Flat Bands, Strong Correlations, and Heavy Fermions

The electronic band structure of hexagonal Kagome materials is predicted to contain coexisting flat bands, van Hove singularities, and Dirac points. Materials in the hexagonal RM$_6$X$_6$ (166) family (R=rare-earth, M=transition metal, X=Ge, Sn) contain Kagome nets of transition metal ions and are of particular interest because their chemical tunability enables access to these interesting band structure features and to novel ground states. We successfully synthesized single crystals of UV$_6$Sn$_6$ and UNb$_6$Sn$_6$. We probed the physical properties of these two compounds with x-ray and neutron diffraction, magnetic susceptibility, electrical resistivity, thermal expansion, and heat capacity. We found a complex magnetic field-temperature phase diagram and two zero-field magnetic transitions at T$_N$=29 K, T$_2$=24 K for UV$_6$Sn$_6$ and T$_N$=46 K, T$_2$=42 K for UNb$_6$Sn$_6$. Neutron and x-ray diffraction measurements point to deviations from the ideal hexagonal P6/mmm structure, a feature often observed in the 166 family due to the large M-X cage-like voids in the structure. Our band structure calculations place the vanadium flat bands 0.25 eV above the Fermi level for UV6Sn6, and suggest an opportunity to expand the U-based 166 family with the goal of tuning 5f and 3d flat bands close to the Fermi level. 2-D van der Waals materials provide the means to explore strong electronic correlations, quantum criticality, and magnetism in the 2-D limit. We will discuss our recent efforts to synthesize and characterize U-based van der Waals materials, which can be exfoliated.

Will be provided later

Flat bands systems have attracted much interest as they may stablize exotic electronic orders and exhibit prominent phenomena by the control of such orders. Here we present our recent work on flat band systems and the effects of magnetic and mulitopole orders. We present the anomalous transport and thermodynamic phenomena as the responses to the electric, magnetic fields and strain in the system hosting the flat bands close to the Fermi energy.

Although no known electronic material definitely exhibits a superconductive electron pairing potential Δ(k) with odd-parity, Δ(-k)=-Δ(k), UTe2 is now the leading candidate. Ideally, the parity of Δ(k) might be established by using Bogoliubov quasiparticle interference (QPI) imaging, a recognized technique for Δ(k) determination in complex superconductors. However, odd-parity superconductors should support a topological, quasiparticle surface band (QSB) on all crystal termination surfaces and only within the superconductive energy gap |E| ≤ Δ. Thus, QPI should be dominated by the QSB electronic structure k(E) and only reveal bulk Δ(k) characteristics exclusively. Here, by using a superconducting scan-tip to greatly enhance QPI sensitivity in UTe2, we discover and visualize in-gap quasiparticle interference patterns of its QSB. Specifically, at the UTe2 (0-11) cleave surface a band of Bogoliubov quasiparticles appears only in the superconducting state T

In crystalline solids, the interactions of charge and spin can result in a variety of emergent quantum ground states, especially in partially filled, topological flat bands such as Landau levels or in “magic angle” graphene layers. Rhombohedral graphite (RG) is perhaps the simplest and structurally most perfect condensed matter system to host a flat band, which is also protected by the symmetry. In this contribution we provide detailed investigation of the flat band in RG by using low temperature Scanning Tunneling Microscopy (STM) measurements combined with electronic structure calculations [1]. We measured the flat surface band of 8,10 and 17 layers of RG at various charge densities and found correlated behavior up to a temperature of 20 K. At charge neutrality we also identified a degenerate ground state, forming a competing domain structure between a sublattice antiferromagnetic insula- tor and a gapless, correlated paramagnet. Our density-matrix renormalization group (DMRG) calculations explained this observation by revealing a degenerate ground state of the system and demonstrate the important role of the correlation effects. Our work establishes RG as a platform to study many-body interactions beyond the mean-field approach, where quantum fluctuations and entanglement dominate. [1] I. Hagymási et al., Observation of competing, correlated ground states in the flat band of rhombohedral graphite.Sci. Adv.8,eabo6879 (2022).

