Bardeen-Cooper-Schrieffer Superconductors Research Articles

Coexistence of Zero-Dimensional Electride State and Superconductivity in AlH2 Monolayer

Electrides, which confine “excess anionic electrons” in subnanometer-sized cavities of a lattice, are exotic ionic crystals. We propose a non-stoichiometric strategy to realize intrinsic two-dimensional (2D) superconducting electride. AlH2 monolayer, which is structurally identical to 1H-MoS2, possesses zero-dimensionally confined anionic electrons in the interstitial sites of Al triangles, corresponding to a chemical formula of [AlH2]+e−. The interaction between interstitial anionic electrons (IAEs) and host cation lattice mainly accounts for stabilization of 1H-AlH2 electride. Impressively, 1H-AlH2 monolayer is an intrinsic Bardeen–Cooper–Schrieffer superconductor with T c = 38 K, which is the direct consequence of strong coupling of the H-dominated high electronic states with Al acoustic branch vibrations and mid-frequency H-derived phonon softening modes caused by Kohn anomalies. Under tensile strain, IAEs transform into itinerant electrons, favoring the formation of stable Cooper pairs. Therefore, T c reaches up to 53 K at a biaxial fracture strain of 5%. Our findings provide valuable insights into the correlation between non-stoichiometric electrides and superconducting microscopic mechanisms at the 2D limit.

Ni-Intercalation-Induced Topological Nodal Line States and Superconductivity in NiTe

Based on symmetry analyses and first-principles calculations, we report the predictions of topological fermions and superconductivity in Ni-intercalated transition metal chalcogenide NiTe. The self-intercalation of Ni introduces nonsymmorphic symmetry operations, protecting a pair of Dirac points and three intersecting Dirac nodal lines near Fermi energy level (EF), which generate spin-textured surface states across EF. Moreover, the Ni-intercalation strongly enhances electron–phonon coupling in NiTe and makes it an anisotropic Bardeen–Cooper–Schrieffer superconductor with a full superconducting gap and a critical temperature Tc ∼1.5 K. The coexistence of topological surface states and superconductivity implies that NiTe is a potential material platform for exploring topological superconductivity.

Investigation of the Electron–Phonon Coupling in Dirac Semimetal PdTe2 via Temperature‐Dependent Raman Spectroscopy

Layered Palladium ditelluride (PdTe2) is an interesting noble‐transition‐metal dichalcogenide with high electrical and thermal conductivity, exhibiting superconductivity and a type‐II Dirac semimetallic phase due to the increased electron–phonon (e–ph) coupling. Herein, the e–ph coupling constant λ of E g (in‐plane) and A 1g (out‐of‐plane) modes in the exfoliated PdTe2 nanoflakes via temperature‐dependent Raman spectroscopy within the temperature range from 80 to 580 K is determined. Both E g mode with a Gaussian line shape and A 1g mode with a Breit–Wigner–Fano line shape show nonlinear frequency redshift and linewidth broadening with temperature. The extracted e–ph coupling constants are = 1.54 and = 0.55, respectively. The Raman results confirm that PdTe2 is a phonon‐mediated Bardeen–Cooper–Schrieffer superconductor.

The absence of superconductivity in the next-to-leading order Ginzburg–Landau functional for Bardeen–Cooper–Schrieffer superconductor

Shortly after the Gor’kov microscopic derivation of the Ginzburg–Landau (GL) model via a small order parameter expansion in Bardeen–Cooper–Schrieffer theory of superconductivity, the derivation was carried to next-to-leading order in that parameter and its spatial derivatives. The aim was to obtain a generalized GL free energy that approximates the microscopic model better. Since 1960s, multiple works have claimed or implicitly assumed that this extended GL model corresponds to the free energy and has solutions in the form of local minima describing superconductivity, such as vortex solutions. In contrast to this, we prove that this extended GL functional does not represent free energy since it does not have any solutions in the form of minima. Accordingly, it cannot be used to describe superconducting states.

Evidence for unconventional superconductivity in twisted bilayer graphene.

