The origin of the anomalous superconducting properties of MgB(2)

Th2Mo2Ir2Si4C: An Intergrown Superconductor by Structure Design

Exploration of new superconductors in multicomponent complex systems remains challenging. Among complex superconductors, those containing distinct superconducting layers are quite rare. In this work, based on the block-layer model together with formation energy calculations, we have designed and successfully synthesized a quinary intermetallic compound, Th2Mo2Ir2Si4C. The new material crystallizes in an intergrowth structure with an alternate stacking of superconducting ThMo2Si2C and ThIr2Si2 block layers along the crystallographic c axis. The interblock-layer interaction is dominated by the Si-Ir bonding, which results in a relatively shorter interlayer distance and a stronger coupling between [Mo2Si2C] and fluorite-type [Si2Ir2] layers. Enhanced superconductivity, with a superconducting transition temperature of Tc = 3.4 K and a zero-temperature upper critical field of Hc2(0) = 9.5 kOe, is revealed by measurements of electrical resistivity, magnetic susceptibility, and specific heat. The strategy of the block-layer design demonstrated here can be extended to other intergrowth systems with various functional motifs.

Superconductivity in ordered Li-Al-B compounds

Using first principles calculations, we show that [Formula: see text] materials have strong electron-phonon coupling, with many having a superconducting critical temperature ([Formula: see text]) that exceeds that of the more familiar [Formula: see text] at ambient pressure. In particular, we find that [Formula: see text] is the most stable member of the family, with [Formula: see text] whilst the peak [Formula: see text] is with [Formula: see text] which has [Formula: see text]. Our results reveal that these materials are both thermodynamically and dynamically stable, with strong electron-phonon coupling, indicating significant potential for practical superconducting applications.

Cavity-enhanced superconductivity in MgB2 from first-principles quantum electrodynamics (QEDFT)

Strong laser pulses can control superconductivity, inducing nonequilibrium transient pairing by leveraging strong-light matter interaction. Here, we demonstrate theoretically that equilibrium ground-state phonon-mediated superconductive pairing can be affected through the vacuum fluctuating electromagnetic field in a cavity. Using the recently developed ab initio quantum electrodynamical density-functional theory approximation, we specifically investigate the phonon-mediated superconductive behavior of MgB[Formula: see text] under different cavity setups and find that in the strong light-matter coupling regime its superconducting transition temperature T[Formula: see text] can be enhanced at most by [Formula: see text]10% in an in-plane (or out-of-plane) polarized and realistic cavity via photon vacuum fluctuations. The results highlight that strong light-matter coupling in extended systems can profoundly alter material properties in a nonperturbative way by modifying their electronic structure and phononic dispersion at the same time. Our findings indicate a pathway to the experimental realization of light-controlled superconductivity in solid-state materials at equilibrium via cavity materials engineering.

Atomic-Scale Mechanism of Enhanced Electron-Phonon Coupling at the Interface of MgB2 Thin Films

In conventional Bardeen-Cooper-Schrieffer (BCS) superconductors, electron-phonon coupling is the fundamental mechanism of superconductivity. For instance, the superconductivity of magnesium diboride (MgB2) comes from the coupling between E2g modes (in-plane boron-boron bond vibrations) and self-doped charge carriers. In thin films and ceramics of BCS superconductors, interfaces with discontinuous chemical bonds may alter the local electron-phonon coupling. However, such effects remain largely unexplored. Here, we investigate the heterointerface of the MgB2 film on the SiC substrate at the atomic scale using electron microscopy and spectroscopy. We detect the presence of a thin MgO layer with a thickness of ∼1 nm between MgB2 and SiC. Atomic-level electron energy loss spectra (EELS) show MgB2-E2g mode splitting and softening near the MgB2/MgO interface, which enhances electron-phonon coupling at the interface. Our findings highlight the potential of interface engineering to enhance superconductivity via modulating local phonon states and/or electron states.

Superconductivity in Monolayer Carbon Allotropes with High Thermal Stability

Intrinsic superconductivity is rarely discovered in sp2-hybridized monolayer carbon allotropes. Here we design a carbon monolayer configured of pentagon, heptagon, and hexagon rings with p2 plane group symmetry. Full-sp2 hybridization is proposed to favor thermal metastability on a low Gibbs free energy. The extremely small thermal expansion coefficient is predicted to the turn negative value to positive with elevating temperature. Carbon polygon structures remain intact at a high thermal temperature of 3,000 K. The high specific surface area is found to approach 2,700 m2/g, with O2-adsorption being advantageous over pristine graphene. We reveal electronic Fermi surfaces mediated by phonon modes of carbon out-of-plane vibrations. By calculating the Eliashberg equation, we evaluate intrinsic superconductivity with a large electron-phonon coupling coefficient. The superconducting transition temperature is estimated to reach 20 K under a high logarithmic average frequency. These first-principles calculations shall stimulate experimentalists' interest in exploring low-dimensional carbon superconductors with gas sensitivity.

Superconductive MgB2 Intercalated Muscovite with Dynamically Tunable Stress

In this study, we utilized a stress-sensitive superconductor MgB2 in combination with a flexible muscovite, a layered silicate, to demonstrate that materials in a reduced-dimension environment could be influenced by external strain. MgB2 nanocrystals were inserted into the muscovite interlayers using gas phase intercalation, creating a two-dimensional cavity-like structure. Several experiments confirmed that the cavity-induced static pressure from the intercalation effect and the external dynamic bending effect can affect the physical properties of MgB2. The results of analyzing the changes in superconducting critical temperature (T c) indicate that the dynamic bending effect corresponds to an applied pressure of approximately 1.2 GPa. This method demonstrates that muscovite intercalation serves as a versatile platform for evaluating the stress effects on functional materials in reduced dimensions under ambient conditions.

Two-Gap Superconductivity and the Decisive Role of Rare-Earth d Electrons in Infinite-Layer Nickelates

We present a theoretical prediction of a phonon-mediated two-gap superconductivity in infinite-layer nickelates Nd_{1-x}Sr_{x}NiO_{2} by performing ab initio GW and GW perturbation theory calculations. Electron GW self-energy effects significantly alter the characters of the two-band Fermi surface and enhance the electron-phonon coupling, compared with results based on density functional theory. Solutions of the fully k-dependent anisotropic Eliashberg equations yield two dominant s-wave superconducting gaps-a large gap on a band of rare-earth Nd d and interstitial orbital characters and a small gap on a band of transition-metal Ni d character. Increasing hole doping induces a non-rigid-band response in the electronic structure, leading to a rapid drop of the superconducting T_{c} in the overdoped regime in agreement with experiments.

