Monday, 12 August 2024
Kagome metals have drawn significant attention in condensed matter physics due to the geometrical arrangement of the lattice that gives rise to a flat band. van Hove singularities (VHS) and Dirac cones. In this talk I will focus on scanning tunneling microscopy (STM) data on the Co termination of the kagome compound Co_3 Sn_2 S_2 (a ferromagnetic Weyl semimetal). The distortion of the surface gives rise to a high order VHS. I will present real space spectroscopic data that is combined with a super sampling technique that allows us to observe the different phases of the electronic wave function. Finally, I will discuss the possibility of a Pomeranchuk instability of the Fermi surface and how it is embedded in quasi-particle interference measurements.
In this talk, I will discuss recent results for charge density wave (CDW) and pair density wave (PDW) instabilities on the kagome lattice near a van Hove singularity. I then discuss the relevance of these results to experimental observations in kagome metals such as CsV_3Sb_5.
In low dimensional superconductors, disorder and many body interactions leads to a veritable zoo of intriguing phases and phase transitions. A exemplar of the same is for instance the highly debated anomalous metallic phase which exists circumventing the celebrated Anderson localisation. On the other hand, disorder itself triggers a host of very intriguing and exotic effects such as the Quantum Griffiths Phase (QGP) that stems from the associated Infinite Randomness Fixed Point (IRFP). In this talk we provide incontrovertible proof of emergence of a QGP in the 2D electron gas formed in the LaScO_3 /SrTiO_2 heterostructure. The signatures of the QGP are embedded in the magneto-resistance exhibited by the sample. In particular, we show that in the Griffiths phase (that obtains at higher temperatures), the effective dynamical exponent diverges as a function of the magnetic field. Further, at lower temperatures we argue that the divergence signalling the QGP is cut-off by interplay of disorder and long range interactions. We present plausible mechanisms that can explain this phenomenon of the emergence of the QGP and also its eventual demise. We also show that the killing-off of the QGP also leads to the destruction of the quantum critical point between the superconductor and the normal state.
Space group symmetries and multipole moments allowed by them can be used to not only classify different phases but also to predict the macroscopic response induced by structural or electronic order parameters. Similarly, magnetic space groups can be utilized to predict macroscopic response induced by magnetic orders. In this talk, we apply similar ideas to possible charge density wave orders in AV3Sb5 Kagome materials with time-reversal symmetry breaking imaginary charge density waves. After showing that charge density wave orders can be represented by magnetic irreducible representations of the space group, we tabulate the different phases induced by them, and predict experimental signatures therein. In particular, we focus on piezomagnetism and spontaneous gyrotropic birefringence and show that these two complimentary tensors can differentiate between most possible phases in Kagome compounds.
The ultranodal superconducting state exhibits very unusual physical properties since it has a strongly enhanced low energy density of states compared to a nodal state. This is due to the existence of a so-called Bogoliubov Fermi surface which is topologically protected and can emerge in a multiband system if a spin singlet pairing gap coexists with a nonunitary interband triplet component. Starting from a microscopic model, I will discuss how such a ultranodal state can be stabilized and examine signatures in the low temperature specific heat, tunneling spectroscopy and spin-relaxation rate pointing towards the existence of Bogoliubov Fermi surfaces. It turns out that FeSe doped with S seems to exhibit a number of these features and might be a strong candidate material to study consequences of Bogoliubov Fermi surfaces.
Tuesday, 13 August 2024
In this talk, I will discuss the charge correlations in two different classes of kagome metals, each with electron fillings near saddle points in their band structures. In the first compound, CsV3Sb5, a dominant breathing mode of the kagome network drives the formation of a metastable charge density state. Charge correlations in this state undergo an unusual evolution upon tuning the carrier filling, suggesting the presence of a nearby nematic instability. In the second compound, ScV6Sn6, charge order is driven by an out-of-plane instability of the Sc-Sn chains that thread through the kagome planes. This drives a form of frustrated charge order likely responsible for the pseudogap and anomalous electronic properties reported in this material. The differing routes to charge order across multiple families of kagome metals will be discussed.
In this talk, I will discuss new progress in understanding electronic loop current states in correlated electron systems. A brief review of this type states will be given for cuprates and Kagome lattice superconductors. We will develop correlated electron models where the loop current states are ground states and discuss the physics behind it.
