Flat bands and high-order Van Hove singularities

We will discuss the formation of flat bands in monolayer graphene, AB stacked bilayer graphene and twisted bilayer graphene structures. We will show how the consideration of excitons via many body Hamiltonian will lead to the formation of such bands in the electronic band structure. The formation of the flat bands in graphene appears at the Dirac point $K$ when considering the phonons and consequent spin-triplet superconductivity. We will show that high-temperature the spin-triplet superconductivity is possible in monolayer graphene in the special parameter regime. The band-gap engineering in AB- bilayers will be discussed in details concerning considering the excitonic pairing effects in the special regime of the electron-electron interaction parameters in the system. We will show how a very large band-gap appear at the Dirac's $K$ point and how this band-gap could be changed when varying the inter-layer separation distance or the interlayer Coulomb interaction. Meanwhile, the excitonic condensation will be discussed in this context. Finally, we consider the excitonic effects in twisted bilayer graphene, and we will show how the flat band appears due to the excitonic formations at the large twist angles. Moreover, we will discuss a doubling effect of Dirac's $K$-point in the weak interaction limit and we will show that one of Dirac's node is stable and the other one changes its position as a function of rotation angle. The results obtained here, could have an unprecedented impact on the technological applications of graphene and graphene-based heterostructures and could open a new direction toward the new type pf electronic devices in suitable parameters regime.

We propose a Kohn-Luttinger-like mechanism for charge density waves with higher angular momentum in correlated electron systems. The mechanism describes an instability in the particle-hole direct channel, which emerges due to the feedback from the particle-hole crossed channel. Like in the original Kohn-Luttinger mechanism for superconductivity, the separation of vertex corrections in different lattice harmonics is the key for getting attractive components out of an initially repulsive interaction. We provide numerical as well as analytical arguments for the realisation of this mechanism in the triangular lattice Hubbard model with higher SU(N) symmetry, which can be implemented, e.g., in cold atomic gases or moiré bilayers of transition metal dichalcogenides.

In altermagnets (AM), flipping spins can be compensated by a rotation, similar to antiferromagnets, where this is accomplished by a translation or by inversion. Even though AM are states of homogeneous order, their symmetry requires that, in sharp contrast to ferromagnets, there is no direct bilinear coupling to a homogeneous magnetic field. However, since many altermagnets display piezomagnetism, a trilinear coupling with magnetic field and strain is generally allowed. This is the case for externally applied, for dynamic, and for random strain. Consequently, in the presence of random strain, a magnetic field behaves as an effective random field conjugate to the AM order parameter, providing a rare realization of a tunable random-field Ising model. Here, we solve the corresponding transverse-field Ising model in the presence of random longitudinal fields via mean-field to gain insight into the impact of a magnetic field on the AM phase diagram. We find two competing effects enabled by an increasing magnetic field: an increasing random-field disorder, which suppresses long-range AM order, and an enhanced coupling to elastic fluctuations, which favors AM order. We discuss the outcome of this competition and determine its fingerprints in various experimentally-accessible quantities, such as the magnetic susceptibility, the elastocaloric effect, the shear modulus, and the AM order parameter.

We explore the possibilities for spin-singlet superconductivity in newly discovered altermagnets. Investigating d-wave altermagnets, we show that finite-momentum superconductivity can easily emerge in altermagnets even though they have no net magnetization, when the superconducting order parameter also has d-wave symmetry with nodes coinciding with the altermagnet nodes. Additionally, we find a rich phase diagram when both altermagnetism and an external magnetic field are considered, including superconductivity appearing at high magnetic fields from a parent zero-field normal state. References: [1] Debmalya Chakraborty and Annica M. Black-Schaffer, arXiv:2309.14427.

Spontaneous symmetry breaking and more recently entanglement are two cornerstones of quantum matter. We introduce the notion of anisotropic entanglement ordered phases, where the spatial profile of spin-pseudospin entanglement spontaneously lowers the four-fold rotational symmetry of the underlying crystal to a two-fold one, while the charge density retains the full symmetry. The resulting phases, which we term entanglement smectic and entanglement stripe, exhibit a rich Goldstone mode spectrum and a set of phase transitions as a function of underlying anisotropies. We discuss experimental consequences of such anisotropic entanglement phases distinguishing them from more conventional charge or spin stripes. Our discussion of this interplay between entanglement and spontaneous symmetry breaking focuses on multicomponent quantum Hall systems realizing textured Wigner crystals, as may occur in graphene or possibly also in moire systems, highlighting the rich landscape and properties of possible entanglement ordered phases.