Raman Spectroscopy Investigation of Phonon Behavior in ZnO-Buffered MgB2 Tapes: Exploring Lattice Dynamics and Anharmonicity

We investigated the phonon behavior of ZnO-buffered MgB2 tapes with varying ZnO buffer layer thicknesses using polarized Raman spectroscopy at room and cryogenic temperatures. Polar plots from integrated angle-resolved polarized Raman spectroscopy (ARPRS) at room temperature revealed substantial distortion in the boron plane geometry due to lattice mismatch among the MgB2 film, ZnO buffer layer, and Hastelloy substrate. This distortion significantly affects the electron-phonon coupling (EPC) constant, λ, which we calculated using the modified McMillan equation by Allen-Dynes in relation to the superconducting transition temperature (Tc) of the sample. At cryogenic temperatures, our investigation of the E2g mode exhibited a notable phonon hardening effect of up to ∼4.1%, correlated with the ZnO buffer layer thickness. Furthermore, analysis of the anharmonic E2g phonon mechanism through line width (full width at half maximum) revealed damping behavior, indicating an additional coupling mechanism within the sample that varies with the temperature. This unique Raman scattering behavior potentially elucidates the high Tc mechanism of MgB2, which is underestimated by traditional EPC calculations. Additionally, increasing the thickness of the ZnO layer is predicted to alleviate the distortion in the boron plane geometry, thereby promoting MgB2 toward its inherent electron-phonon superconducting nature by mitigating the additional coupling mechanisms. Understanding how the ZnO buffer layer influences the phonon dynamics and EPC in MgB2 will provide critical insights into optimizing its superconducting properties and advancing its practical applications in high-performance superconducting devices.

Structural and Electronic Properties of the Magnetic and Nonmagnetic X0.125Mg0.875B2 (X = Nb, Ni, Fe) Materials: A DFT/HSE06 Approach to Investigate Superconductor Behavior

MgB2 material has a simple composition and structure that is well-reported and characterized. This material has been widely studied and applied in the last 20 years as a superconductor in wire devices and storage material for H in the hydride form. MgB2 doped with transition metals improves the superconductor behavior, such as the critical temperature (T cs) or critical current (J sc) for the superconducting state. The results obtained in this manuscript indicate that Nb-, Fe-, and Ni-doping in the Mg site leads to a contraction of the unit cell through the spin polarization on the electronic resonance of the boron layer. Fe and Ni transition metals doping perturb the electronic resonance because of stronger dopant-boron bonds. The unpaired electrons are transferred from 3d orbitals to the empty 2p z orbitals of the boron atoms, locating α electrons in the σ bonds and β electrons in the π orbitals. The observed influence of magnetic dopants on MgB2 enables the proposal of an electronic mechanism to explain the spin polarization of boron hexagonal rings.

A new perspective on ductile high-Tcsuperconductors under ambient pressure: few-hydrogen metal-bonded hydrides

Superconducting materials have garnered widespread attention due to their zero-resistance characteristic and complete diamagnetism. After more than 100 years of exploration, various high-temperature superconducting materials including cuprates, nickelates, iron-based compounds, and ultra-high pressure multi-hydrides have been discovered. However, the practical application of these materials is severely hindered by their poor ductility and/or the need for high-pressure conditions to maintain structural stability. To address these challenges, we first provide a new thought to build high-temperature superconducting materials based on few-hydrogen metal-bonded hydrides under ambient pressure. We then review the related research efforts in this article. Moreover, based on the bonding type of atoms, we classify the existing important superconducting materials and propose the new concepts of pseudo-metal and quasi-metal superconductivity, which are expected to be helpful for the design of new high-temperature superconducting materials in the future.

Surface inducing high-temperature superconductivity in layered metal carborides Li2BC3 and LiBC by metallizing σ electrons

Metallizing σ electrons provides a promising route to design high-temperature superconducting materials, such as MgB2 and high-pressure hydrides. Here, we focus on two MgB2-like layered carborides Li2BC3 and LiBC; their bulk does not have superconductivity because the B-C σ states are far away from the Fermi level (EF), however, based on first-principles calculations, we found that when their bulk systems are cleaved into surfaces with B-C termination, high Tc of ∼80 K could be observed in the exposed B-C layer on the surfaces. Detailed analysis reveals that surface symmetry reduction, due to lattice periodic breaking, not only introduces hole self-doping into surface B-C layers and shifts the σ-bonding states towards the EF - associated with emergent large electronic occupation, but also makes in-plane stretching modes on the surface layer experience significant softness. The enhanced σ states and softened phonon modes work to produce strong coupling, thus yielding high-Tc surface superconductivity, which distinctly differs from the superconducting features of the MgB2 film, which generates phonon stiffness accompanied by suppressed superconductivity. Our findings undoubtedly provide a novel platform to realize high-Tc surface superconductivity, and also clearly elucidate the microscopic mechanism of surface-enhanced superconductivity in favor of creating more high-Tc surface superconductors among MgB2-like layered materials.

Discovery of superconductivity in technetium borides at moderate pressures

Advances in theoretical calculations have boosted the search for high-temperature superconductors, such as sulfur hydrides and rare-earth polyhydrides. However, the required extremely high pressures for stabilizing these superconductors has handicapped further implementation. Based upon thorough structural searches, we identified a series of unprecedented superconducting technetium borides at moderate pressures, including TcB (P63/mmc) with a superconducting transition temperature of Tc = 20.2 K at ambient pressure and TcB2 (P6/mmm) with Tc = 23.1 K at 20 GPa. Superconductivity in these technetium borides mainly originates from the coupling between the low-frequency vibrations of technetium atoms and the dominant technetium-4d electrons at the Fermi level. Our work therefore presents a fresh group in the family of superconducting borides, whose diversified crystal structures suggest rich possibilities in the discovery of other superconducting transition-metal borides.

