Spin Polarons and Ferromagnetism in Doped Dilute Moiré-Mott Insulators.

Moiré heterostructures of transition metal dichalcogenides (TMDs) exhibit Mott-insulating behavior both at half filling as well as at fractional fillings, where electronic degrees of freedom form self-organized Wigner crystal states. An open question concerns magnetic states obtained by lifting the pseudospin-1/2 degeneracy of these states at lowest temperatures. While at half filling virtual hopping is expected to induce (weak) antiferromagnetic exchange interactions, these are strongly suppressed when considering dilute filling fractions. We argue that, instead, a small concentration of doped electrons leads to the formation of spin polarons, inducing ferromagnetic order at experimentally relevant temperatures, consistent with recently observed ferromagnetic states in moiré TMD systems. We predict explicit signatures of polaron formation in the magnetization profile.

Emergence of a Spin Microemulsion in Spin-Orbit Coupled Bose-Einstein Condensates.

We report the first numerical prediction of a "spin microemulsion"-a phase with undulating spin domains resembling classical bicontinuous oil-water-surfactant emulsions-in two-dimensional systems of spinor Bose-Einstein condensates with isotropic Rashba spin-orbit coupling. Using field-theoretic numerical simulations, we investigated the melting of a low-temperature stripe phase with supersolid character and find that the stripes lose their superfluidity at elevated temperature and undergo a Kosterlitz-Thouless-like transition into a spin microemulsion. Momentum distribution calculations highlight a thermally broadened occupation of the Rashba circle of low-energy states with macroscopic and isotropic occupation around the ring. We provide a finite-temperature phase diagram that positions the emulsion as an intermediate, structured isotropic phase with residual quantum character before transitioning at higher temperature into a structureless normal fluid.

Diffusive excitonic bands from frustrated triangular sublattice in a singlet-ground-state system.

Magnetic order in most materials occurs when magnetic ions with finite moments arrange in a particular pattern below the ordering temperature. Intriguingly, if the crystal electric field (CEF) effect results in a spin-singlet ground state, a magnetic order can still occur due to the exchange interactions between neighboring ions admixing the excited CEF levels. The magnetic excitations in such a state are spin excitons generally dispersionless in reciprocal space. Here we use neutron scattering to study stoichiometric Ni2Mo3O8, where Ni2+ ions form a bipartite honeycomb lattice comprised of two triangular lattices, with ions subject to the tetrahedral and octahedral crystalline environment, respectively. We find that in both types of ions, the CEF excitations have nonmagnetic singlet ground states, yet the material has magnetic order. Furthermore, CEF spin excitons from the tetrahedral sites form a dispersive diffusive pattern around the Brillouin zone boundary, likely due to spin entanglement and geometric frustrations.

Cascade of correlated electron states in the kagome superconductor CsV3Sb5.

The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology1-18, which continues to bear surprises. Here, using spectroscopic imaging scanning tunnelling microscopy, we discover a temperature-dependent cascade of different symmetry-broken electronic states in a new kagome superconductor, CsV3Sb5. We reveal, at a temperature far above the superconducting transition temperature Tc ~ 2.5 K, a tri-directional charge order with a 2a0 period that breaks the translation symmetry of the lattice. As the system is cooled down towards Tc, we observe a prominent V-shaped spectral gap opening at the Fermi level and an additional breaking of the six-fold rotational symmetry, which persists through the superconducting transition. This rotational symmetry breaking is observed as the emergence of an additional 4a0 unidirectional charge order and strongly anisotropic scattering in differential conductance maps. The latter can be directly attributed to the orbital-selective renormalization of the vanadium kagome bands. Our experiments reveal a complex landscape of electronic states that can coexist on a kagome lattice, and highlight intriguing parallels to high-Tc superconductors and twisted bilayer graphene.

Frustrated Heisenberg J1-J2 model within the stretched diamond lattice of LiYbO2.

We investigate the magnetic properties of LiYbO2, containing a three-dimensionally frustrated, diamond-like lattice via neutron scattering, magnetization, and heat capacity measurements. The stretched diamond network of Yb3+ ions in LiYbO2 enters a long-range incommensurate, helical state with an ordering wave vector k=(0.384,±0.384,0) that "locks-in" to a commensurate k=(1/3,±1/3,0) phase under the application of a magnetic field. The spiral magnetic ground state of LiYbO2 can be understood in the framework of a Heisenberg J1-J2 Hamiltonian on a stretched diamond lattice, where the propagation vector of the spiral is uniquely determined by the ratio of J2/J1. The pure Heisenberg model, however, fails to account for the relative phasing between the Yb moments on the two sites of the bipartite lattice, and this detail as well as the presence of an intermediate, partially disordered, magnetic state below 1 K suggests interactions beyond the classical Heisenberg description of this material.

