Beryllium was recently discovered to harbor a Dirac nodal line (DNL) in its bulk phase and the DNL-induced non-trivial drumhead-like surface states (DNSSs) on its (0001) surface, rationalizing several already-existing historic puzzles [Phys. Rev. Lett., \textbf{117}, 096401 (2016)]. However, to date the underlying mechanism, as to why its (0001) surface exhibits an anomalously large electron-phonon coupling effect ($λ_{e-ph}^s$ $\approx$ 1.0), remains unresolved. Here, by means of first-principles calculations we have evidenced that the coupling of the DNSSs with the phononic states mainly contributes to its novel surface \emph{e-ph} enhancement. Besides that the experimentally observed $λ_{e-ph}^s$ and the main Eliashberg coupling function (ECF) peaks have been reproduced well, we have decomposed the ECF, $α^{2}$$F$(\emph{k},\textbf{\emph{q}};\emph{v}), and the \emph{e-ph} coupling strength $λ(\emph{k},\textbf{\emph{q}};\emph{v})$ as a function of each electron momentum (\emph{k}), each phonon momentum (\textbf{\emph{q}}) and each phonon mode ($v$), evidencing the robust connection between the DNSSs and both $α^{2}$$F$(\emph{k},\textbf{\emph{q}};\emph{v}) and $λ(\emph{k},\textbf{\emph{q}};\emph{v})$. The results reveal the strong \emph{e-ph} coupling between the DNSSs and the phonon modes, which contributes over 80$\%$ of the $λ_{e-ph}^s$ coefficient on the Be (0001) surface. It highlights that the anomalously large \emph{e-ph} coefficient on the Be (0001) surface can be attributed to the presence of its DNL-induced DNSSs, clarifying the long-term debated mechanism.
In parallel to electronic systems, the concept of topology has been extended to phonons, which has led to the birth of topological phonons. Very recently, nodal point phonons, nodal line phonons, and nodal surface phonons have been proposed, and a handful of candidate materials have been predicted in solid-state materials. In this work, based on symmetry analysis and first-principles calculations, we propose that hourglass Weyl nodal line (HWNL) phonons and Dirac nodal line (DNL) phonons coexist in the phonon dispersion of a single material, KCuS, with a $Pnma$-type structure. The HWNLs and DN…
Topological phonons in crystalline materials have been attracting great interest. However, most cases studied so far are direct generalizations of the topological states from electronic systems. Here, we reveal a novel class of topological phonons -- the symmetry-enforced nodal-chain phonons, which manifest features unique for phononic systems. We show that with $D_{2d}$ little co-group at a non-time-reversal-invariant-momentum point, the phononic nodal chain is guaranteed to exist owing to the vector basis symmetry of phonons, which is a unique character distinct from electronic and other sys…
Topological semimetal states which are constrained by symmetries and give birth to innovative excitations are the frontiers of topological quantum matter. Nodal chains in which two nodal rings connect at one point were first discovered in non-symmorphic electronic systems and then generalized to symmorphic phononic systems. In this work, we identify a new class of planar nodal chains in non-symmorphic phononic systems, where the connecting rings lie in the same plane. The constituting nodal rings are protected by mirror symmetry, their intersection is guaranteed by the combination of time-reve…
Formation of swift heavy ion tracks requires extremely fast energy transfer between excited electrons and a lattice. However, electron-phonon energy exchange is too slow, as known from laser-irradiation experiments and calculations. We resolve this contradiction noticing that electron-phonon coupling is not the sole mechanism of energy exchange between electrons and ions: heating of electrons also alters potential energy surface of atoms, accelerating them and increasing their kinetic energy.
