Session B03: Charge Density Wave and Phonons in Topological Materials

Progress in Understanding the Charge Density Wave in ScV6Sn6

Kagome metals are exciting flat band systems that often combine non-trivial topology with correlated electron physics. For example, the HfFe₆Ge₆ (166) family of materials has been intensively investigated for their intertwined magnetism and topology. Recently, a charge density wave (CDW) was discovered in the 166 compound ScV₆Sn₆ [1].  This prompted an intense investigation of this sytem over the past months. In this talk, I will review our current understanding of the CDW in ScV₆Sn₆ and will also discuss similarities and differences between ScV₆Sn₆ and 135 materials such as CsV₃Sb₅.

[1] H. W. S. Arachchige, et al. Phys. Rev. Lett. 129, 216402 (2022) https://doi.org/10.1103/PhysRevLett.129.216402   

Visualizing electronic nematicity tunable by magnetic field in epitaxial Kagome magnet FeSn films

Kagome lattice, a two-dimensional hexagonal network of corner-sharing triangles, hosts a plethora of quantum states arising from the interplay of topology, spin-orbit coupling, and electron correlations. In this work, we report symmetry-breaking electronic orders tunable by an applied magnetic field in a model Kagome magnet FeSn consisting of alternating stacks of two-dimensional Fe₃Sn Kagome and Sn₂ honeycomb layers. On the Fe₃Sn layer terminated FeSn thin films epitaxially grown on SrTiO₃(111) substrates by MBE, we observed trimerization of the Kagome lattice using scanning tunneling microscopy/spectroscopy, breaking its six-fold rotational symmetry while preserving the translational symmetry. Such a trimerized Kagome lattice shows an energy-dependent contrast reversal in dI/dV maps, which is significantly enhanced by bound states induced by Sn vacancy defects. This trimerized Kagome lattice also exhibits stripe modulations that are energy-dependent and tunable by an applied in-plane magnetic field, indicating symmetry-breaking nematicity from the entangled magnetic and charge degrees of freedom in antiferromagnet FeSn [Nat Commun 14, 6167 (2023)].   

Tuning of electron pairing by uniaxial strain in kagome lattices

Unique topological and correlated phases arise in kagome lattices associated with Dirac fermions and flat dispersions in the energy spectrum [1]. In this work, we study the interplay of attractive electron interactions and topological states in strained kagome lattices via a Hubbard Hamiltonian. It has been shown that the system is driven into a charge density wave state beyond a critical attractive interaction U_c in a mean-field approximation [2]. We study the tunability of U_c employing uniaxial strains and doping levels and find interesting different phases as these physical parameters change. As uniaxial strain breaks the C₃ symmetry of the lattice, we see the onset of a charge density wave ground state even for weak attractive interaction. In the presence of spin-orbit interaction, the system changes from a quantum spin Hall state to a charge density wave at U_c for 1/3 and 2/3 filling, signaling topological phase transitions. We study the stability of these results beyond the mean-field with Density Matrix Renormalization Group calculations. This work illustrates how electronic correlations and single-particle topological structures compete to create fascinating correlated phases in kagome systems.

[1] M. A. Mojarro, and Sergio E. Ulloa. Strain-induced topological transitions and tilted Dirac cones in kagome lattices. 2024 2D Mater. 11 011001

[2] Xingchuan Zhu, Wanpeng Han, Shiping Feng, and Huaiming Guo. Quantum Monte Carlo study of the attractive kagome-lattice Hubbard model. Phys. Rev. Research 5, 023037   

Exploring structural self-dual twisted kagome metamaterials

Fragile topological states of matter are known to lack the protective features usually associated with topology, resulting in relatively weak manifestations. The strength of these states is often influenced by the system's symmetry and boundaries, making them challenging to observe across various symmetries in phononics. These states are generally limited to specific symmetry classes and are not widely studied in the context of phononic media. However, in this study, we present a theoretical prediction of the emergence of fragile topological bands in a twisted kagome lattice in the self-dual configuration. We assume that the hinges are elastic, finite-thickness ligaments that can store bending energy. The interplay between the edge modes in the bandgaps that bound the fragile topological states leads to the emergence of localized non-trivial corner modes at certain corners of a finite domain. This property qualifies the lattice as a second-order topological insulator. To validate our findings, we conducted a series of experiments on a physical prototype using 3D Scanning Laser Doppler Vibrometry. Our results corroborate the theoretical predictions of the emergence of fragile topological states in this specific system, highlighting the potential of these states to manifest in unconventional configurations.   

