Hae-Young Kee

• PhD
• Professor (Full) at University of Toronto

Quantum spin liquids (QSLs) represent exotic states of matter where quantum spins interact strongly yet evade long-range magnetic order down to absolute zero. Characterized by non-local quantum entanglement and resultant fractionalized excitations, QSLs have emerged as a frontier in condensed matter physics, bolstered by the recent identification o...

Motivated by intense research on two-dimensional spin-1/2 Kitaev materials, Kitaev spin chains and ladders, though geometrically limited, have been studied for their numerical simplicity and insights into extended Kitaev models. The phase diagrams under the magnetic field were also explored for these quasi-one dimensional models. For an isotropic K...

Motivated by the time-reversal symmetry breaking signal in muon spin relaxation below a transition temperature without accompanying noticeable magnetic Bragg peaks in $5d^2$ Os double perovskites, a rare ferro-octupolar order was proposed to account for such hidden order. Here we study the phase transitions under a magnetic field in triangular and...

The exactly solvable spin-1/2 Kitaev model on a honeycomb lattice has drawn significant interest, as it offers a pathway to realizing the long-sought after quantum spin liquid. Building upon the Kitaev model, Yao and Lee introduced another exactly solvable model on an unusual star lattice featuring non-abelian spinons. The additional pseudospin deg...

The discovery of Mott insulators and superconductivity in twisted bilayer graphene has ignited intensive research into strong correlation effects in other stacking geometries. Bernal-stacked bilayer graphene (BBG), when subjected to a perpendicular electric field, exhibits phase transitions to a variety of broken-symmetry states. Notably, supercond...

α−RuCl3 is a Kitaev material suggested to be a proximate quantum spin liquid in a certain temperature and magnetic field range. Nonequilibrium measurements of transient dynamics have been proposed to detect fractionalized particles that emerge in the spin liquid and to possibly drive the system into novel photoinduced magnetic states that cannot be...

For many years, CoNb2O6 has served as an exemplar of the one-dimensional Ising model. However, recent experimental and theoretical analyses challenge its applicability to this material. Prior to that, a tailored spin model for 3d7 systems such as Co2+, known as the JKΓ model, has emerged, featuring Heisenberg (J), Kitaev (K), and Gamma (Γ) interact...

The spin-orbit assisted Mott insulator $\alpha$-RuCl3 is proximate to the coveted quantum spin liquid (QSL) predicted by the Kitaev model. In the search for the pure Kitaev QSL, reducing the dimensionality of this frustrated magnet by exfoliation has been proposed as a way to enhance magnetic fluctuations and Kitaev interactions. Here, we perform a...

The recent experimental discovery of the zero-field fractional Chern insulator (FCI) in twisted MoTe2 moiré superlattices has sparked immense interest in this exotic topological quantum state. The FCI has also been observed in previous experiments in magic angle twisted bilayer graphene (TBG) under a finite magnetic field of about 5 Tesla. Generall...

Finite-momentum pairing in a Pauli-limited spin-singlet superconductor arises from the pair-breaking effects of an external Zeeman field, a mechanism which is not applicable in odd-parity spin-triplet superconductors. However, in multiorbital systems, the relevant bands originating from different orbitals are usually separated in momentum space, im...

CrX$_3$ (X = Cl, Br, I) have the same crystal structure and Hamiltonian but different ligand spin-orbit coupling (SOC) constant $\lambda_X$, providing excellent material platform exploring for exotic two-dimensional (2D) spin orders. Their microscopic mechanism underlying 2D spin physics and Hamiltonian remain unestablished, along with experimental...

Recent experiments on kagome metals AV3Sb5 (A=Cs,Rb,K) indicated spontaneous time-reversal symmetry breaking in the charge density wave state in the absence of static magnetization. The loop current order (LCO) is proposed as its cause, but a microscopic model explaining the emergence of LCO through electronic correlations has not been firmly estab...

We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To this end, we present a comprehensive overview of the key exchange interactions in candidate materials with a specific focus on systems fea...

Finding the Kitaev spin liquid in candidate materials involves understanding the entire phase diagram, including other allowed interactions. One of these interactions, called the Gamma (Γ) interaction, causes magnetic frustration and its interplay with the Kitaev ( K ) interaction is crucial to comprehend Kitaev materials. Due to the complexity of...

