s-wave bulk contributions, which leads to a two-fold symmetric superconductivity. Our results provide an exciting paradigm to realize TSC via Rashba effect on surface superconducting bands in layered materials.

Spin-polarized Majorana zero modes in proximitized superconducting penta-silicene nanoribbons

We theoretically propose penta-silicene nanoribbons (p-SiNRs) with induced p-wave superconductivity as a platform for the emergence of spin-polarized Majorana zero-modes (MZMs). The model explicitly considers the key ingredients of well-known Majorana hybrid nanowire setups: Rashba spin-orbit coupling, magnetic field perpendicular to the nanoribbon plane, and first nearest neighbor hopping with p-wave superconducting pairing. The energy spectrum of the system, as a function of chemical potential, reveals the existence of MZMs with a well-defined spin orientation localized at the opposite ends of both the top and bottom chains of the p-SiNR, associated with well-localized and nonoverlapping wave function profiles. Well-established experimental techniques enable the fabrication of highly ordered p-SiNRs, complemented by a thin lead film on top, responsible for inducing p-wave superconductivity through proximity effect. Moreover, the emergence of MZMs with explicit opposite spin orientations for some set of model parameters opens a new avenue for exploring quantum computing operations, which accounts for both MZMs and spin properties, as well as for new MZMs probe devices based on spin-polarized electronic transport mechanisms.

Current redistribution model of anomalous resistance behaviour in superconductor-topological insulator heterostructures

Superconductor-topological insulator (TI) heterostructures are interesting due to induced p-wave superconductivity on the TI surface states near the interface. Transport studies carried out in this work on the TI surface of superconductor-TI (NbN-Bi1.95Sb0.05Se3) heterostructures have revealed anomalous resistance upturn and downturn at millimetre length scales away from the interface. Magnetotransport measurements have indicated that the anomaly is caused due to the superconducting transition of the NbN layer. The strength of the jump in resistance has been found to be strongest at the edges and the sign of the jump found to be opposite along opposite edges. Such resistance upturns and downturns have been previously reported in literature, wherein the upturns have been attributed to the antagonistic ground states of p-wave Cooper pairing and the spin-polarized TI states, and the downturns attributed to induced long-range proximity effects. However, the possibility of long-range superconducting proximity effect has been ruled out in this study through the observation of similar anomaly in NbN-Au and NbN-Al heterostructures. The present study demonstrates that the anomalies in resistance occur due to current redistribution (CRD) effects at the superconducting transition due to the geometry of the heterostructure. Results obtained from finite element analysis using COMSOL software have validated the proposed CRD model of long-range resistance anomalies in superconductor-TI and superconductor-metal heterostructures.

The mixed-state entanglement in holographic p-wave superconductor model

In this paper, we investigate the mixed-state entanglement in a model of p-wave superconductivity phase transition using holographic methods. We calculate several entanglement measures, including holographic entanglement entropy (HEE), mutual information (MI), and entanglement wedge cross-section (EWCS). Our results show that these measures display critical behavior at the phase transition points, with the EWCS exhibiting opposite temperature behavior compared to the HEE. Furthermore, we explore the behavior of thermodynamics and holographic quantum information at the zeroth-order phase transition point and find that it is opposite to that observed in the first-order phase transition. Additionally, we find that the critical exponents of all entanglement measures are twice those of the condensate. Our findings also suggest that the EWCS is a more sensitive indicator of the critical behavior of phase transitions than the HEE. Lastly, we uncover a universal inequality in the growth rates of EWCS and MI near critical points in thermal phase transitions, such as p-wave and s-wave superconductivity, suggesting that MI captures more information than EWCS when a phase transition first occurs.

Holographic p-Wave Superconductor with Excited States in 4D Einstein–Gauss–Bonnet Gravity

We construct a holographic p-wave superconductor with excited states in the 4D Einstein–Gauss–Bonnet gravity using the Maxwell complex vector field model. In the probe limit, we observe that, the higher curvature correction or the higher excited state can hinder the vector condensate to be formed in the full parameter space, which is different from the holographic s-wave superconductor. Regardless of the choice of the vector mass by selecting the value of m2L2 or m2Leff2, we note that the critical chemical potential becomes evenly spaced for the number of nodes and that the difference of the critical chemical potential between the consecutive states depends on the curvature correction. Moreover, we find that the higher curvature correction or the higher excited state will alter the universal relation of the gap frequency, and the pole and delta function of the conductivity for the excited states can be broadened into the peaks with the finite width as the curvature correction increases.

Spin-projected charge conductance in SNN junctions with noncentrosymmetric superconductors

An SNN-junction in which the superconducting potential is a mixture between s-wave and p-wave potentials is investigated using the Usadel equation equipped with Tanaka-Nazarov boundary conditions. The article provides several ways to distinguish between s + chiral and s + helical p-wave superconductors and a way to determine whether a superconductor has a mixed pair potential. Thus, it is of great importance in the determination of the pair potential of superconductors. It is shown that the different spin sectors satisfy independent equations and can thus be calculated separately even if the d-vector depends on the direction of momentum. This greatly simplifies the equations to be solved. It was found that a difference in conductance for sectors with opposite spins arises if both an s-wave and a p-wave component is present, even in the absence of a magnetic field. The results are confirmed by calculations in the ballistic regime. It is shown that the spin conductance for s + chiral p-wave and s + helical p-wave junctions is qualitatively similar. A setup containing two SN junctions is shown to give a clear difference between the two types of superconductivity.