High-Throughput Screening for Boride Superconductors

A high-throughput screening using density functional calculations is performed to search for stable boride superconductors from the existing materials database. The workflow employs the fast frozen-phonon method as the descriptor to evaluate the superconducting properties quickly. Twenty-three stable candidates were identified during the screening. The superconductivity was obtained earlier experimentally or computationally for almost all found binary compounds. Previous studies on ternary borides are very limited. Our extensive search among ternary systems confirmed superconductivity in known systems and found several new compounds. Among these discovered superconducting ternary borides, TaMo2B2 shows the highest superconducting temperature of ∼12 K. Most predicted compounds were synthesized previously; therefore, our predictions can be examined experimentally. Our work also demonstrates that the boride systems can have diverse structural motifs that lead to superconductivity.

Chemical bonding dictates drastic critical temperature difference in two seemingly identical superconductors

Though YB6 and LaB6 share the same crystal structure, atomic valence electron configuration, and phonon modes, they exhibit drastically different phonon-mediated superconductivity. YB6 superconducts below 8.4 K, giving it the second-highest critical temperature of known borides, second only to MgB2. LaB6 does not superconduct until near-absolute zero temperatures (below 0.45 K), however. Though previous studies have quantified the canonical superconductivity descriptors of YB6's greater Fermi-level (Ef) density of states and higher electron-phonon coupling (EPC), the root of this difference has not been assessed with full detail of the electronic structure. Through chemical bonding, we determine low-lying, unoccupied 4f atomic orbitals in lanthanum to be the key difference between these superconductors. These orbitals, which are not accessible in YB6, hybridize with π B-B bonds and bring this π-system lower in energy than the σ B-B bonds otherwise at Ef. This inversion of bands is crucial: the optical phonon modes we show responsible for superconductivity cause the σ-orbitals of YB6 to change drastically in overlap, but couple weakly to the π-orbitals of LaB6. These phonons in YB6 even access a crossing of electronic states, indicating strong EPC. No such crossing in LaB6 is observed. Finally, a supercell (the M k-point) is shown to undergo Peierls-like effects in YB6, introducing additional EPC from both softened acoustic phonons and the same electron-coupled optical modes as in the unit cell. Overall, we find that LaB6 and YB6 have fundamentally different mechanisms of superconductivity, despite their otherwise near-identity.

Structure searches and superconductor discovery in XB2 (X = Sc, Ti, V, Cr, and Tc)

With extensive structure searches for XB2 (X = Sc, Ti, V, Cr, and Tc) under pressures up to 100 GPa, we uncovered that the crystal structures of these compounds with the lowest enthalpy have the same space group (P6/mmm) as MgB2 at ambient pressure. Among them, ScB2, TiB2 and VB2 are dynamically stable at ambient pressure, but they do not superconduct. CrB2 becomes dynamically stable at 108 GPa and shows superconductivity with a transition temperature (Tc) of 26.0 K. TcB2 is not dynamically stable until 9 GPa. At 20 GPa, it has a Tc of 23.5 K. Further calculations indicate that CrB2 and TcB2 are also thermodynamically stable, suggesting that it is highly likely that they can be synthesized successfully in the laboratory. We found that transition metal atoms (Cr/Tc) dominate soft phonon vibrations and make significant contributions to the electron-phonon coupling (EPC) and superconductivity in CrB2/TcB2, which is in strong contrast to the case of MgB2, where high-frequency B vibrations dominate the EPC and superconductivity. Our work enriches the understanding of superconductivity in transition metal borides.

Design and construction of a refrigerator-cooled adiabatic calorimeter for heat capacity measurement in liquid helium temperature region

Heat capacity is a fundamental thermodynamic property of a substance. Although heat capacity values and related thermodynamic functions are available for many materials, low-temperature heat capacity measurements, especially for novel materials, can still provide valuable insights for research in physics, chemistry, thermodynamics, and other fields. Reliable low-temperature heat capacity data are typically measured using classical adiabatic calorimeters, which use liquid helium as the refrigerant to provide a cryogenic environment for heat capacity measurements. However, liquid helium is not only expensive but also not easy to obtain, which greatly limits the application of adiabatic calorimetry. In this work, an accurate adiabatic calorimeter equipped with a Gifford-MacMahon refrigerator was designed and constructed for measuring the heat capacity of condensed matter in the temperature range from 4 to 100 K. The Gifford-MacMahon refrigerator was utilized to provide a stable liquid helium-free cryogenic environment. A simple mechanical thermal switch assembly was designed to facilitate switching between the refrigeration mode and the adiabatic measurement mode of the calorimeter. Based on the measurement results of standard reference materials, the optimized repeatability and accuracy of heat capacity measurements were determined to be within 0.8% and 1.5%, respectively. The heat capacity of α-Fe2O3 nanoparticles was also investigated with this device. Furthermore, this adiabatic calorimeter only requires electricity to operate in the liquid helium temperature range, which may significantly advance the research on low-temperature heat capacity based on adiabatic calorimetry.

Monolayer Borophene Formation on Cu(111) Surface Triggered by ⟨ 1 1 ¯ 0 ⟩ $\langle {1\bar{1}0} \rangle $ Step Edge

Borophene, a promising material with potential applications in electronics, energy storage, and sensors, is successfully grown as a monolayer on Ag(111), Cu(111), and Au(111) surfaces using molecular beam epitaxy. The growth of two-dimensional borophene on Ag(111) and Au(111) is proposed to occur via surface adsorption and boron segregation, respectively. However, the growth mode of borophene on Cu(111) remains unclear. To elucidate this, scanning tunneling microscopy in conjunction with theoretical calculations is used to study the phase transformation of boron nanostructures under post-annealing treatments. Results show that by elevating the substrate temperature, boron nanostructures undergo an evolution from amorphous boron to striped-phase borophene (η = 1/6) adhering to the Cu⟨ 1 1 ¯ 0 ⟩ $\langle {1\bar{1}0} \rangle $ step edge, and finally to irregularly shaped β-type borophene (η = 5/36) either on the substrate surface or embedded in the topmost Cu layer. dI/dV spectra recorded near the borophene/Cu lateral interfaces indicate that the striped-phase borophene is a metastable phase, requiring more buckling and electron transfer to stabilize the crystal structure. These findings offer not only an in-depth comprehension of the β-type borophene formation on Cu(111), but also hold potential for enabling borophene synthesis on weakly-binding semiconducting or insulating substrates with 1D active defects.