The myriad manifestations of topological crystalline phases (TCP), from anomalous higher-order boundary states to obstructed atomic limits, are well understood. A comprehensive understanding of their stability to disorder however remains an open question. We classify such generalized phases (with order-two symmetries) for disorder that breaks the crystalline symmetry, while preserving it on average. We detail novel disordered phases; statistical higher-order phases whose hinge states are subject to backscattering but remain protected from Anderson localization at zero-energy and a novel superconducting phase which concurrently hosts the aforementioned critical zero-energy hinge state along with a stable chiral Majorana hinge mode. We also discover that obstructed atomic limits are stable to disorder if and only if they have a filling anomaly: An observation that results, in contrast to clean TCPs, in disordered TCPs satisfying a complete bulk-boundary correspondence.

We consider the S=1/2 antiferromagnetic Heisenberg model on a frustrated kagome bilayer (the sites of each kagome layer are immediately above one another) when the nearest-neighbor interlayer coupling is large enough. In this regime, the low-energy states can be mapped onto a gas of hard(soft)-core rhombi on a kagome lattice, and the low-temperature magnetothermodynamics of the frustrated quantum spin system appears to be related to counting problems of combinatorics (e.g., dimer covering) and classical lattice-gas or Ising models. We provide finite-size numerics to illustrate the elaborated picture.

In systems belonging to the symmetry class CI, the presence of time-reversal, particle-hole and chiral symmetry allows for the appearance of topologically nontrivial phases. In the case of dx2-y2-wave superconductors, these are characterized by a winding number defined on noncontractable closed loops with fixed k//. For non-zero values, the bulk-edge correspondence guarantees the appearance of Majorana flat-bands at two-dimensional regions of the (110) surface’s Brillouin zone which are bounded by the projections of the superconducting nodes. Here we show the results obtained from tight-binding models as well as our Angle-Resolved Photo-Emission Spectroscopy (ARPES) measurements, where we further demonstrate the use of a recently established approach to cleave crystals for angle-resolved photoemission studies in which the fracture propagation is controlled by means of micro-notches.

Graphene is composed of light-weight atoms, making the spin-orbit coupling (SOC) is weak and yields only tiny band gaps that limit its applications [1]. In planar carbon lattices, a sizable band gap can be opened by quantum confinement (size control), structural elements as coves, chirality (edge control), and by chemical perturbation [2,3]. The Tight Binding (TB) approximation is a suitable method to check the roles of the π orbital in graphene and elucidate its effects in structural change of graphene towards the electronic properties. In this study, variations of defects in graphene were calculated by removing the A and B sublattices of graphene. The same number of sublattice A and B can induce band gap in graphene, while unequal number of sublattices removal induces flat bands on Fermi energy level. A pattern of band gap due to band folding in graphene supercell with vacancy have been observed. In further study, it is essential to compare the results obtained from TB by using a higher level theory such as DFT.

Holey Graphene} (HG) is a widely used graphene material for the synthesis of high-purity and highly crystalline materials. The electronic properties of a periodic distribution of lattice holes are explored here, demonstrating the emergence of flat bands. It is established that such flat bands arise as a consequence of an induced sublattice site imbalance, i.e., by having more sites in one of the graphene's bipartite sublattice than in the other. This is equivalent to the breaking of a path-exchange symmetry. By further breaking the inversion symmetry, gaps and a nonzero Berry curvature are induced, leading to topological bands. In particular, the folding of the Dirac cones from the hexagonal Brillouin zone (BZ) to the holey superlattice rectangular BZ of HG, with sizes proportional to an integer $n$ times the graphene's lattice parameter, leads to a periodicity in the gap formation such that $n \equiv 0$ (mod $3$). A low-energy hamiltonian for the three central bands is also obtained revealing that the system behaves as an effective $\alpha-\mathcal{T}_{3}$ graphene material. Therefore, a simple protocol is presented here that allows for obtaining flat bands at will. Such bands are known to increase electron-electron correlation effects. Therefore, the present work provides an alternative system that is much easier to build than twisted systems, allowing for the production of flat bands and potentially highly correlated quantum phases.

