Superconductivity is commonly destroyed by a magnetic field due to orbital or Zeeman-induced pair breaking. Surprisingly, the spin-valley locking in a two-dimensional superconductor with spin-orbit interaction makes the superconducting state resilient to large magnetic fields. We investigate the spectral properties of such an Ising superconductor in a magnetic field taking into account disorder. The interplay of the in-plane magnetic field and the Ising spin-orbit coupling leads to noncollinear effective fields. We find that the emerging singlet and triplet pairing correlations manifest themselves in the occurrence of "mirage" gaps: at (high) energies of the order of the spin-orbit coupling strength, a gap-like structure in the spectrum emerges that mirrors the main superconducting gap. We show that these mirage gaps are signatures of the equal-spin triplet finite-energy pairing correlations and due to their odd parity are sensitive to intervalley scattering.
We study the electronic structure of magnetic and non-magnetic quantum corrals embedded in s-wave superconductors. We demonstrate that a quantum mirage of an impurity bound state peak can be projected from the occupied into the empty focus of a non-magnetic quantum corral via the excitation of the corral's eigenmodes. We observe an enhanced coupling between magnetic impurities inside the corral, which can be varied through oscillations in the corral's impurity potential. Finally, we discuss the form of eigenmodes in magnetic quantum corrals.
We investigate the local density of states and the order parameter structure inside an elliptic quantum corral on surfaces of isotropic and anisotropic superconductors. The Bogoliubov-de Gennes equations are solved in the presence of non-magnetic and magnetic impurities. We observe and discuss a variety of mirage and anti-mirage phenomena, which specifically reflect the nature of the superconducting pairing state.
We illustrate the importance of many-body effects in the Fourier transformed local density of states (FT-LDOS) of d-wave superconductors from a model of electrons coupled to an Einstein mode with energy Omega_0. For bias energies significantly larger than Omega_0 the quasiparticles have short lifetimes due to this coupling, and the FT-LDOS is featureless if the electron-impurity scattering is treated within the Born approximation. In this regime it is important to include boson exchange for the electron-impurity scattering which provides a `step down' in energy for the electrons and allows for…
An in-plane magnetic field applied to an Ising superconductor converts spin-singlet Cooper pairs to spin-triplet ones. In this work, we study a Josephson junction formed by two Ising superconductors that are proximitized by ferromagnetic layers. This leads to highly tunable spin-triplet pairing correlations which allow to modulate the charge and spin supercurrents through the in-plane magnetic exchange fields. For a junction with a nonmagnetic barrier, the charge current is switchable by changing the relative alignment of the in-plane exchange fields, and a $π$-state can be realized. Furthermo…
Superconductivity and magnetism are generally incompatible because of the opposing requirement on electron spin alignment. When combined, they produce a multitude of fascinating phenomena, including unconventional superconductivity and topological superconductivity. The emergence of two-dimensional (2D)layered superconducting and magnetic materials that can form nanoscale junctions with atomically sharp interfaces presents an ideal laboratory to explore new phenomena from coexisting superconductivity and magnetic ordering. Here we report tunneling spectroscopy under an in-plane magnetic field …
In the theory of dilute magnetic impurities in superconductors, the effect of all impurity spin-components is expressed via a single magnetic scattering rate $Γ_\mathrm{m}$. In a more realistic setting, magnetic impurities are anisotropic. In this case, the spatial randomness of three spin-components of impurities gives rise to generally different scattering rates $Γ_i$ ($i=1,2,3$). We explore the effects of anisotropic magnetic impurities on the in-plane critical field in 2D superconductors. We discuss singlet, triplet and parity-mixed order parameters allowed in systems without the inversion…
We study the Andreev levels, supercurrent and tunnelling conductance in a clean Ising superconductor (ISC)/half metal (HM)/Ising superconductor (ISC) Josephson junction with spin-active interfaces using Bogoliubov-de Gennes equations. We theoretically demonstrate the effect of spin mixing, spin flipping processes and spin-orbit coupling (SOC) of the ISC on Andreev Bound States (ABS) spectra, current phase relation (CPR) and tunnelling conductance in transparent and opaque barrier limit. We witness an additional splitting of the Andreev levels due to SOC of the ISC and $0 - π$ transition for di…