The emergence of superconductivity and correlated insulators in magic-angle twisted bilayer graphene (MATBG) has raised the intriguing possibility that its pairing mechanism is distinct from that of conventional superconductors1-4, as described by the Bardeen-Cooper-Schrieffer (BCS) theory. However, recent studies have shown that superconductivity persists even when Coulomb interactions are partially screened5,6. This suggests that pairing in MATBG might be conventional in nature and a consequence of the large density of states of its flat bands. Here we combine tunnelling and Andreev reflection spectroscopy with a scanning tunnelling microscope to observe several key experimental signatures of unconventional superconductivity in MATBG. We show that the tunnelling spectra below the transition temperature Tc are inconsistent with those of a conventional s-wave superconductor, but rather resemble those of a nodal superconductor with an anisotropic pairing mechanism. We observe a large discrepancy between the tunnelling gap ΔT, which far exceeds the mean-field BCS ratio (with 2ΔT/kBTc ~ 25), and the gap ΔAR extracted from Andreev reflection spectroscopy (2ΔAR/kBTc ~ 6). The tunnelling gap persists even when superconductivity is suppressed, indicating its emergence from a pseudogap phase. Moreover, the pseudogap and superconductivity are both absent when MATBG is aligned with hexagonal boron nitride. These findings and other observations reported here provide a preponderance of evidence for a non-BCS mechanism for superconductivity in MATBG.

Influence of superconductivity on the magnetic moment of quantum impurity embedded in BCS superconductor

We study the influence of superconductivity on the formation of the localized magnetic moment for a single-level quantum impurity embedded in an s-wave Bardeen–Cooper–Schrieffer (BCS) superconducting medium, modeled by single-impurity Anderson Hamiltonian. We have combined Bogoliubov transformation with Green’s function method within self-consistent Hartree–Fock mean field approximation to analyze the conditions necessary in metal (in the superconducting) for the formation of the magnetic moment at the impurity site for the low-frequency limit |ω| ≪ Δsc as well as for the finite superconducting gap Δsc. We have compared these results with other theoretical results and with the single-level quantum impurity embedded in the normal metallic host. Further, we analyze the spectral density of the quantum impurity embedded in a superconducting host to study the sub-gap states as a function of impurity parameters.

Enhancing the critical temperature of strained Niobium films

The study of the high critical temperature (Tc) of hydrogen compounds under high pressure has resulted in a considerable focus on Bardeen–Cooper–Schrieffer superconductors. Nb has the highest Tc among the elemental metals at ambient pressure, so reviewing Nb films again is worthwhile. In this study, we investigated the factors that determine the Tc of Nb films by strain introduction and carrier doping. We deposited Nb films of various thicknesses onto Si substrates and evaluated the Tc variation with thickness. In-plane compressive strain in the (110) plane due to residual stress reduced the Tc. First-principles calculations showed that adjusting the density of states at the Fermi level is key for both strain-induced suppression and doping-induced enhancement of the Nb Tc. The application of hydrostatic pressure compensated for the intrinsic strain of the film and increased its Tc, which could also be enhanced by increasing the hole concentration with an electric double-layer transistor. A liquid electrolyte should be used as a pressure medium for applying hydrostatic pressure to increase the Tc of correlated materials, where this increase results from changes in material structure and carrier concentration.

Superconductivity in noncentrosymmetric Mo3P single crystal

Superconductivity in single crystalline Mo3P has been investigated by the measurement of electrical resistivity, magnetic susceptibility, and specific heat capacity. Its space group is I 4-2 m with lattice parameters a = b = 9.808 4 Å and c = 4.838 2 Å. A bulk superconductivity with a critical temperature of TC = 5.6 ± 0.1 K, an upper critical field of = 13.7 ± 0.1 kOe, and a lower critical field of = 190 ± 2 Oe for ρab were confirmed. A large anisotropic behavior was discovered in the resistivity and upper critical fields. A clear upward curvature in Hc2 was observed, suggesting a multiband superconductivity in Mo3P. The value of the Ginzburg–Landau parameter κGL indicates that Mo3P is a type-II superconductor. ΔC(Tc)/γ Tc = 1.50 and 2Δ/kB Tc = 3.48 from the specific heat analyses indicate that Mo3P is a weak-coupling Bardeen–Cooper–Schrieffer superconductor with fully gapped superconductivity.

