We formulate a general framework for addressing both odd- and even-frequency superconductivity in Dirac semimetals and demonstrate that the odd-frequency or the Berezinskii pairing can naturally appear in these materials because of the chirality degree of freedom. We show that repulsive frequency-dependent interactions favor the Berezinskii pairing while an attractive electron-electron interaction allows for the BCS pairing. In the case of compensated Dirac and Weyl semimetals, both the conventional BCS and odd-frequency Berezinskii pairings require critical coupling. Since these pairings could originate from physically different mechanisms, our findings pave the way for controlling the realization of the Berezinskii superconductivity in topological semimetals. We also present the density of states with several cusp-like features that can serve as an experimentally verifiable signature of the odd-frequency gap.
We revisit the pairing symmetry competition in quasi-one-dimensional systems. We show that spin-triplet s-wave pairing, where the pair is formed by electrons with different times and has an odd-frequency symmetry, can be realized in systems with strong one-dimensionality when the strength of charge fluctuation dominates over spin fluctuation. The present study provides a novel microscopic mechanism for this exotic pairing originally proposed by Berezinskii in 1974.
We study superconductivity driven by screened Coulomb repulsion in three-dimensional Luttinger semimetals with a quadratic band touching and strong spin-orbit coupling. In these semimetals, the Cooper pairs are formed by spin-3/2 fermions with non-trivial wavefunctions. We numerically solve the linear Eliashberg equation to obtain the critical temperature of a singlet s-wave gap function as a function of doping, with account of spin-orbit and self-energy corrections. In order to understand the underlying mechanism of superconductivity, we compute the sensitivity of the critical temperature to …
We propose the metallic and weakly dispersive surface states of half-Heusler semimetals as a possible domain for the onset of unconventional surface superconductivity ahead of the bulk transition. Using density functional theory (DFT) calculations and the random phase approximation (RPA), we analyse the surface band structure of LuPtBi and its propensity towards Cooper pair formation induced by screened electron-electron interactions in the presence of strong spin-orbit coupling. Over a wide range of model parameters, we find an energetically favoured chiral superconducting condensate featurin…
We investigate the impact of s-wave spin-singlet pairing on antiferromagnetic semimetals with Dirac points or nodal loops at the Fermi level. The electron pairing is generally shown to convert the semimetal into a tunable nodal superconductor. The changeover from fully gapped to gapless phases is dictated by symmetry properties of the antiferromagnetic-superconducting state that set the occurrence of a large variety of electronic topological transitions. We provide a general criterion for predicting a series of transitions between nodal and fully gapped superconducting phases. Different types …
The influence of weak disorder on the superconductivity in ordinary metals can be formally described by the Abrikosov-Gorkov diagrammatic approach. The vertex correction is ignored in this approach because an inequality $k_F l \gg 1$, where $k_F$ is the Fermi momentum and $l$ mean free path, is satisfied in ordinary metals with a large Fermi surface. In a Dirac semimetal that has discrete Fermi points, this inequality may break down even for arbitrarily weak disorder since $k_F \rightarrow 0$, and thus the vertex correction could be important. We incorporate the vertex correction into the self…
We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for highly unconventional superconducting states with the coexistence of chiral d-wave superconductivity, charge density waves and pair density waves in the strained graphene. Our results show that the strain-induced flat bands can promote the superconducting transition temperature approximately $50\%$ compared to that of the original doped graphene, which suggests that the flat-band superconductivity is a potential route to get superconductivity with higher critical temperatures. In particular, we…