The few-layer transition metal dichalcogenides (TMDs) have been recently suggested as a platform for controlled unconventional superconductivity. We study the manifestations of unconventional triplet pairing in the density of states of a disordered TMD based monolayer. The conventional singlet pairing attraction is assumed to be the dominant pairing interaction. We map the phase diagrams of disordered Ising superconductors in the plane of temperature and the in-plane magnetic field. The latter suppresses singlet and promote triplet correlations. The triplet order parameters of a trivial (non-t…
Recently it was discovered that superconductivity in transition metal dichalcogenides (TMDs) is strongly affected by an out-of-plane spin-orbit coupling (SOC). In addition, new techniques of fabricating 2d ferromagnets on van der Waals materials are rapidly emerging. Combining these breakthroughs, we propose a realization of nodal topological superconductivity in TMDs by fabricating nanostructured ferromagnets with an in-plane magnetization on the top surface. The proposed procedure does not require application of external magnetic fields and applies to monolayer and multilayer (bulk) systems.…
Ising superconductivity has been recently discovered in 2D transition metal dichalcogenides. We report that such superconductors have unusual optical properties controlled by the in-plane Zeeman field. First, we find several optical gaps visible as peaks of the conductivity and the Raman susceptibility. Moreover, we find that the Ising spin splitting in the spectrum of Bogolubov quasiparticles enables strong population inversion generated by the time-dependent Zeeman field. Ultimately this leads to the possibility of the superconducting laser with magnonic pumping which can be realized in the …
Majorana Kramers pairs emerged on surfaces of time-reversal-invariant topological crystalline superconductors show the Ising anisotropy to an applied magnetic field. We clarify that crystalline symmetry uniquely determines the direction of the Majorana Ising spin for given irreducible representations of pair potential, deriving constraints to topological invariants. Besides, necessary conditions for nontrivial topological invariants protected by the n-fold rotational symmetry are shown.
In a two-dimensional noncentrosymmetric Ising superconductor in the fluctuating regime under the action of a uniform external electromagnetic field there emerge two contributions to the photogalvanic effect due to the trigonal warping of the valleys. The first contribution stems from the current of the electron gas in its normal state, while the second contribution is of Aslamazov-Larkin nature: it originates from the presence of fluctuating Cooper pairs when the ambient temperature approaches (from above) the temperature of superconducting transition in the sample. The way to lift the valley …
Recently, it was experimentally realized that 2D superconducting transition metal dichalcogenides (TMD) such as gated MoS$_2$ and monolayer NbSe$_2$ have in-plane upper critical magnetic fields much higher than the Pauli limit. This is due to the so-called Ising spin-orbit coupling (SOC) of TMD which pins the electron spins along the out-of-plane directions and protects the Cooper pairs from in-plane magnetic fields. However, many TMD materials with extremely large Ising SOC, in the order of a few hundred meV, are not superconducting. In this work, we show that TMD materials can induce strong …
We theoretically study the effect of localized magnetic impurities on two-dimensional topological superconductor (TSC). We show that the local density of states (LDOS) can be tuned by the effective exchange field $m$, the chemical potential $μ$ of TSC, and the distance $Δr$ as well as relative spin angle $α$ between two impurities. The changes in $Δr$ between two impurities alter the interference and result in significant modifications to the bonding and antibonding states. Furthermore, the bound-state spin LDOS induced by single and double magnetic impurity scattering, the quantum corrals, an…
This paper demonstrates that the results of a Monte Carlo simulation of a diluted 2D Ising antiferromagnetic system corresponds with the phase diagram for non conventional superconductors. An energy gap of this system is defined. We also find a strange phenomenon that when the lattice size of simulation increased the crystal structure becomes more like quasi crystal at the low temperature.
We show that an in-plane Zeeman field applied to non-centrosymmetric Ising superconductors converts singlet $s$-wave Cooper pairs to equal-spin triplet $if$ pairs, leading to an enhancement of the critical transition line beyond expected from Ising spin-orbit coupling. Singlet to triplet conversion relates to a phase transformation due to spin rotation by the Zeeman field and has a geometric origin. The discussion is especially relevant, but not limited to monolayer transition metal dichalcogenides.
