Quantum Criticality and Topology in Correlated Electron Systems

I will overview our recent ARPES results on this topic. In particular, the data on LiFeSe, Ba122 and FeSeTe will be discussed.

In the quest to understand the superconductivity in cuprates, a key issue is the nature of the enigmatic pseudogap region of the phase diagram. An especially important question is whether the pseudogap state is a distinct thermodynamic phase characterized by broken symmetries below the onset temperature $T^∗$. We use torque-magnetometry and elastoresistance measurements to test the rotational symmetry breaking in the pseudogap state in single crystals of YBa$_2$Cu$_3$O$_y$ (YBCO) and Bi$_2$Sr$_2$CaCu$_2$O$_8+\delta$ (Bi2212). In YBCO, anisotropic susceptibility within the ab planes was measured by the torque magnetometry with exceptionally high precision [1]. The in-plane anisotropy displays a significant increase with a distinct kink at the pseudogap onset temperature $T^∗$, showing a remarkable scaling behavior with respect to $T/T^∗$ in a wide doping range. Our systematic analysis reveals that the rotational symmetry breaking sets in at $T^∗$ in the limit where the effect of orthorhombicity is eliminated. In Bi2212, the nematic susceptibility that describes the electronic anisotropy response to a uniaxial strain was measured by elastoresistance above $T^∗$ [2]. We find that the nematic susceptibility increases upon cooling with a kink anomaly at $T^∗$, evidencing a second-order transition with neamtic fluctuations. These results provide thermodynamic evidence that the pseudogap in cuprates accompanies an electronic nematic order, which differs from the recently reported charge-density-wave transition that accompanies translational symmetry breaking. [1] Y. Sato {\it et al.}, Nat. Phys. {\bf 13}, 1074 (2017). [2] K. Ishida {\it et al.}, preprint.

A hallmark of the phase diagrams of correlated electronic systems is the existence of multiple electronic ordered states. In many cases, they cannot be simply described as independent competing phases, but instead display a complex intertwinement. A prime example of intertwined states is the case of primary and vestigial phases. While the former is characterized by a multi-component order parameter, the fluctuation-driven vestigial state is characterized by a composite order parameter formed by higher-order, symmetry-breaking combinations of the primary order parameter. This concept has been widely employed to elucidate nematicity in both iron-based and cuprate superconductors. In this talk, I will present a group-theoretical framework, supplemented by microscopic calculations, that extends this notion to a variety of phases, providing a general classification of vestigial orders of unconventional superconductors and density-waves. Electronic states with scalar and vector chiral order, spin-nematic order, Ising-nematic order, time-reversal symmetry-breaking order, and algebraic vestigial order emerge from this simple underlying principle. I will present a rich variety of possible phase diagrams involving the primary and vestigial orders, and discuss possible realizations of these exotic composite orders in different materials.

The cuprate high temperature superconductors develop spontaneous charge density wave (CDW) order below a temperature $T_{\rm CDW}$ and over a wide range of hole doping ($p$). An outstanding challenge in the field is to understand whether this modulated phase is related to the more exhaustively studied pseudogap and superconducting phases [1,2]. To address this issue, it is important to extract the energy scale $\Delta_{\rm CDW}$ associated with the CDW order, and to compare it with the pseudogap (PG) $\Delta_{\rm PG}$ and with the superconducting gap $\Delta_{\rm SC}$. However, while $T_{\rm CDW}$ is well-characterized from earlier work, little is known about $\Delta_{\rm CDW}$ until now. Here, we report the extraction of $\Delta_{\rm CDW}$ for several cuprates using electronic Raman spectroscopy. Crucially, we find that upon approaching the parent Mott state by lowering $p$, $\Delta_{\rm CDW}$ increases in a manner similar to the doping dependence of $\Delta_{\rm PG}$ and $\Delta_{\rm SC}$ [3]. This reveals that the above three phases have a common microscopic origin. In addition, we find that $\Delta_{\rm CDW} \approx \Delta_{\rm SC}$ over a substantial doping range, which suggests that CDW and superconducting phases are intimately related, for example they may be intertwined or connected by an emergent symmetry [1,4-6] [1] E. Fradkin et al., Rev. Mod. Phys. 87, 457 (2015). [2] B. Keimer et al., Nature 518, 179 (2015). [3] B. Loret et al., arXiv:1808.08198 accepted in Nature Physics [4] K. B. Efetov et al., Nat. Phys. 9, 442 (2013). [5] S. Sachdev et al., Phys. Rev. Lett. 111, 027202 (2013). [6] Y. Wang et al., Phys. Rev. Lett. 114, 197001 (2015).