Two-gap topological superconductor LaB2 with high Tc = 30 K

Since two gap superconductivity was discovered in MgB2, research on multigap superconductors has attracted increasing attention because of its intriguing fundamental physics. In MgB2, the Mg atom donates two electrons to the borophene layer, resulting in a stronger gap from the σ band and a weaker gap from the π bond. First-principles calculations demonstrate that the two gap anisotropic superconductivity strongly enhances the transition temperature of MgB2 in comparison with that given by the isotropic model. In this work, we report a three-band (B-σ, B-π, and La-d) two-gap superconductor LaB2 with very high Tc = 30 K by solving the fully anisotropic Migdal-Eliashberg equation. Because of the σ and π-d hybridization on the Fermi surface, the electron-phonon coupling constant λ = 1.5 is significantly larger than the λ = 0.7 of MgB2. Our work paves a new route to enhance the electron-phonon coupling strength of multigap superconductors with d orbitals. On the other hand, our analysis reveals that LaB2 belongs to the weak topological semimetal category, leading to a possible topological superconductor with the highest Tc to date. Moreover, upon applying pressure and/or doping, the topology is tunable between weak and strong with Tc varying from 15 to 30 K, opening up a flexible platform for manipulating topological superconductors.

Electronic Structure and Chemical Bonding of the First-, Second-, and Third-Row-Transition-Metal Monoborides: The Formation of Quadruple Bonds in RhB, RuB, and TcB

Boron presents an important role in chemistry, biology, and materials science. Diatomic transition-metal borides (MBs) are the building blocks of many complexes and materials, and they present unique electronic structures with interesting and peculiar properties and a variety of bonding schemes which are analyzed here. In the first part of this paper, we present a review on the available experimental and theoretical studies on the first-row-transition-metal borides, i.e., ScB, TiB, VB, CrB, MnB, FeB, CoB, NiB, CuB, and ZnB; the second-row-transition-metal borides, i.e., YB, ZrB, NbB, MoB, TcB, RuB, RhB, PdB, AgB, and CdB; and the third-row-transition-metal borides, i.e., LaB, HfB, TaB, WB, ReB, OsB, IrB, PtB, AuB, and HgB. Consequently, in the second part, the second- and third-row MBs are studied via DFT calculations using the B3LYP, TPSSh, and MN15 functionals and, in some cases, via multi-reference methods, MRCISD+Q, in conjunction with the aug-cc-pVQZ-PPM/aug-cc-pVQZB basis sets. Specifically, bond distances, dissociation energies, frequencies, dipole moments, and natural NPA charges are reported. Comparisons between MB molecules along the three rows are presented, and their differences and similarities are analyzed. The bonding of the diatomic borides is also described; it is found that, apart from RhB(X1Σ+), which was just recently found to form quadruple bonds, RuB(X2Δ) and TcB(X3Σ-) also form quadruple σ2σ2π2π2 bonds in their X states. Moreover, to fill the gap existing in the current literature, here, we calculate the TcB molecule.

Stability and superconductivity of freestanding two-dimensional transition metal boridene: M4/3B2

The small atomic mass of boron indicates strong electron-phonon coupling (EPC), so it may have a brilliant performance in superconductivity. Recently, a new 2D boride sheet with ordered metal vacancies and surface terminals (Mo4/3B2-x) was realized in experiments (Zhouet al2021Science373801). Here, the 2D monolayer freestanding Mo4/3B2is evidenced to be thermodynamically stable. Through electronic structure, phonon spectrum and EPC, monolayer Mo4/3B2is found to be an intrinsic phonon-mediated superconductor. The superconducting transition temperature (Tc) is determined to be 4.06 K by the McMillian-Allen-Dynes formula. Remarkably, theTcof monolayer Mo4/3B2can be increased to 6.78 K with an appropriate biaxial tensile strain (+5%). Moreover, we predict that other transition metal replacing Mo atoms is also stable and retaining the superconductivity. Such as monolayer W4/3B2is also a superconductor with theTcof 2.37 K. Our research results enrich the database of 2D monolayer superconductors and boron-related formed materials science.

Two-gap-like anisotropic superconductivity in a bulk boron kagome lattice

Since a report of superconductivity in elemental boron at high pressure [M. I. Eremets et al., Science, 2001, 293, 272-274], many efforts have been devoted to the search for superconductivity in diverse boron allotropes. However, there are few superconducting phenomena to be discovered theoretically and experimentally in elemental bulk boron crystals at normal pressure to date. In this paper, we propose a metastable but dynamically stable metallic bulk boron phase within the kagome lattice, and demonstrate from first principles good superconductivity with a high superconducting critical temperature Tc, e.g., ∼34-39 K, in the elemental bulk boron at ambient pressure. Our calculations indicate that such a high-Tc superconductivity is closely related to the Fermi surface displaying strong electron-phonon coupling with a two-region-like distribution feature, which resulted from two different types of covalent bonding crossing the Fermi level and also gives rise to a two-gap-like superconducting nature in the system. We uncover that the strong electron-lattice coupling is dominated by the transversal acoustic phonon modes around a degenerate softening kink that places the system on the verge of a latent charge density wave. The present findings shed light on a study of the high-Tc superconductivity of the elemental bulk boron phase at normal pressure.

Non-homogeneous pairing in disordered two-orbital s-wave superconductors

We investigate the effects of non-magnetic disorder in a hybridized two-dimensional two-orbital s-wave superconductor (SC) model. The situation in which electronic orbitals overlap such that the hybridizationVi,jamong them is antisymmetric, under inversion symmetry, was taken into account. The on-site disorder is given by a random impurity potentialW. We find that while the random disorder acts to the detriment of superconductivity, hybridization proceeds to favor it. Accordingly, hybridization plays an important role in two-orbital models of superconductivity, in order to hold the long-range order against the increase of disorder. This makes the present model eligible to describe real materials, since the hybridization may be induced by pressure or doping. In addition, the regime from moderate to strong disorder reveals that the system is broken into SC islands with correlated local order parameters. These correlations persist to distances of several order lattice spacing which corresponds to the size of the SC-Islands.