Moiré semiconductors emerged as tunable quantum simulators for strongly correlated phases. The single-particle low-energy physics is ruled by the moiré-periodic superpotential that develops by twisting or stacking layers with different lattice parameters. Signatures of this modulation are observed in the spectral function measured by angle-resolved photoemission spectroscopy (ARPES) in the form of replicas and gaps opening at the nascent zone boundary. In twisted bilayer transition metal dichalcogenides (TMDs), flat bands are reported at the Brillouin zone center and their dispersion is associated to the effective moiré potential experienced by electronic states with large out-of-plane orbital character. Here, we extend this analysis and present the orbital and wave vector dependence of this interaction over the whole Brillouin zone by comparing quantitatively our ARPES data on a TMD heterobilayer with an extended tight-binding model. Our results set the fundaments for future spectroscopic studies of the electronic correlations in moiré systems.

We use unrestricted Hartree-Fock, density matrix renormalization group, and variational projected entangled pair state calculations to investigate the ground state phase diagram of the triangular lattice Hubbard model at ``half doping'' relative to single occupancy, i.e. at a filling of $(1\pm \frac{1}{2})$ electrons per site. The electron-doped case has a nested Fermi surface in the non-interacting limit, and hence a weak-coupling instability towards density-wave orders whose wavevectors are determined by Fermi surface nesting conditions. We find that at moderate to strong interaction strengths other spatially-modulated orders arise, with wavevectors distinct from the nesting vectors. In particular, we identify a series closely-competing itinerant long-wavelength magnetically ordered states, yielding to uniform ferromagnetic order at the largest interaction strengths. For half-hole doping and a similar range of interaction strengths, our data indicate that magnetic orders are most likely absent.

Early theoretical works have predicted that single-layer graphene (SLG) is a superconductor driven by electron-electron interactions when doped to its van Hove singularity. However, although the existence of superconductivity (SC) seems by now established in various twisted and nontwisted graphene multilayers, whether their building block, SLG, also hosts SC, still remains an open question. In this study, we adopt a Random Phase Approximation (RPA) framework based on a Kohn-Luttinger-like (KL) mechanism to investigate superconductivity in heavily-doped SLG. The models are derived from ARPES measurements on Terbium-doped graphene and Density Functional Theory calculations. We predict SC with critical temperatures comparable to those of the non-twisted graphene multilayers (~600 mK at most), and dependent upon the specific dopant. Since different dopants modify SLG's lattice symmetry in different ways, electron-driven SC can potentially arise only for certain types of chemical doping. Our results might serve as a guide for future related experimental efforts.

In perfectly flat bands, phenomena such as superconductivity and Bose-Einstein condensation are possible due to multiband effects which depend on the geometry of the Bloch states. Quantum geometric quantities such as the Berry curvature and quantum metric, sometimes with modifications to ensure basis invariance [1,2,3], appear for instance in the conductivity and the superfluid weight. In fermionic systems, a nonzero integral of the quantum metric over the Brillouin zone can enable superconductivity even on an isolated flat band. In a Bose-Einstein condensate, on the other hand, the quantum metric at the condensation momentum is of particular importance: it is known to affect for instance the speed of sound [4] and the effective mass tensor [5]. We find that it also accounts for a part of the superfluid weight of the Bose-Einstein condensate. However, we also find that fluctuations lead to an often negative contribution dependent on the geometry of the flat band Bloch states throughout the Brillouin zone. We discuss the consequences for the stability of a flat band Bose-Einstein condensate. [1] K.-E. Huhtinen, J. Herzog-Arbeitman, A. Chew, B. A. Bernevig and P. Törmä, Phys. Rev. B 106, 014518 (2022) [2] J. Herzog-Arbeitman, A. Chew, K.-E. Huhtinen, P. Törmä and B. A. Bernevig, arXiv:2209.00007 (2022) [3] J. Yu, C. J. Ciccarino, R. Bianco, I. Errea, P. Narang and B. A. Bernevig, arXiv:2305.02340 (2023) [4] A. Julku, G. M. Bruun and P. Törmä, Phys. Rev. Lett 127, 170404 (2021). [5] M. Iskin, Phys. Rev. A 107, 023313 (2023)

