We consider a moving vortex in a two dimensional superconductor located at a distance $d$ from a metallic overlayer. Starting from the microscopic imaginary time action we integrate out the electronic degrees of freedom to obtain a low energy, long wavelength effective action for the vortex. We focus our attention on the vortex kinetic energy and derive a general expression for the vortex mass. We find that in the limit $d\to \infty$ the Coulomb screening of the density fluctuations, associated with vortex motion, results in a very small vortex mass as has been obtained in earlier studies. In the opposite limit of $d\ll ξ$ where $ξ$ is the coherence length of the superconductor we find that the vortex mass diverges logarithmically with the size of the system as the proximity to the metal makes the screening processes, that usually make the mass small, ineffective. We comment on the relevance of our results to recent experiments which show a dramatic fall in resistance when a metallic gate is placed near a supeconducting film in a magnetic field at low temperature.
We study theoretically the vortex matter structure in low dimensional (LD) systems with superconducting order induced by proximity to a bulk superconductor. We analyze the effects of microscopic coupling mechanisms between the two systems and the effects of possible mismatch in the band structures of these materials on the energy spectrum of vortex-core electrons. The unusual structure of vortex cores is discussed in the context of recent tunneling microscopy/spectroscopy experiments.
The proximity effect in SF structures was examined. It is shown that, due to the oscillations of the induced superconducting order parameter in a ferromagnet, the critical temperature of an SF-bilayer becomes minimal when the thickness of the ferromagnetic layer is close to a quarter of the period of spatial oscillations. It is found that the spontaneous vortex state arisen in the superconductor due to the proximity of the magnetic domain structure of a ferromagnet brings about noticeable magnetoresistive effects.
The structure of a proximity induced vortex core in a two-dimensional (2D) metallic layer covering a superconducting half-space is calculated. We predict formation of a multiple vortex core characterized by two-scale behavior of the local density of states (LDOS). For coherent tunnelling between the 2D layer and the bulk superconductor, the spectrum has two subgap branches while for incoherent tunnelling only one of them remains. The resulting splitting of the zero-bias anomaly and the multiple peak structure in the LDOS should be visible in the tunnelling spectroscopy experiments.
The paradigmatic Mott insulator arises in strongly correlated systems, where strong local repulsion localizes interacting particles in underlying egg-holder-like potential. The corresponding Mott transition reflects delocalization of the charges either by varying parameters of the system and temperature, or by applied current, the latter being referred to as the dynamic Mott transition. Recently, the dynamic Mott transition was experimentally observed on the vortex system trapped by the periodic proximity array and described in terms of non-Hermitian theory of nonequilibrium processes. Here we…
We consider superconductivity nucleation in multiply connected mesoscopic samples such as thin-walled cylinders or rings placed in electrical contact with a ferromagnet. The superconducting critical temperature and order parameter structure are studied on the basis of linearized Usadel equations. We suggest a mechanism of switching between the superconducting states with different vorticities caused by the exchange field and associated with the oscillatory behavior of the Cooper pair wave function in a ferromagnet.
We study the proximity effect in a ferromagnetic nanoparticle having a vortex magnetization pattern. We show that for axisymmetric system consisting of a circular particle and a magnetic vortex situated at the center of it no long range superconducting correlations are induced. It means that induced superconductivity is localized in the small area near the superconducting electrode. However, in the real systems axial symmetry can be broken by either a shift of the magnetic vortex from the origin or geometrical anisotropy of the ferromagnetic particle. In this case a long range proximity effect…
We show that quantum vortex-loop proliferation may be one possible explanation of the super-long-range proximity effect observed in an insulating underdoped cuprate, using the dual theory of quantum vortices. As a test of this scenario, we propose that a dual proximity effect experiment can confirm the superfluid motion of the quantum vortices in the vortex-proliferated insulator and can measure the divergent correlation lengths near the superconductor-insulator transition.
Superconducting vortex loops have so far avoided experimental detection despite being the focus of much theoretical work. We here propose a method of creating controllable vortex loops in the superconducting condensate arising in a normal metal through the proximity effect. We demonstrate both analytically and numerically that superconducting vortex loops emerge when the junction is pierced by a current-carrying insulated wire and give an analytical expression for their radii. The vortex loops can readily be tuned big enough to hit the sample surface, making them directly observable through sc…
We show that in multiband superconductors even small interband proximity effect can lead to a qualitative change in the interaction potential between superconducting vortices by producing long-range intervortex attraction. This type of vortex interaction results in unusual response to low magnetic fields leading to phase separation into domains of a two-component Meissner states and vortex droplets.