Recent experiments on Kagome metals AV$_3$Sb$_5$ (A=Cs,Rb,K) indicated spontaneous time-reversal symmetry breaking in the charge density wave state in the absence of static magnetization. The loop current order (LCO) is proposed as its cause, but a microscopic model explaining the emergence of LCO through electronic correlations has not been firmly...

We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To that end, we give a comprehensive overview of the most relevant exchange interactions in $d^5$ and $d^7$ iridates and similar compounds, a...

Understanding the nature of charge density wave (CDW) and superconductivity in the kagomé metal AV3Sb5 (A= Cs,Rb,K) is a recent subject of intensive study. Due to the presence of van Hove singularities, electron-electron interaction has been suggested to play an important role in the formation of such broken-symmetry states. Recent experiments show...

In a cubic environment, the ground state of spin-orbit coupled 5d2 ions is a non-Kramers Eg doublet, which hosts quadrupole and octupole moments. A series of 5d2 osmium double perovskites Ba2MOsO6 (M=Mg, Ca, Zn, Cd) have recently been proposed to exhibit multipolar orders. We investigate the structural properties of these materials using ab initio...

While a complete understanding of the phase-diagram of Kitaev materials has yet to be achieved, important insights can be gained from studying low-dimensional models such as chains and ladders. Here we focus on the Kitaev-Gamma ladder with both Kitaev ($K$) and Gamma ($\Gamma$) couplings. We first report two new phases near $K$=0, $\Gamma\mathord{>...

Kitaev-type spin chains have been demonstrated to be fertile playgrounds in which exotic phases and unconventional phase transitions are ready to appear. In this work, we use the density-matrix renormalization-group method to study the quantum phase diagram of a spin-1 Kitaev chain with a tunable negative single-ion anisotropy (SIA). When the stren...

The Kitaev-type spin chains have been demonstrated to be fertile playgrounds in which exotic phases and unconventional phase transitions are ready to appear. In this work, we use the density-matrix renormalization group method to study the quantum phase diagram of a spin-1 Kitaev chain with a tunable negative single-ion anisotropy (SIA). When the s...

In a cubic environment, the ground state of spin-orbit coupled $5d^2$ ions is a non-Kramers $E_g$ doublet, which hosts quadrupole and octupole moments. A series of $5d^2$ osmium double perovskites Ba$_2M$OsO$_6$ (M = Mg, Ca, Zn, Cd) have recently been proposed to exhibit multipolar orders. We investigate the structural properties of these materials...

Entangling a pair of far-distant qubits in many-body systems has been a challenging task in quantum computing. A robust entanglement was predicted in the rainbow states and generating nonlocal Bell pairs protected by a mirror symmetry was recently proposed. We investigate a way to create entangled Majorana fermions in the spin-12 Kitaev chain with...

An intriguing chiral soliton phase has recently been identified in the S=12 Kitaev spin chain. Here we show that for S = 1, 2, 3, 4, 5 an analogous phase can be identified, but contrary to the S=12 case the chiral soliton phases appear as islands within the sea of the polarized phase. In fact, a small field applied in a general direction will adiab...

The bond-dependent Ising interaction present in the Kitaev model has attracted considerable attention. The appearance of an unexpected intermediate phase under a magnetic field is particularly intriguing, and one may wonder if a similar phase occurs in the Kitaev spin chain with alternating x- and y-bond Ising interactions. Previous studies have fo...

Understanding the nature of charge density wave (CDW) and superconductivity in kagome metal AV$_3$Sb$_5$ (A=Cs,Rb,K) is a recent subject of intensive study. Due to the presence of van Hove singularities, electron-electron interaction has been suggested to play an important role in the formation of such broken symmetry states. Recent experiments sho...

Recently, honeycomb cobaltates with 3d7 were proposed to display Kitaev physics despite weak spin-orbit coupling. However, other theoretical and experimental works found leading XXZ Heisenberg and negligible Kitaev interactions in BaCo2(AsO4)2 (BCAO), which calls for further study to clarify the origin of the discrepancies. Here we derive the analy...

An intriguing chiral soliton phase has recently been identified in the $S$=1/2 Kitaev spin chain. Here we show that for $S$=1,2,3,4,5 an analogous phase can be identified, but contrary to the $S$=1/2 case the chiral soliton phases appear as islands within the sea of the polarized phase. In fact, a small field applied in a general direction will adi...