I will discuss recent theoretical investigations of disorder response and the spin susceptibility of unconventional superconductivity on the kagome lattice. Despite the existence of a sign-changing gap structure, which sums to zero over the Fermi surface, such unconventional pairing states remain robust to disorder and exhibit a Hebel-Slichter peak in the temperature-dependent spin-relaxation rate. It originates from destructive interference effects peculiar to the kagome lattice. For the same reason, unconventional pairing states on the kagome lattice do not exhibit a neutron resonance peak. These results build on previous theoretical studies of the surprising robustness of unconventional pairing states to disorder on the kagome lattice. Taken together these results imply that unconventional superconductivity on the kagome lattice is deceptive in the sense that its properties may appear similar to conventional non-sign-changing superconductivity. These results may be of relevance to the superconducting state of the kagome superconductors $A$V$_3$Sb$_5$ ($A$: K, Rb, Cs) and CsTi$_3$Bi$_5$.
van Hove singularities (vHS) -- momenta for which the group velocity of a Bloch state vanishes, and the density of states diverges -- have a dramatic impact on interaction effects when located near the Fermi level, resulting in a rich competition between superconductivity and charge order. While the presence of vHS near the Fermi level is typically unusual, it appears to be a ubiquitous feature of many recently discovered kagome metals. In this talk I will relate the novel properties of many of these materials to the nature of their vHS. Firstly I will discuss AV3Sb5, in which ARPES identifies twofold vHS near the Fermi level with opposite concavity. The opposite concavity of the vHS results in a weak-coupling instabilitly towards excitonic order, hybridising the two bands. Landau theory predicts the coexistence of charge density wave and excitonic order, offering a possible explanation of many of the unconventional responses seen in AV3Sb5. Second, I will discuss ScV6Sn6. Recent STM experiments have provided smoking gun evidence of excitonic gapping of two opposite concavity vHS, and I present a minimal interacting analysis to explain the observation of nematicity. Lastly, I will discuss the surface states of kagome metals. I show that certain kinds of surface termination exhibit a distortion of the kagome lattice, resulting in surface states in which the vHS flattens to produce a ``higher-order'' vHS. I relate this effect to ongoing STM experiments, and propose several untested applications of this idea.
Coulomb interactions among charge carriers have a profound impact on the macroscopic properties of materials. At sufficient strength, these interactions can give rise to captivating phenomena such as quantum criticality, Mott-Hubbard states, and unconventional superconductivity. Consequently, the search for new families of strongly correlated materials hosting a diverse range of quantum phases is a central research theme in condensed matter physics. In this work, we present experimental evidence obtained from scanning tunneling microscopy measurements for a cascade of strongly correlated states appearing in the partially occupied kagome flat bands of Co1−xFexSn with finite Fe doping x. Unlike in conventional strongly correlated materials, the kagome flat bands arise from a quantum interference effect imparted by geometric frustration [1]. At elevated temperatures (T ≥ 16 K), we observe that strong local Coulomb interactions (U > 100 meV) blend the states of two kagome flat bands across a broad doping range, resulting in an inter-band state that exhibits a nematic order parameter. This strongly coupled state serves as the parent phase of a Mott-Hubbard state, which arises in samples with ideal Fe doping (x = 0.17) and descends into charge ordered states upon doping with both electrons and holes [2]. These observations suggest a significant degree of electronic interactions within the partially filled kagome flat bands over a wide doping range, driven by the combination of strong Coulomb repulsion and the orbital degeneracy of the Co atoms. Our research expands the realm of Mott-Hubbard states to unconventional flat bands and introduces a new avenue for investigating strongly correlated quantum phases of matter.
We gratefully acknowledge support by the Hong Kong RGC and the Croucher Foundation.
[1] C. Chen et al., Phys. Rev. Research 5, 043269 (2023)
[2] C. Chen et al., submitted (2024)
Many-body instabilities in correlated quantum systems, such as charge density waves and electronic nematicity are pillars to understand the underlying energy scales necessary to tune both their electronic and magnetic properties. Kagome lattices have been shown to host a vast array of collective excitations, involving electrons, orbitals, and spins degrees of freedom. Here, we will focus on how optical experiments performed in a pump-and-probe configuration can be a valuable resource to shed light on the dynamics of such correlated phases. In particular, by using a bilayer kagome metal ScV6Sn6 as a platform, we probe directly the amplitude mode associate to its unconventional charge density wave transition, by bringing the system out of equilibrium conditions and, subsequently, studying the relaxation process. Additionally, we benchmark the limits within which the charge density wave can be modulated mechanically by use of uniaxial strain, and we show how the frequency of the amplitude mode point at an enhancement of the acclaimed transition. In this talk, finally, I aim to discuss about possible future perspectives of pump and probe experiments combined with techniques different from optical spectroscopy, which might be relevant for the relaxation dynamics of topological states.