In a p-wave Fermi superfluid suffering from the nonmagnetic impurity scatterings, a coefficient of a gradient term becomes divergent upon cooling. Consequences of this divergent rigidity in the stable vortices in the B phase in globally isotropic aerogel are considered where the "impurity scattering" events are brought by the aerogel structure. For a moderately strong "impurity scatterings", the superfluid transition line T_c(P) has a quantum critical point at a low but finite pressure. We find that, with decreasing T_c via the lowering of the pressure, the distance between the half cores comp…
An array of superconducting proximity islands has been shown to be highly tunable by electric and magnetic fields. Indeed, a small change in the electric and magnetic field can tune the system from a vortex Mott insulator to a vortex metal. This transition from localized to a non-localized state can occur as soon as the density of the superconducting vortices matches the density of the pinning sites in a non defective structure. The possibility of further modulation of non-localized superconducting states via enhancement of the superconducting order parameter or modulation of the Josephson pla…
It is shown that the order parameter $Δ$ induced in the normal part of superconductor-normal-superconductor proximity system is modulated in the magnetic field differently from vortices in bulk superconductors. Whereas $Δ$ turns zero at vortex centers, the magnetic structure of these vortices differs from that of Abrikosov's.
Made of a thin non-superconducting metal (N) sandwiched by two superconductors (S), SNS Josephson junctions enable novel quantum functionalities by mixing up the intrinsic electronic properties of N with the superconducting correlations induced from S by proximity. Electronic properties of these devices are governed by Andreev quasiparticles [1] which are absent in conventional SIS junctions whose insulating barrier (I) between the two S electrodes owns no electronic states. Here we focus on the Josephson vortex (JV) motion inside Nb-Cu-Nb proximity junctions subject to electric currents and m…
We consider an isolated vortex in the two-dimensional proximity-induced superconducting state formed at the interface of a three-dimensional strong topological insulator (TI) and an s-wave superconductor (sSC). Prior calculations of the bound states of this system famously revealed a zero-energy state that is its own conjugate, a Majorana fermion bound to the vortex core. We calculate, not the bound states, but the scattering states of this system, and ask how the spin-momentum-locked massless Dirac form of the single-particle Hamiltonian, inherited from the TI surface, affects the cross secti…
The design of artificial vortex pinning landscapes is a major goal towards large scale applications of cuprate superconductors. While disordered nanometric inclusions have shown to modify their vortex phase diagram and to produce enhancements of the critical current1,2, the effect of ordered oxide nanostructures remains essentially unexplored. This is due to the very small nanostructure size imposed by the short coherence length, and to the technological difficulties in the nanofabrication process. Yet, the novel phenomena occurring at oxide interfaces open a wide spectrum of technological opp…
We calculate the effective mass of a single quantized vortex in the BCS superconductor at finite temperature. Using the effective action for a vortex, we arrive at the mass formula as the integral of the spectral function $J(ω)/ω^3$ over frequency. The spectral function is given in terms of the transition elements of the gradient of the Hamiltonian between Bogoliubov-deGennes eigenstates. We show that core-core, and core-extended transitions yield the vortex mass, near T=0, of order of electron mass displaced by the normal core. The extended-extended states contributions are linearly divergent…
Recently, interest in Superconductor (S)-Normal (N) interfaces was renewed by the observation of exotic proximity effects in various systems, including S/semiconductor, S/ferromagnet, and S/topological insulator. In general, the proximity effect is enhanced in transparent weak links where coherent Andreev reflection is possible. Also, it is a common knowledge that the proximity effect is, by definition, is a localized phenomenon that can only be active in each S/N interface region. However, here we show that a three-dimensional (3D) macroscale proximity effect is realized in few-micrometer-thi…
We use local and global magnetometry measurements to study the influence of magnetic domain width w on the domain-induced vortex pinning in superconducting/ferromagnetic bilayers, built of a Nb film and a ferromagnetic Co/Pt multilayer with perpendicular magnetic anisotropy, with an insulating layer to eliminate proximity effect. The quasi-periodic domain patterns with different and systematically adjustable width w, as acquired by a special demagnetization procedure, exert tunable vortex pinning on a superconducting layer. The largest enhancement of vortex pinning, by a factor of more than 10…