Prediction of superconductivity in sandwich XB4 (X = Li, Be, Zn and Ga) films

Borophenes and 2D boron allotropes are metallic and exhibit a BCS superconducting state, unlike graphene. In-plane stretching vibrational modes in bulk MgB2 boron layers induce phonon-mediated superconductivity. However, the effect of stretching vibrational phonon modes on transition temperature (Tc) still requires further investigations. Here, we use first-principles calculations combined with conventional BCS theory to explore the superconducting properties in a series of dynamically stable boron-based sandwich films that have not been realized experimentally. The sandwich films of XB4 (where X = Li, Be, Zn, Ga) are predicted to exhibit good phonon-mediated superconductivity with high Tc values of 25.1 K, 28.7 K, 38.7 K, and 36.2 K, respectively. The origin of the superconducting states is mainly caused by the high metallicity and strong electron-phonon coupling (EPC), which can be attributed to the presence of intercalated atoms within the borophene layers. It is further demonstrated in the XB4 compounds (where X = Li, Be, Zn, Ga) that the pronounced EPC is not solely attributable to the in-plane vibrations of B atoms, but it is also influenced significantly by the out-of-plane vibrations of B atoms. Sandwich (Li,Be,Zn,Ga)B4 films may be a great choice for nanoscale superconductors as the electron-phonon coupling parameter becomes greater than unity, thereby providing a powerful approach for investigating these systems with high critical temperatures.

Anisotropy and isotope effect in superconducting solid hydrogen

Elucidating the phase diagram of solid hydrogen is a key objective in condensed matter physics. Several decades ago, it was proposed that at low temperatures and high pressures, solid hydrogen would be a metal with a high superconducting transition temperature. This transition to a metallic state can happen through the closing of the energy gap in the molecular solid or through a transition to an atomic solid. Recent experiments have managed to reach pressures in the range of 400-500 GPa, providing valuable insights. There is strong evidence suggesting that metallization via either of these mechanisms occurs within this pressure range. Computational and experimental studies have identified multiple promising crystal phases, but the limited accuracy of calculations and the limited capabilities of experiments prevent us from determining unequivocally the observed phase or phases. Therefore, it is crucial to investigate the superconducting properties of all the candidate phases. Recently, we reported the superconducting properties of theC2/c-24,Cmca-12,Cmca-4 andI41/amd-2 phases, including anharmonic effects. Here, we report the effects of anisotropy on superconducting properties using Eliashberg theory. Then, we investigate the superconducting properties of deuterium and estimate the size of the isotope effect for each phase. We find that the isotope effect on superconductivity is diminished by anharmonicity in theC2/c-24 andCmca-12 phases and enlarged in theCmca-4 andI41/amd-2 phases. Our anharmonic calculations of theC2/c-24 phase of deuterium agree closely with the most recent experiment by Loubeyreet al(2022Phys. Rev. Lett.29035501), indicating that theC2/c-24 phase remains the leading candidate in this pressure range, and has a strong anharmonic character. These characteristics can serve to distinguish among crystal phases in experiment. Furthermore, expanding our understanding of superconductivity in pure hydrogen holds significance in the study of high-Tchydrides.

Bilayer Two-Orbital Model of La_{3}Ni_{2}O_{7} under Pressure

The newly discovered Ruddlesden-Popper bilayer La_{3}Ni_{2}O_{7} reaches a remarkable superconducting transition temperature T_{c}≈80  K under a pressure of above 14 GPa. Here we propose a minimal bilayer two-orbital model of the high-pressure phase of La_{3}Ni_{2}O_{7}. Our model is constructed with the Ni-3d_{x^{2}-y^{2}}, 3d_{3z^{2}-r^{2}} orbitals by using Wannier downfolding of the density functional theory calculations, which captures the key ingredients of the material, such as band structure and Fermi surface topology. There are two electron pockets, α, β, and one hole pocket, γ, on the Fermi surface, in which the α, β pockets show mixing of two orbitals, while the γ pocket is associated with Ni-d_{3z^{2}-r^{2}} orbital. The random phase approximation spin susceptibility reveals a magnetic enhancement associated with the d_{3z^{2}-r^{2}} state. A higher energy model with O-p orbitals is also provided for further study.

Few-Hydrogen High-Tc Superconductivity in (Be4)2H Nanosuperlattice with Promising Ductility under Ambient Pressure

The multi-hydrogen lanthanum hydride LaH10 is well recognized as having the highest critical temperature (Tc) of 250-260 K under unrealistically ultrahigh pressures of about 170-200 GPa. Here, we propose a novel idea for designing a new ambient-pressure high-Tc superconductor by inserting a hexagonal H-monolayer into two close-packed Be monolayers to form a new and stable few-hydrogen metal-bonded layered beryllium hydride (Be4)2H nanosuperlattice, with better ductility than multi-hydrogen, cuprate, and iron-based superconductors, completely contrary to the conventional design strategy for multi-hydrogen covalent high-Tc superconductors with poor ductility at several hundred GPa. We find that (Be4)2H is a phonon-mediated Eliashberg superconductor with a large electron-phonon coupling constant of 1.41 and a high Tc of 84-72 K with Coulomb repulsion pseudopotential μ* = 0.07-0.13. Importantly, (Be4)2H is the only new high-Tc superconductor and fills the gap in the absence of ambient-pressure superconductors around the liquid-nitrogen temperature with good ductility, which is highly beneficial for practical applications.

Search for ambient superconductivity in the Lu-N-H system

Motivated by the recent report of room-temperature superconductivity at near-ambient pressure in N-doped lutetium hydride, we performed a comprehensive, detailed study of the phase diagram of the Lu-N-H system, looking for superconducting phases. We combined ab initio crystal structure prediction with ephemeral data-derived interatomic potentials to sample over 200,000 different structures. Out of the more than 150 structures predicted to be metastable within ~50 meV from the convex hull we identify 52 viable candidates for conventional superconductivity, for which we computed their superconducting properties from Density Functional Perturbation Theory. Although for some of these structures we do predict a finite superconducting Tc, none is even remotely compatible with room-temperature superconductivity as reported by Dasenbrock et al. Our work joins the broader community effort that has followed the report of near-ambient superconductivity, confirming beyond reasonable doubt that no conventional mechanism can explain the reported Tc in Lu-N-H.

Signatures of superconductivity near 80 K in a nickelate under high pressure

Although high-transition-temperature (high-Tc) superconductivity in cuprates has been known for more than three decades, the underlying mechanism remains unknown1-4. Cuprates are the only unconventional superconductors that exhibit bulk superconductivity with Tc above the liquid-nitrogen boiling temperature of 77 K. Here we observe that high-pressure resistance and mutual inductive magnetic susceptibility measurements showed signatures of superconductivity in single crystals of La3Ni2O7 with maximum Tc of 80 K at pressures between 14.0 GPa and 43.5 GPa. The superconducting phase under high pressure has an orthorhombic structure of Fmmm space group with the [Formula: see text] and [Formula: see text] orbitals of Ni cations strongly mixing with oxygen 2p orbitals. Our density functional theory calculations indicate that the superconductivity emerges coincidently with the metallization of the σ-bonding bands under the Fermi level, consisting of the [Formula: see text] orbitals with the apical oxygen ions connecting the Ni-O bilayers. Thus, our discoveries provide not only important clues for the high-Tc superconductivity in this Ruddlesden-Popper double-layered perovskite nickelates but also a previously unknown family of compounds to investigate the high-Tc superconductivity mechanism.