We study superconductivity in a three-dimensional zero-density Dirac semimetal in proximity to a ferroelectric quantum critical point. We find that the interplay of criticality, inversion-symmetry breaking, and Dirac dispersion gives rise to a robust superconducting state at the charge-neutrality point, where no Fermi surface is present. Using Eliashberg theory, we show that the ferroelectric quantum critical point is unstable against the formation of a ferroelectric density wave (FDW), whose fluctuations, in turn, lead to a first-order superconducting transition. Surprisingly, long-range supe…
Topological superconductivity in multiband systems has received much attention due to a variety of possible exotic superconducting order parameters as well as non-trivial bulk and surface states. While the impact of coexisting magnetic order on superconductivity has been studied for many years, such as ferromagnetic superconductors, the implication of coexisting multipolar order has not been explored much despite the possibility of multipolar hidden order in a number of $f$-electron materials. In this work, we investigate topological properties of multipolar superconductors that may arise when…
In the search of high-temperature superconductivity one option is to focus on increasing the density of electronic states. Here we study both the normal and $s$-wave superconducting state properties of periodically strained graphene, which exhibits approximate flat bands with a high density of states, with the flatness tunable by the strain profile. We generalize earlier results regarding a one-dimensional harmonic strain to arbitrary periodic strain fields, and further extend the results by calculating the superfluid weight and the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature …
Superconductivity in a doped topological insulator (TI) is a very interesting phenomenon and constitute a new finding of the modern day condensed matter physics. Here we have investigated the physical and transport properties of such an intercalated TI, namely, Bi$_2$Se$_3$ via a strong coupling route. The unique bandstructure of Bismuth Selenide with a dirac cone is strongly influenced with the intercalation by Silver (Ag) (Gold (Au) is included to compare and contrast) at high densities, along with novel structural effects, leading to the emergence of orbital selective metal insulator transi…
Two-dimensional (2D) transition-metal dichalcogenide (TMDs) MoTe2 has attracted much attention due to its predicted Weyl semimetal (WSM) state and a quantum spin Hall insulator in bulk and monolayer form, respectively. We find that the superconductivity in MoTe2 single crystal can be much enhanced by the partial substitution of the Te ions by the S ones. The maximum of the superconducting temperature TC of MoTe1.8S0.2 single crystal is about 1.3 K. Compared with the parent MoTe2 single crystal (TC=0.1 K), nearly 13-fold in TC is improved in MoTe1.8S0.2 one. The superconductivity has been inves…
The recently discovered Dirac and Weyl semimetals are new members of topological materials. Starting from them, topological superconductivity may be achieved, e.g. by carrier doping or applying pressure. Here we report high-pressure resistance and X-ray diffraction study of the three-dimensional topological Dirac semimetal Cd3As2. Superconductivity with Tc ~ 2.0 K is observed at 8.5 GPa. The Tc keeps increasing to about 4.0 K at 21.3 GPa, then shows a nearly constant pressure dependence up to the highest pressure 50.9 GPa. The X-ray diffraction measurements reveal a structure phase transition …
A feasible strategy to realize the Majorana fermions is searching for a simple compound with both bulk superconductivity and Dirac surface states. In this paper, we performed calculations of electronic band structure, the Fermi surface and surface states, as well as measured the resistivity, magnetization, specific heat for TlSb compound with a CsCl-type structure. The band structure calculations show that TlSb is a Dirac semimetal when spin-orbit coupling is taken into account. Meanwhile, we first found that TlSb is a type-II superconductor with $T_c$ = 4.38 K, $H_{c1}$(0) = 148 Oe, $H_{c2}$(…
This work presents the emergence of superconductivity in Ir - doped Weyl semimetal T$_d$ - MoTe$_{2}$ with broken inversion symmetry. Chiral anomaly induced planar Hall effect and anisotropic magneto-resistance confirm the topological semimetallic nature of Mo$_{1-x}$Ir$_{x}$Te$_{2}$. Observation of weak anisotropic, moderately coupled type-II superconductivity in T$_d$ -Mo$_{1-x}$Ir$_{x}$Te$_{2}$ makes it a promising candidate for topological superconductor.