Kagome lattices are known for their outstanding lattice-driven band structure properties, which may give rise to a plethora of different physical properties, such as electronic correlations, charge and spin density waves, superconductivity, and topological states of matter [1]. Due to its Star-of-David atomic arrangement, it is expected to obtain saddle points, flat bands, and Dirac cones in its band structure independent of the details of the compounds [1]. Although some reports claim the presence of Dirac points and saddle points close to the Fermi level, it is still a rare occurrence to obtain a kagome lattice with a flat band located at the Fermi level [2-5]. Interestingly, in this condi-tion, it would be possible to unravel quantum criticality, which raises questions about correlations, topology, and unconventional superconductivity [6]. In this work, we locally explore a potential candidate with flat bands near the Fermi level through scanning tunneling microscopy/spectroscopy (STM/S). We are able to directly make our measurements in the kagome termination, which brings important insights to our STS. Our point STS shows clear many-body phenomena signatures, which are corroborated by temperature and magnetic field dependencies measurements. Additionally, through spectroscopic imaging STS and a direct comparison to ab initio band structure calculations, we can identify the dominating scattering bands near the Fermi level. Finally, we constructed a supercell [7] from our spectroscopic imaging STS, unraveling the unique positioning of the flat band at the kagome layer. In the end, we discuss the possible implications of flat bands and the appearance of a correlated metal phase.
1. J.-X. Yin, B. Lian, and M. Z. Hasan, Nature 612, 647-657 (2022).
2. L. Ye et al., Nature 555, 638-642 (2018).
3. Y. Hu et al., Nat. Commun. 13, 2220 (2022).
4. L. Ye, Nat. Phys. 20, 610-614 (2024).
5. Y. Guo et al., arXiv 2406.05293 (2024).
6. L. Chen et al., arXiv 2307.09431 (2023).
7. I. Zeljkovic et al., Nat. Mater. 11, 585-589 (2012).
Wednesday, 14 August 2024
Electronic flat band systems have gained considerable attention as a platform to realize quantum matter phenomena including the fractional quantum Hall effect, topological phases, unconventional superconductivity, and new forms of magnetism. Electrons in a flat band are characterized by a quenched kinetic energy (bandwidth), a diverging effective mass, and localized wave functions, leading to strong correlation physics in the presence of Coulomb interactions. In recent years, significant efforts have been directed at realizing electronic flat bands in special ‘line graph’ lattices, which under certain conditions exhibit eigenstates that are spatially ‘trapped’ by the total destructive interference of hopping pathways (compact localized states). The realization of new flat band systems and their tuning via chemical composition, carrier doping, or lattice geometry (dimensionality) is an exciting frontier for engineering quantum phases of matter at potentially high temperatures.
In this talk, I will discuss how flat bands are not just a textbook realization of the line-graph band structure toy model in the noninteracting limit, but rather can support strong correlation physics in two paradigmatic lattices – the kagome and pyrochlore lattice. We investigated the electronic band structure in kagome and pyrochlore metals using angle-resolved photoemission spectroscopy (ARPES). I will first discuss the general phenomenology of flat bands in a few representative kagome and pyrochlore intermetallics [1,2]. Next, I will present evidence for one-dimensional flat bands giving rise to heavy fermion-like behavior in kagome metal Ni3In [3]. Last, I will show recent work elucidating the band structure of ‘f electron-free’ heavy-fermion compound LiV2O4, and the role of flat bands in this system [4].
[1] M. Kang, et al., Topological flat bands in frustrated kagome lattice CoSn. Nature Comm. 11, 4004 (2020).
[2] J. Wakefield, et al., Three-dimensional flat bands in pyrochlore metal CaNi2, Nature 623, 301 (2023).
[3] L. Ye, et al., A flat band-induced correlated kagome metal. Nature Phys. 20, 610 (2020).
[4] D. Oh, et al., in preparation.
In this talk, I will report our recent progress on Kagome superconductor AV3Sb5 (A=K, Rb, and Cs). As the first-step toward understanding of their largely unconventional natures, we conducted systematic analyses based on density functional theory calculation. Tight-binding parameters computed by maximally localized Wannier functions technique demonstrates that the out-of-plane Sb out -p orbital is a key element for the description of Van Hove singularity structures known in this material near Fermi level. Correlation strengths are also found to be largely determined by Sb out -p states. Based on constrained random phase approximation, we found that on- site and inter-site interaction parameter are both significantly affected by Sb out -p screenings. The chemical effect on the van Hove singularity structure and the possible suggestion of detecting time reversal symmetry breaking phase will be presented and discussed.