As a consequence of strong correlations, many aspects of the complex phase diagram of the cuprate high-temperature superconductors are still under debate. In the first part of the talk, I will discuss a non-Abelian gauge theory that we propose [1] as an effective field theory for the cuprates near optimal doping. In this theory, spin-density-wave order is fractionalized into Higgs fields while all low-energy fermionic excitations are electron-like and gauge neutral. The conventional Fermi-liquid state corresponds to the confining phase of the theory at large doping and there is a quantum phase transition to a Higgs phase, describing the pseudogap, at low doping. It will be shown that the topological order of the pseudogap state is very naturally intertwined with charge-density-wave, Ising-nematic, and scalar spin-chirality order. We will also discuss the deconfined quantum criticality in the limit of large numbers of Higgs flavors. The second part of the talk deals with the thermal Hall effect in related gauge theories of the square-lattice antiferromagnet [2,3]. I will show that these approaches can yield a sizeable thermal Hall response, similar to what has recently been seen in experiment [4]. [1] Phys. Rev. B 99, 054516 (2019). [2] Phys. Rev. B 99, 165126 (2019). [3] arXiv:1903.01992 (2019). [4] arXiv:1901.03104 (2019).

We show that a random interacting model exhibits solvable non-Fermi liquid behavior and exotic pairing behavior. The model describes the random Yukawa coupling between $N$ quantum dots each hosting $M$ flavors of fermions and $N^2$ bosons that becomes critical at low energies. This diagrammatic expansion is controlled by $1/MN$, and the results become exact in a large-$M$, large-$N$ limit. We find that pairing only develops within a region of the $(M,N)$ plane --- even though the pairing interaction is strongly attractive, the incoherence of the fermions can spoil the forming of Cooper pairs{, rendering the system a non-Fermi liquid down to zero temperature}. By solving the Eliashberg equation and renormalization group analysis, we show that the transition into the pairing phase exhibits Kosterlitz-Thouless quantum-critical behavior.

I report measurements of resistivity, Hall Effect, magnetoresistance and thermopower in the electron-doped cuprate La2-xCexCuO4 for 0.19≥ x ≥0.08 as a function of temperature. The new and unconventional results are: 1) The normal state magnetoresistance exhibits an anomalous linear-in-H behavior [1] at the same doping and temperature where a linear-in-T resistivity was previously observed for H>Hc2 [2], i.e. above the Fermi surface reconstruction at x =0.14 up to the end of the superconducting dome (x ~ 0.175). For doping above the dome conventional Fermi liquid behavior is found (but, with intrinsic Ferromagnetism below 4K--arXiv:1902.11235). 2) The normal state Seebeck coefficient, S/T, exhibits an unconventional low temperature –lnT dependence at the same doping where linear-in-T and linear-in-H resistivity is found [3]. Conventional S/T = constant behavior is found above the superconducting dome. 3) The normal state resistivity above Tc, from 80 K to 400 K, follows an anomalous ~A(x)T2 behavior at zero field for all doping(x), with no indication of a MIR limit. Fermi liquid theory cannot explain any of these results. Moreover, the magnitude of the anomalous magnetoresistance and thermopower scales with Tc, suggesting that the origin of the superconductivity is correlated with the anomalous normal state properties. 1. T. Sarkar et al., Sci. Adv. 2019 2. K. Jin et al. , Nature 476, 73 (2012) 3. P. R. Mandal et al., PNAS 116, 5991 (2019) 4. T. Sarkar, R. L. Greene, and S. Das Sarma, Phys. Rev. B 98, 224503 (2018)