Tuning the electron-phonon coupling in MX2 system

Whereas electron-phonon scattering relaxes the electron’s momentum in metals, a perpetual exchange of momentum between phonons and electrons may conserve total momentum and lead to a coupled electron-phonon liquid. In a previous study, we presented evidence of such an electron-phonon liquid in NbGe₂ [1], which could be a platform for observing electron hydrodynamics. Here we provide evidence on tuning the strength of electron-phonon coupling by replacing Ge with Si and Nb with Ta. We combine de Haas-van Alphen (dHvA), electron transport, Raman scattering, and first-principles calculations in this MX₂ topological semimetal family where M=Nb, Ta and X=Ge, Si [2]. Tuning electron-phonon coupling increases the transport mobilities from nearly balanced to an order magnitude larger than quantum mobilities, with crystal structure or topology unchanged, and small differences in electron Fermi surface. Simultaneously, Raman scattering and first-principles calculations demonstrate a dominant phonon-drag effect only in MGe2 compounds. Our study suggests phonon-drag as a mechanism for achieving electron-phonon hydrodynamics.   

High field magnetotransport measurements of the Weyl semi-metal and charge density wave compound TaTe4

The study of the coupling between topological states of matter and correlated states such as superconductivity or density waves in quantum materials has been an active field of research in experimental condensed matter physics in recent years.  In this sense, TaTe₄, a representative of the family of transition metal tetrachalcogenides, appears as a perfect standpoint to study this kind of interplay, since it is a long known-charge density wave system and a predicted Weyl semi-metal. Here we present a detailed study of the electronic band structure of this compound, through a combination of high field magnetotransport measurements and density functional theory calculations. We provide evidence for the presence of Fermi surface sections not previously reported and analyze their connection with the predicted topological states for this compound.   

In-Plane Anisotropy in the Layered Topological Insulator Ta2Ni3Te5 Investigated via TEM and Polarized Raman Spectroscopy

Ta₂M₃Te₅, (M = Pd, Ni) has emerged as a platform to study 2D topological insulators, which have unusual properties such as gapless surface states and spin-momentum locking. In particular, Ta₂Ni₃Te₅ has been shown to host superconductivity under pressure and is predicted to host second-order topology. In this work, we use TEM and polarized Raman spectroscopy (PRS) to study the anisotropic properties of exfoliated few-layer Ta₂Ni₃Te₅. Electron diffraction and TEM imaging were used to probe the structural anisotropic response of the material. Angle-resolved PRS was used to investigate the vibrational modes of the material, including their angular dependence, symmetries, and excitation energy dependence.   

Identifying Raman modes in few-layer WS2 using Polarized Raman Spectroscopy

The anisotropic properties of low-symmetry 2D materials hold significant promise for next-generation electronics and optoelectronics. 2M-WS₂, as a newly discovered topological superconductor, has attracted substantial interest in recent years. Yet, a comprehensive study of its anisotropic features and the corresponding Raman modes remains to be conducted. In this work, we delve into the Raman modes and their corresponding polarization dependence in 2M-WS₂ thin layers using Raman spectroscopy. Preliminary findings suggest that the intensity of Raman spectra for 2M-WS₂ layers amplifies inversely with sample thickness. Furthermore, a detailed analysis of the polarization-dependent Raman spectra, using two distinct laser excitations, allowed us to identify specific Raman modes, encompassing both A_g and B_g, in few-layer 2M-WS₂. A notable observation is that the different Raman modes demonstrate a clear anisotropic dependence on the laser wavelengths. This study deepens our insight into the anisotropic properties of 2M-WS₂ and highlights the pivotal role of laser wavelength in discerning its crystallographic orientation through Raman spectroscopy.   