Quantum spin liquids are fascinating phases of matter, hosting fractionalized spin excitations and unconventional long-range quantum entanglement. Usually, spin liquids exist in Mott insulators at half-filling. Here, we investigate the influence of a single mobile hole in the ground state of paradigmatic spin liquid models using techniques based on matrix product states. We find that several phases compete that can destroy the quantum spin liquid ground state towards an ordered state. However, if the spin liquid survives the hole insertion, the hole spectral function, as measured by angle-resolved photoemission spectroscopy, provides a useful tool to characterize quantum spin liquids. In this case, the single hole separates into a spinon and chargon. These fractional excitations then determine the low energy properties of the system.

We present a systematic study of Majorana modes in the quantum Hall effect by introducing anisotropic hopping integrals for a tight-binding model on the honeycomb lattice in a magnetic field. It is shown that a tunneling current of the Majorana modes localized at the boundaries is a spin current. The spin current has singular behavior, its amplitude is proportional to the square root of the magnetic field magnitude. The persistent current in one-dimensional superconductors is also determined by the Majorana modes localized on the surface, so the $4\pi$-persistence current is a spin current.

Motivated by the observation of partial magnetic order (or partial Kondo screening) in certain Kondo lattices, we propose and investigate an effective Hamiltonian to describe the physics of partial magnetic order. The model is investigated on square as well as triangular lattices via a Hybrid Monte Carlo method that allows for simulations of classical degrees of freedom coupled to lattice fermions. The model and its treatment allows for the possibility of spontaneous formation of Kondo singlets on an arbitrary number of lattice sites and hence partially ordered states can spontaneously emerge in the ground state. We find various exotic magnetic ground states coexisting with partial singlet formation. One of the intriguing results is the formation of new effective lattices that support van Hove singularities and/or flat bands. The connection of the proposed model with the Kondo-lattice model will be discussed. The theoretical/numerical results obtained thus far on this effective Hamiltonian suggest that a new mechanism for the flat-band formation on lattices may exist in certain Kondo systems. Examples of possible candidate materials will also be discussed.

We investigate the crossover from an ordinary Van Hove singularity (OVHS) to a higher order Van Hove singularity (HOVHS) in a model applicable to Bernal bilayer graphene and rhombohedral trilayer graphene in a displacement field. At small doping, these systems possess three spin-degenerate Fermi pockets near each Dirac point K and K'; at larger doping, the three pockets merge into a single one. The transition is of Lifshitz type and includes Van Hove singularities. Depending on system parameters, there are either three separate OVHS or a single HOVHS. We model this behavior by a one-parameter dispersion relation, which interpolates between OVHS and HOVHS. In each case, the diverging density of states triggers various electronic orders (superconductivity, pair density wave, valley polarization, ferromagnetism, spin, and charge density wave). We apply parquet renormalization group (pRG) technique and analyze how the ordering tendencies evolve between OVHS and HOVHS. We report rich system behavior caused by disappearance/reemergence and pair production/annihilation of the fixed points of the pRG flow.

Recent observations of the fractional anomalous quantum Hall effect in moiré materials have reignited the interest in fractional Chern insulators (FCIs). The chiral limit in which analytic Landau level-like single-particle states form an "ideal" Chern band and local interactions lead to Laughlin-like FCIs at 1/3 filling, has been very useful for understanding these systems by relating them to the lowest Landau level. We show, however, that, even in the idealized chiral limit, a fluctuating quantum geometry is associated with strongly broken symmetries and a phenomenology very different from that of Landau levels. In particular, particle-hole symmetry is strongly violated and e.g. at 2/3 filling an emergent interaction driven Fermi liquid state with no Landau level counterpart is energetically favoured. In fact, even the exact Laughlin-like zero modes at 1/3 filling have a non-uniform density tracking the underlying quantum geometry. Moreover, by switching to a Coulomb interaction, the ideal Chern band features charge density wave states with no lowest Landau level counterpart.