Pressure-induced superconductivity at 32 K in MoB2

Since the discovery of superconductivity in MgB2 (Tc ∼ 39 K), the search for superconductivity in related materials with similar structures or ingredients has never stopped. Although about 100 binary borides have been explored, only a few of them show superconductivity with relatively low Tc. In this work, we report the discovery of superconductivity up to 32 K, which is the highest Tc in transition-metal borides, in MoB2 under pressure. The Tc of MoB2 in the α phase can be well explained by theoretical calculations in the framework of electron-phonon coupling. Furthermore, the coupling between the d electrons of Mo and the out-of-plane Mo-phonon modes are the main driving force of the 32 K superconductivity of MoB2. Our study sheds light on the exploration of high-Tc superconductors in transition metal borides.

Enhancement in High-Field J c Properties and the Flux Pinning Mechanism of ZnO-Buffered MgB2 Films

We investigated the flux pinning properties in terms of the critical current density (J _c) and pinning force density (F _p) of MgB₂ films with ZnO buffer layers of various thicknesses. At higher thicknesses of the buffer layer, significantly larger J _c values are observed in the high-field region, whereas J _c values in the low- and intermediate-field regions remain largely unaffected. A secondary point-pinning mechanism other than primary grain boundary pinning is observed in the F _p analysis, which depends on the thickness of the ZnO buffer layer. Moreover, a close relationship between the Mg and B bond ordering and the fitting parameter of secondary pinning is obtained, indicating that the local structural distortion of MgB₂ induced by ZnO buffer layers with different thicknesses may contribute to flux-pinning enhancement in the high-field region. Discovering further advantages of ZnO as a buffer layer other than the delamination resistance it provides will help to develop a MgB₂ superconducting cable with a high J _c for power applications.

Surface Superconductivity with High Transition Temperatures in Layered CanBn+1Cn+1 Films

Proposed by Ginzberg nearly 60 years ago, surface superconductivity refers to the emergent phenomenon that the electrons on or near the surface of a material becomes superconducting despite its bulk is nonsuperconducting. Here, based on first-principles calculations within density functional theory, we predict that the superconducting transition temperature T_c at the surfaces of Ca_nB_n+1C_n+1 (n = 1, 2, 3, ...) films can be drastically enhanced to ∼90 K from 8 K for bulk CaBC. Our detailed analyses reveal that structural symmetry reduction at surfaces induces pronounced carrier self-doping into the surface B-C layer of the films and shifts the σ-bonding states toward the Fermi level; furthermore, the in-plane stretching modes of the surface layers experience significant softening. These two effects work collaboratively to strongly enhance the electron-phonon coupling, which in turn results in much higher T_c values than the McMillian limit. These findings point to new material platforms for realizing unusually high-T_c surface superconductivity.

Measurements of Surface Impedance in MgB2 in DC Magnetic Fields: Insights in Flux-Flow Resistivity

We present the multifrequency measurements of the surface resistance of spark-plasma-sintered MgB2 performed through a dielectric loaded resonator operating at 16.5 and 26.7 GHz. By normally applying magnetic fields ≤1.2 T to the sample surface, we drove it in the mixed state. By means of data-rooted analysis, we found that the sample vortex dynamics could be fully described within a single-component approach. Pinning phenomena were present and characterized by a depinning frequency smaller than the measurement ones. The multiband nature of the superconductor emerged in the flux-flow resistivity, whose field dependence could be interpreted well within theoretical models. By exploiting them, the upper critical field was extracted in the low-temperature range, which exhibited a consistent temperature trend with the values obtained at the onset of the resistive transition near Tc, and was well in line with literature data on other polycrystalline samples.

A family of superconducting boron crystals made of stacked bilayer borophenes

Monolayer borophenes tend to be easily oxidized, while thicker borophenes have stronger antioxidation properties. Herein, we proposed four novel metallic boron crystals by stacking the experimentally synthesized borophenes, and one of the crystals has been reported in our previous experiments. Bilayer units tend to act as blocks for crystals as determined by bonding analyses. Their kinetic, thermodynamic and mechanical stabilities are confirmed by our calculated phonon spectra, molecular dynamics and elastic constants. Our proposed allotropes are more stable than the boron α-Ga phase below 1000 K at ambient pressure. Some of them become more stable than the α-rh or γ-B₂₈ phases at appropriate external pressure. More importantly, our calculations show that three of the proposed crystals are phonon-mediated superconductors with critical temperatures of about 5-10 K, higher than those of most superconducting elemental solids, in contrast to typical boron crystals with significant band gaps. Our study indicates a novel preparation method for metallic and superconducting boron crystals dispensing with high pressure.

THz/Far infrared synchrotron observations of superlattice frequencies in MgB2

THz/Far Infrared synchrotron absorption experiments on pure and doped MgB₂ samples show that the absorption spectral weight at low wavenumber (i.e., <110 cm^-1) evolves as the temperature is reduced to 10 K. Distinct spectral peak intensities increase as the temperature of MgB₂ and doped MgB₂ approaches, and then crosses, the superconducting transition temperature. These experimental data suggest a strong link to superconductivity induced by subtle shifts in structural symmetry. Significant increases in absorption are observed at frequencies that correspond to the superconducting gaps for doped and pure MgB₂, and at fractions of these frequency (or energy) values. This low wavenumber spectral transition is consistent with the notion that superlattice frequencies contribute to the optic modes of the MgB₂ phonon dispersion and are critical to the superconducting transition for this structure. Key integer ratios are identified in real and reciprocal spaces that link bonding character, Fermi vectors and Fermi surfaces as well as phonon properties with geometric parameters and specific superlattice symmetries for MgB₂. Similarly consistent spectral data at low wavenumber are also obtained for carbon doped Mg¹¹B₂. Density Functional Theory calculations of superlattice phonon dispersions result in folded mode frequencies that match these observed low wavenumber experiments. These results show that symmetry reductions, largely electronic in character although coupled to vibrations, occur with change in temperature and imply strong links to superconductivity mechanisms.