Spread complexity and topological transitions in the Kitaev chain

A number of recent works have argued that quantum complexity, a well-known concept in computer science that has re-emerged recently in the context of the physics of black holes, may be used as an efficient probe of novel phenomena such as quantum chaos and even quantum phase transitions. In this article, we provide further support for the latter, using a 1-dimensional p-wave superconductor — the Kitaev chain — as a prototype of a system displaying a topological phase transition. The Hamiltonian of the Kitaev chain manifests two gapped phases of matter with fermion parity symmetry; a trivial strongly-coupled phase and a topologically non-trivial, weakly-coupled phase with Majorana zero-modes. We show that Krylov-complexity (or, more precisely, the associated spread-complexity) is able to distinguish between the two and provides a diagnostic of the quantum critical point that separates them. We also comment on some possible ambiguity in the existing literature on the sensitivity of different measures of complexity to topological phase transitions.

Two-dimensional superconductors with intrinsic p-wave pairing or nontrivial band topology

Over the past fifteen years, tremendous efforts have been devoted to realizing topological superconductivity in realistic materials and systems, predominately propelled by their promising application potentials in fault-tolerant quantum information processing. In this article, we attempt to give an overview on some of the main developments in this field, focusing in particular on two-dimensional crystalline superconductors that possess either intrinsic p-wave pairing or nontrivial band topology. We first classify the three different conceptual schemes to achieve topological superconductor (TSC), enabled by real-space superconducting proximity effect, reciprocal-space superconducting proximity effect, and intrinsic TSC. Whereas the first scheme has so far been most extensively explored, the subtle difference between the other two remains to be fully substantiated. We then move on to candidate intrinsic or p-wave superconductors, including Sr2RuO4,UTe2,Pb3Bi, and graphene-based systems. For TSC systems that rely on proximity effects, the emphases are mainly on the coexistence of superconductivity and nontrivial band topology, as exemplified by transition metal dichalcogenides, cobalt pnictides, and stanene, all in monolayer or few-layer regime. The review completes with discussions on the three dominant tuning schemes of strain, gating, and ferroelectricity in acquiring one or both essential ingredients of the TSC, and optimizations of such tuning capabilities may prove to be decisive in our drive towards braiding of Majorana zero modes and demonstration of topological qubits.

What lies beyond the horizon of a holographic p-wave superconductor

We study the planar anti-de Sitter black hole in the p-wave holographic superconductor model. We identify a critical coupling value which determines the type of phase transition. Beyond the horizon, at specific temperatures flat spacetime emerges. Numerical analysis close to these temperatures demonstrates the appearance of a large number of alternating Kasner epochs.

Detecting Majorana Zero Modes via Strong Field Dynamics.

We propose a protocol to detect topological phase transitions of one-dimensional p-wave superconductors from their harmonic emission spectra in strong fields. Specifically, we identify spectral features due to radiating edge modes, which characterize the spectrum and the density of states in the topological phase and are absent in the trivial phase. These features allow us to define a measurable signature, obtained from emission measurements, that unambiguously differentiates between the two phases. Local probing provides insight into the localized and topologically protected nature of the modes. The presented results establish that high-harmonic spectroscopy can be used as an all-optical tool for the detection of Majorana zero modes.

Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires.

In most naturally occurring superconductors, electrons with opposite spins form Cooper pairs. This includes both conventional s-wave superconductors such as aluminium, as well as high-transition-temperature, d-wave superconductors. Materials with intrinsic p-wave superconductivity, hosting Cooper pairs made of equal-spin electrons, have not been conclusively identified, nor synthesized, despite promising progress1-3. Instead, engineered platforms where s-wave superconductors are brought into contact with magnetic materials have shown convincing signatures of equal-spin pairing4-6. Here we directly measure equal-spin pairing between spin-polarized quantum dots. This pairing isproximity-induced from an s-wave superconductor into a semiconducting nanowire with strong spin-orbit interaction. We demonstrate such pairing by showing that breaking a Cooper pair can result in two electrons with equal spin polarization. Our results demonstrate controllable detection of singlet and triplet pairing between the quantum dots. Achieving such triplet pairing in a sequence of quantum dots will be required for realizing an artificial Kitaev chain7-9.

Spin-triplet pairing induced by near-neighbor attraction in the extended Hubbard model for cuprate chain

In quantum materials, the electronic interaction and the electron-phonon coupling are, in general, two essential ingredients, the combined impact of which may drive exotic phases. Recently, an anomalously strong electron-electron attraction, likely mediated by phonons, has been proposed in one-dimensional copper-oxide chain Ba2−xSrxCuO3+δ. Yet, it is unclear how this strong near-neighbor attraction V influences the superconductivity pairing in the system. Here we perform accurate many-body calculations to study the extended Hubbard model with on-site Coulomb repulsion U > 0 and near-neighbor attraction V < 0 that could well describe the cuprate chain and likely other similar transition-metal materials with both strong correlations and lattice effects. We find a rich quantum phase diagram containing an intriguing Tomonaga-Luttinger liquid phase — besides the spin density wave and various phase separation phases — that can host dominant spin-triplet pairing correlations and divergent superconductive susceptibility. Upon doping, the spin-triplet superconducting regime can be further broadened, offering a feasible mechanism to realize p-wave superconductivity in realistic cuprate chains.

Anisotropic superconducting spin transport at magnetic interfaces

We present a theoretical investigation of anisotropic superconducting spin transport at a magnetic interface between a p-wave superconductor and a ferromagnetic insulator. Our formulation describes the ferromagnetic resonance modulations due to spin current generation depending on spin-triplet Cooper pair, including the frequency shift and enhanced Gilbert damping, in a unified manner. We find that the Cooper pair symmetry is detectable from the qualitative behavior of the ferromagnetic resonance modulation. Our theory paves the way toward anisotropic superconducting spintronics.