The proximity coupled topological insulator / superconductor (TI/SC) bilayer system is a representative system to realize topological superconductivity. In order to better understand this unique state and design devices from the TI/SC bilayer, a comprehensive understanding of the microscopic properties of the bilayer is required. In this work, a microwave Meissner screening study, which exploits a high-precision microwave resonator technique, is conducted on the SmB6/YB6 thin film bilayers as an example TI/SC system. The study reveals spatially dependent electrodynamic screening response of th…
It is shown that the temperature of the resistive transition $T_r$ of a superconducting film can be increased by a thin superconducting or normal overlayer. For instance, deposition of a highly conductive thin overlayer onto a dirty superconducting film can give rise to an "anti-proximity effect" which manifests itself in an initial increase of $T_r(d_2)$ with the overlayer thickness $d_2$ followed by a decrease of $T_r(d_2)$ at larger $d_2$. Such a nonmonotonic thickness dependence of $T_r(d_2)$ results from the interplay of the increase of a net superfluid density mitigating phase fluctuatio…
The vortex dynamics and the specific heat of a type II superconducting system with quasi-periodic geometry is studied theoretically for different values of interaction parameters using the numerical simulation technique, where the vortex-vortex interaction potential is considered in the form of the modified Bessel's function of first kind. The dynamics of the system is analysed by phase space trajectories of the vortex for both high and low values as well as for both high and low mismatch of vortex-vortex and vortex-pinning interaction parameters. The specific heat variation with temperature i…
We have numerically investigated the dynamics of vortices in a clean layered superconductor placed in a perpendicular magnetic field. We describe the energetics using a Ginzburg-Landau free energy functional in the lowest Landau level approximation. The dynamics are determined using the time-dependent Ginzburg-Landau approximation, and thermal fluctuations are incorporated via a Langevin term. The c-axis conductivity at nonzero frequencies, as calculated from the Kubo formalism, shows a strong but not divergent increase as the melting temperature $T_M$ is approached from above, followed by an …
Vortex matter in mesoscopic superconductors is known to be strongly affected by the geometry of the sample. Here we show that in nanoscale superconductors with coherence length comparable to the Fermi wavelength the shape resonances of the order parameter results in an additional contribution to the quantum topological confinement - leading to unconventional vortex configurations. Our Bogoliubov-de Gennes calculations in a square geometry reveal a plethora of asymmetric, giant multi-vortex, and vortex-antivortex structures, stable over a wide range of parameters and which are very different fr…
We show that the intrinsic chiral $d_{x^2-y^2} \pm id_{xy}$-wave superconducting pairing in doped graphene is significantly strengthened in the core region of a doubly quantized s-wave superconducting vortex produced in a graphene-superconductor hybrid structure. The chiral d-wave state is induced by proximity effect, which transfers the center-of-mass angular momentum of the s-wave vortex to the orbital angular momentum of the chiral d-wave Cooper pairs. The proximity effect is enhanced by the circular geometry of the vortex and we find a $[1 + (T-T_{c,J})^2]^{-1}$ temperature dependence for …
Much interest in the superconducting proximity effect in three-dimensional (3D) topological insulators (TIs) has been driven by the potential to induce Majorana bound states at the interface. Most candidate materials for 3D TI, however, are bulk metals, with bulk states at the Fermi level coexisting with well-defined surface states exhibiting spin-momentum locking. In such topological metals, the proximity effect can differ qualitatively from that in TIs. By studying a model topological metal-superconductor (TM-SC) heterostructure within the Bogoliubov-de Gennes formalism, we show that the pai…
Superconductivity and vortex structure on Bi$_{2}$Te$_{3}$/FeTe$_{0.55}$Se$_{0.45}$ heterostructures with different thickness of Bi$_{2}$Te$_{3}$ films
We argue that by inducing superconductivity in graphene via the proximity effect, it is possible to observes the "quantum valley Hall effect". In the presence of magnetic field, supercurrent causes "valley pseudospin" to accumulate at the edges of the superconducting strip. This, and the structure of the superconducting vortex core, provide possibilities to experimentally observe aspects of the "deconfined quantum criticality".