Condensed matter systems contain both fermionic and bosonic quasiparticles. Owing to the constraint imposed by the Fermi level, ideal material candidate for the emergent particles with higher-dimensional degeneracy manifold (i.e., nodal lines and nodal surfaces) has not been found in electronic systems. This paper demonstrates that according to the first-principle calculations and symmetry analysis, realistic ternary nitride Li$_6$WN$_4$ features ideal (nearly flat) nodal-surface and nodal-line structures in its phonon spectra. These nodal degeneracies are shaped like lanterns, and their exist…
The Raman exponent of single-molecular magnetic relaxation may take various unexpected values because of rich phonon spectrum and spin-phonon coupling of molecular crystals. We systematically examine the origins of different abnormalities, and clarify misunderstandings in the past, particularly the appropriateness of the fitting procedures for the exponents. We find that exponential laws raised by optical phonons can yield spurious power laws with low exponents. This observation indicates long-standing misunderstandings for origins of low Raman exponents in a large bulk of single-molecule magn…
With the successful synthesis of the two-dimensional (2D) gallium nitride (GaN) in a planar honeycomb structure, the phonon transport properties of 2D GaN have been reported. However, it remains unclear for the thermal transport in Ga-based materials by substituting N to other elements in the same main group, which is of more broad applications. In this paper, based on first-principles calculations, we performed a comprehensive study on the phonon transport properties of 2D GaX (X = N, P, and As) with planar or buckled honeycomb structures. The thermal conductivity of GaP (1.52 Wm-1K-1) is fou…
While condensed matter systems host both Fermionic and Bosonic quasi-particles, reliably predicting and empirically verifying topological states is only mature for Fermionic electronic structures, leaving topological Bosonic excitations sporadically explored. This is unfortunate, as Bosonic systems such a phonons offer the opportunity to assess spinless band structures where nodal lines can be realized without invoking special additional symetries to protect against spin-orbit coupling. Here we combine first-principles calculations and meV-resolution inelastic x-ray scattering to demonstrate t…
Based on first-principles calculations, we predict that the superconducting MgB$_2$ with a AlB$_2$-type centrosymmetric lattice host the so-called phononic topological Weyl nodal lines (PTWNLs) on its bulk phonon spectrum. These PTWNLs can be viewed as countless Weyl points (WPs) closely aligned along the straight lines in the $-$H-K-H direction within the three-dimensional Brillouin zone (BZ). Their topological non-trivial natures are confirmed by the calculated Berry curvature distributions on the planes perpendicular to these lines. These lines are highly unique, because they exactly locate…
We study electron-phonon interaction and related transport properties of nodal-line semimetal ZrSiS using first-principles calculations. We find that ZrSiS is characterized by a weak electron-phonon coupling on the order of 0.1, which is almost energy independent. The main contribution to the electron-phonon coupling originates from long-wavelength optical phonons, causing no significant renormalization of the electron spectral function. At the charge neutrality point, we find that electrons and holes provide a comparable contribution to the scattering rate. The phonon-limited resistivity calc…
Topological materials provide an exclusive platform to study the dynamics of relativistic particles in table-top experiments and offer the possibility of wide-scale technological applications. ZrSiS is a newly discovered topological nodal-line semimetal and has drawn enormous interests. In this report, we have investigated the lattice dynamics and electron-phonon interaction in single crystalline ZrSiS using Raman spectroscopy. Polarization and angle resolved measurements have been performed and the results have been analyzed using crystal symmetries and theoretically calculated atomic vibrati…
Based on first-principles calculations and effective model analysis, all possible straight nodal-line phonons in symmorphic space groups are uncovered. A classification of two-band ${\textbf{k}}\cdot {\textbf{p}}$ models at an arbitrary point on the nodal lines is carried out, and these nodal-line phonons are found to locate along the high symmetry lines of the Brillouin zone. According to our classification, there are two types of nodal-line phonons in symmorphic space groups. The first type possesses a linear dispersion perpendicular to the nodal lines, while the second type exhibits a quadr…
