Simple cubic phosphorus exhibits superconductivity with a maximum $T_c$ of up to 12 K under pressure. The pressure dependence of $T_c$ cannot be consistently explained with a simple electron-phonon mechanism, which has stimulated investigations into the role of electronic correlations and plasmonic contributions. Here, we solve the gap equation of density functional theory for superconductors using different electron-electron and electron-phonon contributions to the kernel. We find that the phonon contribution alone yields an overestimation of $T_c$, while the addition of the static electronic contribution results in an underestimation. Taking into account the full frequency dependence of the screened interaction, the one-shot $GW$ approximation predicts $T_c$ values in good agreement with the experiments in the pressure range appropriate for the cubic phase. We also explore the use of quasi-particle bands in the calculation of the electronic and phononic kernels, and show that this modification significantly improves $T_c$ in the high-pressure region.
Co-doping of lanthanum and phosphorus in CaFe2As2 induces superconductivity at 45 K. This superconducting transition temperature is higher than the 38 K transition in Ba1-xKxFe2As2, which is the maximum found thus far among the 122 phases. Superconductivity with a substantial shielding volume fraction was observed at 0.12 $\leq$ x $\leq$ 0.18 and y = 0.06 in Ca1-xLaxFe2(As1-yPy)2. The superconducting phase of the present system seems to be not adjacent to an antiferromagnetic phase.
The effects of phosphorus doping on the structural and superconducting phase transitions of BaNi$_2$(As$_{1-x}$P$_x$)$_2$ were studied. The specific heat, resistivity, and magnetic susceptibility were measured. The results revealed an abrupt increase in the superconducting transition temperature ($T_c$) from 0.6 K in the triclinic phase (space group P$\bar{1}$) with less phosphorus (0 $\leq$ $x$ $\leq$ 0.067) to 3.3 K in the tetragonal phase (space group I4/mmm) with more phosphorus ($x$ $\geq$ 0.067). Our data analysis suggests that a doping-induced softening related to an in-plane Ni and As(…
We have studied EuFe$_{2}$(As$_{0.7}$P$_{0.3}$)$_{2}$ by the measurements of x-ray diffraction, electrical resistivity, thermopower, magnetic susceptibility, magnetoresistance and specific heat. Partial substitution of As with P results in the shrinkage of lattice, which generates chemical pressure to the system. It is found that EuFe$_{2}$(As$_{0.7}$P$_{0.3}$)$_{2}$ undergoes a superconducting transition at 26 K, followed by ferromagnetic ordering of Eu$^{2+}$ moments at 20 K. This finding is the first observation of superconductivity stabilized by internal chemical pressure, and supplies a r…
The influence of carrier type on superconductivity has been an important issue for understanding both conventional and unconventional superconductors [1-7]. For elements that superconduct, it is known that hole-carriers govern the superconductivity for transition and main group metals [8-10]. The role of hole-carriers in elements that are not normally conducting but can be converted to superconductors, however, remains unclear due to the lack of experimental data. Here we report the first in-situ high pressure Hall effect measurements on single crystal black phosphorus, measured up to ~ 50 GPa…
Two-dimensional (2D) boron has been predicted to show superconductivity. However, intrinsic 2D carbon and phosphorus have not been reported to be superconductors, which, inspires us to seek superconductivity in their mixture. Here we perform first-principles calculations of the electronic structure, phonon dispersion, and electron-phonon coupling of the metallic phosphorus carbide monolayer, the $β_{0}$-PC. Results show that it is an intrinsic phonon-mediated superconductor, with estimated superconducting temperature $T_{c}$ to be $\sim$13 K. The main contribution to the electron-phonon coupli…
First-principles calculations predicted monolayer blue phosphorus to be an alternative two-dimensional allotrope of phosphorus, like the recently discovered monolayer black phosphorus. Due to its unique crystalline and electronic structure, blue phosphorus may be a promising candidate as a BCS-superconductor after proper intercalation. In this study, using first-principles calculations, the favorable intercalation sites for some alkali metals and alkaline earths have been identified for Blue-P bilayer and the stacking configuration of bilayer is changed. Then the blue phosphorus bilayer transf…