The structural and magneto-transport properties of type-II Dirac semimetal candidate Ir2In8S have been investigated under high pressure. The ambient tetragonal structure (P4_2/mnm) is found to be stable up to 7 GPa, above which the system takes an orthorhombic Pnnm structure, possibly destroying the Dirac cones due to the loss of the four-fold screw symmetry. In the tetragonal structure, a gradual suppression of the transverse magneto-resistance and a rapid change in the magnetic field dependence above 50K suggest possible T-dependent Fermi surface modification. In the high pressure phase, the…
A large number of half-Heusler compounds have been recently proposed as three-dimensional (3D) topological insulators (TIs) with tunable physical properties.However, no transport measurements associated with the topological surface states have been observed in these half-Heusler candidates due to the dominating contribution from bulk electrical conductance. Here we show that, by reducing the mobility of bulk carriers, a two-dimensional (2D) weak antilocalization (WAL) effect, one of the hallmarks of topological surface states, was experimentally revealed from the tilted magnetic field dependen…
Time-reversal invariant topological superconductors are a new state of matter which have a bulk superconducting gap and robust Majorana fermion surface states. These have not yet been realized in solid state systems. In this paper, we propose that this state can be realized in doped Weyl semimetals or Weyl metals. The Fermi surfaces of a Weyl metal carry Chern numbers, which is a required ingredient for such a topological superconductor. By applying the fluctuation-exchange approach to a generic model of time-reversal invariant Dirac and Weyl semimetals, we investigate what microscopic interac…
Weyl semimetal defines a material with three dimensional Dirac cones which appear in pair due to the breaking of spatial inversion or time reversal symmetry. Superconductivity is the state of quantum condensation of paired electrons. Turning a Weyl semimetal into superconducting state is very important in having some unprecedented discoveries. In this work, by doing resistive measurements on a recently recognized Weyl semimetal TaP under pressure up to about 100 GPa, we observe superconductivity at about 70 GPa. The superconductivity retains when the pressure is released. The systematic evolut…
In two-dimensional Dirac semimetals, Cooper pairing instability occurs only when the attractive interaction strength $|u|$ is larger than some critical value $|u_{c}|$ because the density of states vanishes at Dirac points. Disorders enhance the low-energy density of states but meanwhile shorten the lifetime of fermions, which tend to promote and suppress superconductivity, respectively. To determine which of the two competing effects wins, we study the interplay of Cooper pairing interaction and disorder scattering by means of renormalization group method. We consider three types of disorders…
Topological semimetals with superconducting properties provide an emergent platform to explore the properties of topological superconductors. We report magnetization, and magneto-transport measurements on high quality single crystals of transition metal dichalcogenide SnTaS2. It is a nodal line semimetal with superconducting transition below Tc = 2.9 K. Moderate anisotropy (3.1) is observed in upper critical fields along H||c and H||ab plane. In the normal state we observe large magneto-resistance and weak anti-localization effect that provide unambiguous confirmation of topological features i…
Recently topological superconductors emerge as a platform to realise Majorana Fermions which has potential application in topological quantum computation. Superconductivity in these materials can be realised by chemical doping, high pressure or proximity effect. Herein we report the emergent superconductivity in single-crystals of Re doped type-II Weyl semimetal NiTe2. The magnetic and transport measurements highlight that Re substitution in Ni-site induces superconductivity at a maximum temperature of 2.36 K. Hall effect and specific heat measurements indicate that Re substitution is doping h…
The combination with superconductivity and topological nontrivial band structure provides a promising route towards novel quantum states such as topological superconductivity. Here, we report the first observation of superconductivity (4.1 K) in Ba5In4Bi5 single crystal, a noncentrosymmetric topological semimetal featuring nodal chain loops at the high-symmetry points R and X. The magnetization, resistivity, and specific heat capacity measurements reveal that Ba5In4Bi5 is a moderately coupled type-II Bardeen-Cooper-Schrieffer superconductor. Bulk superconductivity is suggested from the magneti…
YPtBi, a topological semimetal with very low carrier density, was recently found to be superconducting below $T_\mathrm{c} = 0.77$\,K. In the conventional theory, the nearly vanishing density of states around the Fermi level would imply a vanishing electron-phonon coupling and would therefore not allow for superconductivity. Based on relativistic density functional theory calculations of the electron-phonon coupling in YPtBi it is found that carrier concentrations of more than $10^{21}$\,cm$^{-3}$ are required to explain the observed critical temperature with the conventional pairing mechanism…