Topological interpretations of phonons facilitate a new platform for novel concepts in phonon physics. Though there are ubiquitous set of reports on topological electronic excitations, the same for phonons are extremely limited. Here, we propose a new candidate material, KMgBO 3 , which showcase the co-existence of several multifold and multidimensional topological phonon excitations, which are protected by spatial and non-spatial symmetries. This includes zero dimensional double, triple and quadratic Weyl phonon nodes, one dimensional nodal line/loop and two dimensional doubly degenerate noda…
This year, Liu \textit{et al}. [Phys. Rev. B \textbf{104}, L041405 (2021)] proposed a new class of topological phonons (TPs; i.e., one-nodal surface (NS) phonons), which provides an effective route for realizing one-NSs in phonon systems. In this work, based on first-principles calculations and symmetry analysis, we extended the types of NS phonons from one- to three-NS phonons. The existence of three-NS phonons (with NS states on the $k_{i}$ = $π$ ($i$ = $x$, $y$, $z$) planes in the three-dimensional Brillouin zone (BZ)) is enforced by the combination of two-fold screw symmetry and time rever…
Hourglass dispersion is generally believed to be solely protected by nonsymmorphic symmetries, because these symmetries can introduce high-dimensional projective representations. Here, based on symmetry arguments, we propose that the hourglass dispersion can be jointly protected by symmorphic and nonsymmorphic symmetries, instead of the only conventional nonsymmorphic symmetry. Moreover, using first-principles calculations, we realize our proposal in phonon spectra of realistic materials that share an antiperovskite structure with space group \emph{P}4/\emph{nmm}. Importantly, the neck points …
Carbon, a basic versatile element in our universe, exhibits rich varieties of allotropic phases, most of which possess promising nontrivial topological fermions. In this work, we identify a distinct topological phonon phase in a realistic carbon allotrope with a body-centered cubic structure, termed bcc-C$_{8}$. We show by symmetry arguments and effective model analysis that there are three intersecting phonon nodal rings perpendicular to each other in different planes. The intersecting phonon nodal rings are protected by time-reversal and inversion symmetries, which quantize the corresponding…
The topological metal states in electronic systems have been extensively studied, but topological phonons were explored only in few examples so far. Here, we expose for the first time that the topological nodal gimbal phonons, type-I and type-II Weyl phonons are simultaneously present in T-carbon, a recently realized new allotrope of carbon. At about 15.2 THz, we find that there exist three mutually intersecting nodal loops (named as nodal gimbal phonons) around Γ point, and two pairs of type-I Weyl phonons on the boundary of Brillouin zone around each X point. In addition, there exist three p…
Based on the dimension of degeneracy, topological electronic systems can roughly be divided into three parts: nodal point, line and surface materials corresponding to zero-, one- and two-dimensional degeneracy, respectively. In parallel to electronic systems, the concept of topology was extended to phonons, promoting the birth of topological phonons. Till date, few nodal point, line and surface phonons candidates have been predicted in solid-state materials. In this study, based on symmetry analysis and first-principles calculation, for the first time, we prove that zero-, one- and two-dimensi…
Despite being the most studied nodal line semimetal, a clear understanding of the transient state relaxation dynamics and the underlying mechanism in ZrSiS is lacking. Using time and angle resolved photoemission spectroscopy, we study the ultrafast relaxation dynamics in ZrSiS and reveal a unique relaxation in the bulk nodal-line state which is well captured by a simple model based on optical and acoustic phonon cooling. We find linear decay processes for both optical and acoustic phonon relaxations with acoustic cooling suppressed at high temperatures. Our results reveal different decay mecha…