Quantum fluctuations related to a T = 0 quantum critical point (QCP) result from the frustration of magnetic order, as well as instabilities of the moment-bearing electrons themselves. The interplay of both types of quantum fluctuations at T = 0 is the basis of generic phase diagrams, so far focused largely on the stability of magnetic order in three-dimensional (3D) correlated electron systems that are QC. Strong quantum fluctuations limit magnetic correlations in one-dimensional (1D) systems, however it has not been possible to integrate them into this same rubric, due to the lack of correlated metals that are robustly one-dimensional. We present here experimental evidence for 1D excitations in Ti4MnBi2, a moderately correlated metal consisting of well-separated chains of spin S = 1/2 moments. Detailed comparison of inelastic neutron scattering (INS) measurements and Density Matrix Renormalization Group (DMRG) calculations show that Ti4MnBi2 is well described by the frustrated J1-J2 1D XXZ Hamiltonian, and naturally forms in a gapped vector chiral phase, located near a T = 0 phase boundary to a gapless ferromagnetic phase. The 1D character of Ti4MnBi2 is confirmed by the observation of spinons, while proximity to this quantum phase transition, the weakness of interchain coupling, and the possible suppression of the magnetic moments by the Kondo effect all act to minimize the growth of long-ranged and long-lived correlations that would otherwise lead to long-ranged order. Evidence for a field driven quantum critical point will be presented. This work is a collaboration with Xiyang Li, Alberto Nocera, Kateryna Foyetsova, and George Sawatzky. This research was supported by the National Science Foundation through grant NSF-DMR-1807451, by the Natural Sciences and Engineering Research Council of Canada (NSERC), and by the Stewart Blusson Quantum Matter Institute by the Canada First Research Excellence Fund (CFREF).

Realizing robust topological electronic phases at zero magnetic field has been a longstanding quest since Haldane’s theoretical proposal of the quantum anomalous Hall (QAH) state. Moiré superlattices in van der Waals (vdW) materials, which arise from small rotational misalignment between layers in vdW heterostructures, provide a powerful way to control the interactions and topology of electronic bands. This tunability has made them an active platform for pursuing novel topological states. My talk will focus on QAH states that emerge in twisted graphene multilayers. In contrast to magnetically doped topological insulators, the QAH states in these moiré systems are driven by intrinsic strong interactions, which polarize the electrons into a single moiré miniband with non-zero Chern number. The magnetization of these “orbital Chern insulators” (OCI) arises predominantly from the orbital motion of the electrons rather than the electron spin. This orbital character endows OCIs with curious magnetic properties and enables novel effects, such as non-volatile electrical switching of the magnetic and topological orders using gate voltages or currents. Strong Coulomb interaction at partial fillings of flat topological moiré bands may also lead to additional topological gapped states with integer or fractional quantized Hall conductivity.

Moiré materials built on transition metal dichalcogenide semiconductors have emerged as a tunable platform for simulating the Hubbard model on a triangular lattice. A natural question arises: Can the platform be tuned to yield a phase diagram similar to that in high-temperature cuprate superconductors? In this talk, I will discuss the emergence of “high-temperature” superconductivity near the Mott transition in a triangular moiré lattice with intermediate coupling strength. The emergent doping-temperature phase diagram looks remarkably similar to that in cuprate superconductors. I will also discuss the evolution of the phase diagram by tuning the band structure of the material by gating. The results could provide a new angle for understanding the phenomenon of high-temperature superconductivity in strongly correlated materials.

We demonstrate that a disordered magnetic Weyl semimetal may be mapped onto a two-dimensional array of coupled replicated Hubbard chains, where the Hubbard $U$ is directly related to the variance of the disorder potential. This is a three-dimensional generalization of a similar mapping of the two-dimensional quantum Hall plateau transition to a one-dimensional Hubbard chain. We demonstrate that this mapping leads to the conclusion that the Weyl semimetal becomes a diffusive metal with a nonzero density of states at arbitrarily weak disorder, in agreement with recent work. We also discuss the absence of localization in strongly disordered Weyl semimetals from the viewpoint of this mapping and rederive the nonlinear sigma model with a topological term, which describes interacting diffusion modes in this three-dimensional topological metal.

