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Nematic superconductivity in twisted bilayer graphene

Twisted bilayer graphene displays insulating and superconducting phases caused by exceptional flattening of its lowest energy bands. Superconductivity with highest T c appears near half filling of the valence band (n ≈ –2). The data show that in the large part of the superconducting dome near n = –2, threefold lattice rotation symmetry is broken in the superconducting phase, i.e., a superconductor is also a nematic. We perform a comprehensive analysis of superconductivity in twisted-bilayer graphene within an itinerant approach and present a mechanism for nematic superconductivity. We take as an input the fact that at dopings, where superconductivity has been observed, the Fermi energy lies in the vicinity of twist-induced Van Hove singularities in the density of states. We argue that the low-energy physics can be properly described by patch models with either six or twelve Van Hove points. We obtain pairing interactions for the patch models in terms of parameters of the microscopic model for the flat bands, which contains both local and twist-induced nonlocal interactions. Here, we show that the latter give rise to attraction in different superconducting channels. For six Van Hove points, there is just one attractive d-wave channel, and we find chiral d ± id superconducting order, which breaks time-reversal symmetry but leaves the lattice rotation symmetry intact. For twelve Van Hove points, we find two attractive channels, g and i waves, with almost equal coupling constants. We show that both order parameters are nonzero in the ground state and explicitly demonstrate that in this co-existence state the threefold lattice rotation symmetry is broken, i.e., the superconducting state is also a nematic. We find two possible nematic states, one is time-reversal symmetric, the other additionally breaks time-reversal symmetry. We apply our scenario to twisted bilayer graphene near n = –2 and argue that it is applicable also to other systems with two (or more) attractive channels with similar couplings as our reasoning for a nematic superconductivity is based on generic symmetry considerations.

36 MATERIALS SCIENCE↗

A V 3 Sb 5 kagome superconductors

Here, the recent discovery of the AV 3 Sb 5 (A = K, Rb, Cs) kagome superconductors launched a growing field of research investigating the interplay between superconductivity and charge-density wave order in kagome metals. Specifically, the AV 3 Sb 5 family of materials naturally exhibits a Fermi level close to the Van Hove singularities associated with the saddle points formed from the prototypical kagome band structure. The charge-density wave and superconducting states that form within the kagome networks of these compounds exhibit a number of anomalous properties reminiscent of theoretical predictions of exotic states in kagome metals tuned close to their Van Hove fillings. In this Review, we discuss the key structural and electronic features of AV 3 Sb 5 compounds and survey the status of investigations of their unconventional electronic phase transitions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Cascade of transitions in twisted and non-twisted graphene layers within the van Hove scenario

Abstract Motivated by measurements of compressibility and STM spectra in twisted bilayer graphene, we analyze the pattern of symmetry breaking for itinerant fermions near a van Hove singularity. Making use of an approximate SU(4) symmetry of the Landau functional, we show that the structure of the spin/isospin order parameter changes with increasing filling via a cascade of transitions. We compute the feedback from different spin/isospin orders on fermions and argue that each order splits the initially 4-fold degenerate van Hove peak in a particular fashion, consistent with the STM data and compressibility measurements, providing a unified interpretation of the cascade of transitions in twisted bilayer graphene. Our results follow from a generic analysis of an SU(4)-symmetric Landau functional and are valid beyond a specific underlying fermionic model. We argue that an analogous van Hove scenario explains the cascade of phase transitions in non-twisted Bernal bilayer and rhombohedral trilayer graphene.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Uniaxial strain tuning of charge modulation and singularity in a kagome superconductor

Tunable quantum materials hold great potential for applications. Of special interest are materials in which small lattice strain induces giant electronic responses. The kagome compounds AV 3 Sb 5 (A = K, Rb, Cs) provide a testbed for electronic tunable states. In this study, through angle-resolved photo- emission spectroscopy, we provide comprehensive spectroscopic measure- ments of the electronic responses induced by compressive and tensile strains on the charge-density-wave (CDW) and van Hove singularity (VHS) in CsV 3 Sb 5 . We observe a tripling of the CDW gap magnitudes with ~ 1% strain. Simulta- neously, changes of both energy and mass of the VHS are observed. Combined, this reveals an anticorrelation between the unconventional CDW order para- meter and the mass of the VHS, and highlight the role of the latter in the superconducting pairing. The substantial electronic responses uncover a rich strain tunability of the versatile kagome system in studying quantum inter- plays under lattice variations.