Entangling a pair of far-distance qubits in many-body systems has been a challenging task in quantum computing. A persistent entanglement was suggested in the rainbow states and generating nonlocal Bell pairs protected by a mirror symmetry was recently proposed. We investigate a way to create entangled Majorana fermions in the spin-1/2 Kitaev chain...

The Kitaev model, characterized by bond-dependent Ising spin interactions among spin-orbit entangled dipole moments in Mott insulators, offered a new approach to quantum spin liquids. Motivated by another type of bond-dependent interaction among quadrupole moments in 5d2 Mott insulators, we provide a microscopic route to uncover the Kitaev multipol...

The Kitaev interaction in a honeycomb lattice with higher-spin S has been one of the central attractions, as it may offer quantum spin liquids. A microscopic theory showed that when the Hund's coupling at the transition metal generates S>12, the spin-orbit coupling at the heavy ligands provides a route to the Kitaev interaction. However, there have...

The superconducting state of Sr2RuO4 was once thought to be a leading candidate for p-wave superconductivity. A constant Knight shift below the transition temperature provided evidence for spin-triplet pairing, and a π phase shift observed in Josephson junction tunneling experiments suggested odd-parity pairing, both of which are described by p-wav...

Thermal Hall conductivity originating from topological magnons is observed in the Kitaev candidate $\alpha$-RuCl$_3$ in broad intervals of temperature and in-plane magnetic field, raising questions on the role of the Majorana mode in heat conduction.

Thermal Hall conductivity originating from topological magnons is observed in the Kitaev candidate α-RuCl3 in broad intervals of temperature and in-plane magnetic field, raising questions on the role of the Majorana mode in heat conduction.

Recently, honeycomb cobaltates with 3$d^7$ were proposed to display Kitaev physics despite weak spin-orbit coupling. However, other theoretical and experimental works found leading XXZ Heisenberg and negligible Kitaev interactions in the rhombohedral cobaltates, which calls for a further study to clarify the origin of the discrepancies. Here we der...

The Bloch wave functions have been playing a crucial role in the diagnosis of topological phases in noninteracting systems. However, the Bloch waves are no longer applicable in the presence of finite Coulomb interaction and alternative approaches are needed to identify the topological indices. In this paper, we focus on three-dimensional higher-ord...

The superconducting state of Sr$_2$RuO$_4$ was once thought to be a leading candidate for $p$-wave superconductivity. A constant Knight shift below the transition temperature provided evidence for spin-triplet pairing, and a $\pi$ phase shift observed in Josephson junction tunneling experiments suggested odd-parity pairing, both of which are descri...

The bond-dependent Ising interaction present in the Kitaev model has attracted considerable attention. The appearance of an unexpected intermediate phase under a magnetic field is particularly intriguing, and one may wonder if a similar phase occurs in the Kitaev spin chain with alternating $x$- and $y$-bond Ising interactions. Previous studies hav...

The Kitaev interaction in a honeycomb lattice with higher-spin $S$ has been one of the central attractions, as it may offer quantum spin liquids. A microscopic theory showed that when the Hund's coupling at the transition metal generates $S> \frac{1}{2}$, the spin-orbit coupling at the heavy ligands provides a route to the Kitaev interaction. Howev...

An effective spin model for Mott insulators is determined by the symmetries involved among magnetic sites, electron fillings, and their interactions. Such a spin Hamiltonian offers insight to mechanisms of magnetic orders and magnetic anisotropy beyond the Heisenberg model. For a spin moment S bigger than 1/2, single-ion anisotropy is in principle...

We study the nearest neighboring spin-1/2 Kitaev-Heisenberg-Gamma ($KJ\Gamma$) model on the honeycomb lattice in the parameter region of ferromagnetic (FM) Kitaev and antiferromagnetic (AFM) Heisenberg couplings relevant for honeycomb iridates, using a coupled-chain analysis. Starting from the gapless Luttinger liquid phase of a decoupled $KJ\Gamma...

Recent experiments on Kitaev spin liquid candidate materials reported nonmonotonic behavior of thermal conductivity as a function of magnetic field, which lead to conflicting interpretations of its origin. Motivated by this development, we study the magnetic field dependence of thermal conductivity of a generalized Kitaev model, which allows the ph...