The established and highly successful description of metals is based on Landau’s Fermi liquid theory. The relevant phase space for electron-electron collisions is determined by the Pauli blocking of a degenerate Fermi gas due to its Fermi surface. In some strongly correlated systems narrow bands form and the energetics of the system at elevated energies or temperatures becomes dominated by strong interactions and is no longer restricted by Fermi-surface phase-space effects. To develop a well-controlled approach of this regime is an important question in the theory of strongly correlated electrons. In this talk I will give an overview over the description of incoherent and critical electronic systems using the Sachdev-Ye-Kitaev approach. We consider versions of the model where electrons interact with each other, with boson collective modes, and even with phonons. We also comment on the very direct relation to holographic approaches to strongly coupled quantum theories. Finally we address the emergence of superconductivity in such an incoherent metal and show that pairing and superconductivity of a fully incoherent electronic system is allowed and leads to a pairing state with high transition temperature but low condensation energy.

We study the 4Hb structure of TaS$_2$ which is an alternating stack of a Mott insulator, recently reported as a gapless spin-liquid (1T-TaS$_2$), and a 2D superconductor (1H-TaS$_2$). We find a superconducting transition at T$_c$ =2.7 K, which is signicantly elevated compared to the value in bulk 2H-TaS$_2$, 0.7 K. Muon spin relaxation experiments show that 4Hb-TaS2 exhibits signatures of time-reversal symmetry breaking insetting abruptly at T$_c$. This suggests that 4Hb-TaS2 is a chiral superconductor and promotes the question of the mutual influence of superconductivity and gapless spin-liquid states.

The past year has seen rapid developments in our understanding of the long-studied unconventional superconductor Sr 2 RuO 4. I will report on our group's measurements of the strain dependence of the heat capacity and angle-resolved photoemission, and on collaborative work on the strain dependence of muon spin rotation and the NMR Knight shift. The results of the last project have completely rewritten our understanding of the superconducting order parameter, by reversing famous experimental data from 1998 that was a mainstay of the evidence for spin triplet superconductivity. I will attempt to assess where things stand at present in light of this revised experimental situation.

Despite its low Tc, Sr2RuO4 has been one of the most important seed materials and inspiration for contemporary research on unconventional superconductivity, encompassing triplet pairing, Majorana zero modes in vortices, chiral Majorana edge states, and chiral topological bulk order. In order to appropriately take into account the enhanced diversity of experimental evidence, the theoretical modelling of superconductivity in Sr2RuO4 necessitates refinement at several levels. This includes the consideration of spin-orbit coupling, uniaxial strain, and the systematic treatment of Fermi surface instabilities and electronic flucutations beyond the mere weak coupling domain. I review the state of the art of several current frontiers along these lines, and how functional renormalization group has the potential to reach an accurate description of electron pairing in Sr2RuO4 in the physically relevant parametric window of intermediate interaction strength.

According to standard theory, low-density metals, such as doped semiconductors and semimetals, are not expected to become superconducting for two main reasons: (1) Their density of states is very low. (2) Their Fermi energy is small and can be even smaller than the Debye frequency. Nonetheless, superconductivity is observed in a wide range of low-density metals. In this talk I will first discuss possible resolutions of this puzzle using different pairing mechanisms. I will then focus on a specific example, where I will show how the coupling between an arbitrarily small Fermi surface in a Dirac semimetal, and a quantum critical point of the ferroelectric type, leads to strong electronic pairing and superconductivity in-spite the fulfillment of points (1) & (2).

Superconductivity mediated by dynamical fluctuations of a quantum-critical nematic order-parameter is characterized by the existence of multiple pairing states with closely spaced transition temperatures. These states are topologically distinct, with pairing gaps that differ by the number of nodes on the Fermi surface. Nevertheless, they are all in the same lattice symmetry, usually s-wave. I will discuss how the superconducting phase below $T_c$ is a superposition of many such states, and how interference effects modify superconducting properties such as the Fermi surface gap anisotropy.

A topic of interplay between disorder and competing electronic phases in multiband superconductors have recently got renewed interest in the context of iron-based superconductors. In my talk I will present a theory of disordered unconventional superconductor with competing magnetic order. My discussion will be based on the results obtained for on a two-band model with quasi-two-dimensional Fermi surfaces, which allows for the coexistence region in the phase diagram between magnetic and superconducting states in the presence of intraband and interband scattering induced by doping. Within the quasi-classical approximation I will present the analysis of the quasi-classical Eilenberger’s equations which include weak external magnetic field. I will demonstrate that disorder has a crucial effect on the temperature dependence of the magnetic pen- etration depth as well as critical current, which is especially pronounced in the coexistence phase.