electronic properties and materials↗

Interacting Dirac magnons in the van der Waals ferromagnet CrBr 3

We study the effects of magnon-magnon interactions in the two-dimensional van der Waals ferromagnet CrBr 3 focusing on its honeycomb lattice structure. Motivated by earlier theoretical predictions of temperature-induced spectral shifts and van Hove singularities in the magnon dispersion [S. S. Pershoguba et al., Phys. Rev. X 8, 011010 (2018)], we go beyond the commonly used thermal magnon approximation by applying second-order perturbation theory in a fully numerical framework. Our analysis uncovers significant deviations from previous analysis: in particular, the predicted singularities are absent, consistent with recent inelastic neutron scattering measurements [S. E. Nikitin et al ., Phys. Rev. Lett. 129, 127201 (2022)]. Moreover, we find that the temperature dependence of the renormalized magnon spectrum exhibits a distinct 𝑇 3 behavior for the optical magnon branch, while retaining 𝑇 2 behavior for the acoustic or down magnon band. This feature sheds light on the collective dynamics of Dirac magnons and their interactions. We further compare the honeycomb case with a triangular Bravais lattice, relevant for ferromagnetic monolayer MnBi 2 ⁢Te 4 , and show that both systems lack singular features while displaying quite distinct thermal trends.

Holstein-Primakoff method↗

Electrical Transport Interplay with Charge Density Waves, Magnetization, and Disorder Tuned by 2D van der Waals Interface Modification via Elemental Intercalation and Substitution in ZrTe 3 , 2H-TaS 2 , and Cr 2 Si 2 Te 6 Crystals

Electrical transport in 2D materials exhibits unique behaviors due to reduced dimensionality, broken symmetries, and quantum confinement. It serves as both a sensitive probe for the emergence of coherent electronic phases and a tool to actively manipulate many-body correlated states. Exploring their interplay and interdependence is crucial but remains underexplored. This review integratively cross-examines the atomic and electronic structures and transport properties of van der Waals-layered crystals ZrTe 3 , 2H-TaS 2 , and Cr 2 Si 2 Te 6 , providing a comprehensive understanding and uncovering new discoveries and insights. A common observation from these crystals is that modifying the atomic and electronic interface structures of 2D van der Waals interfaces using heteroatoms significantly influences the emergence and stability of coherent phases, as well as phase-sensitive transport responses. In ZrTe 3 , substitution and intercalation with Se, Hf, Cu, or Ni at the 2D vdW interface alter phonon–electron coupling, valence states, and the quasi-1D interface Fermi band, affecting the onset of CDW and SC, manifested as resistance upturns and zero-resistance states. We conclude here that these phenomena originate from dopant-induced variations in the lattice spacing of the quasi-1D Te chains of the 2D vdW interface, and propose an unconventional superconducting mechanism driven by valence fluctuations at the van Hove singularity, arising from quasi-1D lattice vibrations. Short-range in-plane electronic heterostructures at the vdW interface of Cr 2 Si 2 Te 6 result in a narrowed band gap. The sharp increase in in-plane resistance is found to be linked to the emergence and development of out-of-plane ferromagnetism. The insertion of 2D magnetic layers such as Mn, Fe, and Co into the vdW gap of 2H-TaS 2 induces anisotropic magnetism and associated transport responses to magnetic transitions. Overall, 2D vdW interface modification offers control over collective electronic behavior, transport properties, and their interplays, advancing fundamental science and nanoelectronic devices.

2D van der Waals interfaces↗

Fluidic Flow Assisted Deterministic Folding of Van der Waals Materials

Origami offers a distinct approach for designing and engineering new material structures and properties. The folding and stacking of atomically thin van der Waals (vdW) materials, for example, can lead to intriguing new physical properties including bandgap tuning, Van Hove singularity, and superconductivity. On the other hand, achieving well-controlled folding of vdW materials with high spatial precision has been extremely challenging and difficult to scale toward large areas. In this paper, a deterministic technique is reported to fold vdW materials at a defined position and direction using microfluidic forces. Electron beam lithography (EBL) is utilized to define the folding area, which allows precise control of the folding geometry, direction, and position beyond 100 nm resolution. Using this technique, single-atomic-layer vdW materials or their heterostructures can be folded without the need for any external supporting layers in the final folded structure. In addition, arrays of patterns can be folded across a large area using this technique and electronic devices that can reconfigure device functionalities through folding are also demonstrated. Such scalable formation of folded vdW material structures with high precision can lead to the creation of new atomic-scale materials and superlattices as well as opening the door to realizing foldable and reconfigurable electronics.