The interplay between interactions and topology in quantum materials is a topic of much current interest. For metallic systems, the question of whether and how electron correlations can drive topological states without any noninteracting counterpart is an open and pressing challenge. The concept of the Weyl-Kondo semimetal, introduced concurrently through theoretical and experimental efforts [1], has established a foundation for progress in this area. This is especially so because heavy fermion systems exhibit extremely strong correlations for such non-perturbative effect as strange metallicity [2]. In this work, we demonstrate how non-Fermi liquid single-particle excitations in heavy-fermion systems provide a means to realize the nontrivial correlated topological matter. We propose topological semimetals without quasiparticles both in a quantum critical phase and at a quantum critical point [3]. The quantum critical phase arises in a multi-channel Kondo lattice while the quantum critical point develops from a competition between the RKKY and Kondo interactions. The enabling methodological notion we introduce here [3] (and generalize elsewhere [4]) is that symmetry constraints on topology proceed through the electron spectral functions and the associated Green’s function eigenfunctions. Our work opens a new avenue for investigating gapless topological phases across a wide range of strongly correlated materials and models. [1] H.-H. Lai et al., “Weyl-Kondo semimetal in heavy fermion systems'', PNAS 115, 93 (2018); S. Dzsaber et al., “Kondo insulator to semimetal transformation tuned by spin-orbit coupling'', Phys. Rev. Lett. 118, 246601 (2017); L. Chen et al., “Topological semimetal driven by strong correlations and crystalline symmetry”, Nat. Phys. 18, 1341 (2022). [2] Haoyu Hu, L. Chen, Q. Si, “Quantum critical metals and loss of quasiparticles”, Nat. Phys. 20, 1863 (2024); S. Paschen, Q. Si, “Quantum phases driven by strong correlations “, Nat. Rev. Phys. 3, 9 (2021); Q. Si et al, “Locally-critical quantum phase transitions in strongly correlated metals'', Nature 413, 804 (2001). [3] Haoyu Hu et al., “Topological semimetals without quasiparticles”, arXiv:2110.06182; L. Chen, Haoyu Hu, et al., unpublished. [4] C. Setty, Haoyu Hu et al., “Symmetry constraints and spectral crossing in a Mott insulator with Green’s function zeros”, Phys. Rev. Research 6, L032018 (2024).

Heavy fermion systems exhibit a number of intriguing properties, from strange metal behavior and unconventional superconductivity to correlation-driven topology [1]. On their own, these features are comparably well understood within the context of Kondo physics, which has lately been suggested to play a more general role across many different material platforms [2]. The Weyl-Kondo semimetal state [3-5] realized in Ce$_3$Bi$_4$Pd$_3$ [3,5] is the first example of a gapless topological phase driven by the Kondo effect. Using the genuinely quantum critical heavy fermion semimetal CeRu$_4$Sn$_6$ [6] we address the open question whether such a topological phase can still be realized when the Fermi liquid framework breaks down, e.g at a quantum critical point of beyond-order parameter type [1]. Our experiments find a topological semimetal phase that emerges from the system's quantum critical state, with a dome-like shape as a function of pressure and magnetic field. We understand these results by generalizing Weyl crossings as non-quasiparticle spectral functions overlapping in energy at specific points in momentum space [7]. This provides a foundation for a new design principle for correlation-driven topological phases: emergent topological phases from quantum criticality. [1] S. Paschen and Q. Si, Nat. Rev. Phys. 3, 9 (2021). [2] J. G. Checkelsky et al., Nat. Rev. Mater. 9, 509 (2024) [3] S. Dzsaber et al., Phys. Rev. Lett., 118, 246601 (2017) [4] H.-H. Lai et al., Proc. Natl. Acad. Sci. U.S.A. 115, 93 (2018) [5] S. Dzsaber et al., Proc. Natl. Acad. Sci. U.S.A. 118, e2013386118 (2021) [6] W. T. Fuhrman et al., Sci. Adv. 7, eabf9134 (2021) [7] D. M. Kirschbaum, L. Chen et al., arXiv:2404.15924 (2024) *This work was supported by the Austrian Science Fund (FWF grants I4047, SFB F 86 "Q-M&S", and I5868-N/FOR 5249 "QUAST"), the European Microkelvin Platform (H2020 project 824109), and the European Research Council (ERC Advanced Grant 101055088-CorMeTop).