Canonical pair condensation in a flat-band BCS superconductor

The standard approach of the Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity is to introduce a self-consistent mean-field approximation, and a variational ansatz for the many-body ground state. The resulting mean-field Hamiltonian no longer commutes with the total number operator, and the variational search takes place in Fock space rather than in a Hilbert space of states with fixed number of particles. This is a disadvantage when studying small systems where the canonical ensemble predictions differ from the corresponding grand-canonical results. To remedy this, alternative approaches such as Richardson’s method have been put forward. Here, we derive the exact many-body ground state of a model Hamiltonian corresponding to the deep-BCS or flat-band regime, without having to resort to Richardson’s set of coupled nonlinear equations. This allows to write the exact many-body ground state in a way that makes the difference with the BCS variational wave function particularly clear. We show that the exact wave function consists of a superposition of many-pair states in such a way that the mean-field averaging corresponds to a summation over these many-pair states. This explains why many expectation values calculated with the BCS variational wave function give the same result as when calculated with the exact wave function, even though these wave functions are different. In the canonical (fixed-number) approach, pairing is investigated using the second-order reduced density matrix and calculating its largest eigenvalue. When interpreted as the order parameter of the superconducting state, this can be compared directly to the behavior of the mean-field gap. Finally, we show that a clear difference between the canonical approach and the BCS grand canonical estimates appears when evaluating pair condensate fluctuations as well as the pair entanglement entropy.

Thermodynamic properties of superconducting GeH3 under high pressure

Chemical precompression can reduce the pressure required for structure metallization and for the subsequent existence of a superconducting state in hydrogen-rich compounds. In this study, we determined the thermodynamic properties of the superconducting state in germanium hydride GeH3. Stable structures of this compound crystallize at 175 GPa during the chemical decomposition of GeH4. Computations were conducted within the formalism of the Eliashberg theory of superconductivity. This approach allowed us to analyze thermodynamic quantities such as the transition temperature (Tc), free energy, entropy, and specific heat difference (ΔF, ΔS, ΔC) between the superconducting and normal states. Results were obtained for three stable structures comprising A15 (Pm3¯n, fcc), Cccm (orthorhombic), and P42/mmc (tetragonal) for GeH3 at 180 GPa. The transition temperature for μ⋆ = 0.1 indicated substantial changes between the crystal structures, where A15 had the highest Tc (194 K). The Cccm and P42/mmc systems had similar critical temperatures of 147.2 K and 132.9 K, respectively. The advantageous superconducting state properties of the A15 system in terms of the thermodynamic quantities make this structure more desirable for industrial use. In particular, the free energy difference representing the thermodynamic stability of the superconducting state was two times larger in A15 compared with the other systems. The results obtained for the critical temperatures were compared with the values obtained using the McMillan (MM) and Allen–Dynes (AD) analytic formulae. The difference between the results obtained using the Eliashberg formalism and MM approach was well above 60 K for the A15 structure (TcMM = 133 K, TcAD = 159 K). Further analysis with the Bardeen–Cooper–Schrieffer (BCS) constants (RΔ, RC, RH) showed that GeH3 cannot be considered as a BCS superconductor.

Superconducting Ti15Zr15Nb35Ta35 High-Entropy Alloy With Intermediate Electron-Phonon Coupling

The body-centered cubic (BCC) Ti15Zr15Nb35Ta35 high-entropy alloy showed superconducting behavior at around 8 K. The electronic specific heat coefficient and the lattice specific heat coefficient β were determined to be γ=9.3±0.1 mJ/mol K2 and β=0.28±0.01 mJ/mol K4, respectively. It was found that the electronic specific heat Ces does follow the exponential behavior of the Bardeen-Cooper-Schrieffer (BCS) theory. Nevertheless, the specific heat jump (ΔC/γTc ) at the superconducting transition temperature which was determined to be 1.71 deviates appreciably from that for a weak electron-phonon coupling BCS superconductor. Within the framework of the strong-coupled theory, our analysis suggests that theTi15Zr15Nb35Ta35 HEA is an intermediate electron-phonon coupled BCS-type superconductor.

Superconductivity in a misfit compound (PbSe)1.12(TaSe2)

We report the discovery of superconductivity with a maximum Tc ≈ 1.28 K in Br-doped (PbSe)1.12(TaSe2), which is a new misfit compound consisting of alternating layers of distorted rocksalt PbSe and dichalcogenide TaSe2. It is found that the Br-doping is required for the formation of this misfit compound and superconductivity can be tuned by the Br content. The large anisotropic parameter of resistivity ≈ 100 and that of the upper critical field = ≈ 10 are obtained. The estimated c-axis coherence length ≈ 6.3 nm, larger than the c-axis lattice constant, which implies that this compound is an anisotropic three-dimensional superconductor. The Hall coefficient measurements suggest that the charge transport is dominated by the hole-type charge carrier and there is a charge transfer from the PbSe layer to the conducting TaSe2 layer. The small normalized specific heat jump ΔC/γ Tc = 1.16 and electron–phonon coupling constant λep ≈ 0.61 indicate that Br-doped (PbSe)1.12(TaSe2) is a weak coupling Bardeen–Cooper–Schrieffer superconductor.