Be-Be π bonding and predicted superconductivity in MBe2 (M=Zr, Hf)

Beryllium, an s-block element, forms an aromatic network of delocalized Be-Be π bonds in alloys ZrBe2 and HfBe2. This gives rise to a structure that fits description as stacked [Be2]4- layers with tetravalent cations in between. The [Be2]4- sublattice is isoelectronic and isostructural to graphite, as well as the [B]-2 sublattice in MgB2, and it bears identical manifestations of π bonding in its electronic band structure. These come in the form of degeneracies at K and H in the Brillouin zone, separated in energy as the result of interlayer orbital interactions. Zr and Hf use their valence d orbitals to form bonds with the layers, leading to nearly identical band structures. Like MgB2, ZrBe2 and HfBe2 are computed to be phonon-mediated superconductors at ambient pressures, with respective critical temperatures of 11.4 K and 8.8 K. The coupling strength between phonons and free electrons is very similar, so that the difference in critical temperatures is controlled by the mass of constituent interlayer ions.

The Emergence and Evolution of Borophene

Neighboring carbon and sandwiched between non-metals and metals in the periodic table of the elements, boron is one of the most chemically and physically versatile elements, and can be manipulated to form dimensionally low planar structures (borophene) with intriguing properties. Herein, the theoretical research and experimental developments in the synthesis of borophene, as well as its excellent properties and application in many fields, are reviewed. The decade-long effort toward understanding the size-dependent structures of boron clusters and the theory-directed synthesis of borophene, including bottom-up approaches based on different foundations, as well as up-down approaches with different exfoliation modes, and the key factors influencing the synthetic effects, are comprehensively summarized. Owing to its excellent chemical, electronic, mechanical, and thermal properties, borophene has shown great promise in supercapacitor, battery, hydrogen-storage, and biomedical applications. Furthermore, borophene nanoplatforms used in various biomedical applications, such as bioimaging, drug delivery, and photonic therapy, are highlighted. Finally, research progress, challenges, and perspectives for the future development of borophene in large-scale production and other prospective applications are discussed.

A low noise cryogen-free scanning tunneling microscope-superconducting magnet system with vacuum sample transfer

Imaging atomically resolved surfaces and performing spectroscopy of exotic surfaces at cryogenic temperature in the presence of the magnetic field is an engineering challenge. Additionally, performing these measurements in an all-cryogen-free environment compounds the above complexity due to the associated vibration and acoustic noise generated by the running of cryogenic cold heads. We here report successful integration of a cryogen-free scanning tunneling microscope (STM) with a cryogen-free superconducting vector-magnet, connected to an ultra-high vacuum cluster assembly for in situ sample transfer. We present details of the integration involving vibration and electrical noise isolation procedures allowing for operation of the STM at extremely low noise levels below 30 fA/Hz during normal operations of the complete vacuum-line assembly with multiple turbomolecular pumps. We demonstrate the above STM capability at cryogenic temperature and in the presence of the magnetic field through atomic resolution imaging of graphite and thin films of gold on the mica substrate transferred in situ to the STM chamber. We also demonstrate spectroscopy signatures of the superconducting gap in MgB₂ thin films. The design of our in-house customized cluster-vacuum-line assembly provides unsought opportunities in continuous uninterrupted imaging of ultra-clean in-vacuum grown surfaces without the need for cryogenic refills in either the STM or the magnet.

Spectroscopic signature of two superconducting gaps and their unusual field dependence in RuB2

Recently RuB2was shown to be a possible two-gap, type-I superconductor. Temperature dependent heat capacity measurements revealed a two-gap superconducting ground state, while magnetic field dependent magnetization measurements indicated surprizing type-I superconductivity with a very low experimental critical field (Hc) ∼120 Oe. In this paper, we report direct spectroscopic evidence of two superconducting energy gaps in RuB2. We have measured scanning tunnelling spectra exhibiting signature of two gaps on different grains of polycrystalline RuB2, possibly originating from multiple bands. Analysis of the temperature dependent tunnelling spectra revealed that the gaps from different bands evolve differently with temperature before disappearing simultaneously at a singleTc. Interestingly, our experiments also reveal that the gaps in quasiparticle density of states survive up to magnetic fields much higher than the bulkHcand they evolve smoothly with field, unlike what is expected for a type-I superconductor, indicating the existence of a 'mixed state'.

Ultrafast Hot Phonon Dynamics in MgB_{2} Driven by Anisotropic Electron-Phonon Coupling

The zone-center E_{2g} modes play a crucial role in MgB_{2}, controlling the scattering mechanisms in the normal state as well the superconducting pairing. Here, we demonstrate via first-principles quantum-field theory calculations that, due to the anisotropic electron-phonon interaction, a hot-phonon regime where the E_{2g} phonons can achieve significantly larger effective populations than other modes, is triggered in MgB_{2} by the interaction with an ultrashort laser pulse. Spectral signatures of this scenario in ultrafast pump-probe Raman spectroscopy are discussed in detail, revealing also a fundamental role of nonadiabatic processes in the optical features of the E_{2g} mode.

Relation between Crystal Structure and Transition Temperature of Superconducting Metals and Alloys

Using the Roeser–Huber equation, which was originally developed for high temperature superconductors (HTSc) (H. Roeser et al., Acta Astronautica 62 (2008) 733), we present a calculation of the superconducting transition temperatures, T c , of some elements with fcc unit cells (Pb, Al), some elements with bcc unit cells (Nb, V), Sn with a tetragonal unit cell and several simple metallic alloys (NbN, NbTi, the A15 compounds and MgB 2 ). All calculations used only the crystallographic information and available data of the electronic configuration of the constituents. The model itself is based on viewing superconductivity as a resonance effect, and the superconducting charge carriers moving through the crystal interact with a typical crystal distance, x. It is found that all calculated T c -data fall within a narrow error margin on a straight line when plotting ( 2 x ) 2 vs. 1 / T c like in the case for HTSc. Furthermore, we discuss the problems when obtaining data for T c from the literature or from experiments, which are needed for comparison with the calculated data. The T c -data presented here agree reasonably well with the literature data.

Crystal phase-dependent electrocatalytic hydrogen evolution performance of ruthenium–boron intermetallics

Four crystal phases of ruthenium–boron intermetallics, including Ru₇B₃, RuB, Ru₂B₃ and RuB₂, are selectively synthesized and their activity trends toward the HER are investigated.