We propose that propagating one-dimensional Majorana fermions will develop in the vortex cores of certain iron-based superconductors, most notably Li(Fe1−xCox)As. A key ingredient of this proposal are the 3D Dirac cones recently observed in ARPES experiments [P. Zhang et al., Nat. Phys. 15, 41 (2019)]. Using an effective Hamiltonian around the Gamma − Z line we demonstrate the development of gapless one-dimensional helical Majorana modes, protected by C4 symmetry. A topological index is derived which links the helical Majorana modes to the presence of monopoles in the Berry curvature of the normal state. We present various experimental consequences of this theory and discuss its possible connections with cosmic strings.

The quantum Hall effect (QHE) is one of the most remarkable phenomena in contemporary condensed matter physics, which rivals superconductivity in its fundamental significance as a manifestation of quantum mechanics on a macroscopic scale.　The quantum Hall state is a topological property of quantum matter. There are two classes of the QHE, where integer and fractional electrical conductance are measured in units of $e^2/h$. Here we report a novel type of quantization of the Hall effect caused by charge neutral quasiparticles, i.e. Majorana fermions, in an insulating two-dimensional (2D) quantum magnet, $\alpha$-RuCl$_3$ with honeycomb lattice[1][2]. This material has been suggested to be a candidate of Kitaev quantum spin liquid (QSL), where significant entanglement of quantum spins is expected. In the low-temperature regime of the QSL state, the 2D thermal Hall conductance reaches a quantum plateau as a function of the applied magnetic field. The plateau attains a quantization value $\kappa_{xy}/T=1/2(\pi^2k_B^2/3h)$, which is exactly half of that in the integer QHE. In stark contrast to the quantum Hall effect in 2D electron gas, the half-integer thermal quantum Hall effect occurs even in the magnetic field parallel to 2D plane [3]. These observations are direct signatures of topologically protected chiral edge currents of emergent Majorana fermions and non-Abelian anyons in the bulk. [1]Y. Kasahara {\it et al}. Phys. Rev. Lett. 120, 217205 (2018). [2]Y. Kasahara {\it et al}. Nature 559, 227 (2018). [3]T. Yokoi {\it et al}. in preparation.

Motivated by the ongoing effort to search for high-resolution signatures of quantum spin liquids, we investigate the temperature dependence of the Raman and the indirect resonant inelastic x-ray scattering response for the Kitaev honeycomb model. We find that, as a result of spin fractionalization, the dynamical response changes qualitatively at two well-separated temperature scales, TL and TH, which correspond to the characteristic energies of the two kinds of fractionalized excitations.

I will discuss various instances in which anomalous transport can be captured with simple scattering mechanisms. I will focus on charge transport in ruthenates, and heat transport in complex insulators such as perovskites.

I will describe theoretical progress on understanding transport in several models of strange metals.

An overview of recent progress in the field will be given.

https://arxiv.org/pdf/1906.07123.pdf

Historically materials discovery has been the result of serendipity or painstaking exploration of a large phase space of chemically synthesized compounds. A new era of materials started with the breakthrough isolation of a free standing 2D material, graphene, followed by many others. The distinctive characteristic of these 2D materials is that, with all the atoms residing at the surface, it is possible to access and manipulate their properties without changing their chemical composition. I will discuss methods of transforming the electronic structure of graphene: inducing magnetism and Kondo screening by removing single Carbon atoms; generating flat bands and pseudo-magnetic fields by introducing a twist between layers, by buckling or by introducing strain.