Dynamical Signatures of Quasiparticle Interactions in Quantum Spin Chains.

We study the transverse dynamical susceptibility of an antiferromagnetic spin-1/2 chain in the presence of a longitudinal Zeeman field. In the low magnetization regime in the gapless phase, we show that the marginally irrelevant backscattering interaction between the spinons creates a nonzero gap between two branches of excitations at small momentum. We further demonstrate how this gap varies upon introducing a second neighbor antiferromagnetic interaction, vanishing in the limit of a noninteracting "spinon gas." In the high magnetization regime, as the Zeeman field approaches the saturation value, we uncover the appearance of two-magnon bound states in the transverse susceptibility. This bound state feature generalizes the one arising from string states in the Bethe ansatz solution of the integrable case. Our results are based on numerically accurate, unbiased matrix-product-state techniques as well as analytic approximations.

Noncollinear phases in moiré magnets.

We introduce a general framework to study moiré structures of two-dimensional Van der Waals magnets using continuum field theory. The formalism eliminates quasiperiodicity and allows a full understanding of magnetic structures and their excitations. In particular, we analyze in detail twisted bilayers of Néel antiferromagnets on the honeycomb lattice. A rich phase diagram with noncollinear twisted phases is obtained, and spin waves are further calculated. Direct extensions to zigzag antiferromagnets and ferromagnets are also presented. We anticipate the results and formalism demonstrated to lead to a broad range of applications to both fundamental research and experiments.

Three-Magnon Bound State in the Quasi-One-Dimensional Antiferromagnet α-NaMnO_{2}.

Here we report on the formation of a three-magnon bound state in the quasi-one-dimensional antiferromagnet α-NaMnO_{2}, where the single-ion, uniaxial anisotropy inherent to the Mn^{3+} ions in this material provides a binding mechanism capable of stabilizing higher order magnon bound states. While such states have long remained elusive in studies of antiferromagnetic chains, neutron scattering data presented here demonstrate that higher order n>2 composite magnons exist, and, specifically, that a weak three-magnon bound state is detected below the antiferromagnetic ordering transition of NaMnO_{2}. We corroborate our findings with exact numerical simulations of a one-dimensional Heisenberg chain with easy-axis anisotropy using matrix-product state techniques, finding a good quantitative agreement with the experiment. These results establish α-NaMnO_{2} as a unique platform for exploring the dynamics of composite magnon states inherent to a classical antiferromagnetic spin chain with Ising-like single ion anisotropy.

CsV_{3}Sb_{5}: A Z_{2} Topological Kagome Metal with a Superconducting Ground State.

Recently discovered alongside its sister compounds KV_{3}Sb_{5} and RbV_{3}Sb_{5}, CsV_{3}Sb_{5} crystallizes with an ideal kagome network of vanadium and antimonene layers separated by alkali metal ions. This work presents the electronic properties of CsV_{3}Sb_{5}, demonstrating bulk superconductivity in single crystals with a T_{c}=2.5 K. The normal state electronic structure is studied via angle-resolved photoemission spectroscopy and density-functional theory, which categorize CsV_{3}Sb_{5} as a Z_{2} topological metal. Multiple protected Dirac crossings are predicted in close proximity to the Fermi level (E_{F}), and signatures of normal state correlation effects are also suggested by a high-temperature charge density wavelike instability. The implications for the formation of unconventional superconductivity in this material are discussed.

Chiral domain walls of Mn3Sn and their memory.

Magnetic domain walls are topological solitons whose internal structure is set by competing energies which sculpt them. In common ferromagnets, domain walls are known to be of either Bloch or Néel types. Little is established in the case of Mn3Sn, a triangular antiferromagnet with a large room-temperature anomalous Hall effect, where domain nucleation is triggered by a well-defined threshold magnetic field. Here, we show that the domain walls of this system generate an additional contribution to the Hall conductivity tensor and a transverse magnetization. The former is an electric field lying in the same plane with the magnetic field and electric current and therefore a planar Hall effect. We demonstrate that in-plane rotation of spins inside the domain wall would explain both observations and the clockwise or anticlockwise chirality of the walls depends on the history of the field orientation and can be controlled.

Quantization of the Thermal Hall Conductivity at Small Hall Angles.