2D materials↗

Tunable Second Harmonic Generation in Twisted Bilayer Graphene

Twisted stacking of van der Waals (vdW) materials introduces a new way in bandstructure engineering and has given rise to numerous extraordinary physical phenomena. Despite the absence of second harmonic generation (SHG) in non-gated monolayer graphene, artificially twisted bilayer graphene (tBLG) possesses more possible point-group symmetries including those with broken inversion-symmetry. Here, we report twist-angle-dependent SHG from tBLG, which is the first demonstration of an elemental material with intrinsically tunable nonlinearity. We show that depending on the twist angle, the susceptibility of the dominant chiral tensor component of tBLGs can vary from 0 to 28×10 4 pm 2 /V, which is at the same order of magnitude as on-resonance susceptibility of monolayer MoS 2 . These results shed light on the underlying symmetry of tBLG systems and electronic band-structure near van Hove singularities (vHs). More importantly, they introduce a new degree of freedom, the twisting, in creating efficient second-order nonlinear material form centrosymmetric constituents

36 MATERIALS SCIENCE↗

Effect of Fermi surface topology change on the Kagome superconductor CeRu 2 under pressure

The cubic Laves phase compound CeRu 2 with a Kagome substructure of Ru has been investigated to understand myriad fascinating phenomena resulting from competition among its various physical and geometric features. Such phenomena include flat bands, van Hove singularities, Dirac cones, reentrant superconductivity, magnetism, the Fulde–Ferrell–Larkin–Ovchinnikov state, valence fluctuations, time-irreversible anisotropic s-state superconductivity, etc. Extensive studies have thus been carried out since 1958 when the highly unusual coexistence of superconductivity and ferromagnetism was proposed for the mixed compounds (Ce,Gd)Ru 2 . Activity has accelerated in recent years due to increasing interest in topological states in superconductors. However, there has been little investigation of the mutual influence of these fascinating states. Therefore, we systematically investigated the superconductivity and possible Fermi surface topological change in CeRu 2 via magnetic, resistivity, and structural measurements under pressure up to ~168 GPa. An unusual phase diagram that suggests an intriguing interplay between the compound’s superconducting order and Fermi surface topological order has been constructed. A resurgence in its superconducting transition temperature was observed above 28 GPa. Our experiments have identified a structural transition above 76 GPa and a few tantalizing phase transitions driven by high pressure. Our high-pressure results further suggest that superconductivity and Fermi surface topology in CeRu 2 are strongly intertwined.

36 MATERIALS SCIENCE↗

A Metastable CaSH 3 Phase Composed of HS Honeycomb Sheets that is Superconducting Under Pressure

Evolutionary searches have predicted a number of ternary Ca–S–H phases that could be synthesized at pressures of 100–300 GPa. P6 3 /mmc CaSH 2 , Pnma CaSH 2 , Cmc2 1 CaSH 6 , and I$\bar{4}$CaSH 20 were composed of a Ca–S lattice along with H 2 molecules coordinated in a “side-on” fashion to Ca. The H–H bond lengths in these semiconducting phases were elongated because of H 2 σ → Ca d donation, and Ca d → H 2 σ* back-donation, via a Kubas-like mechanism. P$\bar{6}$m2 CaSH 3 , consisting of two-dimensional HS and CaH 2 sheets, was metastable and metallic above 128 GPa. The presence of van Hove singularities increased its density of states at the Fermi level and concomitantly the superconducting critical temperature, which was estimated to be as high as ~100 K at 128 GPa. Furthermore, this work will inspire the search for superconductivity in materials based upon honeycomb HX (X = S, Se, Te) and MH 2 (M = Mg, Ca, Sr, Ba) layers under pressure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Symmetry-Protected Moiré Band Engineering and Enhanced Electron–Phonon Coupling in Xe/Bi 2 Se 3 Superlattices: Path to Topological Superconductivity