The superconductor PdTe$_2$ was recently classified as a Type II Dirac semimetal, and advocated to be an improved platform for topological superconductivity. Here we report magnetic and transport measurements conducted to determine the nature of the superconducting phase. Surprisingly, we find that PdTe$_2$ is a Type I superconductor with $T_c = 1.64$ K and a critical field $μ_0 H_c (0) = 13.6$ mT. Our crystals also exhibit the intermediate state as demonstrated by the differential paramagnetic effect. For $H > H_c$ we observe superconductivity of the surface sheath. This calls for a close exa…
In topological materials, Dirac fermions can split into two Weyl fermions with opposite chiralities due to the breaking of space inversion symmetry, while in non-centrosymmetric superconductors, novel superconducting electron pairing mechanisms arise because of the antisymmetric spin-orbit coupling. In this work, we report the pressure-introduced superconductivity in a typical noncentrosymmetric Weyl semimetal LaAlX (X=Si and Ge). Superconductivity was observed at around 65 GPa without structural phase transition. A typical dome-shape phase diagram is obtained with the maximum Tc of 2.5 K (2.1…
The search for unconventional superconductivity in Weyl semimetal materials is currently an exciting pursuit, since such superconducting phases could potentially be topologically nontrivial and host exotic Majorana modes. The layered material TaIrTe4 is a newly predicted time-reversal invariant type II Weyl semimetal with minimum number of Weyl points. Here, we report the discovery of surface superconductivity in Weyl semimetal TaIrTe4. Our scanning tunneling microscopy/spectroscopy (STM/S) visualizes Fermi arc surface states of TaIrTe4 that are consistent with the previous angle-resolved phot…
Dirac semimetals host bulk band-touching Dirac points and a surface Fermi loop. We develop a theory of superconducting Dirac semimetals. Establishing a relation between the Dirac points and the surface Fermi loop, we clarify how the nontrivial topology of Dirac semimetals affects their superconducting state. We note that the unique orbital texture of Dirac points and a structural phase transition of the crystal favor symmetry-protected topological superconductivity with a quartet of surface Majorana fermions. We suggest possible application of our theory to recently discovered superconducting …
The Weyl semimetal MoTe$_2$ offers a rare opportunity to study the interplay between Weyl physics and superconductivity. Recent studies have found that Se substitution can boost the superconductivity up to 1.5K, but suppress the Td structure phase that is essential for the emergence of Weyl state. A microscopic understanding of possible coexistence of enhanced superconductivity and the Td phase has not been established so far. Here, we use scanning tunneling microscopy (STM) to study a optimally doped new superconductor MoTe$_{1.85}$Se$_{0.15}$ with bulk Tc ~ 1.5K. By means of quasiparticle in…
Type I superconductivity has recently been reported for the Dirac semimetal PdTe$_2$ (Tc approximately 1.6K) with, remarkably, multiple critical fields and a complex phase diagram. Here, measurements of the specific heat utilizing a thermal relaxation technique are presented. Conventional weak-coupling BCS superconductivity is confirmed by examining the temperature dependence of the specific heat in zero field. By probing the latent heat accompanying the superconducting transition, thermodynamic evidence for type I superconductivity is attained. The presence of the intermediate state is observ…
We report the observation of superconductivity with multiple magnetic ordering and Rashba-type spin-orbit coupling in a layered polar semimetal EuAuBi. Magnetic transition is observed at 4 K, followed by a superconducting transition at 2.2 K, which is sensitive to the crystal surface conditions. The upper critical field Hc2 of 9.8 T for the out-of-plane field is three times higher than that for the in-plane field, which can be associated with the two-dimensional structure or the surface state. On the basis of first-principles calculations, it is found that the characteristic Hc2 possibly refle…
Very recently, NiTe2 has been reported to be a type II Dirac semimetal with Dirac nodes near the Fermi surface. Furthermore, it is unveiled that NiTe2 presents the Hall Effect, which is ascribed to orbital magnetoresistance. The physical properties behavior of NiTe2 under high pressure attracts us. In this paper, we investigate the electrical properties of polycrystalline NiTe2 by application of pressure ranging from 3.4GPa to 54.45Gpa. Superconductivity emerges at critical pressure 12GPa with a transition temperature of 3.7K, and Tc reaches its maximum, 6.4 K, at the pressure of 52.8GPa. Comp…
We discuss the evolution from BCS to Bose superconductivity versus carrier density in gated two-dimensional s-wave superconductors. We show that the transition from the normal to the superconducting state is controlled by the Berezinskii-Kosterlitz-Thouless vortex-antivortex pairing mechanism, and that the evolution from high carrier density (BCS pairing) to low carrier density (Bose pairing) is just a crossover in s-wave systems. We compare our results to recent experiments on the superconductor LixZrNCl, a lithium intercalated layered nitride, and obtain very good quantitative agreement at l…