Vortices in an unconventional superconductor are an important subject for the fundamental study of superconductivity. A spin counterflow half-quantum vortex (HQV) was predicted theoretically for odd-parity, spin-triplet superconductors. Cantilever torque magnetometry measurements revealed previously experimental evidence for HQVs in doubly connecte...

The Kitaev model, characterized by bond-dependent Ising spin interactions among spin-orbit entangled dipole moments in Mott insulators, offered a new approach to quantum spin liquids. Motivated by another type of bond-dependent interaction among quadrupole moments in 5$d^{2}$ Mott insulators, we provide a microscopic route to uncover the Kitaev mul...

The Bloch wave functions have been playing a crucial role in the diagnosis of topological phases in non-interacting systems. However, the Bloch waves are no longer applicable in the presence of finite Coulomb interaction and alternative approaches are needed to identify the topological indices. In this paper, we focus on three-dimensional higher-or...

In candidate Kitaev materials, the off-diagonal Γ and Γ′ interactions are identified to come from the spin-orbit coupling and trigonal distortion, respectively. They have generated intense research efforts because of their intimate relation to the field-induced magnetically disordered state reported in α−RuCl3. Theoretically, while a plethora of fi...

The Kitaev spin liquid, a ground state of the bond-dependent Kitaev model in a honeycomb lattice has been a center of attraction, since a microscopic theory to realize such an interaction in solid-state materials was discovered. A challenge in real materials though is the presence of the Heisenberg and another bond-dependent Gamma interactions detr...

The ruthenate family of layered perovskites has been a topic of intense interest, with much work dedicated to the superconducting state of Sr2RuO4. Another long-standing puzzle is the lack of superconductivity in its sister compound, Sr3Ru2O7, which constrains the possible mechanisms of Sr2RuO4. Here we address a microscopic mechanism that unifies...

The simulation of fermionic relativistic physics, e.g., Dirac and Weyl physics, has led to the discovery of many unprecedented phenomena in photonics, of which the optical-frequency realization is, however, still challenging. Here, surprisingly, we discover that the woodpile photonic crystals commonly used for optical frequency applications host ex...

In candidate Kitaev materials, the off-diagonal $\Gamma$ and $\Gamma'$ interactions are identified to come from the spin-orbit coupling and trigonal distortion, respectively. They have generated intense research efforts because of their intimate relation to the reported field-induced magnetically disordered state in $\alpha$-RuCl$_3$. Theoretically...

Recently, there has been a renewed interest in properties of the higher-spin Kitaev models, especially their low-dimensional analogs with additional interactions. These quasi-one-dimensional systems exhibit rich phase diagrams with symmetry-protected topological phases, Luttinger liquids, hidden order, and higher-rank magnetism. However, the nature...

An effective spin model for Mott insulators is determined by the symmetries involved among magnetic sites, electron fillings, and their interactions. Such a spin Hamiltonian offers insight to mechanisms of magnetic orders and magnetic anisotropy beyond the Heisenberg model. For a spin moment S bigger than 1/2, single-ion anisotropy is in principle...

The Kitaev spin liquid, a ground state of the bond-dependent Kitaev model in a honeycomb lattice has been a centre of attraction, since a microscopic theory to realize such interaction in solid-state materials was discovered. A challenge in real materials though is the presence of the Heisenberg and another bond-dependent Gamma interactions detrime...

Recent experiments on Kitaev spin liquid candidate materials reported non-monotonic behavior of thermal conductivity as a function of magnetic field, which lead to conflicting interpretations of its origin. Motivated by this development, we study the magnetic field dependence of thermal conductivity of a generalized Kitaev model, which allows the p...

Frustrated magnets with highly degenerate ground states are at the heart of hunting exotic states of matter. Recent studies in spin-orbit coupled honeycomb magnets have generated immense interest in bond-dependent interactions, appreciating a symmetric off-diagonal Γ interaction which exhibits a macroscopic degeneracy in the classical limit. Here,...

In 5d2 Mott insulators with strong spin-orbit coupling, the lowest pseudospin states form a non-Kramers doublet, which carries quadrupolar and octupolar moments. A family of double perovskites where magnetic ions form a face-centered cubic (fcc) lattice was suggested to unveil an octupolar order offering a rare example in d-orbital systems. The pro...