Cuprate superconductors have attracted a lot of attention due to their high Tc’s, reaching up to 130 K at ambient pressure. However, the physics underlying their properties has remained obscured by (i) multitudes of complex orders that appear near the superconducting phase, and (ii) the inseparable effects of the disorder that is introduced by the doping mechanisms. Decades of past research have identified one promising candidate, Tl2Ba2CuO6+x, that can be used to explore this superconductivity in the (seemingly less complicated) overdoped region of the cuprate phase diagram, with minimal effects of disorder [1,2]. We have grown high-quality single crystals of Tl2Ba2CuO6+x with negligible orthorhombicity (<0.1%) that can be annealed reversibly across a very wide doping range (p = 0.05-0.29) and have relatively large dimensions (up to ~1200⨉500⨉80 μm). This indicates that our samples are close to having perfect cation stoichiometry and no substitutional defects - solving some of the major issues faced by the previous efforts. Additionally, we are able to exploit a multitude of powerful techniques that have been developed recently, including: membrane-based AC nanocalorimetry [3], scanning SQUID measurements [4], FIB microstructuring and cleanroom recipes for magneto-transport device fabrication [5], nano-ARPES on preferentially-cleaving microstructures [6], strain-free membrane-based microstructuring procedures [7], etc. This puts us in position to map out the full phase diagram of clean cuprates, and thus take the crucial first step towards resolving the origin of their high Tc superconducting order. References: [1] N E Hussey et al., Nature, 425 (2005) 814 [2] M Plate et al., Physical Review Letters, 95 (2005) 077001 [3] S Tagliati, PhD Thesis, Stockholm University (2011) [4] E Persky et al., Annu. Rev. Condens. Matter Phys., 13 (2022) 385 [5] P J W Moll, Annu. Rev. Condens. Matter Phys., 9 (2018) 147 [6] A Hunter et al., arXiv:2311.13458v1 (2023) [7] C Guo et al., Nature, 611 (2022) 461

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

We explore the possible weak coupling instabilities of the 2D Hubbard model with existing altermagnetic order, within a truncated unity functional renormalization group (tUfRG) framework. We find that as a function of chemical potential the system exhibits instabilities towards distinct SDW orders that coexist with the altermagnetic order. We also find that the system exhibits a d-wave superconducting instability as the next nearest neighbor hopping is tuned.

A strange metal can be identified by its low temperature resistivity differing from the conventional $T^{2}$ behaviour expected of a typical Fermi liquid, with a linear-in-$T$ temperature dependence being the most commonly observed scaling [1-3]. This behaviour is strongly connected to the Planckian scattering rate [1], though the microscopic origin of this link has remained elusive. The Fermi liquid picture breaks down when thermal broadening of the Fermi surface saturates the entire band, a case not encountered in conventional metals. In strange metals like Sr${}_{3}$Ru${}_{2}$O${}_{7}$, the Fermi surface is formed across multiple bands with vastly different properties where thermal broadening can vary greatly between the different bands. Electrons whose Fermi velocity is large (cold electrons) are expected to dominate the transport properties of the system in comparison to those with small Fermi velocities (hot electrons). Recently, a phase space argument based upon second-order perturbation theory suggested that a linear-in-$T$ scattering rate can arise from scattering between these two electron species [4]. We present a microscopic description detailing how scattering between the hot and cold electron species can modify the $T^{2}$ Fermi liquid scattering rate due to thermal saturation of the hot electron bands. Our theory accounts for all electron-electron scattering processes contained within the RPA, ladder, and rainbow diagrammatic series to compare with the recent phase space predictions [4]. \textbf{References} [1] J.A.N. Bruin, H. Sakai, R.S. Perry, and A.P. Mackenzie, "Similarity of Scattering Rates in Metals Showing $T$-Linear Resistivity", Science \textbf{339}, 804 (2013). [2] Y. Cao, D. Chowdhury, D. Rodan-Legrain, O. Rubies-Bigorda, K. Watanabe, T. Taniguchi, T. Senthil, and P. Jarillo-Herrero, "Strange Metal in Magic-Angle Graphene with near Planckian Dissipation", Phys. Rev. Lett. \textbf{124}, 076801 (2020). [3] C. Lester, S. Ramos, R. S. Perry, T. P. Croft, M. Laver, R. I. Bewley, T. Guidi, A. Hiess, A. Wildes, E. M. Forgan, and S. M. Hayden, "Magnetic-field-controlled spin fluctuations and quantum criticality in Sr${}_{3}$Ru${}_{2}$O${}_{7}$", Nat. Commun. \textbf{12}, 5798 (2021). [4] C. H. Mousatov, E. Berg, and S. A. Hartnoll, "Theory of the Strange Metal Sr${}_{3}$Ru${}_{2}$O${}_{7}$", Proc. Natl. Acad. Sci. U.S.A. \textbf{117}, 2852 (2020).