The phase diagram of the kagome metal family AV3Sb5 (A = K, Rb, Cs) features both super- conductivity and charge density wave (CDW) instabilities, which have generated tremendous attention. We've studied the temperature evolution and demise of the CDW state using low resolution X-ray diffraction x-ray scattering study of CsV3Sb5 over a broad range of temperatures from 300 K to ∼ 2 K, below the onset of its super-conductivity at Tc ∼ 2.9 K. Such measurements are optimized for diffuse X-ray scattering. Order parameter measurements of the 2 × 2 × 2 CDW structure show an unusual and extended linear temperature dependence onsetting at T ∗ ∼ 160 K, much higher than the susceptibility anomaly associated with CDW order at TCDW = 94 K. This implies strong CDW fluctuations exist to ∼ 1.7 × TCDW. The CDW order parameter is also observed to be constant from T = 16 K to 2 K, implying that the CDW and superconducting order co-exist below Tc, and, at ambient pressure, any possible competition between the two order parameters is manifested at temperatures well below Tc, if at all. These low resolution X-ray measurements will be put into the context of other studies of diffuse scattering and long range order in quantum materials.
Quantum properties, like superposition, entanglement, and fractionalization, enable fascinating functionalities for quantum technologies. However, it remains unclear whether these properties are exclusive to quantum concepts or can be generalized to the classical vector space. This talk addresses this question. We introduce a generic symmetry group construction built from a vector field in a plaquette of classical spins, demonstrating how classical spins superpose in the irreducible representations (irreps). The corresponding probability amplitudes serve as order parameters and local spins as fragmented excitations. Moreover, the formalism offers a many-body vector field representation for diverse ground states, encompassing spin liquids and fragmented phases described as degenerate ensembles of irreps. Finally, we apply the theory in a square Kagome lattice, showing how the spin liquid state is unstable to either vortex orderings or fragmented phases with any finite Dzyaloshinskii-Moria interaction.
Ref: K. B. Yogendra, S Karmakar, TD, arXiv:2403.15090
Competing many-body phases and chiral superconductivity on the triangular lattice
We derive a minimal low-energy model for Bernal bilayer graphene and related rhombohedral graphene multilayers at low electronic densities by constructing Wannier orbitals defined in real-space supercells of the original primitive cell. Starting from an ab-initio electronic structure theory comprising the atomic carbon $p_z$-orbitals, momentum locality of the Fermi surface pockets around $K,K'$ is circumvented by backfolding the $\pi$-bands to the concomitant mini-Brillouin zone of the supercell, reminiscent of their (twisted) moiré counterparts. The supercell Wannier functions reproduce the spectral weight and Berry curvature of the microscopic model and offer an intuitive real-space picture of the emergent physics at low electronic densities being shaped by flavor-polarized wave packets with mesoscopic extent. By projecting an orbital-resolved, dual-gated Coulomb interaction to the effective Wannier basis, we find that the low-energy physics of Bernal bilayer graphene is governed by weak electron-electron interactions. Our study bridges between existing continuum theories and ab-initio studies of small Fermi pocket systems like rhombohedral graphene stacks by providing a symmetric lattice description of their low-energy physics.
Friday, 16 August 2024
Two dimensional di-chalcogenide materials with Ising spin orbit coupling often show enhanced charge density wave transition temperature and signatures of unconventional superconductivity unlike their three dimensional bulk counterparts. Some of these experiments in monolayer NbSe2 include enhancement of superconducting transition temperature with increasing disorder concentration, observation of two fold symmetric gap in the presence of in plane magnetic field, and observation of Leggett modes in tunnelling experiments.
In this talk, we will first present our calculation of 3Q CDW ordering and role of disorder in normal state of monolayer NbSe2. We will then present our results for the superconducting state assuming a spin fluctuation mediated pairing scenario and explore the dominant gap functions within this theory. Finally, we will discuss the effects of an in-plane Zeeman field on the homogenous superconducting state.
Indian Institute Of Technology Ma
Kagome materials have emerged as a promising platform to study novel quantum phases of matter that arise from the interplay between lattice geometry, band topology, and electronic correlations. They host a variety of electronic and structural instabilities, with charge density waves being a prominent example.
In this talk, I will describe how first principles calculations can be used to explore the rich physics associated with charge density waves. Using bilayer kagome metal ScV6Sn6 as an illustrative example, I will explore competing charge density waves, the role of anharmonic phonon-phonon interactions in the charge density wave transition, and the control of charge density waves by external parameters such as pressure and doping.