Ultrathin Bismuth Film on High-Temperature Cuprate Superconductor Bi2Sr2CaCu2O8+δ as a Candidate of a Topological Superconductor.

One of the key challenges in condensed-matter physics is to establish a topological superconductor that hosts exotic Majorana fermions. Although various heterostructures consisting of conventional BCS (Bardeen-Cooper-Schrieffer) superconductors as well as doped topological insulators were intensively investigated, no conclusive evidence for Majorana fermions has been provided. This is mainly because of their very low superconducting transition temperatures ( Tc) and small superconducting-gap magnitude. Here, we report a possible realization of topological superconductivity at very high temperatures in a hybrid of Bi(110) ultrathin film and copper oxide superconductor Bi2Sr2CaCu2O8+δ (Bi2212). Using angle-resolved photoemission spectroscopy and scanning tunneling microscopy, we found that three-bilayer-thick Bi(110) on Bi2212 exhibits a proximity-effect-induced s-wave energy gap as large as 7.5 meV which persists up to Tc of Bi2212 (85 K). The small Fermi energy and strong spin-orbit coupling of Bi(110), together with the large pairing gap and high Tc, make this system a prime candidate for exploring stable Majorana fermions at very high temperatures.

Radiation-Induced Oscillating Gap States of Nonequilibrium Two-Dimensional Superconductors**Supported by the National Basic Research Program of China under Grant No 2015CB921101, and the National Natural Science Foundation of China under Grant No 11325416.

We study the effects of infrared radiation on a two-dimensional Bardeen–Cooper–Schrieffer superconductor coupled with a normal metal substrate through a tunneling barrier. The phase transition is analyzed by inspecting the stability of the system against perturbations of pairing potentials. We find an oscillating gap phase with a frequency not directly related to the radiation frequency, but instead resulting from the asymmetry of electron density of states of the system as well as the tunneling amplitude. When such a superconductor is in contact with another superconductor, gives rise to an unusual alternating Josephson current.

Single Crystal Growth and Physical Property Characterization of Non-centrosymmetric Superconductor PbTaSe2**Supported by the National Basic Research Program of China under Grant Nos 2015CB921303, 2011CBA00100 and 2012CB821404, the Strategic Priority Research Program (B) of Chinese Academy of Sciences under Grant Nos XDB07020100 and XDB07020200, and the National Natural Science Foundation of China under Grant No 11174350.

We report on the single crystal growth and superconducting properties of PbTaSe2 with the non-centrosymmetric crystal structure. By using the chemical vapor transport technique, centimeter-size single crystals are successfully obtained. The measurement of temperature dependence of electrical resistivity ρ(T) in both normal and superconducting states indicates a quasi-two-dimensional electronic state in contrast to that of polycrystalline samples. Specific heat C(T) measurement reveals a bulk superconductivity with Tc ≃ 3.75 K and a specific heat jump ratio of 1.42. All these results are in agreement with a moderately electron–phonon coupled, type-II Bardeen–Cooper–Schrieffer superconductor.

Coherence factors beyond the BCS result

The dynamics of BCS (Bardeen-Cooper-Schrieffer) superconductors is fairly well understood due to the availability of a mean-field solution for the pairing Hamiltonian, a solution which gives the quantum state of a superconductor as a state of almost-free fermions interacting only with a condensate. As a result, transition probabilities may be computed, and expressed in terms of matrix elements of electron creation and annihilation operators between approximate eigenstates. These matrix elements are also called ``coherence factors.'' Mean-field theory is however not sufficient to describe all eigenstates of a superconductor, a deficiency which is hardly important in (or very close to) equilibrium, but one that becomes relevant in certain out-of-equilibrium situations. We report here on a computation of matrix elements (coherence factors) for the pairing Hamiltonian between any ``two-arc'' eigenstates in the thermodynamic limit.

Dynamic Hubbard model: kinetic energy driven charge expulsion, charge inhomogeneity, hole superconductivity and Meissner effect