Observation of superconductivity, magnetism, and correlated insulating phases driven by the moiré potential in twisted graphene bilayer has opened the exciting new field of “twistronics”. Even richer physics is expected if moiré superlattice could be generated on topological insulators; however, until now, experimental studies have been scarce. Here, we demonstrate topological moirés generated by adsorbing a monolayer of noble gas on a topological insulator. By angle-resolved photoemission spectroscopy, we show that the moiré potential replicates the topological surface state and affects it in a way fundamentally different from the trivial states. Replicated Dirac cones generally avoid crossings, except at the time-reversal invariant momenta that remain gapless. This creates van Hove singularities at the moiré Brillouin zone corners, providing the mechanism of enhancing correlations. Indeed, we observe a strong enhancement of the electron–phonon coupling strength that, if properly tuned, might lead to topological superconductivity and Majorana Fermions.

36 MATERIALS SCIENCE↗

Excitonic density wave and spin-valley superfluid in bilayer transition metal dichalcogenide

Artificial moiré superlattices in 2 d van der Waals heterostructures are a new venue for realizing and controlling correlated electronic phenomena. Recently, twisted bilayer WSe 2 emerged as a new robust moiré system hosting a correlated insulator at moiré half-filling over a range of twist angle. In this work, we present a theory of this insulating state as an excitonic density wave due to intervalley electron–hole pairing. We show that exciton condensation is strongly enhanced by a van Hove singularity near the Fermi level. Our theory explains the remarkable sensitivity of the insulating gap to the vertical electric field. In contrast, the gap is weakly reduced by a perpendicular magnetic field, with quadratic dependence at low field. The different responses to electric and magnetic field can be understood in terms of pair-breaking versus non-pair-breaking effects in a BCS analog of the system. We further predict superfluid spin transport in this electrical insulator, which can be detected by optical spin injection and spatial-temporal imaging.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Visualizing delocalized correlated electronic states in twisted double bilayer graphene

Abstract The discovery of interaction-driven insulating and superconducting phases in moiré van der Waals heterostructures has sparked considerable interest in understanding the novel correlated physics of these systems. While a significant number of studies have focused on twisted bilayer graphene, correlated insulating states and a superconductivity-like transition up to 12 K have been reported in recent transport measurements of twisted double bilayer graphene. Here we present a scanning tunneling microscopy and spectroscopy study of gate-tunable twisted double bilayer graphene devices. We observe splitting of the van Hove singularity peak by ~20 meV at half-filling of the conduction flat band, with a corresponding reduction of the local density of states at the Fermi level. By mapping the tunneling differential conductance we show that this correlated system exhibits energetically split states that are spatially delocalized throughout the different regions in the moiré unit cell, inconsistent with order originating solely from onsite Coulomb repulsion within strongly-localized orbitals. We have performed self-consistent Hartree-Fock calculations that suggest exchange-driven spontaneous symmetry breaking in the degenerate conduction flat band is the origin of the observed correlated state. Our results provide new insight into the nature of electron-electron interactions in twisted double bilayer graphene and related moiré systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Pomeranchuk instability from electronic correlations in CsTi 3 Bi 5 kagome metal

Electronic nematicity, the spontaneous breaking of rotational symmetry, has emerged as a key instability in correlated quantum systems. CsTi 3 Bi 5 , a kagome metal of the AV 3 Sb 5 (A = K, Rb, Cs) family, hosts rich unconventional electronic phases, yet the origin of its nematicity remains unsettled. Here, we combine polarization-dependent angle-resolved photoemission spectroscopy with functional renormalization group calculations on a fully interacting ab initio model. We reveal an orbital-selective nematic deformation in the low-energy band structure and identify a finite angular momentum (d-wave) Pomeranchuk instability driven by electronic correlations in specific orbital channels and detuning from Van Hove singularities. Our results establish a direct link between orbital selectivity and symmetry-breaking instabilities in CsTi 3 Bi 5 , providing a microscopic framework for nematic order in kagome systems.