The magnetization process of a superconductor is determined by the potential barrier for vortex nucleation and escape. In multicomponent superconductors, fractional vortices with a winding in the phase of only one of the components can be stable topological solitons that carry a fraction of the flux quantum. While the formation of such objects in the bulk costs logarithmically or linearly divergent energy, these objects were shown to be stable near samples' boundaries in the two-component London model. Therefore, the conventional Bean-Livingston picture of magnetic flux entry does not apply to…
Proximity-induced superconductivity in a 3D topological insulator represents a new avenue for observing zero-energy Majorana fermions inside vortex cores. Relatively small gaps and low transition temperatures of conventional s-wave superconductors put the hard constraints on these experiments. Significantly larger gaps and higher transition temperatures in cuprate superconductors might be an attractive alternative to considerably relax these constraints, but it is not clear whether the proximity effect would be effective in heterostructures involving cuprates and topological insulators. Here, …
We study the superconducting density of states and vortex lattice of single crystals of CaKFe$_4$As$_4$ using a scanning tunneling microscope (STM). This material has a critical temperature of $T_c= 35\,$ K, which is one of the highest among stoichiometric iron based superconductors (FeBSC) and is comparable to $T_c$ found near optimal doping in other FeBSC. Using quasi-particle interference we identify the hole sheets around the zone center and find that two superconducting gaps open in these sheets. The scattering centers are small defects that can be localized in the surface topography and …
We study the energy spectrum of a vortex core in a two-dimensional semiconductor with Rashba spin-orbit interaction and proximity-coupled to a conventional superconductor and a ferromagnetic insulator. We perform self-consistent calculations using the microscopic tight-binding Bogoliubov-de Gennes method on a lattice and confirm the existence of Majorana fermions in the non-trivial topological phase. We also find two different topologically trivial bulk superconducting phases, only differing in the type of vortex core structure they support and separated by a zero-energy excitation. Furthermor…
Pinning interactions between superconducting vortices in Nb and magnetic Ni dots were studied as a function of current and temperature to clarify the nature of pinning mechanisms. A strong current dependence is found for a square array of dots, with a temperature dependent optimum current for the observation of periodic pinning, that decreases with temperature as (1-T/Tc)3/2. This same temperature dependence is found for the critical current at the first matching field with a rectangular array of dots. The analysis of these results allows to narrow the possible pinning mechanisms to a combinat…
After more than a decade, direct observation of the odd frequency triplet pairing state in super- conducting hybrid structures remains elusive. We propose an experimentally feasible setup that can unambiguously reveal the zero energy peak due to proximity-induced equal spin superconducting triplet correlations. We theoretically investigate a two dimensional Josephson junction in the diffu- sive regime. The nanostructure consists of a normal metal sandwiched between two ferromagnetic layers with spiral magnetization patterns. By applying an external magnetic field perpendicular to the junction …
We argue that the low- frequency quantum oscillations observed recently in the vortex state of underdoped ortho II-YBCO have the same origin as in other strongly correlated electronic systems. Superconductivity driven by strong interactions on several Fermi surfaces creates proximity gaps on the other. The gap transferred on a small-sized pocket from larger Fermi surfaces is small. In case of unconventional pairing symmetry the induced gap is proportional to ratio of the oscillations' frequencies for small and large Fermi surfaces. The gap is in inverse proportion to mass enhancement on the la…
Dynamic ordering of driven vortex matter has been investigated in the peak effect regime of both amorphous MoGe films and 2H-NbSe2 crystals by mode locking (ML) and dc transport measurements. ML features allow us to trace how the shear rigidity of driven vortices evolves with the average velocity. Determining the onset of ML resonance in different magnetic fields and/or temperatures, we find that the dynamic ordering frequency (velocity) exhibits a striking divergence in the higher part of the peak effect regime. Interestingly, this phenomenon is accompanied by a pronounced peak of dynamic cri…
Majorana Fermions, strange particles that are their own antiparticles, were predicted in 1937 and have been sought after ever since. In condensed matter they are predicted to exist as vortex core or edge excitations in certain exotic superconductors. These are topological superconductors whose order parameter phase winds non-trivially in momentum space. In recent years, a new and promising route for realizing topological superconductors has opened due to advances in the field of topological insulators. Current proposals are based on semiconductor heterostructures, where spin-orbit coupled band…