We will present the possible effects of topological properties on the low energy physics of the Moire graphene lattices

Correlated states at different fillings have been observed in twisted bilayer graphene upon doping a graphene bilayer with a small twist angle, creating a lot of excitement in the scientific community. The stacking misorientation produces a moiré pattern with a superlattice modulation corresponding to thousands of atoms per unit cell. When the rotation angle is close to the so-called magic angle, the low energy electronic bands of the moiré become almost flat. The insulating states, believed to be due to electronic correlations, arise when the system is doped with an integer number of electrons or holes per moire unit cell. The superconducting states are intercalated between the insulating ones and show nematic features. More recently STM experiments have uncovered a new correlated state with flat band splitting. Many different theoretical proposals have been put forward to explain these correlated states and the origin of superconductivity. Understanding the nature of these ordered phases requires the use of different techniques. To date most of the experimental data is coming from transport experiments and a few STM experiments. Optical conductivity is one of the techniques which can be used to analyze these systems. I will discuss the features in the optical conductivity spectrum which can help identifying the nature of the correlated states.

When two sheets of graphene are stacked at a small twist angle, the resulting flat superlattice minibands are expected to strongly enhance electron-electron interactions. Here we present evidence that near three-quarters (3/4) filling of the conduction miniband these enhanced interactions drive the twisted bilayer graphene into a ferromagnetic state. In a narrow density range around an apparent insulating state at 3/4, we observe emergent ferromagnetic hysteresis, with a giant anomalous Hall (AH) effect and indications of chiral edge states. Surprisingly, the magnetization of the sample can be reversed by applying a small DC current. Although the AH resistance is not quantized and dissipation is significant, our measurements suggest that the system may be an incipient Chern insulator. We further present magnetotransport measurements in tilted field that may hold clues to the nature of the magnetism, and briefly discuss the appearance of a similar phenomenon in an ABC-stacked trilayer graphene/hexagonal boron nitride moiré superlattice.

Twisted bilayer graphene exhibits an unusual metallic phase with an anomalously low charge carrier density near the Mott insulator, which is reminiscent of the pseudogap phase in underdoped cuprates. Here we present theoretical results for a two-species quantum dimer model on the triangular lattice, which provides a simple effective description of a metallic state with topological order (i.e. a fractionalized Fermi liquid). This state exhibits a small charge carrier concentration as observed in experiments, without breaking any symmetries. We develop an exact solution of this model and use it to predict ordering wave-vectors of potential CDW instabilities.

I will discuss my recent theoretical work on the interplay between band topology and strong correlations in moire graphene systems, and its implications for experiments.

Recent experiments on the twisted bilayer graphene have discovered the correlated insulator phase and the neighboring superconductivity with certain fillings of the charge carriers. To understand the correlation effects, we build the localized Wannier states (WSs) for the four narrow bands around the charge neutrality point and construct the corresponding low energy tight binding model. Furthermore, we project the gate-screened Coulomb interaction onto the constructed localized WSs. Due to the nontrivial topological properties of the four narrow bands, the projected interaction becomes nonlocal and contains new terms beyond the cluster Hubbard model. These new terms lead to strong correlations between different lattice sites even without the hoppings. At the one-quarter filling, the largely degenerate ground states are found to be SU(4) ferromagnetic in the strong coupling limit. The kinetic terms select the ground state in which the two valleys with opposite spins are equally mixed, with vanishing magnetic moment per particle. Our results suggest the fundamental difference between the twisted bilayer graphene and other unconventional superconductors described by the Hubbard model.

Graphene in the presence of a strong external magnetic field is a special attraction for investigations of the fractional quantum Hall (fQH) states with odd and even denominators of the fraction. Most of the attempts to understand Graphene in strong field regime were made through exploiting the universal low-energy effective description of Dirac fermions emerging from the nearest-neighbor hopping model of electrons on a honeycomb lattice. We highlight that accounting for the nextnearest-neighbor hopping terms in doped Graphene can lead to a unique redistribution of magnetic fuxes within the unit cell of the lattice. While this affects all the fQH states, it has a striking effect at a half-filled Landau-level state: it leads to a composite fermion state that is equivalent to the doped topological Chern insulator on a honeycomb lattice. At energies comparable to the Fermi energy, this state possesses a Haldane gap in the bulk proportional to the next-nearest-neighbor hopping and density of dopants. We propose experiments to detect this gap; the associated chiral boundary mode; and encourage cold-atom setups to test other predictions of the theory.