We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising anyons (e.g., Kitaev's non-Abelian spin liquid on the honeycomb lattice). This is especially important in the regime in which the longitudinal bulk heat conductivity κ_{xx} due to phonons is much larger than the expected quantized thermal Hall conductance κ_{xy}^{q}=(πT/12)(k_{B}^{2}/ℏ) of the ideal isolated edge mode, so that the thermal Hall angle, i.e., the angle between the thermal current and the temperature gradient, is small. By modeling the interaction between a Majorana edge and bulk phonons, we show that the exchange of energy between the two subsystems leads to a transverse component of the bulk current and thereby an effective Hall conductivity. Remarkably, the latter is equal to the quantized value when the edge and bulk can thermalize, which occurs for a Hall bar of length L≫ℓ, where ℓ is a thermalization length. We obtain ℓ∼T^{-5} for a model of the Majorana-phonon coupling. We also find that the quality of the quantization depends on the means of measuring the temperature and, surprisingly, a more robust quantization is obtained when the lattice, not the spin, temperature is measured. We present general hydrodynamic equations for the system, detailed results for the temperature and current profiles, and an estimate for the coupling strength and its temperature dependence based on a microscopic model Hamiltonian. Our results may explain recent experiments observing a quantized thermal Hall conductivity in the regime of small Hall angle, κ_{xy}/κ_{xx}∼10^{-3}, in α-RuCl_{3}.

Floquet Engineering of Multiorbital Mott Insulators: Applications to Orthorhombic Titanates.

We consider driving multiorbital Mott insulators using laser radiation. We derive general expressions for periodically driven spin-orbital models using time-dependent perturbation theory in the strong interaction limit. We show that the effective exchange interactions of the Floquet spin-orbital Hamiltonian are highly tunable via variations of the frequency, amplitude, and polarization of the laser. We also take the effect of a finite bandwidth of excitations into account and study possible heating effects. We further apply our formalism to orthorhombic titanates YTiO_{3} and LaTiO_{3} based on first-principles calculations, and we find that the spin exchange interactions in these compounds can be engineered to a large extent by tuning the frequency and electric-field amplitude of the laser.

Topological Superconductivity in Twisted Multilayer Graphene.

We study a minimal Hubbard model for electronically driven superconductivity in a correlated flat miniband resulting from the superlattice modulation of a twisted graphene multilayer. The valley degree of freedom drastically modifies the nature of the preferred pairing states, favoring spin triplet d+id order with a valley singlet structure. We identify two candidates in this class, which are both topological superconductors. These states support half-vortices carrying half the usual superconducting flux quantum hc/(4e), and have topologically protected gapless edge states.

Amplitude mode in the planar triangular antiferromagnet Na0.9MnO2.

Amplitude modes arising from symmetry breaking in materials are of broad interest in condensed matter physics. These modes reflect an oscillation in the amplitude of a complex order parameter, yet are typically unstable and decay into oscillations of the order parameter's phase. This renders stable amplitude modes rare, and exotic effects in quantum antiferromagnets have historically provided a realm for their detection. Here we report an alternate route to realizing amplitude modes in magnetic materials by demonstrating that an antiferromagnet on a two-dimensional anisotropic triangular lattice (α-Na0.9MnO2) exhibits a long-lived, coherent oscillation of its staggered magnetization field. Our results show that geometric frustration of Heisenberg spins with uniaxial single-ion anisotropy can renormalize the interactions of a dense two-dimensional network of moments into largely decoupled, one-dimensional chains that manifest a longitudinally polarized-bound state. This bound state is driven by the Ising-like anisotropy inherent to the Mn3+ ions of this compound.

Strongly Correlated Metal Built from Sachdev-Ye-Kitaev Models.

Prominent systems like the high-T_{c} cuprates and heavy fermions display intriguing features going beyond the quasiparticle description. The Sachdev-Ye-Kitaev (SYK) model describes a (0+1)D quantum cluster with random all-to-all four-fermion interactions among N fermion modes which becomes exactly solvable as N→∞, exhibiting a zero-dimensional non-Fermi-liquid with emergent conformal symmetry and complete absence of quasiparticles. Here we study a lattice of complex-fermion SYK dots with random intersite quadratic hopping. Combining the imaginary time path integral with real time path integral formulation, we obtain a heavy Fermi liquid to incoherent metal crossover in full detail, including thermodynamics, low temperature Landau quasiparticle interactions, and both electrical and thermal conductivity at all scales. We find linear in temperature resistivity in the incoherent regime, and a Lorentz ratio L≡(κρ/T) varies between two universal values as a function of temperature. Our work exemplifies an analytically controlled study of a strongly correlated metal.