Superconductivity intrinsic to the intercalated black phosphorus (BP) with a transition temperature Tc of 3.8 K, independent of the intercalant, whether an alkali or an alkaline earth element, has been reported recently by R. Zhang et al. (2017). However, the reported Tc and the field effect on the superconducting (SC) transition both bear great similarities to those for the pure Sn, which is commonly used for BP synthesis under the vapor transport method. We have therefore decided to determine whether a minute amount of Sn is present in the starting high purity BP crystals and whether it is t…
Hydrogen-rich compounds have been extensively studied both theoretically and experimentally in the quest for novel high-temperature superconductors. Reports on sulfur-hydride attaining metallicity under pressure and exhibiting superconductivity at temperatures as high as 200 K have spurred an intense search for room-temperature superconductors in hydride materials. Recently, compressed phosphine was reported to metallize at pressures above 45 GPa, reaching a superconducting transition temperature (T$_{c}$) of 100 K at 200 GPa. However, neither the exact composition nor the crystal structure of…
In the recent years, three-dimensional (3D) high-temperature superconductors at ultrahigh pressure have been reported, typical examples are the polyhydrides H$_{3}$S, LaH$_{10}$, and YH$_{9}$, etc. To find high-temperature superconductors in two-dimensional (2D) at atmosphere pressure is another research hotspot. Here, we investigated the possible superconductivity in a hydrogenated monolayer phosphorus carbide based on first-principles calculations. The results reveal that monolayer PC$_{3}$ transforms from a semiconductor to a metal after hydrogenation. Interestingly, the C-$π$-bonding band …
The tetragonal Mo$_5$PB$_2$ compound was recently reported to show superconductivity with a critical temperature up to 9.2 K. In search of evidence for multiple superconducting gaps in Mo$_5$PB$_2$, comprehensive measurements, including magnetic susceptibility, electrical resistivity, heat capacity, and muon-spin rotation and relaxation ($μ$SR) measurements were carried out. Data from both low-temperature superfluid density and electronic specific heat suggest a nodeless superconducting ground state in Mo$_5$PB$_2$. Two superconducting energy gaps $Δ_0$ = 1.02 meV (25%) and 1.49 meV (75%) are …
Simple cubic (sc) black phosphorus (denoted BP), stable at P>10GPa, seems an ordinary metal. It has electron-phonon-driven superconductivity with Tc 5-10 K. The A17 phase, stable at atmospheric pressure, has a narrow gap, becomes semimetallic at P=1 GPa, and has a smooth transition to topological metal behavior at P ~ 5 GPa. The A7 phase, stable for 5<P<10 GPa, is metallic, superconducting, and less conventional than the sc phase. Some insights are extracted from analysis of resistivity versus temperature at various pressures. A surprising order-of-magnitude disagreement between theory and exp…
The effects of copper doping on the structural and superconducting phase transitions of Ba(Ni$_{1-x}$Cu$_{x}$)$_{2}$As$_{2}$ were studied by examining the resistivity, magnetic susceptibility, and specific heat. We found an abrupt increase in the superconducting transition temperature $T_{\rm c}$ from 0.6 K in the triclinic phase with less copper ($x$ $\leq$ 0.16) to 2.5-3.2 K in the tetragonal phase with more copper ($x$ $>$ 0.16). The specific-heat data suggested that doping-induced phonon softening was responsible for the enhanced superconductivity in the tetragonal phase. All of these obse…
Novel structural building blocks in compounds could induce interesting physical and chemical properties. Although phosphorus tends to form very different motifs, the existence of lone pair electrons has always prevented the formation of graphenelike structures. Here, the application of first-principles swarm structural calculations has allowed us to predict the stability of pressure-induced hexagonal LaP2H2 containing graphenelike phosphorus, which derives from the trigonal bipyramid configuration of P atoms regulated by symmetric hydrogen bonds. LaP2 in LaP2H2 has the same configuration as Mg…
Polycrystalline samples and single crystals of SmFeAs1-xPxO1-y were synthesized and grown employing different synthesis methods and annealing conditions. Depending on the phosphorus and oxygen content, the samples are either magnetic or superconducting. In the fully oxygenated compounds the main impact of phosphorus substitution is to suppress the Néel temperature TN of the spin density wave (SDW) state, and to strongly reduce the local magnetic field in the SDW state, as deduced from muon spin rotation measurements. On the other hand the superconducting state is observed in the oxygen deficie…