By means of first-principles calculations and modeling analysis, we have predicted that the traditional 2D-graphene hosts the topological phononic Weyl-like points (PWs) and phononic nodal line (PNL) in its phonon spectrum. The phonon dispersion of graphene hosts three type-I PWs (both PW1 and PW2 at the BZ corners \emph{K} and \emph{K}', and PW3 locating along the $Γ$-\emph{K} line), one type-II PW4 locating along the $Γ$-\emph{M} line, and one PNL surrounding the centered $Γ$ point in the $q_{x,y}$ plane. The calculations further reveal that Berry curvatures are vanishingly zero throughout t…
Weyl-Dirac nodal line phonons with type-selective surface states
Inner Mongolia University（内蒙古大学）；Research Center for Quantum Physics and Technologies, School of Physical Science and Technology, Inner Mongolia University（内蒙古大学物理科学与技术学院量子物理与技术研究中心）；Key Laboratory of Semiconductor Photovoltaic Technology and Energy Materials at Universities of Inner Mongolia Autonomous Region, Inner Mongolia University（内蒙古自治区高校半导体光伏技术与能源材料重点实验室（内蒙古大学））
Here we report an ultrafast optical spectroscopic study of the nodal-line semimetal ZrSiTe. Our measurements reveal that, converse to other compounds of the family, the sudden injection of electronic excitations results in a strongly coherent response of an $A_{1g}$ phonon mode which dynamically modifies the distance between Zr and Te atoms and Si layers. "Frozen phonon" DFT calculations, in which band structures are calculated as a function of nuclear position along the phonon mode coordinate, show that large displacements along this mode alter the material's electronic structure significantl…
Topological semimetals with several types of three-dimensional (3D) fermion of electrons, such as Dirac fermions, Weyl fermions, Dirac nodal lines and triply degenerate nodal points have been theoretically predicted and then experimentally discovered in the electronic structures of a series of solid crystals. In analogy of various typical fermions, topological mechanical states with two type of bosons, Dirac and Weyl bosons, were also experimentally reported in some macroscopic systems of kHz frequency and with a type of doubly-Weyl phonons in atomic vibrational framework of THz frequency of s…
We study the temperature relaxation dynamics of nodal-line semimetals after a sudden excitation in the presence of acoustic and optical phonon modes. We find that the nodal line constrains the electron momenta in scattering processes and, as a result, the temperature relaxation due to acoustic phonons is exponential as a function of time. However, depending on initial conditions, other functional forms are possible. In typical pump-probe experiments, the temperature relaxation is linear due to acoustic phonons with rates that vary as $\sim n^{1/2}$ with density. The temperature relaxation due …
Perovskite oxides exhibit a rich variety of structural phases hosting different physical phenomena that generate multiple technological applications. We find that topological phonons, i.e., nodal rings, nodal lines, and Weyl points, are ubiquitous in oxide perovskites in terms of structures (tetragonal, orthorhombic, and rhombohedral), compounds (BaTiO3, PbTiO3, and SrTiO3), and external conditions (photoexcitation, strain, and temperature). In particular, in the tetragonal phase of these compounds, all types of topological phonons can simultaneously emerge when stabilized by photoexcitation, …
ZrSiS, an intriguing candidate of topological nodal line semimetals, was discovered to have exotic surface floating two-dimensional (2D) electrons [Phys. Rev. X 7, 041073 (2017)], which are likely to interact with surface phonons. Here, we reveal a prominent Kohn anomaly in a surface phonon branch by mapping out the surface phonon dispersions of ZrSiS using high-resolution electron energy loss spectroscopy. Theoretical analysis via an electron-phonon coupling (EPC) model attributes the strong renormalization of the surface phonon branch to the interactions with the surface floating 2D electron…
Symmetry-Protected Phonon Topology and Low Lattice Thermal Conductivity in Square-Octagonal Chalcogenides
Khalifa University（哈利法大学）；Seoul National University（首尔国立大学）；Indian Institute of Technology, Bombay（印度理工学院孟买分校）；Research and Innovation Center for Graphene and 2D materials (RIC2D)（石墨烯与二维材料研究与创新中心）
$T_{3}$Pb$_{2}Ch_{2}$ ($T$=Pd,Pt and $Ch$=S,Se) with transition metal kagome net: Dynamical properties, phonon nodal line, phonon surface states, and chiral phonons
Recently, magnetic topological semimetals have received a lot of attention due to their potential applications in the field of spintronics. By using first-principles calculations, we propose that two ferromagnetic spinel materials of X2MnO4 (X=Li, Na) have Weyl-type nodal chains around the Fermi level. Their stabilities are validated by cohesive energies, phonon dispersions, and elastic constants. The nodal chains are composed of two types of nodal loops, which are protected by the glide operation Mz, the mirror operation M101 and their equivalent. The drumhead surface states are observed on t…