TBD

The microscopic mechanism of superconductivity in the magic-angle twisted graphene family, including magic-angle twisted trilayer graphene (MATTG), is poorly understood. Properties of MATTG, like Pauli limit violation, suggest unconventional superconductivity. Theoretical studies propose proximal magnetic states in the phase diagram, but direct experimental evidence is lacking. We show direct evidence for an in-plane magnetic order proximal to the superconducting state using two complementary electrical transport measurements. First, we probe the superconducting phase by using statistically significant switching events from superconducting to the dissipative state of MATTG. The system behaves like a network of Josephson junctions due to lattice relaxation-induced moiré inhomogeneity in the system. We observe non-monotonic and hysteretic responses in the switching distributions as a function of temperature and in-plane magnetic field. Second, in normal regions doped slightly away from the superconducting regime, we observe hysteresis in magnetoresistance with an in-plane magnetic field; showing evidence for in-plane magnetic order that vanishes ∼900 mK. Additionally, we show a broadened Berezinskii-Kosterlitz-Thouless transition due to relaxation-induced moiré inhomogeneity. We find superfluid stiffness Js∼0.15 K with strong temperature dependence. Theoretically, the magnetic and superconducting order arising from the magnetic order's fluctuations have been proposed - we show direct evidence for both. Our observation that the hysteretic magnetoresistance is sensitive to the in-plane field may constrain possible intervalley-coherent magnetic orders and the resulting superconductivity that arises from its fluctuations.

The emergence of field-reinforced superconductivity in UTe2 is coincident with a metamagnetic transition into a spin-polarized state. Understanding the connection between magnetism and superconductivity is key to determining the superconducting order parameter and the pairing mechanism. However, little is known about the magnetism in UTe2 as it seems to straddle the boundary between local moment and itinerant Kondo physics. We explore the magnetotropic susceptibility of UTe2 in high magnetic fields over a broad range of field angles. We find that a large change in magnetic anisotropy onsets at ~20 T -- roughly the same energy scale as the Kondo temperature, signifying a crossover from itinerant to local physics in high fields. Notably, the magnetic field component along the c-axis drives a large change in the transverse magnetic susceptibility (i.e. a large susceptibility in the ab-plane for large fields along the c-axis). This suggests the emergence of a local easy-plane anisotropy that surrounds the high-field metamagnetic and superconducting phases of UTe2.

Twist-angle engineering of 2D materials has led to the recent discoveries of novel many-body ground states in moiré systems such as correlated insulators, unconventional superconductivity, strange metals, orbital magnetism and topologically nontrivial phases. These systems are clean and tuneable, where all phases can coexist in a single device, which opens up enormous possibilities to address key questions about the nature of correlation induced superconductivity and topology, and allows to create entirely novel quantum phases with enhanced interactions. In this talk we will introduce some of the main concepts underlying these systems, concentrating on magic angle twisted bilayer graphene (MATBG) and show how we can engineer strongly interacting, topological and superconducting states. We will further discuss our recent effort to explore the vast library of novel bilayer moiré materials (TMDs etc.) using a novel high-throughput quantum twisted microscope (QTM) technique, which will allow us to search for novel exotic ground states with ever higher interactions energy and temperatures. Last but not least we will show some recent quantum technology developments that were enabled by the ultra-low carrier density superconducting states in MATBG, culminating in the demonstration of highly tuneable single photon detectors.

Frustration, resulting from competing interactions that cannot be simultaneously satisfied, has emerged as a key mechanism for stabilizing novel electronic phases of matter. In this talk, I will explore how frustration stabilizes electronic flat band states, which arise from constrained electron hopping on specific lattice geometries. These flat bands are particularly intriguing due to a large degeneracy in the electronic manifold, creating a fertile platform for the emergence of correlated states. I will present experimental realizations of these flat band states in a class of materials termed kagome metals, highlighting their unique properties as revealed by spectroscopic and transport measurements [1,2], including the discovery of an unconventional non-Fermi liquid "strange metallic" phase [2]. Toward the end of the talk, I will also discuss our recent efforts to uncover novel physical properties stemming from frustrated magnetic states. [1] M. Kang et al., Nat. Commun. 11, 4004 (2020) [2] LY et al., Nat. Phys. 20, 610 (2024)