The pair-fluctuation contribution reduces the electrostatic screening length in superconductivity as compared to the normal state. When a conductor possesses a static background charge distribution, superconductivity arises even in the absence of an explicit pairing interaction, such that the Coulomb repulsion is reduced and the total energy is lowered. We demonstrate that the superconducting gap increases with increased background charge at first, after which the mixing of the Higgs and plasma modes suppresses superconductivity in the pseudogap phase. This indicates that the mechanism may be …
Binary hydrides formed by the pnictogens of phosphorus, arsenic and antimony are studied at high pressures using first principles methods. Stable structures are predicted and their electronic, vibrational and superconducting properties are investigated. We predict that SbH$_{4}$ and AsH$_{8}$ will be high-temperature superconductors at megabar pressures, with critical temperatures in excess of 100 K. The highly symmetric hexagonal SbH$_{4}$ phase is predicted to be stabilized above about 150 GPa, which is readily achievable in diamond anvil cell experiments. We find that all phosphorus hydride…
Anisotropic pairing interactions mediated by phonons are examined in layer systems. It is shown that the screening effects become weaker when the layer spacing increases. Then the anisotropic components of the pairing interactions increase with the screening length since the momentum dependence changes. As a result, various types of anisotropic superconductivity occur depending on the parameter region. For example, p-wave superconductivity occurs when the short-range part of Coulomb repulsion is strong and the layer spacing is large. Two kinds of inter-layer pairing may occur when the layer sp…
We study within a first-principle approach the band structure, vibrational modes and electron-phonon coupling in boron, aluminum and phosphorus doped silicon in the diamond phase. Our results provide evidences that the recently discovered superconducting transition in boron doped cubic silicon can be explained within a standard phonon-mediated mechanism. The importance of lattice compression and dopant related stretching modes are emphasized. We find that T$_C$ can be increased by one order of magnitude by adopting aluminum doping instead of boron.
Evidence against superconductivity in flux trapping experiments on hydrides under high pressure & On magnetic field screening and expulsion in hydride superconductors
Pressure-induced superconductivity and structural phase transitions in phosphorous (P) are studied by resistivity measurements under pressures up to 170 GPa and fully $ab-initio$ crystal structure and superconductivity calculations up to 350 GPa. Two distinct superconducting transition temperature (T$_{c}$) vs. pressure ($P$) trends at low pressure have been reported more than 30 years ago, and for the first time we are able to reproduce them and devise a consistent explanation founded on thermodynamically metastable phases of black-phosphorous. Our experimental and theoretical results form a …
We report the realization of superconductivity by an isovalent doping with phosphorus in LaFeAsO. X-ray diffraction shows that, with the partial substitution of P for As, the Fe$_2$As$_2$ layers are squeezed while the La$_2$O$_2$ layers are stretched along the c-axis. Electrical resistance and magnetization measurements show emergence of bulk superconductivity at $\sim$10 K for the optimally-doped LaFeAs$_{1-x}$P$_{x}$O ($x=0.25\sim0.3$). The upper critical fields at zero temperature is estimated to be 27 T, much higher than that of the LaFePO superconductor. The occurrence of superconductivit…
We have clarified how the enhanced superconductivity, often referred to as the 3-K phase superconductivity, develops in the Sr2RuO4-Ru eutectic system. From the detailed ac and dc susceptibility measurements on well-characterized crystals, we revealed strongly anisotropic shielding, governed by the direction of the screening current dominated within the RuO2 plane rather than by the orientation of the Ru lamellae. The onset temperature of the 3-K phase superconductivity probed by diamagnetic screening is as high as 3.5 K. The temperature dependence of the diamagnetic shielding above around 2 K…