Finite-length one-dimensional topological superconductor wires host localized Majorana zero modes at their ends. In realistic models, these appear only after a topological quantum critical point is crossed by external tuning of parameters. Thus, there is a universal finite-size scaling, governed by the critical point, that dictates the evolution of the energy of the Majorana modes near the transition. We first describe this scaling, then apply it in detail to an explicit synthetic topological superconductor model. Our work not only connects Ising quantum criticality with realistic nanowires in…
Van der Waals materials like NbSe$_2$ or TaS$_2$ have demonstrated Ising superconductivity down to atomically thin layers. Due to the spin-orbit coupling, these superconductors have the in-plane upper critical magnetic field far beyond the Pauli limit. We theoretically demonstrate that, twisted bilayer Ising superconductors separated by a ferromagnetic buffer layer can naturally host chiral topological superconductivity with Chern numbers, which can be realized in heterostructures like $\mathrm{NbSe_2/CrCl_3/NbSe_2}$. Under appropriate experimental conditions the topological superconducting ga…
We study the superconducting instability in disordered non-centrosymmetric monolayers with intrinsic Ising spin-orbit coupling (SOC) subjected to an in-plane Zeeman magnetic field. The pairing interaction contains the channels allowed by crystal symmetry, such that in general, the pairing state is a mixture of singlet and triplet Cooper pairs. The joint action of SOC and Zeeman field selects a specific in-plane $\mathbf{d}$-vector triplet component to couple with the singlets, which gains robustness against disorder through the coupling. The out-of-plane $\mathbf{d}$-vector component, that in …
Ising spin-orbital coupling is usually easy to identify in the Ising superconductors via an in-plane critical field enhancement, but we show that the Ising spin-orbital coupling also manifests in the vortex physics for perpendicular magnetic fields. By self-consistently solving the Bogoliubov-de Gennes equations of a model Hamiltonian built on the honeycomb lattice with the Ising spin-orbital coupling pertinent to the transition metal dichalcogenides, we numerically investigate the local breaking of the spin and sublattice degeneracies in the presence of a perpendicular magnetic field. It is r…
We theoretically study the electronic transport through a ferromagnet-Ising superconductor junction. A tight-binding Hamiltonian describing the Ising superconductor is presented. Then by combing the non-equilibrium Green's function method, the expressions of Andreev reflection coefficient and conductance are obtained. A strong magnetoanisotropic spin-triplet Andreev reflection is shown, and the magnetoanisotropic period is $π$ instead of $2π$ as in the conventional magnetoanisotropic system. We demonstrate a significant increase of the spin-triplet Andreev reflection for the single-band Ising …
The metallic ground state in two-dimensional (2D) superconductors has attracted much attention but is still under intense scrutiny. Especially, the measurements in ultralow temperature region are challenging for 2D superconductors due to the sensitivity to external perturbations. In this work, the resistance saturation induced by external noise, named as "extrinsic anomalous metallic state", is observed in 2D transition metal dichalcogenide (TMD) superconductor 4Ha-TaSe2 nanodevices. However, with further decreasing temperature, credible evidence of intrinsic anomalous metallic state is obtain…
An external magnetic field is needed to drive a nanowire in proximity to an s-wave superconductor into a topological regime which supports Majorana end states. However, a magnetic field generally suppresses the proximity superconducting gap induced on the nanowire. In recent experiments using InSb nanowires coupled to Al, the induced proximity gap vanishes at magnetic fields B~1T. This results in a small superconducting gap on the wire and a narrow topological regime which is proportional to the strength of the magnetic field. In this work, we show that by placing nanowires in proximity to rec…
Distinguishing nodal and nonunitary superconductivity in quasiparticle interference of an Ising superconductor with Rashba spin-orbit coupling: an example of NbSe$_2$
We study a mechanism for superconductivity in quasi-one-dimensional materials with Ising anisotropy. In an isolated chain Ising anisotropy opens a spin gap; if inter-chain coupling is sufficiently weak, single particle hopping is suppressed and the physics of coupled chains is controlled by a competition between pair hopping and exchange interaction. Spin density wave and triplet superconductivity phases are found separated by a first order phase transition. For particular parameter values a second order transition described by SO(4) symmetry is found.