Two-dimensional (2D) materials have received widespread attention over the past 20 years due to their remarkable physical, mechanical and chemical properties, and our ability to integrate them into devices. In this seminar, I will detail our recent work in the development of the next generation of 2D materials. I will begin by introducing the synthesis and electronic properties of CeSiI, the first van der Waals (vdW) metal with a heavy fermion ground state. Conceptually, our synthetic design takes a traditional 3D intermetallic structure and slices it into atomically-thin vdW sheets by incorporating iodine into the structure. The resulting material is cleavable and effectively electronically 2D. I will then discuss a new approach for realizing long-sought electronic structures of geometrically frustrated lattice models (e.g. kagome and pyrochlore), by “decorating” un-frustrated, primitive lattices with a particular set of atomic orbitals. In the process, we identify the vdW intermetallic compound Pd5AlI2 as the first material to realize the electronic structure of the 2D Lieb lattice – featuring Dirac-like bands intersected by a flat band – persisting in ambient conditions down to the monolayer limit. I will discuss how this unique electronic structure gives rise to compact localized states and bound states in continuum (BICs), which could provide a platform for lossless and topologically protected electronic processes.

UTe2 has been the focus of numerous experimental and theoretical studies in recent years, as it is recognized as an odd-parity bulk superconductor. Its surface has also been probed, revealing charge density wave (CDW), pair density wave (PDW), and time-reversal symmetry-breaking (TRSB). In this work, we propose that the interplay between the order parameters observed on the surface and in the bulk of UTe2 may be crucial in explaining some of the unusual features detected by surface probes in this material. Through a phenomenological analysis, we can account for three distinctive experimental signatures observed on the surface of UTe2: i) the apparent suppression of CDW order at the upper critical field of the bulk superconducting state; ii) the magnetic field-induced imbalance of the Fourier peaks associated with the CDW; iii) the onset of TRSB at the bulk superconducting critical temperature and its field-trainability. Furthermore, we propose specific experimental checks to validate our conjecture, which we believe could be promptly achieved.

While the recent advances in topology have led to a classification scheme for electronic bands described by the standard theory of metals, a similar scheme has not emerged for strongly correlated systems such as Mott insulators in which a partially filled band carries no current. This talk will address this deficiency by including interactions into the three dominant models for topological states, the Haldane and KM/BHZ models. We show that all of these models possess a quarter-filled state that is an insulator once the interactions exceed the bandwidth. We obtain this result by solving analytically a model in which the interactions are local in momentum space and then numerically by quantum Monte Carlo simulations on the corresponding Hubbard model. Both yield the same result: For sufficiently large interaction strengths, the quarter-filled Haldane/KM/BHZ models form a topological Mott insulator with ferromagentic correlations with a Chern number of unity. Recent experiments on the anomalous quantum Hall effect in transition metal dichalcogenides are discussed in this context.

We study the effect of quasiperiodic perturbations on one-dimensional all-bands-flat lattice models. Such networks can be diagonalized by a finite sequence of local unitary transformations parameterized by angles . Without loss of generality, we focus on the case of two bands with bandgap . Weak perturbations lead to an effective Hamiltonian with both on- and off-diagonal quasiperiodic terms that depend on . For some angle values, the effective model coincides with the extended Harper model. By varying the parameters of the quasiperiodic potentials, we observe localized insulating states and an entire parameter range hosting critical states with subdiffusive transport. For finite quasiperiodic potential strength, the critical-to-insulating transition becomes energy dependent with what we term fractality edges separating localized from critical states. Critical-to-insulator transitions and fractality edges in perturbed flat bands S Lee, A Andreanov, S Flach Physical Review B 107 (1), 014204 (2023)

We investigate the emergence of topological features in the charge excitations of Mott insulators in the Chern-Hubbard model. In the strong correlation regime, treating electrons as the sum of holons and doublons excitations, we compute the topological phase diagram of Mott insulators at half-filling using composite operator formalism. The Green function zeros manifest as the tightly bound pairs of such elementary excitations of the Mott insulators. Our analysis examines the winding number associated with the occupied Hubbard bands and the band of Green's function zeros. We show that both the poles and zeros show gapless states and zeros, respectively, in line with bulk-boundary correspondence. The gapless edge states emerge in a junction geometry connecting a topological Mott band insulator and a topological Mott zeros phase. These include an edge electronic state that carries a charge and a charge-neutral gapless zero mode. Our study is relevant to several twisted materials with flat bands where interactions play a dominant role.