In this paper we investigate the role of the electronic correlation on the hole doping dependence of electron-phonon and superconducting properties of cuprates. We introduce a simple analytical expression for the one-particle Green's function in the presence of electronic correlation and we evaluate the reduction of the screening properties as the electronic correlation increases by approaching half-filling. The poor screening properties play an important role within the context of the nonadiabatic theory of superconductivity. We show that a consistent inclusion of the reduced screening proper…
The exploration of superconductivity dominated by structural units is of great interest in condense matter physics. MgB2, consisting of graphene-like B, becomes a typical representative of traditional superconductors. Phosphorus demonstrates diverse non-planar motifs through sp3 hybridization in allotropes and phosphides. Here, we report that a pressure-stabilized LaP2, isostructural to MgB2, shows superconductivity with a predicted Tc of 22.2 K, which is the highest among already known transition metal phosphides. Besides electron-phonon coupling of graphene-like P, alike the role of B layer …
A theoretical analysis of the superconductivity observed recently in Carbon nanotubes is proposed. We argue that ultra-small (diameter $ \sim 0.4 nm$) single wall carbon nanotubes (with transition temperature $T_c\sim 15 ^{o}K$) and entirely end-bonded multi-walled ones ($T_c\sim 12 ^{o}K$) can superconduct by an electronic mechanism, basically the same in both cases. By a Luttinger liquid -like approach, one finds enhanced superconducting correlations due to the strong screening of the long-range part of the Coulomb repulsion. Based on this finding, we perform a detailed analysis on the resul…
A combination of strong Cooper pairing and weak superconducting fluctuations is crucial to achieve and stabilize high-Tc superconductivity. We demonstrate that a coexistence of a shallow carrier band with strong pairing and a deep band with weak pairing, together with the Josephson-like pair transfer between the bands to couple the two condensates, realizes an optimal multicomponent superconductivity regime: it preserves strong pairing to generate large gaps and a very high critical temperature but screens the detrimental superconducting fluctuations, thereby suppressing the pseudogap state. S…
We report our $^{23}$Na and $^{75}$As NMR studies on isovalent phosphorus-doped NaFeAs$_{0.8}$P$_{0.2}$ ($T_c=$ 33 K) single crystals. Our data suggest a dramatic enhancement of the electron density of states on the Fermi surface, and a large residual electron density of state below $T_c$. However, evidence of antiferromagnetic spin fluctuations is shown by the spin-lattice relaxation rate. The penetration depth, revealed from $^{23}$Na NMR linewidth, follows the universal Uemura relation in iron pnictides. These observations suggest that the correlation effects are still important for the sup…
Phonon-driven nodal surface superconductivity of Fermi arcs
Leibniz Institute for Solid State and Materials Research, IFW Dresden（德累斯顿亥姆霍兹固体与材料研究所）；Department of Mathematics, City St George’s, University of London（伦敦大学城市圣乔治学院数学系）；Würzburg-Dresden Cluster of Excellence ctd.qmat（维尔茨堡-德累斯顿卓越集群 ctd.qmat）
A quantitative description of Coulomb interactions is developed for two-dimensional superconducting materials, enabling us to compare intrinsic with external screening effects, such as those due to substrates. Using the example of a doped monolayer of MoS2 embedded in a tunable dielectric environment, we demonstrate that the influence of external screening is limited to a length scale, bounded from below by the effective thickness of the quasi-two-dimensional material and from above by its intrinsic screening length. As a consequence, it is found that unconventional Coulomb-driven superconduct…
The 2D screening is investigated in a simple single band square tight-binding model which qualitatively resembles the known electronic structure in high temperature superconductors. The Coulomb kernel for the two particle Bethe-Salpeter equation in the single loop (RPA) approximation for the polarization can be evaluated in a strong tight binding limit. The results indicate an intense screening of the Coulomb repulsion between the particles, which becomes stronger and anisotropic when the Fermi level approach half filling (or equivalently, when the Fermi surface approach the Van Hove singulari…