Lately, the three-dimensional (3D) Dirac semimetal, which possesses 3D linear dispersion in electronic structure as a bulk analogue of graphene, has generated widespread interests in both material science and condensed matter physics. Very recently, crystalline Cd3As2 has been proposed and proved to be one of 3D Dirac semimetals which can survive in atmosphere. Here, by controlled point contact (PC) measurement, we observe the exotic superconductivity around point contact region on the surface of Cd3As2 crystal. The observation of zero bias conductance peak (ZBCP) and double conductance peaks …
Weyl nodal loop semimetals (WNLs) host a closed nodal line loop Fermi surface in the bulk, protected zero-energy flat band, or drumhead, surface states, and strong spin-polarization. The large density of states of the drumhead states makes WNL semimetals exceedingly prone to electronic ordering. At the same time, the spin-polarization naively prevents conventional superconductivity due to its spin-singlet nature. Here we show the complete opposite: WNLs are extremely promising materials for superconducting Josephson junctions, entirely due to odd-frequency superconductivity. By sandwiching a W…
Motivated by the experimental detection of superconductivity in the low-carrier density half-Heusler compound YPtBi, we study the pairing instabilities of three-dimensional strongly spin-orbit coupled semimetals with a quadratic band touching point. In these semimetals the electronic structure at the Fermi energy is described by spin j=3/2 quasiparticles, which are fundamentally different from those in ordinary metals with spin j=1/2. We develop a general approach to analyzing pairing instabilities in j=3/2 materials by decomposing the pair scattering interaction into irreducible channels, pro…
The effects of a strain-induced pseudomagnetic field on inter-node spin-triplet superconducting states in Weyl semimetals are studied by using the quasiclassical Eilenberger formalism. It is found that the Cooper pairing with spins parallel to the pseudomagnetic field has the lowest energy among the spin-triplet states and its gap does not depend on the strength of the field. In such a state, both electric and chiral superconducting currents are absent. This is in contrast to the superconducting states with the spins of Cooper pairs normal to the field, which support a nonzero chiral current a…
The conductance of a junction between a normal metal and a superconductor having the symmetry proposed by Berezinskii is studied theoretically. The main feature of this symmetry is the odd frequency dependence of the anomalous Green function, which makes possible the s-wave triplet superconducting state (the Berezinskii superconductor). The Andreev reflection (which links positive and negative energies) is sensitive to the energetic symmetry; as a result, the conductance of the junction involving the Berezinskii superconductor is qualitatively different from the case of a conventional supercon…
We study superconducting states of doped inversion-symmetric Weyl semimetals. Specifically, we consider a lattice model realizing a Weyl semimetal with an inversion symmetry and study the superconducting instability in the presence of a short-ranged attractive interaction. With a phonon-mediated attractive interaction, we find two competing states: a fully gapped finite-momentum (FFLO) pairing state and a nodal even-parity pairing state. We show that, in a BCS-type approximation, the finite-momentum pairing state is energetically favored over the usual even-parity paired state and is robust ag…
Bulk superconductivity in a topological semimetal is a first step towards realizing topological superconductors, which can host Majorana fermions allowing us to achieve quantum computing. Here, we report superconductivity and compensation of electrons and holes in single crystals of the nodal-line semimetal CaSb$_2$. We characterize the superconducting state and find that Cooper pairs have moderate-weak coupling, and the superconducting transition in specific heat down to 0.22 K deviates from that of a BCS superconductor. The non-saturating magnetoresistance and electron-hole compensation at l…
Superconductors with broken time-reversal symmetry represent arguably one of the most promising venues for realizing highly sought-after topological superconductivity that is vital to fault-tolerant quantum computation. Here, by using extensive muon-spin relaxation and rotation measurements, we report that the isostructural silicide superconductors (Ta, Nb)OsSi spontaneously break time-reversal symmetry at the superconducting transition while surprisingly showing a fully-gapped superconductivity characteristic of conventional superconductors. The first-principles calculations show that (Ta, Nb…
Two-dimensional superconductors attract great interest both for their fundamental physics and for their potential applications, especially in the rapidly growing field of quantum computing. Despite intense theoretical and experimental efforts, materials with a reasonably high transition temperature are still rare. Even more rare are those that combine superconductivity with a non-trivial band topology, to potentially host exotic states of matter such as Majorana fermions. Here, we predict a remarkably high superconducting critical temperature of 21-28 K in the easily exfoliable, topologically …