Despite the intensive efforts for determining the mechanism that causes high-temperature superconductivity in copper oxide materials, no consensus on the pairing mechanism has been reached. Recent advances in high resolution angle-resolved photoemission spectroscopies have suggested that a sizeable electron-phonon coupling exists as the principal cause for kinks in the dispersion relations (energy versus wave vector) of the electronic states. Here, we report on a systematic study about the influence of the electron-phonon coupling parameter "$λ$" in the electronic quasiparticle dispersions alo…
The sudden change of the velocity, so-called "kink," of the dispersing peak in angle resolved photoelectron spectroscopy is a well-known feature in the high temperature superconducting cuprates. Currently, the origin of the kink is being much debated, but a consensus has not emerged yet. Here, we present a study of the momentum evolution of the kink structure from the nodal region towards the anti-nodal region, for optimally doped Bi2212 sample. We show that the observed temperature dependence of the kink structure in both regions of the momentum space is consistent with a scenario in which ph…
Mechanism for Nodal Topological Superconductivity on PtBi$_2$ Surface
Institute for Theoretical Physics and Astrophysics, University of Würzburg（维尔茨堡大学理论物理与天体物理研究所）；Würzburg-Dresden Cluster of Excellence ctd.qmat（维尔茨堡-德累斯顿卓越集群ctd.qmat）
Research on topological physics of phonons has attracted enormous interest but demands appropriate model materials. Our {\it ab initio} calculations identify silicon as an ideal candidate material containing extraordinarily rich topological phonon states. In silicon, we identify various topological nodal lines protected by glide mirror or mirror symmetries and characterized by quantized Berry phase $π$, which gives drumhead surface states observable from any surface orientations. Remarkably, a novel type of topological nexus phonon is discovered, which is featured by double Fermi-arc-like surf…
NaAlSi and NaAlGe are isostructural and isoelectronic semimetals with topological nodal lines close to the Fermi level. Despite having virtually identical electronic structures, NaAlSi exhibits superconductivity below Tc = 6.8 K, whereas NaAlGe does not. We investigate NaAlGe by measuring its electrical resistivity, Hall effect, magnetic susceptibility, and heat capacity using single crystals. It is revealed that NaAlGe is not a simple semimetal but rather has an unusual ground state with a small pseudogap of approximately 100 K close to the Fermi level. We argue that the formation of the pseu…
Rare-earth pyrochlores, commonly exhibiting anomalously low lattice thermal conductivities, are considered as promising topcoat materials for thermal barrier coatings. However the structural origin underlying their low thermal conductivities remain unclear. In the present study, we investigated the phonon properties of two groups of RE pyrochlores, Ln2Zr2O7 (Ln = La, Nd, Sm, Gd) and Gd2T2O7 (T = Zr, Hf, Sn, Pb) employing density functional theory and quasi harmonic approximation. Through the relaxation time approximation (RTA) with Debye model, the thermal conductivities of those RE pyrochlore…
Phonons are an ideal platform for realizing stable spinless two-dimensional (2D) Dirac points because they have a bosonic nature and hard-to-break time-reversal symmetry. It should be noted that the twofold degenerate nodal points in the phonon dispersions of almost all reported 2D materials are misclassified as 'Dirac points' owing to a historical issue. The correct name for these twofold degenerate nodal points should be 'Weyl' because 2D phononic systems are essentially spinless and because each twofold degenerate point is described by a Weyl model in two dimensions. To date, there have bee…
We examine an effect of acoustic phonon scattering on an electric conductivity of single-component molecular conductor [Pd(dddt)$_2$] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate) with a half-filled band by applying the previous calculation in a two-dimensional model with Dirac cone [Phys. Rev. B {\bf 98},161205 (2018)], where the electric transport by the impurity scattering exhibits the noticeable interplay of the Dirac cone and the phonon scattering,resulting in a maximum of the conductivity with increasing temperature. The conductor shows a nodal line semimetal where the band crossing of…