Pressure-induced phase transitions and superconductivity in magnesium carbides

Crystal structure prediction and in silico physical property observations guide experimental synthesis in high-pressure research. Here, we used magnesium carbides as a representative example of computational high-pressure studies. We predicted various compositions of Mg–C compounds up to 150 GPa and successfully reproduced previous experimental results. Interestingly, our proposed MgC₂ at high pressure >7 GPa consists of extended carbon bonds, one-dimensional graphene layers, and Mg atomic layers, which provides a good platform to study superconductivity of metal intercalated graphene nano-ribbons. We found that this new phase of MgC₂ could be recovered to ambient pressure and exhibited a strong electron-phonon coupling (EPC) strength of 0.6 whose corresponding superconductivity transition temperature reached 15 K. The EPC originated from the cooperation of the out-of-plane and the in-plane phonon modes. The geometry confinement and the hybridization between the Mg s and C p_z orbitals significantly affect the coupling of phonon modes and electrons. These results show the importance of the high-pressure route to the synthesis of novel functional materials, which can promote the search for new phases of carbon-based superconductors.

Multi-Band Superconductivity and the Steep Band/Flat Band Scenario

The basic features of multi-band superconductivity and its implications are derived. In particular, it is shown that enhancements of the superconducting transition temperature take place due to interband interactions. In addition, isotope effects differ substantially from the typical BCS scheme as soon as polaronic coupling effects are present. Special cases of the model are polaronic coupling in one band as realized e.g., in cuprates, coexistence of a flat band and a steep band like in MgB2, crossovers between extreme cases. The advantages of the multiband approach as compared to the single band BCS model are elucidated and its rather frequent realization in actual systems discussed.

Synthetically Tuned Pd-Based Intermetallic Compounds and their Structural Influence on the O2 Dissociation in Benzylamine Oxidation

Intermetallic compounds (IMCs) have diverse electronic and geometrical properties to offer. However, the synthesis of intermetallic nanoparticles is not always easy; developing new methodologies that are conventional for many systems can be challenging, especially when incorporating highly electropositive metals to reduce to IMCs using solution synthesis methodologies. In this study, we report a comprehensive approach to access nanocrystalline Pd_xM_y (M = Cu, Zn, Ga, Ge, Sn, Pb, Cd, In) intermetallic (IM) via the coreduction method employing sodium borohydride as the reductant. A combination of diffraction, spectroscopic, and microscopic techniques were performed to characterize the formed nanoparticles in terms of their phase composition, purity, particle size distribution, and surface oxidation properties of metals, respectively. IMCs of Pd with the elements such as Cu, Zn, Ga, and Ge exhibited higher catalytic activity that with elements such as In, Sn, Pb, and Cd. The DFT studies on these compounds revealed that the adsorption of benzylamine at the Pd site and the dissociative adsorption of O₂ on the IM surface play a significant effect on catalytic activity. Among them, PdCu IM exhibited an excellent conversion of benzylamine (94.0%), with 92.2% of dibenzylimine selectivity compared to other IMCs. Moreover, PdCu exhibited decent recyclability and activity for the oxidation of different substituted primary amines.

Self-Consistent Two-Gap Description of MgB2 Superconductor

A self-consistent two-gap γ -model is used to quantitatively describe several thermodynamic properties of MgB 2 superconductor. The superconducting coupling matrix, ν i j , was obtained from the fitting of the superfluid density in the entire superconducting temperature range. Using this input, temperature-dependent superconducting gaps, specific heat, and upper critical fields were calculated with no adjustable parameters and compared with the experimental data as well as with the first-principles calculations. The observed agreement between fit and data shows that γ -model provides adequate quantitative description of the two-gap superconductivity in MgB 2 and may serve as a relatively simple and versatile self-consistent description of the thermodynamic quantities in multi-gap superconductors.

Viewpoint: the road to room-temperature conventional superconductivity

It is a honor to write a contribution on this memorial for Sandro Massidda. For both of us, at different stages in our lives, Sandro was first and foremost a friend. We both admired his humble, playful and profound approach to life and physics. In this contribution we describe the route which permitted to meet a long-standing challenge in solid state physics, i.e. room temperature superconductivity. In less than 20 years the critical temperature of conventional superconductors, which in the last century had been widely believed to be limited to 25 K, was raised from 40 K in MgB₂ to 265 K in LaH₁₀. This discovery was enabled by the development and application of computational methods for superconductors, a field in which Sandro Massidda played a major role.

First-principles prediction of phonon-mediated superconductivity in XBC (X = Mg, Ca, Sr, Ba)

From first-principles calculations, we predict four new intercalated hexagonal XBC (X = Mg, Ca, Sr, Ba) compounds to be dynamically stable and phonon-mediated superconductors. These compounds form a LiBC like structure but are metallic. The calculated superconducting critical temperature, Tc, of MgBC is 51 K. The strong attractive interaction between σ-bonding electrons and the B1g phonon mode gives rise to a larger electron-phonon coupling constant (1.135) and hence high Tc; notably, higher than that of MgB2. The other compounds have a low superconducting critical temperature (4-17 K) due to the interaction between σ-bonding electrons and low energy phonons (E2u modes). Due to their energetic and dynamic stability, we envisage that these compounds can be synthesized experimentally.

Surface termination of MgB2 unveiled by a combination of adsorption experiments and theoretical calculations

Superconductivity in polycrystalline and thin-film MgB2 is strongly affected by the termination of its surface, but a reliable determination of the surface termination is still a challenging task of surface chemistry. Here, the surface properties of superconducting MgB2 were investigated using a combination of inverse gas chromatography and van der Waals corrected density functional theory calculations. The dispersive surface energy was measured as a function of the surface coverage and its value (58 mJ m-2 to 48 mJ m-2) was verified by high-level non-local EXX + RPA calculations, which predicted that the dispersive contribution to the cleavage energy was 56 mJ m-2. The isosteric adsorption enthalpies of cyclohexane, dioxane, acetone and acetonitrile molecules were measured on an MgB2 sample and compared to the DFT calculated enthalpies for the Mg-terminated MgB2, B-terminated MgB2 and MgO(001) surfaces. The close agreement between theory and experiment for the Mg-terminated surface suggested that the magnesium termination is the dominant surface phase of MgB2. Thus, combining inverse gas chromatography experiments with theoretical calculations may provide information about the surface termination.