Crafting synthetic two-dimensional (2D) functional materials with novel quantum char- acteristics is a key focus of contemporary condensed matter physics. The adaptability to manipulate both the lattice arrangements and electronic band configurations of these artificially designed materials presents a distinct opportunity to control their properties externally. Among these, the Metal-Organic Framework (MOF) and Covalent Organic Framework (COF) have attracted substantial attention due to their potential applications in organic electronics, spintronics, and topological materials [1]. Characterized by a pair of dispersive bands, a Fermi level-linked flat energy band, and a Dirac cone at the M- point, the Lieb lattice [3] design has been experimentally realized recently in sp2C-COF and sp2N-COF [2]. In addition to the topologically nontrivial band structures, this lat- tice model exhibits flat bands, which could give rise to exotic strongly correlated electron states even for relatively weak interaction strength [3]. Our investigation explores the distinct quantum phases that result from the interplay of the electronic and spin degrees of freedom in the Lieb lattice. Our approach involves coupling an s-wave superconductor to a lattice of localized magnetic spins using Kondo in- teractions. This interplay creates a “Magnetic Superconductor ” characterized by the coex- istence of magnetic and superconducting orders. Using a comprehensive model that unifies a 2D attractive Hubbard framework with Kondo interactions, we harness the spectroscopic signatures to explore the evolution of the Fermi surface across distinct parameter regimes. By analyzing the ground state phase diagram with precision, we observe the emergence and coexistence of gapped and gapless superconducting states with anti-ferromagnetic and non-collinear magnetic orders, as well as the transition from anti-ferromagnetic to non- collinear magnetic phases. Here we discover that the superconducting order parameter has a non-monotonic dependence on the number density, which is a significant feature of flat band superconductivity. At half filling, the superconductivity is solely contributed by the geometric weight of the quantum metric, as the conventional contribution of dispersive bands become insignificant. References [1] Xiaojuan Ni, Huaqing Huang, Chemistry of Materials 10, 1021 (2022). [2] Bin Cui, Xingwen Zheng, Nature Communications 11, 66 (2020). [3] C. Weeks , M. Franz, Phys. Rev. B. 82, 085310 (Aug 2010).

Quantum materials featuring both itinerant and localized degrees of freedom exhibit numerous exotic phases and transitions that deviate from the Ginzburg-Landau paradigm. This work uses the composite operator formalism to examine the bilayer strongly correlated Hubbard model. We observe the spontaneous breaking of layer symmetry, where the electron density in one of the layer reaches half-filling, resulting in a layer selective Mott phase (LSMP). This broken symmetry phase becomes unstable at a critical average electronic density away from half-filling. Furthermore, significant layer differentiation persists up to a moderate inter-layer hopping, beyond which the system abruptly transitions to an layer uniform phase (LUP). In the LSMP phase, the electrons in the two layers are weakly hybridized, resulting in a small Fermi surface. The volume of the Fermi surface jumps at the transition from the LSMP to the uniform phase. We also discuss the physical mechanisms leading to the collapse of the LSMP phase under different perturbations.

In recent years, the condensed matter community has witnessed the discovery of highly interesting superconducting properties in layered nickel oxides. In 2019, a stable electron-pairing phase has been identified in thin-films of Sr-doped NdNiO$_2$ by Li et al. [1], with a formal Ni-$3d^{9-x}$ oxidation state. And in 2023, a bilayer nickelate of formal Ni-$3d^{8-x}$ valence was detected superconducting under pressure [2]. Notably, the $T_c$ of the latter nickelate is reported close to 80K, whereas for the low-valence nickelates it is measured to be about 15K. Interestingly, while differing in the nominal $3d$ valence count, according to our theoretical investigations [3,4] these superconducting nickelates have in common that they are driven by a correlated Ni-$e_g$ multiorbital low-energy regime. We will show how an advanced combination of density functional theory (DFT) and dynamical mean-field theory (DMFT) provides unique access to this novel playground of oxide superconductivity. Thereby, unique correlation effects together with a relevant flat-band character may provide a way to connect the various superconducting nickelates. This will especially be exemplified by the intriguing properties of the La$_3$Ni$_2$O$_6$ compound [5]. [1] D. Li et al., Nature 572, 624 (2019). [2] H. Sun et al., Nature 621, 493 (2023). [3] F. Lechermann, Physical Review B 101, 081110 (2020). [4] F. Lechermann, J. Gondolf, S. Bötzel, I. M. Eremin, Phys. Rev. B 108, L201121 (2023). [5] F. Lechermann, S. Bötzel, I. M. Eremin, arXiv:2412.19617 (2024).