In iron-based superconductors, band inversion of $d$- and $p$-orbitals yields Dirac semimetallic states. We theoretically investigate their topological properties in normal and superconducting phases, based on the tight-binding model involving full symmetry of the materials. We demonstrate that a Cooper pair between electrons with $d$- and $p$-orbitals relevant to the band structure yields odd-parity superconductivity. Moreover, we present the typical surface states by solving the Bogoliubov-de Gennes equation and characterize them by topological invariants defined with crystal symmetry. It is…
Resilient $j$=3/2 superconductivity in topological semimetal YPtBi
University of Maryland, College Park（马里兰大学帕克分校）；Missouri University of Science and Technology（密苏里科技大学）；National High Magnetic Field Laboratory（国家高磁场实验室）
CaSb2 is a topological nodal-line semimetal that becomes superconducting below 1.6 K, providing an ideal platform to investigate the interplay between topologically nontrivial electronic bands and superconductivity. In this work, we investigated the superconducting order parameter of CaSb2 by measuring its magnetic penetration depth change Δλ(T) down to 0.07 K, using a tunneling diode oscillator (TDO) based technique. Well inside the superconducting state, Δλ(T) shows an exponential activated behavior, and provides direct evidence for a nodeless superconducting gap. By analyzing the temperatur…
Superconducting Weyl semimetals present a novel and promising system to harbor new forms of unconventional topological superconductivity. Within the context of time-reversal symmetric Weyl semimetals with $d$-wave superconductivity, we demonstrate that the number of Majorana cones equates to the number of intersections between the $d$-wave nodal lines and the Fermi arcs. We illustrate the importance of nodal line-arc intersections by demonstrating the existence of locally stable surface Majorana cones that the winding number does not predict. The discrepancy between Majorana cones and the wind…
We show that the charge and thermal transport measurements on ultraclean crystals of URu2Si2 reveal a number of unprecedented superconducting properties. The uniqueness is best highlighted by the peculiar field dependence of thermal conductivity including the first order transition at Hc2 with a reduction of entropy flow. This is a consequence of multi-band superconductivity with compensated electronic structure in the hidden order state of this system. We provide strong evidence for a new type of unconventional superconductivity with two distinct gaps having different nodal topology.
Conventional phonon-electron interaction induces either triplet or one of two (degenerate) singlet pairing states in time reversal and inversion invariant 3D Dirac semi - metal. Investigation of the order parameters and energies of these states at zero temperature in wide range of values of chemical potential $μ$, the effective electron-electron coupling constant $λ$ and Debye energy $T_{D}$ demonstrates that when the exchange interaction is neglected the singlet always prevails, however in significant portions of the $\left( μ,λ,T_{D}\right) $ parameter space the energy difference is very sma…
Motivated by recent experiments indicating strong superconductivity and intricate correlated insulating and flavor-polarized physics in mirror-symmetric twisted trilayer graphene, we study the effects of interactions in this system close to the magic angle, using a combination of analytical and numerical methods. We identify asymptotically exact correlated many-body ground states at all integer filling fractions $ν$ of the flat bands. To determine their fate when moving away from these fine-tuned points, we apply self-consistent Hartree-Fock numerics and analytic perturbation theory, with good…
We theoretically study intrinsic superconductivity in doped Dirac semimetals. Dirac semimetals host bulk Dirac points, which are formed by doubly degenerate bands, so the Hamiltonian is described by a $4 \times 4$ matrix and six types of $k$-independent pair potentials are allowed by the Fermi-Dirac statistics. We show that the unique spin-orbit coupling leads to characteristic superconducting gap structures and $d$ vectors on the Fermi surface and the electron-electron interaction between intra and interorbitals gives a novel phase diagram of superconductivity. It is found that when the inter…
Topological superconductivity with Majorana bound states, which are critical to implement nonabelian quantum computation, may be realized in three-dimensional semimetals with nontrivial topological feature, when superconducting transition occurs in the bulk. Here, we report pressure-induced superconductivity in a transition-metal dipnictide NbAs2. The emergence of superconductivity is not accompanied by any structural phase transition up to the maximum experimental pressure of 29.8 GPa, as supported by pressure-dependent synchrotron X-ray diffraction and Raman spectroscopy. Intriguingly, the R…