Kagome metals are known to host Dirac fermions and a saddle point Van Hove singularity positioned close to Fermi level. In the framework of a minimal two-pocket model (Dirac node + Van Hove singularity) we suggest that electron-electron interaction between two nodes is greatly enhanced and determines the microscopic transport properties. We present the full semiclassical description of kinetic phenomena with the help of Boltzmann equation, and demonstrate that internode electron-electron interaction leads to sublinear in $T$ results for both thermal and electrical conductivity at low temperatures. We also predict that for higher temperatures, thermal and electric current would relax in different scattering channels, making a ground for Wiedemann-Franz law violation. Our theory agrees well with the recent experiment [1]. [1] L. Ye, S. Fang, M. Kang, J. Kaufmann, Y. Lee, C. John, P. M. Neves, S. F. Zhao, J. Denlinger, C. Jozwiak, et al., Hopping frustration-induced flat band and strange metallicity in a kagome metal, Nature Physics, 1 (2024).

Spin-ordered states close to metal-insulator transitions are poorly understood theoretically and challenging to probe in experiments. Here, we propose that the quantum twisting microscope, which provides direct access to the energy-momentum resolved spectrum of single-particle and collective excitations, can be used as a novel tool to distinguish between different types of magnetic order. To this end, we calculate the single-particle spectral function and the dynamical spin-structure factor for both a ferromagnetic and antiferromagnetic generalized Wigner crystal formed in fractionally filled moir{\'e} superlattices of transition metal dichalcogenide heterostructures. We demonstrate that magnetic order can be clearly identified in these response functions. Furthermore, we explore signatures of quantum phase transitions in the quantum twisting microscope response. We focus on the specific case of triangular moir{\'e} lattices at half filling, which have been proposed to host a topological phase transition between a chiral spin liquid and a 120 degree ordered state. Our work demonstrates the potential for quantum twisting microscopes to characterize quantum magnetism in moir{\'e} heterostructures.

We study the hydrodynamic properties of ultraclean interacting two-dimensional Dirac electrons with Keldysh quantum field theory. We demonstrate that long-range Coulomb interactions play two independent roles: (i) they provide the inelastic and momentum-conserving scattering mechanism that leads to fast local equilibration; (ii) they facilitate the emergence of collective excitations, for instance plasmons, that contribute to transport properties on equal footing with electrons. Our approach is based on an effective field theory of the collective field coupled to electrons. Within a conserving approxima- tion for the coupled system we derive a set of coupled quantum-kinetic equations. This builds the foundation of the derivation of the Boltzmann equations for the interacting system of electrons and plasmons. We demonstrate that plasmons show up in thermo-electric transport properties as well as in quantities that enter the energy-momentum tensor, such as the viscosity.

We consider a two-dimensional lattice model of altermagnetic metal on a square lattice. We show that for $d$-wave and $d_{xy}$ altermagnetic form factors, the electron bands contain spin-split van-Hove (vH) singularities at the mid-points of the Brillouin zone boundaries. The inequivalent vH points are related by combined $4$-fold rotation and time-reversal symmetry, and exhibit Fermi-surface nesting. Following the approach in Nature Physics 8 (2) (2012) 158–163, we then investigate the superconducting instability of the altermagnets with repulsive interactions, arising from coupling of BCS to nesting channels between inequivalent vH points.

Magic-angle twisted bilayer graphene is a tunable material with remarkably flat energy bands near the Fermi level, leading to fascinating transport properties and correlated states at low temperatures. However, grown pristine samples of this material tend to break up into landscapes of twist-angle domains, strongly influencing the physical properties of each individual sample. This poses a significant problem to the interpretation and comparison between measurements obtained from different samples. In this work, we study numerically the effects of twist-angle disorder on quantum electron transport in mesoscopic samples of magic-angle twisted bilayer graphene. We find a significant property of twist-angle disorder that distinguishes it from onsite-energy disorder: it leads to an asymmetric broadening of the energy-resolved conductance. The magnitude of the twist-angle variation has a strong effect on conductance, while the number of twist-angle domains is of much lesser significance. We further establish a relationship between the asymmetric broadening and the asymmetric density of states of twisted bilayer graphene at angles smaller than the first magic angle. Our results show that the qualitative differences between the types of disorder in the energy-resolved conductance of twisted bilayer graphene samples can be used to characterize them at temperatures above the critical temperatures of the correlated phases, enabling systematic experimental studies of the effects of the different types of disorders also on the other properties such as the competition of the different types of correlated states appearing at lower temperatures.