Recently, Cd3As2 has attracted intensive research interest as an archetypical Dirac semimetal, hosting three-dimensional linear-dispersive electronic bands near the Fermi level. Previous studies have shown that single-crystalline Cd3As2 has an anomalously low lattice thermal conductivity, ranging from 0.3 W/mK to 0.7 W/mK at 300 K, which has been attributed to point defects. In this work, we combine first-principles lattice dynamics calculations and temperature-dependent high-resolution Raman spectroscopy of high-quality single-crystal thin films grown by molecular beam epitaxy to reveal the e…
In most materials, transport can be described by the motion of distinct species of quasiparticles, such as electrons and phonons. Strong interactions between quasiparticles, however, can lead to collective behaviour, including the possibility of viscous hydrodynamic flow. In the case of electrons and phonons, an electron-phonon fluid is expected to exhibit strong phonon-drag transport signatures and an anomalously low thermal conductivity. The Dirac semi-metal PtSn4 has a very low resistivity at low temperatures and shows a pronounced phonon drag peak in the low temperature thermopower; it is …
The ultrafast optical response of two nodal-line semimetals, ZrSiS and ZrSiSe, was studied in the near-infrared using transient reflectivity. The two materials exhibit similar responses, characterized by two features, well resolved in time and energy. The first transient feature decays after a few hundred femtoseconds, while the second lasts for nanoseconds. Using Drude-Lorentz fits of the materials' equilibrium reflectance, we show that the fast response is well-represented by a decrease of the Drude plasma frequency, and the second feature by an increase of the Drude scattering rate. This di…
We analyze the band topology of acoustic phonons in 2D materials by considering the interplay of spatial and internal symmetries with additional constraints that arise from the physical context. These supplemental constraints trace back to the Nambu-Goldstone theorem and the requirements of structural stability. We show that this interplay can give rise to previously unaddressed non-trivial nodal charges that are associated with the crossing of the acoustic phonon branches at the center ($Γ$-point) of the phononic Brillouin zone. We moreover apply our perspective to the concrete context of gra…
Topological semimetals (TSMs) have attracted numerous attention due to their exotic physical properties and great application potentials. Silicon-based TMSs are of particularly importance because of their high abundance, nontoxicity and natural compatibility with current semiconductor industry. In this work, an ideal low-energy topological nodal-line semimetal (TNLSM) silicon (I4/mcm-Si$_{48}$) with a clean band crossing at Fermi level is screened from thousands of silicon allotropes by the transferable tight-binding and DFT-HSE calculations. The results of formation energy, phonon dispersion,…
Topological insulators constitute one of the most intriguing phenomena in modern condensed matter theory. The unique and exotic properties of topological states of matter allow for unidirectional gapless electron transport and extremely accurate measurements of the Hall conductivity. Recently, new topological effects occurring at Dirac/Weyl points have been better understood and demonstrated using artificial materials such as photonic and phononic crystals, metamaterials and electrical circuits. In comparison, the topological properties of nodal lines, which are one-dimensional degeneracies in…
The acoustic phonons in the organic-inorganic lead halide perovskites have been reported to have anomalously short lifetimes over a large part of the Brillouin zone. The resulting shortened mean free paths of the phonons have been implicated as the origin of the low thermal conductivity. We apply neutron spectroscopy to show that the same acoustic phonon energy linewidth broadening (corresponding to shortened lifetimes) occurs in the fully inorganic CsPbBr$_{3}$ by comparing the results on the organic-inorganic CH$_{3}$NH$_{3}$PbCl$_{3}$. We investigate the critical dynamics near the three zon…
High-Throughput Discovery of Chiral Carbon-Boron Semimetals with Weyl Topology and Phonon-Mediated Superconductivity
University of Science and Technology of China（中国科学技术大学）；Wuhan Institute of Technology（武汉工程大学）；Hefei University of Technology（合肥工业大学）；Hanhai Lingchao Intelligent Computing (Shanghai) Technology Services Co., Ltd.（瀚海凌潮智能计算（上海）科技有限公司）