I will present aspects of our theoretical and numerical work in the area of frustrated magnetism [1,2], particularly in the context of the kagome geometry. This area has seen a flurry of research activity owing to several near-ideal material realizations. My focus will be on the existence of an exactly solvable point in the XXZ-Heisenberg model for the ratio of Ising to transverse coupling $J_z/J=-1/2$ [2]. This point in the phase diagram has "three-coloring" states as its exact quantum ground states and is macroscopically degenerate. It exists for all magnetizations and is the origin or "mother" of many of the observed phases of the kagome antiferromagnet. I will revisit aspects of the contentious (and experimentally relevant) Heisenberg case and provide a framework to understand multiple results in terms of three-coloring states [2,3]. [1] K. Kumar, H. J. Changlani, B. K. Clark, E. Fradkin, Phys. Rev. B 94, 134410 (2016). [2] H. J. Changlani, D. Kochkov, K. Kumar, B. K. Clark, E. Fradkin, Phys. Rev. Lett. 120, 117202 (2018). [3] H. J. Changlani, S. Pujari, C.M. Chung, B. K. Clark, Phys. Rev. B 99, 104433 (2019).

The exploration of novel phases of interacting electrons (correlated electrons) has long been a major stream of condensed-matter research. Many-body interactions among electrons give rise to a huge variety of phases, grouped into electron-solid, -liquid-crystal, -liquid and -gas states. The wealth of possibilities arises from a complicated interplay of lattice geometry, quantum effects and the multiple degrees of freedom of the electron (charge, spin and orbital). In the past, the two dominant areas of exploration have been the 3d transition-metal (TM) oxides and the 4f intermetallic compounds but recently 5d TM oxides and related compounds have emerged as the next arena of correlated-electron physics. Significant new physics is expected due to the presence of a large spin-orbit coupling in heavy 5d elements, tying together the otherwise independent spin and orbital degrees of freedom. This can be of order 0.5eV and is often larger than the crystal-field splitting of the orbital states, resulting in a spin-orbital-entangled state of correlated electrons. The nature of the spin-orbital entanglement depends significantly on the d-electron number and the chemical bonding, and it is anticipated that, in combination with electron correlations, a rich variety of novel electronic phases are waiting to be discovered. To name just a few, the proposed phases include Kitaev quantum spin liquids, correlated topological semimetals, excitonic magnets and multipolar-ordered states. In this talk, I will present our recent exploration of such exotic faces of spin-orbital entangled matter in 5d (and 4d) transition metal oxides. Topics will include the following. (I) Spin-orbital quantum liquid on honeycomb lattice in 5d5H(D)3LiIr2O61,2. (II) Non-magnetic Jeff = 0 Mott insulating state3 in 4d4 Ru4+ honeycomb oxides and pressure-induced excitonic magnetism. (III) Multipolar ordering in 5d1 cubic Cs(Rb)2TaCl34. References 1. K. Kitagawa, T. Takayama, Y. Matsumoto, A. Kato, R. Takano, Y. Kishimoto, S. Bette, R. Dinnebier, G. Jackeli, and H. Takagi, Nature, 554, 341–345 (2018). 2. H. Takagi, T. Takayama, G. Jackeli, G. Khaliullin, and S. N. Nagler, Nature Reviews Physics 1, 264–280 (2019). 3. G. Khaliullin, Phys. Rev. Lett. 111, 197201 (2013). 4. H. Ishikawa, T. Takayama, R. Kremer, J. Nuss, R. Dinnebier, K. Kitagawa, K. Ishii and H. Takagi, submitted. arXiv:1807.08311

There has been a great interest in magnetic field induced quantum spin liquids and other competing phases in Kitaev materials. In particular, discovery of neutron scattering continuum and half quantized thermal Hall effect in α-RuCl3, have prompted a number of theoretical studies on the effect of magnetic field in various local moment models with dominant Kitaev interaction. We provide classical and semiclassical analyses of some of such models for large system sizes in two dimensions and compare the results with numerical computations of quantum models for small system sizes. We show emergence of magnetic orders with fairly large unit cells and discuss possible relation to quantum spin liquids. We also discuss some preliminary results on quantum models and thermal Hall conductivity in the context of recent experiments on α-RuCl3.

We develop a hydrodynamic theory that allows one to compute various physical properties of the quantum Hall states near filling factors 1/2 and 1/4.