Conventional Hubbard models do not take into account the fact that the wavefunction of an electron in an atomic orbital expands when a second electron occupies the orbital. Dynamic Hubbard models have been proposed to describe this physics. These models reflect the fact that electronic materials are generically not electron–hole symmetric, and they give rise to superconductivity driven by lowering of kinetic energy when the electronic energy band is almost full, with higher transition temperatures resulting when the ions are negatively charged. We show that the charge distribution in dynamic Hubbard models can be highly inhomogeneous in the presence of disorder, and that a finite system will expel negative charge from the interior to the surface, and that these tendencies are largest in the parameter regime where the models give rise to highest superconducting transition temperatures. High Tc cuprate materials exhibit charge inhomogeneity and they exhibit tunneling asymmetry, a larger tendency to emit electrons rather than holes in normal–insulating–superconducting tunnel junctions. We propose that these properties, as well as their high Tc, are evidence that they are governed by the physics described by dynamic Hubbard models. Below the superconducting transition temperature the models considered here describe a negatively charged superfluid and positively charged quasiparticles, unlike the situation in conventional Bardeen–Cooper–Schrieffer superconductors where quasiparticles are charge neutral on average. We examine the temperature dependence of the superfluid and quasiparticle charges and conclude that spontaneous electric fields should be observable in the interior and in the vicinity of superconducting materials described by these models at sufficiently low temperatures. We furthermore suggest that the dynamics of the negatively charged superfluid and positively charged quasiparticles in dynamic Hubbard models can provide an explanation for the Meissner effect observed in high Tc and low Tc superconducting materials.

Superconductivity with Rashba spin–orbit coupling and magnetic field

Two-dimensional electron systems at oxide interfaces are often influenced by a Rashba type spin–orbit coupling, which is tunable by a transverse electric field. Ferromagnetism near the interface can simultaneously induce strong local magnetic fields. This combination of spin–orbit coupling and magnetism leads to asymmetric two-sheeted Fermi surfaces, on which either intra- or inter-band pairing is favored. The superconducting order parameters are derived within a microscopic pairing model realizing both the Bardeen–Cooper–Schrieffer superconductor with inter-band pairing and a mixed parity state with finite-momentum intra-band pairing. We present a phase diagram for the superconducting groundstates and analyze the density of states, the spectra, and the momentum distribution functions of the different phases. The results are discussed in the context of superconductivity and ferromagnetism at LaAlO3–SrTiO3 interfaces and superconductors with broken inversion symmetry.

Magnetic form factor, field map, and field distribution for a BCS type-II superconductor near itsBc2(T)phase boundary

We review the magnetic form factor deduced by Delrieu from Gorkov's equation for a Bardeen-Cooper-Schrieffer (BCS) type-II superconductor near its ${B}_{\mathrm{c}2}$ phase boundary, i.e., when its magnetization is small. A numerical study of the form factor, field map, and field distribution follows. The characteristics of the transition from the low-temperature BCS to the high-temperature Ginzburg-Landau vortex lattices is studied. The exotic shape of the component field distribution and the form factor at low temperature and as a function of the external field intensity are discussed. Our numerical work should be helpful for the analyzing of small-angle neutron scattering and muon spin rotation vortex-lattice data recorded for BCS superconductors and may be other superconductors in the clean limit.

Superconductivity in the vicinity of ferromagnetism in oxygen free perovskite MgCNi3: An experimental and density functional theory study

We report synthesis, structural, magnetic, specific heat, and density functional theory (DFT) studies on the MgCNi3 superconductor. Polycrystalline MgCNi3 samples are synthesized through the standard solid state reaction route and found to crystallize in the cubic perovskite structure with space group Pm3m, without any detectable trace of Ni impurity. Both AC and DC magnetization exhibited superconducting transition (Tc) at around 7.25 K. The lower critical field (Hc1) and irreversibility field (Hirr) are around 140 Oe and 11 kOe, respectively, at 2 K. The upper critical field (Hc2) being determined from in-field AC susceptibility measurements is 11.6 kOe and 91.70 kOe with 50% and 90% diamagnetism criteria, respectively. Heat capacity (Cp) measurements are carried out under an applied field of up to 140 kOe and down to 2 K. The Sommerfeld constant (γ) and Debye temperature (ΘD) as determined from low temperature fitting of Cp(T) data to the Sommerfeld-Debye model are 36.13 mJ/mol K2 and 263.13 K, respectively. The Bardeen-Cooper-Schrieffer (BCS) parameter (2Δ/KBTc) is around 3.62, suggesting MgCNi3 to be an intermediate coupled BCS superconductor with value λ = 0.69. Although the DFT calculations exhibited the compound to be non-magnetic but with spin fluctuations, the experimental isothermal magnetization MH loops at 20, 50, 100, 200, and 300 K showed some ferromagnetic nature in this compound with coercive field (Hc) of around 50 Oe at 20 K. The Ni3d states play dominant roles near the Fermi levels and there is strong hybridization between Ni3d and C2p states. It seems that MgCNi3 is superconducting in close proximity of ferromagnetism.