Monolayer 1T VSe2, a transition-metal dichalcogenide, hosts an anomalous charge-density-wave (CDW) whose origin and ordering wavevector have been the subject of much debate [1,2,3]. The observed [1] decoupling of the CDW from the lattice, as well as its emerging only in the strict 2-D limit, suggest that it may be driven by electron-electron interactions – this is an exciting prospect from the viewpoint of tunable strongly correlated phases, and would be an experimental counterexample to the belief that all CDWs are driven by the Peierls mechanism. We first examine a recently proposed [4] electronic mechanism for the CDW based on a particular Fermi-surface nesting, and present arguments against it. Then, using fits to ARPES data we demonstrate and discuss the presence in the band structure of an extended flat band region around $\Gamma$, lying just below the Fermi level. Based on an extended Hubbard model, we construct mean-field-theoretic phase diagrams utilising the full Fermi surface and investigate thereby the competition between superconducting, charge and spin orders. Our results provide tentative insight into the origins of the anomalous CDW and address the question of why the flat band region doesn’t cause ferromagnetism to dominate the other orders.

Twisted double bilayer graphene (TDBG) offers electric field tunable topological bands, making it an ideal platform to study the effects of band topology and valley Chern transition therein. We investigate the role of the Berry curvature dipole (BCD) in TDBG by studying its effects on electronic transport. Our work experimentally detect the topological valley Chern transition of the Z$_2$ index of flat bands by measuring the BCD from the non-linear Hall effect in twisted double bilayer graphene. In addition, by probing the BCD, we investigate the differences between TDBG with ABAB and ABBA stacking configurations, which have very similar band structures but exhibit different chirality and undergo different valley Chern transitions under the influence of a perpendicular electric field. Our analysis shows that the differences in the valley Chern transitions can be attributed to the different stacking configurations, highlighting the importance of understanding the role of stacking in the topological properties of TDBG.

Bernal bilayer graphene (BLG) hosts several spontaneous symmetry broken phases such as Stoner ferromagnetic, spin-polarized superconducting, a quantum anomalous Hall octet and a topologically non-trivial Wigner-Hall crystal phase [1-3]. Increasing the ratio of the Coulomb and kinetic energy of carriers by a divergent density of states (DoS) near Lifshitz transitions and the formation of flat bands can stabilize these interaction-driven phases. The low-energy bandstructure of trigonally warped BLG features one centre and three off-centre Dirac cones in each valley, transforming into a ‘Mexican hat’-like shape with increasing vertical electric displacement field ($D$-field) [4]. Therefore, BLG offers a rich playground for correlated phases by inducing charge density and $D$-field driven Lifshitz transitions. Here, we report on quantum Hall and electrical resistance measurements in trigonally warped BLG encapsulated in hexagonal boron-nitride in a dual-gated architecture with graphite gates and graphite contacts at low charge densities ($\sim 10^{11} \mathrm{cm}^{-2}$), high $D$-fields ($\sim 0.5-0.7$ V nm$^{-1}$) and temperatures from 10 mK to 25 K. We find critical scaling behaviour of the electrical resistance near the phase transition between a correlated insulating (potentially Wigner crystal) and Stoner ferromagnetic phase. As this phase transition can be induced either by charge density or by $D$-field, we extract the critical exponents $z\nu$ for both charge density and $D$-field dependent scaling parameters $T_{0}$. References: [1] Seiler, A. M. et al. Nature 608, 298-302 (2022). [2] de la Barrera, S. C. et al. Nat. Phys. 18, 771–775 (2022). [3] Zhou, H. et al. Science 375, 774-778 (2022). [4] McCann, E. & Koshino, M. Rep. Prog. Phys. 76, 056503 (2013).