Witnessing topological spin textures in GdRu2Ge2 centrosymmetric magnet

Magnetic skyrmions are topologically protected spin swirls that are appreciated as a source of emergent electromagnetism. Their topological property and stable particle nature ensure skyrmion is a suitable candidate for low-power spin-based technologies. Particularly in centrosymmetric systems, magnetic skyrmions are mainly driven by long-range Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interactions assisted by geometrically frustrated lattice frameworks. One such goldmine for skyrmions in centrosymmetric systems is the Gd square lattice. GdRu₂Si₂ has recently been shown to host skyrmion lattice around T < 20 K and 2 T ≤ μ₀H ≤ 2.5 T.¹ Herein, we studied GdRu₂Ge₂ in order gain a deeper understanding of how increased spin-orbit coupling in the Ge analog influences the formation of skyrmions. Results from magnetoentropic mapping, topological Hall effect, and heat capacity measurements suggest the formation of skyrmions. We performed density functional theory calculations on both GdRu₂Ge₂ and GdRu₂Si₂ to connect and contrast the relationships between the spin-polarized band structures of these materials and their skyrmion evolution. In this presentation, we will share the knowledge gained from this research from both experimental and theoretical perspectives.

(1) Khanh, N. D.; Nakajima, T.; Yu, X.; Gao, S.; Shibata, K.; Hirschberger, M.; Yamasaki, Y.; Sagayama, H.; Nakao, H.; Peng, L. Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet. Nature Nanotechnology 2020, 15 (6), 444-449.   

Observation of domain wall in chiral antiferromagnet Mn3Sn realized perpendicular magnetization

Magnetic domain wall in chiral antiferromagnet is an important factor in developing fast magnetic memory. The fast speed of the domain wall driven by the current guarantees the perpendicular magnetic memory to move fast, but the domain wall structure, the physics background, has yet to be revealed. Here, we observed the domain wall between perpendicular magnetization of cluster magnetic octupole in Mn₃Sn. Magnetic domains with over hundreds nm scale are observed using nanoscale scanning diamond magnetometry. Reconstructed magnetization is the most consistent with perpendicular polarization in all axes, including the tilted. The domain wall dominated by exchange interaction, not grain boundary, tells us the physical properties and the domain wall chirality. The magnetization axis in the domain wall rotates in the Kagome plane, which suggests that the magnetic octupole is preserved in the domain wall. The estimated domain wall width is much shorter than that of the bulk crystal. Detailed observation of the domain wall powerfully assists in developing materials and devices. Simultaneous revealing of the physical background contributes to understanding the non-trivial domain and spin structure.   

Local structure and magnetic order in Magnetic Weyl semimetal Mn3Sn

Mn₃Sn, a noteworthy kagome-lattice magnetic Weyl semimetal, has recently drawn considerable attention due to its intriguing properties. Even at room temperature, Mn₃Sn exhibits a large anomalous Hall effect, and the presence of magnetic Weyl fermions has been verified by angle-resolved photo-emission spectroscopy (ARPES) and magnetoresistance measurements. In this talk, I will present a comprehensive analysis of crystal structure, magnetic order, and atomic/magnetic pair distribution function analysis using X-ray diffraction and neutron total scattering. Single crystal x-ray diffraction confirmed the hexagonal Mg₃Cd-type average structure at 293 K. The material undergoes a magnetic transition at T_N1 ≈ 420 K to a 120° antiferromagnetic order (k=0) and forms an incommensurate helical magnetic order below T_N2 ≈ 280 K with two propagation vectors, (0,0,0.0877) and (0,0,0.1049). These two propagation vectors exhibit opposite temperature dependence upon cooling, merging to one k vector and separating at lower temperatures. We further observed changes in the pair distribution function patterns associated with the commensurate-incommensurate magnetic transition. This work uncovers the structural and magnetic correlations in local and average length scales and sheds light on understanding the spin-lattice coupling in Mn₃Sn.