We theoretically study the Josephson current in Ising superconductor-half-metal-Ising superconductor junctions. By solving the Bogoliubov-de Gennes equations, the Josephson currents contributed by the discrete Andreev levels and the continuous spectrum are obtained. For very short junctions, because the direct tunneling of the Cooper pair dominates the Josephson current, the current-phase difference relation is independent of the magnetization direction, which is the same as the conventional superconductor-ferromagnet-superconductor junctions. On the other hand, when the length of the half-met…
In monolayer transition metal dichalcogenides (TMDs), electrons in opposite $K$ valleys are subject to opposite effective Zeeman fields, which are referred to as Ising spin-orbit coupling (SOC) fields. The Ising SOC, originated from in-plane mirror symmetry breaking pins the electron spins in out-of-plane directions, and results in the newly discovered Ising superconducting states with strongly enhanced upper critical fields. In this work, we show that the Ising SOC generates equal-spin triplet Cooper pairs with spin polarization in the in-plane directions. Importantly, the spin-triplet Cooper…
A topological insulator (TI) interfaced with an s-wave superconductor has been predicted to host an unusual form of superconductivity known as topological superconductivity (TSC). Molecular beam epitaxy (MBE) has been the primary approach in the scalable synthesis of the TI/superconductor heterostructures. Although the growth of epitaxial TI films on s-wave superconductors has been achieved, it remains an outstanding challenge for synthesizing atomically thin TI/superconductor heterostructures, which are critical for engineering the TSC phase. Here, we used MBE to grow Bi2Se3 films with the co…
Motivated by recent neutron scattering experiments, we study the ordering of spins in the iron-based superconductors La(O_{1-x}F_x)FeAs, assuming them in proximity to a Mott insulator in the phase diagram. The ground state of the parent system with x = 0 is a spin density wave with ordering wave vector Q = (0, π) or (π, 0). Upon raising the temperature, we find the system to restore SU(2) symmetry, while an Ising symmetry remains broken, explaining the experimentally observed lattice distortion to a monoclinic crystal structure. Upon further temperature increase, the spins finally disorder at …
We here examine the relation between odd-frequency spin-triple even-parity (OTE) Cooper pairs and anomalous surface magnetic response in time-reversal invariant (TRI) spin-triplet superfluids and superconductors. The spin susceptibility generally consists of two contributions: Even-frequency odd-parity pair amplitudes and odd-frequency even-parity pair amplitudes. The OTE pair amplitudes are absent in the bulk region, but ubiquitously exist in the surface and interface region as Andreev bound states. We here clarify that additional discrete symmetries, originating from the internal symmetry an…
Recently, Ising superconductors which possess in-plane upper critical fields much larger than the Pauli limit field are under intense experimental study. Many monolayer or few layer transition metal dichalcogenides are shown to be Ising superconductors. In this work, we show that in a wide range of experimentally accessible regimes where the in-plane magnetic field is higher than the Pauli limit field but lower than $H_{c2}$, a 2H-structure monolayer NbSe$_2$ or simiarly TaS$_2$ becomes a nodal topological superconductor. The bulk nodal points appear on the $Γ- M$ lines of the Brillouin zone w…
Systems that simultaneously exhibit superconductivity and spin-orbit coupling are predicted to provide a route toward topological superconductivity and unconventional electron pairing, driving significant contemporary interest in these materials. Monolayer transition-metal dichalcogenide (TMD) superconductors in particular lack inversion symmetry, enforcing a spin-triplet component of the superconducting wavefunction that increases with the strength of spin-orbit coupling. In this work, we present an experimental and theoretical study of two intrinsic TMD superconductors with large spin-orbit …
Non-equilibrium studies of two-dimensional (2D) superconductors (SCs) with Ising spin-orbit coupling are prerequisite for their successful application to equilibrium spin-triplet Cooper pairs and, potentially, Majorana fermions. By taking advantage of the recent discoveries of 2D SCs and their compatibility with any other materials, we fabricate here non-local magnon devices to examine how such 2D Ising superconductivity affects the conversion efficiency of magnon spin to quasiparticle charge in superconducting flakes of 2H-NbSe2 transferred onto ferrimagnetic insulating Y3Fe5O12. Comparison w…
Hybrid Ising superconductor-ferromagnetic insulator heterostructures provide a unique opportunity to explore the interplay between proximity-induced magnetism, spin-orbit coupling and superconductivity. Here we use a combination of first-principles calculations of NbSe$_{2}$/CrBr$_{3}$ heterostructures and an analytical theory of Ising superconductivity to analyze the existing experiments and provide a complete explanation of highly nontrivial and largely counterintuitive effects: an increase in the magnitude of the superconducting gap accompanied by the broadening of the tunneling peaks; hyst…