Perspectives on Magnetic/Superconductor Hybrid Systems: Long-range Electromagnetic Phenomena Induced by Proximity Effect and Interfacial Spin-orbit Coupling
Institute for Physics of Microstructures, Russian Academy of Sciences（俄罗斯科学院微观物理研究所）；Moscow Institute of Physics and Technology (National Research University)（莫斯科物理技术学院（国立研究型大学））；Institute for Computer Science and Mathematical Modeling, Sechenov First Moscow State Medical University（谢切诺夫第一莫斯科国立医科大学计算机科学与数学建模研究所）；University Bordeaux, LOMA UMR-CNRS 5798（波尔多大学，LOMA CNRS联合研究实验室）
The helical electron states on the surface of topological insulators or elemental Bismuth become unstable toward superconducting pairing formation when coupled to the charge or magnetic fluctuations. The latter gives rise to pairing instability in chiral channels $d_{xy}\pm i d_{x^2-y^2}$, as has been observed recently in epitaxial Bi/Ni bilayer system at relatively high temperature, while the former favors a pairing with zero total angular momentum. Motivated by this observation we study the vortex bound states in these superconducting states. We consider a minimal model describing the superc…
The interplay of time-reversal and $n$-fold rotation symmetries ($n=2,4,6$) is known to bring a new class of topological crystalline insulators (TCIs) having $n$ surface Dirac cones due to surface rotation anomaly. We show that the proximity-induced $s$-wave superconductivity on the surface of these TCIs yields a topological superconducting phase in which two Majorana zero modes are bound to a vortex, and that $n$-fold rotation symmetry ($n=2,4,6$) enriches the topological classification of a superconducting vortex from $\mathbb{Z}_2$ to $\mathbb{Z}_2\times\mathbb{Z}_2$. Using a model of a thr…
We report a study of the basal-plane anisotropy of the superfluid density in underdoped YBa$_{2}$Cu$_{4}$O$_{8}$ (Y124), showing the effects of both the CuO$_{2}$ planes and the fully occupied CuO chains. From small-angle neutron scattering measurements of the vortex lattice, we can infer the superconducting (SC) properties for a temperature ($T$) range $T=$ 1.5 K to $T_{\rm c}$ and magnetic induction $B$ from 0.1 to 6 T. We find that the superfluid density along \textbf{a} has a simple $d$-wave T-dependence. However, along \textbf{b} (the chain direction) the superfluid density falls much mor…
We examine the idea, postulated by Phillips et al., that a finite resistivity in $T \to 0$ limit in disordered granular superconducting (SC) films is explained as a consequence of the absence of phase stiffness in a phase glass (PG) peculiar to granular systems. It is found that a coupling between the nonzero PG order and the ordinary SC fluctuation makes the conductivity divergent. However, an actual drop of resistivity is argued to occur due to another SC glass ordering, induced by the precursory PG fluctuation, corresponding to the vortex-glass transition in a nonzero magnetic field.
Magnetization noncollinearity in ferromagnet-superconductor (F/S) heterostructures is expected to enhance the superconducting transition temperature (Tc) according to the domain-wall superconductivity theory, or to suppress Tc when spin-triplet Cooper pairs are explicitly considered. We study the proximity effect in F/S structures where the F layer is a Sm-Co/Py exchange-spring bilayer and the S layer is Nb. The exchange-spring contains a single, controllable and quantifiable domain wall in the Py layer. We observe an enhancement of superconductivity that is nonmonotonic as the Py domain wall …
Interest in superconducting proximity effect has been revived by the exploitation of Andreev states and by the possible emergence of Majorana bound states at the interface. Spectroscopy of these states has been so far restricted to just a handful of superconductor-metal systems in the diffusion regime, whereas reports in otherwise clean superconductor-superconductor heterojunctions are scarce. Here, we realize molecular beam epitaxy growth of atomically sharp planar heterojunctions between Pb and a topological superconductor candidate RhPb2 that allows us to spectroscopically image the proximi…
We theoretically study superconducting proximity effect between a topological insulator (TI) and a high-temperature d-wave superconductor (dSC). When the TI-dSC heterostructure violates 90 degree-rotation and certain reflection symmetries, we show that a sizable s-wave pairing, coexisting with a d-wave one, emerges in the proximity-induced superconductivity in the TI's top surface states. Weak disorder further suppresses d-wave pairing but not s-wave one in the TI's surface states. More importantly, the pairing gap in surface states is found to be nodeless and nearly-isotropic when the Fermi p…
