Observability of Higgs Mode in a system without Lorentz invariance

We study the observability of the Higgs mode in BEC-BCS crossover. The observability of Higgs mode is investigated by calculating the spectral weight functions of the amplitude fluctuation below the critical transition temperature. At zero temperature, we find that there are two sharp peaks on the spectral function of the amplitude fluctuation attributed to Goldstone and Higgs modes respectively. As the system goes from BCS to BEC side, there is strong enhancement of spectral weight transfer from the Higgs to Goldstone mode. However, even at the unitary regime where the Lorentz invariance is lost, the sharp feature of Higgs mode still exists. We specifically calculate the finite temperature spectral function of amplitude fluctuation at the unitary regime and show that the Higgs mode is observable at the temperature that present experiments can reach.Comment: 5 pages, 2 figure

Crossover from Non-Fermi-Liquid to Pseudogap Behavior in the Spectral of Local Impurity in Power-Law Diverging Multichannel Kondo Model

Motivated by the emergence of higher-order van Hove singularities (VHS) with power-law divergent density of states (DOS) ($\rho_c(\omega)=\rho_0/|\omega|^{r}$, $0<r<1$) in materials, we investigate a multichannel Kondo model involving conduction electrons near the higher-order van Hove filling. This model considers $M$ channel and $N$ spin degrees of freedom. Employing a renormalization group analysis and dynamical large-$N$ approach, our results reveal a crossover from a non-Fermi liquid to pseudogap behavior in the spectral properties of the local impurity at the overscreened fixed point. At this critical fixed point, we precisely determine the conditions under which the crossover occurs, either by tuning the exponent $r$ or the ratio $\kappa=M/N$ to a critical value. The results of this study provide novel insights into the non-Fermi liquid and pseudogap behaviors observed in strongly correlated systems, shedding light on the intriguing interplay between higher-order van Hove singularities and multichannel Kondo physics.Comment: 5 pages, 5 fugure

Coexistence of Tri-Hexagonal and Star-of-David Pattern in the Charge Density Wave of the Kagome Superconductor AV3_3Sb5_5

The recently discovered layered kagome metals AV$_3$Sb$_5$(A=K, Rb, Cs) have attracted much attention because of their unique combination of superconductivity, charge density wave (CDW) order, and nontrivial band topology. The CDW order with an in-plane 2x2 reconstruction is found to exhibit exotic properties, such as time-reversal symmetry breaking and rotational symmetry breaking. However, the nature of the CDW, including its dimensionality, structural pattern, and effect on electronic structure, remains elusive despite intense research efforts. Here, using angle-resolved photoemission spectroscopy, we unveil for the first time characteristic double-band splittings and band reconstructions, as well as the band gap resulting from band folding, in the CDW phase. Supported by density functional theory calculations, we unambiguously show that the CDW in AV$_3$Sb$_5$ originates from the intrinsic coexistence of Star-of-David and Tri-Hexagonal distortions. The alternating stacking of these two distortions naturally leads to three-dimensional 2x2x2 or 2x2x4 CDW order. Our results provide crucial insights into the nature and distortion pattern of the CDW order, thereby laying down the basis for a substantiated understanding of the exotic properties in the family of AV$_3$Sb$_5$ kagome metals

Spectroscopic Evidence for a Three-Dimensional Charge Density Wave in Kagome Superconductor CsV3_3Sb5_5

The recently discovered AV3Sb5 (A=K, Rb, Cs) family, possessing V kagome nets, has received considerable attention due to the topological electronic structure and intriguing correlated phenomena, including an exotic charge density wave (CDW) and superconductivity. Detailed electronic structure studies are essential to unravel the characteristics and origin of the CDW as well as its interplay with superconductivity. Here, we present angle-resolved photoemission spectroscopy (ARPES) measurements for CsV3Sb5 at multiple temperatures and photon energies to reveal the nature of the CDW from an electronic structure perspective. We present evidence for a three-dimensional (3D) CDW order. In the process we also pinpoint a surface state attributed to a Cs terminated surface. This state was previously attributed to band folding band due to a CDW along the c direction or a quantum well state from quantum confinement. The CDW expected 2-fold lattice reconstruction along c axis is observed to be a quadrupling of the unit cell, thus for the first time directly demonstrating the 3D nature of the CDW from the electronic structure perspective. Moreover, this 3D CDW configuration originates from two distinct types of distortions in adjacent kagome layers. These present results not only provide key insights into the nature of the unconventional CDW in CsV3Sb5 but also provides an important reference for further studies on the relationship between the CDW and superconductivity.Comment: 19 pages, 4 figure

Phonon promoted charge density wave in topological kagome metal ScV6_{6}Sn6_{6}

Charge density wave (CDW) orders in vanadium-based kagome metals have recently received tremendous attention due to their unique properties and intricate interplay with exotic correlated phenomena, topological and symmetry-breaking states. However, the origin of the CDW order remains a topic of debate. The discovery of ScV$_{6}$Sn$_{6}$, a vanadium-based bilayer kagome metal exhibiting an in-plane $\sqrt{3}$ x $\sqrt{3}$ $\textit{R}$30${\deg}$ CDW order with time-reversal symmetry breaking, provides a novel platform to explore the underlying mechanism behind the unconventional CDW. Here, we combine high-resolution angle-resolved photoemission spectroscopy, Raman scattering measurements and density functional theory to investigate the electronic structures and phonon modes of ScV$_{6}$Sn$_{6}$ and their evolution with temperature. We identify topologically nontrivial Dirac surface states and multiple van Hove singularities (VHSs) in the vicinity of the Fermi level, with one VHS near the K point exhibiting nesting wave vectors in proximity to the $\sqrt{3}$ x $\sqrt{3}$ $\textit{R}$30${\deg}$ CDW wave vector. Additionally, Raman measurements indicate a strong intrinsic electron-phonon coupling in ScV$_{6}$Sn$_{6}$, as evidenced by the presence of a two-phonon mode and a large frequency amplitude mode. Our findings highlight the fundamental role of lattice degrees of freedom in promoting the CDW in ScV$_{6}$Sn$_{6}$ and provide important insights into the fascinating correlation phenomena observed in kagome metals

Phonon promoted charge density wave in topological kagome metal ScV₆Sn₆

Charge density wave (CDW) orders in vanadium-based kagome metals have recently received tremendous attention, yet their origin remains a topic of debate. The discovery of ScV 6 Sn 6 , a bilayer kagome metal featuring an intriguing $$\sqrt{3}\times\sqrt{3}\times3$$ 3 × 3 × 3 CDW order, offers a novel platform to explore the underlying mechanism behind the unconventional CDW. Here, we combine high-resolution angle-resolved photoemission spectroscopy, Raman scattering and density functional theory to investigate the electronic structure and phonon modes of ScV 6 Sn 6 . We identify topologically nontrivial surface states and multiple van Hove singularities (VHSs) in the vicinity of the Fermi level, with one VHS aligning with the in-plane component of the CDW vector near the $$\bar{K}$$ K ¯ point. Additionally, Raman measurements indicate a strong electron-phonon coupling, as evidenced by a two-phonon mode and new emergent modes. Our findings highlight the fundamental role of lattice degrees of freedom in promoting the CDW in ScV 6 Sn 6