Bigi, Chiara [Synchrotron SOLEIL, Saint-Aubin (Fra↗

Crystalline symmetry-protected non-trivial topology in prototype compound BaAl 4

The BaAl 4 prototype crystal structure is the most populous of all structure types, and is the building block for a diverse set of sub-structures including the famous ThCr 2 Si 2 family that hosts high-temperature superconductivity and numerous magnetic and strongly correlated electron systems. The MA 4 family of materials (M = Sr, Ba, Eu; A = Al, Ga, In) themselves present an intriguing set of ground states including charge and spin orders, but have largely been considered as uninteresting metals. We predict the exemplary compound BaAl 4 to harbor a three-dimensional Dirac spectrum with non-trivial topology and possible nodal lines crossing the Brillouin zone, wherein one pair of semi-Dirac points with linear dispersion along the k z direction and quadratic dispersion along the k x / k y direction resides on the rotational axis with C 4 v point group symmetry. An extremely large, unsaturating positive magnetoresistance in BaAl 4 despite an uncompensated band structure is revealed, and quantum oscillations and angle-resolved photoemission spectroscopy measurements confirm the predicted multiband semimetal structure with pockets of Dirac holes and a Van Hove singularity (VHS) remarkably consistent with the theoretical prediction. We thus present BaAl 4 as a topological semimetal, casting its prototype status into a role as a building block for a vast array of topological materials.

36 MATERIALS SCIENCE↗

CrRhAs: a member of a large family of metallic kagome antiferromagnets

Abstract Kagome lattice materials are an important platform for highly frustrated magnetism as well as for a plethora of phenomena resulting from flat bands, Dirac cones and van Hove singularities in their electronic structures. We study the little known metallic magnet CrRhAs, which belongs to a vast family of materials that includes 3 d , 4 f , and 5 f magnetic elements, as well as numerous nonmagnetic metals and insulators. Using noncollinear spin density functional calculations (mostly spin spirals), we extract a model magnetic Hamiltonian for CrRhAs. While it is dominated by an antiferromagnetic second nearest neighbor coupling in the kagome plane, the metallic nature of the compound leads to numerous nonzero longer range couplings and to important ring exchange terms. We analyze this Hamiltonian and find unusual ground states which are dominated by nearly isolated antiferromagnetic triangles that adopt 120 ∘ order either with positive or with negative vector chirality. We discuss the connection to the few known experimental facts about CrRhAs. Finally, we give a brief survey of other interesting magnetic members of this family of kagome compounds.

36 MATERIALS SCIENCE↗

Nature of charge density wave in kagome metal ScV6Sn6

Abstract Recently, kagome lattice materials have emerged as a new model material platform for discovering and engineering novel quantum phases of matter. In this work, we elucidate the driving mechanism of the $$\sqrt{{{3}}}$$ 3 × $$\sqrt{{{3}}}$$ 3 charge order in a newly discovered kagome metal ScV 6 Sn 6 . Through multimodal investigations combining angle-resolved photoemission spectroscopy, phonon dispersion calculations, and phase diagram study, we identify the central role of unstable planar Sn and Sc phonon modes, while the electronic instability and van Hove singularities originating from the V kagome lattice have a marginal influence. Our results highlight that the $$\sqrt{{{3}}}$$ 3 × $$\sqrt{{{3}}}$$ 3 charge order in ScV 6 Sn 6 is fundamentally distinguished from the electronically driven 2 × 2 charge order in the canonical kagome system AV 3 Sb 5 , uncovering a new mechanism to induce symmetry-breaking phase transition in kagome lattice materials.

36 MATERIALS SCIENCE↗

Nanoscale visualization and spectral fingerprints of the charge order in ScV 6 Sn 6 distinct from other kagome metals

Charge density waves (CDWs) in kagome metals have been tied to many exotic phenomena. Here, using spectroscopic-imaging scanning tunneling microscopy and angle-resolved photoemission spectroscopy, we study the charge order in kagome metal ScV 6 Sn 6 . The similarity of electronic band structures of ScV 6 Sn 6 and TbV 6 Sn6 (where charge ordering is absent) suggests that charge ordering in ScV 6 Sn 6 is unlikely to be primarily driven by Fermi surface nesting of the Van Hove singularities. In contrast to the CDW state of cousin kagome metals, we find no evidence supporting rotation symmetry breaking. Differential conductance dI/dV spectra show a partial gap Δ 1 CO ≈ 20 meV at the Fermi level. Interestingly, dI/dV maps reveal that charge modulations exhibit an abrupt phase shift as a function of energy at energy much higher than Δ 1 CO , which we attribute to another spectral gap. Our experiments reveal a distinctive nature of the charge order in ScV 6 Sn 6 with fundamental differences compared to other kagome metals.

36 MATERIALS SCIENCE↗