Ultrathin $\rm Bi_2Se_3$-NbN bilayers comprise a simple proximity system of a topological insulator and an s-wave superconductor for studying gating effects on topological superconductors. Here we report on 3 nm thick NbN layers of weakly connected superconducting islands, overlayed with 10 nm thick $\rm Bi_2Se_3$ film which facilitates enhanced proximity coupling between them. Resistance versus temperature of the most resistive bilayers shows insulating behavior but with signs of superconductivity. We measured the magnetoresistance (MR) of these bilayers versus temperature with and without a …
The search for a Majorana Fermion has been an area of intense interest in condensed matter research of late. This elusive particle, predicted to exist in 1937, has been sought after for both fundamental and practical reasons. On the fundamental level, no particle to date has been observed to be a Majorana fermion, meanwhile on the practical level a Majorana fermion, if found, would represent a non-abelian anyon and could thus be used to build a quantum computer. The search for a Majorana Fermion has recently shifted to topological superconductivity. Topological superconductors are categorized …
Majorana zero modes (MZMs) have been predicted to exist in the topological insulator (TI)/superconductor (SC) heterostructure. Recent spin polarized scanning tunneling microscope (STM) experiment$^{1}$ has observed spin-polarization dependence of the zero bias differential tunneling conductance at the center of vortex core, which may be attributed to the spin selective Andreev reflection, a novel property of the MZMs theoretically predicted in 1-dimensional nanowire$^{2}$. Here we consider a helical electron system described by a Rashba spin orbit coupling Hamiltonian on a spherical surface wi…
We study a new type of three-dimensional topological superconductors that exhibit Majorana zero modes (MZM) protected by a magnetic group symmetry, a combined antiunitary symmetry composed of a mirror reflection and time-reversal. This new symmetry enhances the noninteracting topological classification of a superconducting vortex from $Z_2$ to $Z$, indicating that multiple MZMs can coexist at the end of one magnetic vortex of unit flux. Specially, we show that a vortex binding two MZMs can be realized on the $(001)$-surface of a topological crystalline insulator SnTe with proximity induced BCS…
Spin-polarized supercurrents can be generated with magnetic inhomogeneity at a ferromagnet/spin-singlet-superconductor interface. In such systems, complex magnetic inhomogeneity makes it difficult to functionalise the spin-polarized supercurrents. However, spin-polarized supercurrents in ferromagnet/spin-triplet-superconductor junctions can be controlled by angle between magnetization and spin of Copper pairs ($d$-vector), that can effectively be utilized in developing of a field of research known as superconducting spintronics. Recently, we found induction of spin-triplet correlation into a f…
This is an analytical study of pinning and spontaneous vortex phase is a system consisting of a superconducting thin film pierced by a long ferromagnetic columnar defect of finite radius $R$. The magnetic fields, screening currents, energy and pinning forces for this system are calculated. The interaction between the magnetic field of vortices and the magnetization outside the plane of the film and its close proximity enhances vortex pinning significantly. Spontaneous vortex phase appears when the magnetization of the columnar defect is increased above a critical value. Transitions between pha…
Among the different platforms to engineer Majorana fermions in one-dimensional topological superconductors, topological insulator nanowires remain a promising option. Threading an odd number of flux quanta through these wires induces an odd number of surface channels, which can then be gapped with proximity induced pairing. Because of the flux and depending on energetics, the phase of this surface pairing may or may not wind around the wire in the form of a vortex. Here we show that for wires with discrete rotational symmetry, this vortex is necessary to produce a fully gapped topological supe…
Topological insulators (TIs) having intrinsic or proximity-coupled s-wave superconductivity host Majorana zero modes (MZMs) at the ends of vortex lines. The MZMs survive up to a critical doping of the TI at which there is a vortex phase transition that eliminates the MZMs. In this work, we show that the phenomenology in higher-order topological insulators (HOTIs) can be qualitatively distinct. In particular, we find two distinct features. (i) We find that vortices placed on the gapped (side) surfaces of the HOTI, exhibit a pair of phase transitions as a function of doping. The first transition…
In 2D chiral p-wave superconductors, the zero-energy Majorana fermion excitations trapped at vortex cores follow non-Abelian statistics which can be potentially exploited to build a topological quantum computer. The Majorana states are protected from the thermal effects by the mini-gap, $Δ^2/ε_F$ ($Δ$:bulk gap, $ε_F$: Fermi energy), which is the excitation gap to the higher-energy, non-topological, bound states in the vortex cores. Robustness to thermal effects is guaranteed only when $T \ll Δ^2/ε_F \sim 0.1$ mK, which is a very severe experimental constraint. Here we show that when s-wave sup…