The strong variations in superconducting critical temperature among complex cuprate perovskites, that have identical hole density, indicates the importance of lattice modulation effects. The one-dimensional incommensurate lattice modulation of Bi2Sr2CaCu2O8+y, where the average atomic positions are perturbed beyond the unit cell, is an ideal case where to study the interplay between superconductivity and the one-dimensional incommensurate lattice fluctuations. Here we report nano X-ray diffraction imaging of incommensurate lattice structure in a bulk Bi2Sr2CaCu2O8+y (Tc = 90 K) down to a 2 u.c van der Waals heterostructure. Despite the atomically thin heterostructure, the superconducting critical transition temperature is identical to the bulk devices and the long- and short range incommensurate lattice modulations are still detected. The incommensurate lattice modulations are spatially correlated and fluctuate respect the average wavevector, showing a strain dependence with the substrate. We correlate the structural and transport data by measuring the Hall-effect down to two unit cells. We establish quantitative agreement between theory and data through the observation of the the Hall sign reversal far above Tc of even the optimally doped bulk crystal. We have thus bridged the gap between low temperature superconducting films (where Hall sign reversal occurs above Tc due to superconducting fluctuations) and cuprates (where Hall sign reversal was previously believed to occur below Tc and as the result of vortex dynamics). The newly developed techniques that allow the atomically thin incorporation of BSCCO into van der Waals heterostructures opens the possibility of a new generation of extremely sensitive nanodevices for the search and study of high temperature superconductivity and their interplay with other van der Waals crystal systems.

We will discuss mesoscopic and anomalous quantum transport effects at the onset of superconducting transition focusing on the observed large Nernst-Ettinghausen signal in disordered thin films. (i) In the vicinity of transition, as the Ginzburg-Landau coherence length of preformed Cooper pairs diverges, short-ranged mesoscopic fluctuations are equivalent to local fluctuations of the critical temperature. As the result, the dynamical susceptibility function of pair propagation acquires singular mesoscopic component and consequently superconducting correlations give rise to enhanced mesoscopic fluctuations of thermodynamic and transport characteristics. In contrast to disordered normal metals, root-mean-square value of mesoscopic conductivity fluctuations ceases to be universal and displays strong dependence on dimensionality, temperature, and under certain conditions can exceed its quantum normal state value by a large factor. Interestingly, we find different universality as magnetic susceptibility, conductivity, and transverse magnetic thermopower coefficients all display the same temperature dependence. We will discuss an enhancement of mesoscopic effects in the Seebeck thermoelectricity and Hall conductivity fluctuations as mediated by emergent superconductivity. (ii) We will also discuss how skew-scattering due to spin-orbit interaction gives rise to a new fluctuation-induced effect to the Hall conductance and Nernst coefficient near the superconducting transition point.

In the hydrodynamic regime it is possible to investigate the universal collision-dominated dynamics of the isolated electron fluid, while the couplings to the lattice and to impurities becomes secondary. An important transport property is the shear viscosity which describes whether the electron fluid behaves laminar or turbulent. The ratio shear viscosity over entropy is bounded from below and is an indicator for how strongly the system is interacting [Kovtun]. We determine the shear viscosity in Luttinger metals which are semimetals with a quadratic energy dispersion. Especially we focused on the determination of the shear viscosity in the Luttinger-Abrikosov-Beneslavskii phase [Moon]. This phase occurs upon adding the long-range Coulomb interaction to the system and it is an interacting, scale invariant, and non-Fermi-liquid phase. Upon combining the Boltzmann formalism with an RG analysis, we find that the ratio viscosity over entropy comes very close to the lower bound which makes the Luttinger metals a nearly perfect electron fluid. [Kovtun2005] P. K. Kovtun, D. T. Son, and A. O. Starinets, Phys. Rev. Lett. 94, 111601 (2005). [Moon] E.-G. Moon, C. Xu, Y. B. Kim, and L. Balents, Phys. Rev. Lett. 111, 206401 (2013).