Coulomb screening of superconductivity in magic-angle twisted bilayer graphene
School of Physics & Astronomy, University of Manchester（曼彻斯特大学物理与天文学学院）；National Graphene Institute, University of Manchester（曼彻斯特大学国家石墨烯研究所）；Department of Physics, Washington University in St. Louis（华盛顿大学圣路易斯分校物理系）；Department of Physics and Astronomy, University of Pennsylvania（宾夕法尼亚大学物理与天文学系）；Department of Physics, University of Antwerp（安特卫普大学物理系）；Henry Royce Institute for Advanced Materials, The University of Manchester（曼彻斯特大学亨利·罗伊斯先进材料研究所）；National Institute for Materials Science（国立材料研究所）；Department of Materials Science and Engineering, National University of Singapore（新加坡国立大学材料科学与工程系）；Department of Physics, National University of Singapore（新加坡国立大学物理系）
We consider the Ginzburg-Landau mean field theory of ferromagnetic superconductors with complex order parameter $ψ_i, i=1,2,3$. Below the critical temperature superconductivity is generated by means of a tachyonic term in the free energy $-α|ψ_i|^2$ $(α>0)$, stabilized by a $ψ^4$-term. However, we show that when $α$ becomes negative superconductivity can also be generated spontaneously by the magnetic field through the Zeeman like coupling between the field and the spin of the order parameter, in analogy with what happens in W-meson condensation. We also show that this mechanism leads to a vor…
We develop a theory for strain control of Majorana zero energy modes and Josephson effect in black phosphorus (BP) devices proximity coupled to a superconductor. Employing realistic values for the band parameters subject to strain, we show that the strain closes the intrinsic band gap of BP, however the proximity effect from the superconductor reopens it and creates Dirac and Weyl nodes. Our results illustrate that Majorana zero energy flat bands connect the nodes within the band-inverted regime in which their associated density of states is localized at the edges of the device. In a ferromagn…
Motivated by the recent report of superconductivity above 200 K in ultra-dense hydrogen sulfide, we search for high-\tc\ conventional superconductivity in the phase diagram of the binary Li-S system, using {\em ab-initio} methods for crystal structure prediction and linear response calculations for the electron-phonon coupling. We find that at pressures higher than 20 GPa, several new compositions, besides the known Li$_2$S, are stabilized; many exhibit electride-like {\em interstitial} charge localization observed in other alkali metal compounds. Of all predicted phases, only Li$_3$S at P > 6…
Bulk TiSe$_2$ is an intrinsically layered transition metal dichalcogenide (TMD) hosting both superconducting and charge density wave (CDW) ordering. Motivated by the recent progress in preparing two-dimensional TMDs, we study these frustrated orderings in {\it single} trilayer of TiSe$_2$ within a renormalization group approach. We establish that a novel state with time-reversal symmetry broken chiral superconductivity can emerge from the strong competition between CDW formation and superconductivity. Its stability depends on the precise strength and screening of the electron-electron interact…
Bulk FeSe becomes superconducting below 9\,K, but the critical temperature (T$_{c}$) is enhanced almost universally by a factor of $\sim$4-5 when it is intercalated with alkali elements. How intercalation modifies the structure is known from in-situ X-ray and neutron scattering techniques, but why T$_{c}$ changes so dramatically is not known. Here we show that there is one-to-one correspondence between the enhancement in magnetic instabilities at certain $\bf q$ vectors and superconducting pairing vertex, even while the nuclear spin relaxation rate ${1}/{(T_{1}T)}$ may not reflect this enhance…
We consider competition of Kondo effect and s-wave superconductivity in heavy fermion and mixed valence superconductors, using the phenomenological approach for the periodic Anderson model. Similar to the well known results for single-impurity Kondo effect in superconductors, we have found principal possibility of a re-entrant regime of the superconducting transition temperature, $T_c$, in heavy fermion superconductors in a narrow range of model parameters and concentration of f-electrons. Suppression of $T_c$ in mixed valence superconductors is much weaker. Our theory has most validity in the…