Anomalous Hall Effect and Topological Defects in Antiferromagnetic Weyl Semimetals: Mn_{3}Sn/Ge.

We theoretically study the interplay between bulk Weyl electrons and magnetic topological defects, including magnetic domains, domain walls, and Z_{6} vortex lines, in the antiferromagnetic Weyl semimetals Mn_{3}Sn and Mn_{3}Ge with negative vector chirality. We argue that these materials possess a hierarchy of energy scales, which allows a description of the spin structure and spin dynamics using an XY model with Z_{6} anisotropy. We propose a dynamical equation of motion for the XY order parameter, which implies the presence of Z_{6} vortex lines, the double-domain pattern in the presence of magnetic fields, and the ability to control domains with current. We also introduce a minimal electronic model that allows efficient calculation of the electronic structure in the antiferromagnetic configuration, unveiling Fermi arcs at domain walls, and sharp quasibound states at Z_{6} vortices. Moreover, we have shown how these materials may allow electronic-based imaging of antiferromagnetic microstructure, and propose a possible device based on the domain-dependent anomalous Hall effect.

Spin-Orbit Dimers and Noncollinear Phases in d

We formulate and study a spin-orbital model for a family of cubic double perovskites with d^{1} ions occupying a frustrated fcc sublattice. A variational approach and a complementary analytical analysis reveal a rich variety of phases emerging from the interplay of Hund's rule and spin-orbit coupling. The phase digram includes noncollinear ordered states, with or without a net moment, and, remarkably, a large window of a nonmagnetic disordered spin-orbit dimer phase. The present theory uncovers the physical origin of the unusual amorphous valence bond state experimentally suggested for Ba_{2}BMoO_{6} (B=Y, Lu) and predicts possible ordered patterns in Ba_{2}BOsO_{6} (B=Na, Li) compounds.

Bilayer Graphene as a Platform for Bosonic Symmetry-Protected Topological States.

Bosonic symmetry protected topological (BSPT) states, the bosonic analogue of topological insulators, have attracted enormous theoretical interest in the last few years. Although BSPT states have been classified by various approaches, there is so far no successful experimental realization of any BSPT state in two or higher dimensions. In this paper, we propose that a two-dimensional BSPT state with U(1)×U(1) symmetry can be realized in bilayer graphene in a magnetic field. Here the two U(1) symmetries represent total spin S^{z} and total charge conservation, respectively. The Coulomb interaction plays a central role in this proposal-it gaps out all the fermions at the boundary, so that only bosonic charge and spin degrees of freedom are gapless and protected at the edge. Based on the above conclusion, we propose that the bulk quantum phase transition between the BSPT and trivial phase, which can be driven by applying both magnetic and electric fields, can become a "bosonic phase transition" with interactions. That is, only bosonic modes close their gap at the transition, which is fundamentally different from all the well-known topological insulator to trivial insulator transitions that occur for free fermion systems. We discuss various experimental consequences of this proposal.

Disorder-Induced Quantum Spin Liquid in Spin Ice Pyrochlores.

We propose that in a certain class of magnetic materials, known as non-Kramers "spin ice," disorder induces quantum entanglement. Instead of driving glassy behavior, disorder provokes quantum superpositions of spins throughout the system and engenders an associated emergent gauge structure and set of fractional excitations. More precisely, disorder transforms a classical phase governed by a large entropy, classical spin ice, into a quantum spin liquid governed by entanglement. As the degree of disorder is increased, the system transitions between (i) a "regular" Coulombic spin liquid, (ii) a phase known as "Mott glass," which contains rare gapless regions in real space, but whose behavior on long length scales is only modified quantitatively, and (iii) a true glassy phase for random distributions with large width or large mean amplitude.

Fracton Topological Phases from Strongly Coupled Spin Chains.

We provide a new perspective on fracton topological phases, a class of three-dimensional topologically ordered phases with unconventional fractionalized excitations that are either completely immobile or only mobile along particular lines or planes. We demonstrate that a wide range of these fracton phases can be constructed by strongly coupling mutually intersecting spin chains and explain via a concrete example how such a coupled-spin-chain construction illuminates the generic properties of a fracton phase. In particular, we describe a systematic translation from each coupled-spin-chain construction into a parton construction where the partons correspond to the excitations that are mobile along lines. Remarkably, our construction of fracton phases is inherently based on spin models involving only two-spin interactions and thus brings us closer to their experimental realization.