Strange metallicity with $T$-linear electrical resistance, preceding high-$T_c$ superconductivity is an enigmatic, yet crucial, signature of correlation physics. We study the hydrostatic pressure dependence of ferromagnetism in the kagome metal CrNiAs by electrical transport and magnetization measurements up to 50~GPa. In contrast to other kagome ferromagnets, a linear suppression of the Curie temperature is found, resulting in a ferromagnetic quantum critical point at a critical pressure $p_{\rm{c}} \approx 12.5$~GPa. Remarkably, from $p_{\rm{c}}$ up to the maximal measured pressure, a broad strange metal phase arises, which at low temperatures can be converted to a Fermi liquid in applied magnetic field, phenomenologically described by a zero-field quantum critical line in the $T$-$p$ phase diagram. This establishes pressurized kagome ferromagnets as intriguing platform for strange metal behavior.

Flatband systems form a new class of materials that challenge the conventional wisdom of transport. The intrinsically strong electronic correlations combined with the vanishing kinetic energy scale suggest a sensitive dependence of transport properties on the flat band states and make interacting flat bands promising candidates for exotic quantum transport. Utilizing the Drude weight, we investigate the low-frequency spectral properties of the electrical conductivity, demonstrating the potential of a quantum geometric approach for interacting systems and intermediate temperatures. The derived spectral weight yields unexplored 4-point geometric contributions unrelated to the quantum metric, which questions the previously proposed projection methods. For long-ranged interactions, we show that the low-frequency spectral weight reduces to the variance of the Berry curvature.

Motivated by recent discovery of additional topologically non-trivial phases of matter in lattice models beyond established classification schemes, we generalise the framework of the quantum Hall effect (QHE) to that of the quantum skyrmion Hall effect (QSkHE). This involves one key generalisation: considering particles on a two-sphere, which see a U(1) monopole, one can project to the lowest Landau level (LLL). Upon performing such a projection, the position coordinates become proportional to SU(2) generators by quenching of kinetic energy. An almost point-like LLL corresponds to matrix representation size for the SU(2) generators of N by N, with N small. The key generalisation is that such an almost point-like LLL with small orbital degeneracy can still host an intrinsically 2+1 dimensional topologically non-trivial many-body state. Equivalently, in regimes in which spin has previously been treated as a label (small N), spin encodes some finite number of spatial dimensions, in general. This many-body state can play the role, in the QSkHE, that a charged particle plays in the QHE.

Superconductivity usually emerges from a metallic normal state which follows the Fermi-liquid paradigm. If, in contrast, the normal state is a fractionalized non-Fermi liquid, then pairing may either eliminate fractionalization via a Higgs-type mechanism leading to a conventional superconducting state, or pairing can occur in the presence of fractionalization. Here we discuss a simple model for the latter case: Using a combination of perturbation theory and functional renormalization group, we show that the Kitaev–Kondo lattice model displays a fractionalized superconducting phase at weak Kondo coupling. This phase is characterized by Cooper pairing of conventional electronic quasiparticles, coexisting with a spin-liquid background and topological order.

I will present recent advances in very low temperature scanning tunneling microscopy. I will first discuss the layered, WTe2, which stands out as a semimetal presenting quantum oscillations in most measured quantities under magnetic fields. Band structure calculations, photoemission and transport experiments in devices show that WTe2 can be a higher order topological insulator. However, the connection between Landau quantization and the topological properties of the band structure is not established. Studies of the electronic band structure by quasiparticle interference with Scanning Tunneling Microscopy (STM) are used to determine, with the support of Density Functional Theory (DFT), the whole set of electron and hole bands crossing the Fermi level. Landau quantization of Dirac quasiparticles in surface states is also observed. I will also discuss new insight into the charge density modulation of UTe2 and comment on advances in the understanding of the Josephson effect at atomic scale, relevant for the study of unconventional superconductors.