We study the Cooper instability in jellium model in the controlled regime of small to intermediate values of the Coulomb parameter $r_s \leq 2$. We confirm that superconductivity naturally emerges from purely repulsive interactions described by the Kukkonen-Overhauser vertex function. By employing the implicit renormalization approach we reveal that even in the small-$r_s$ limit, the dominant mechanism behind Cooper instability is based on dynamic screening of the Coulomb interaction--accurately captured by the random phase approximation, whereas the Kohn-Luttinger contribution is negligibly s…
The electrochemical gating technique is a powerful tool to tune the \textit{surface} electronic conduction properties of various materials by means of pure charge doping, but its efficiency is thought to be hampered in materials with a good electronic screening. We show that, if applied to a metallic superconductor (NbN thin films), this approach allows observing reversible enhancements or suppressions of the \emph{bulk} superconducting transition temperature, which vary with the thickness of the films. These results are interpreted in terms of proximity effect, and indicate that the effective…
At ambient pressure CrAs undergoes a first-order transition into a double-helical magnetic state at TN = 265 K, which is accompanied by a structural transition. The recent discovery of pressure-induced superconductivity in CrAs makes it important to clarify the nature of quantum phase transitions out of its coupled structural/helimagnetic order. Here we show, via neutron diffraction on the single-crystal CrAs under hydrostatic pressure (P), that the combined order is suppressed at Pc ~ 10 kbar, near which bulk superconductivity develops with a maximal transition temperature Tc ~ 2 K. We furthe…
The ability to control the strength of interaction is essential for studying quantum phenomena emerging from a system of correlated fermions. For example, the isotope effect illustrates the effect of electron-phonon coupling on superconductivity, providing an important experimental support for the BCS theory. In this work, we report a new device geometry where the magic-angle twisted bilayer graphene (tBLG) is placed in close proximity to a Bernal bilayer graphene (BLG) separated by a 3 nm thick barrier. Using charge screening from the Bernal bilayer, the strength of electron-electron Coulomb …
We investigate the spin-triplet superconductivity mediated by phonons in quasi-one-dimensional (Q1D) systems with open Fermi surfaces. We obtain the ground state phase diagrams. It is found that spin-triplet superconductivity occurs for weak screening and strong on-site Coulomb interaction, even in the absence of any additional nonphonon pairing interactions. We find that the nodeless spin-triplet state is more favorable than the spin-triplet state with line nodes, for the parameter values of the Q1D superconductors (TMTSF)_2X. We also find that Q1D open Fermi surface, which is the specific fe…
Superconducting characteristics such as the Meissner-Ochsenfeld state, screening supercurrents and hysteresis loops of type-II superconductors were observed from the temperature and magnetic field dependences of the magnetic moment, m(T, H), in graphite powders reacted with sulfur for temperatures below 9.0 K. The temperature dependence of the lower critical field Hc1(T) was determined and the zero-temperature penetration depth, lambda(0), was estimated (lambda (0) = 227 nm). The superconductivity was observed to be highly anisotropic and to coexist with a ferromagnetic state that has a Curie …
Monolayer films of FeSe grown on SrTiO$_3$ substrates exhibit significantly higher superconducting transition temperatures than those of bulk FeSe. Interaction of electrons in the FeSe layer with dipolar SrTiO$_3$ phonons has been suggested as the cause of the enhanced transition temperature. In this paper we systematically study the coupling of SrTiO$_3$ longitudinal optical phonons to the FeSe electron, including also electron-electron Coulomb interactions at the random phase approximation level. We find that the electron-phonon interaction between FeSe and SrTiO$_3$ substrate is almost enti…
For two-dimensional superconductors, the high stability in ambient conditions is critical for experiments and applications. Few-layer antimonene can be non-degradative over a couple of months, which is superior to the akin black phosphorus. Based on the anisotropic Migdal-Eliashberg theory and maximally-localised Wannier functions, this work predicts that electron-doping and Ca-intercalation can transform $β$-Sb bilayer from a semimetal to a superconductor. However, the stability of antimonene bilayer in air trends to be decreased due to the electron doping. To overcome this drawback, two kind…