Many recent experiments addressed manifestations of electronic crystals, particularly the charge density waves, in nano-junctions, under electric field effect, at high magnetic fields, together with real space visualizations by STM and micro X-ray diffraction. This activity returns the interest to stationary or transient states with static and dynamic topologically nontrivial configurations: electronic vortices as dislocations, instantons as phase slip centers, and ensembles of microscopic solitons. Describing and modeling these states and processes calls for an efficient phenomenological theory which should take into account the degenerate order parameter, various kinds of normal carriers and the electric field. Here we notice that the commonly employed time-depend Ginzburg-Landau approach suffers with violation of the charge conservation law resulting in unphysical generation of particles which is particularly strong for nucleating or moving electronic vortices. We present a consistent theory which exploits the chiral transformations taking into account the principle contribution of the fermionic chiral anomaly to the effective action. The resulting equations clarify partitions of charges, currents and rigidity among subsystems of the condensate and normal carriers. On this basis we perform the numerical modeling of a spontaneously generated coherent sequence of phase slips - the space-time vortices - serving for the conversion among the injected normal current and the collective one.

The strange metal in unconventional superconductors is thought to be connected to an underlying quantum critical point. Although the phenomenology is consistent with this idea, the absence of measurement that show a diverging correlation length of a symmetry breaking order parameter seems to contradict this connection. We show that the nature of the quantum critical point in a class of heavy fermion superconductors is not associated with any kind of symmetry breaking. Rather, it is a critical point connecting two unusual Fermi liquids that have well defined quasiparticles everywhere in the phase diagram except at the transition itself.

Motivated by the prediction of fractonic topological defects in a quantum crystal, I will discuss a novel U(1) vector gauge theory description of fractons. The fractionalized mobility is simply imposed by gauge invariance. In a specific gauge, at low energies this vector gauge theory reduces to the previously studied fractonic symmetric tensor gauge theory.

We study the effect of electron interaction in an electronic system with a high-order Van Hove singularity, where the density of states shows a power-law divergence. Owing to scale invariance, we perform a renormalization group (RG) analysis to find a nontrivial metallic behavior where various divergent susceptibilities coexist but no long-range order appears. We term such a metallic state as a supermetal. Our RG analysis reveals the Gaussian fixed point and a nontrivial interacting fixed point, which draws an analogy to the ϕ^4 theory. We further present a finite anomalous dimension at the interacting fixed point by a controlled RG analysis, thus establishing an interacting supermetal as a non-Fermi liquid. We discuss experimental evidence of supermetal in moire materials based on graphene and transition metal dichalcogenide.

We present a lattice model of fermions with $N$ flavors and random interactions which describes a Planckian metal at low temperatures, $T \rightarrow 0$, in the solvable limit of large $N$. We begin with quasiparticles around a Fermi surface with effective mass $m^\ast$, and then include random interactions which lead to fermion spectral functions with frequency scaling with $k_B T/\hbar$. The resistivity, $\rho$, obeys the Drude formula $\rho = m^\ast/(n e^2 \tau_{\textrm{tr}})$, where $n$ is the density of fermions, and the transport scattering rate is $1/\tau_{\textrm{tr}} = f \, k_B T/\hbar$; we find $f$ of order unity, and essentially independent of the strength and form of the interactions. The random interactions are a generalization of the Sachdev-Ye-Kitaev models; it is assumed that processes non-resonant in the bare quasiparticle energies only renormalize $m^\ast$, while resonant processes are shown to produce the Planckian behavior.

Claudia Felser, Johannes Gooth, Kaustuv Manna, Enke Liu and Yan Sun Max Planck Institute Chemical Physics of Solids, Dresden, Germany Topology a mathematical concept became recently a hot topic in condensed matter physics and materials science. One important criteria for the identification of the topological material is in the language of chemistry the inert pair effect of the s-electrons in heavy elements and the symmetry of the crystal structure. Beside of Weyl and Dirac new fermions can be identified compounds via linear and quadratic 3-, 6- and 8- band crossings stabilized by space group symmetries. In magnetic materials the Berry curvature and the classical AHE helps to identify interesting candidates. Magnetic Heusler compounds were already identified as Weyl semimetals such as Co$_2$YZ , in Mn$_3$Sn and Co$_3$Sn$_2$S$_2$. The Anomalous Hall angle helps to identify even materials in which a QAHE should be possible in thin films. Besides this k-space Berry curvature, Heusler compounds with non-collinear magnetic structures also possess real-space topological states in the form of magnetic antiskyrmions, which have not yet been observed in other materials.