A family of spin–orbit coupled honeycomb Mott insulators offers a playground to search for quantum spin liquids (QSLs) via bond-dependent interactions. In candidate materials, a symmetric off-diagonal Γ term, close cousin of Kitaev interaction, has emerged as another source of frustration that is essential for complete understanding of these system...

The ruthenate family of layered perovskites has been a topic of intense interest with much work dedicated to understanding the superconducting state of the single layer, Sr$_2$RuO$_4$. Another longstanding puzzle is the lack of superconductivity in its sister compound, Sr$_3$Ru$_2$O$_7$, which constrains the possible superconducting mechanisms of S...

Recently there has been a renewed interest in properties of the higher-spin Kitaev models, especially their low-dimensional analogues with additional interactions. These quasi-1D systems exhibit rich phase diagrams with symmetry-protected topological phases, Luttinger liquids, hidden order, and higher-rank magnetism. However, the nature of the pure...

Even-parity interorbital spin-triplet pairing emerges as an intriguing candidate in multiorbital superconductors with significant Hund's and spin-orbit coupling. Within such a state, the pairing is dominated by the intraband pseudospin-singlet component via the spin-orbit coupling, distinguishing it from a pure spin triplet and motivating the name,...

In the pseudospin-12 honeycomb Mott insulators with strong spin-orbit coupling, there are two types of bond-dependent exchange interactions, named Kitaev (K) and Γ, leading to strong frustration. While the ground state of the Kitaev model is a quantum spin liquid with fractionalized excitations, the ground state of the Γ model remains controversial...

In 5$d^2$ Mott insulators with strong spin-orbit coupling, the lowest pseudospin states form a non-Kramers doublet, which carries quadrupolar and octupolar moments. A family of double-perovskites where magnetic ions form a face-centered cubic (FCC) lattice, was suggested to unveil an octupolar order offering a rare example in d-orbital systems. The...

We develop a microscopic theory of multipole interactions and orderings in 5d2 transition metal ion compounds. In a cubic environment, the ground state of 5d2 ions is a non-Kramers Eg doublet, which is nonmagnetic but hosts quadrupole and octupole moments. We derive low-energy pseudospin one-half Hamiltonians describing various spin-orbital exchang...

Simulation of fermionic relativistic physics (such as Dirac and Weyl points) has led the dicovery of versatile and exotic phenomena in photonics, of which the optical-frequency realization is, however, still a challenging aim. Here we discover that the commonly-used woodpile photonic crystals for optical-frequency applications host novel fermionic...

One-dimensional gapped phases that avoid any symmetry breaking have drawn enduring attention. In this paper, we study such phases in a bond-alternating spin-1 K−Γ chain built of a Kitaev (K) interaction and an off-diagonal Γ term. In the case of isotropic bond strength, a Haldane phase, which resembles the ground state of a spin-1 Heisenberg chain,...

Even-parity inter-orbital spin-triplet pairing emerges as an intriguing candidate in multi-orbital superconductors with significant Hund's and spin-orbit coupling. Within such a state, the pairing is dominated by the intra-band pseudospin-singlet component via the spin-orbit coupling, distinguishing it from a pure spin triplet and motivating the na...

In the pseudospin-$\frac{1}{2}$ honeycomb Mott insulators with strong spin-orbit coupling, there are two types of bond-dependent exchange interactions named Kitaev ($K$) and $\Gamma$ leading to strong frustration. While the ground state of the Kitaev model is a quantum spin liquid with fractionalized excitations, the ground state of the $\Gamma$ mo...

Despite decades of intense theoretical, experimental and computational effort, a microscopic theory of high-temperature superconductivity is not yet established. Eight researchers share their contributions to the search for a better understanding of unconventional superconductivity and their hopes for the future of the field.

We develop a microscopic theory of multipole interactions and orderings in 5$d^2$ transition metal ion compounds. In a cubic environment, the ground state of 5$d^2$ ions is a non-Kramers $E_g$ doublet, which is nonmagnetic but hosts quadrupole and octupole moments. We derive pseudospin one-half Hamiltonians describing various spin-orbital exchange...

The one-dimensional gapped phases that avoid any symmetry breaking have drawn enduring attention. In this work, we study such phases in a bond-alternating spin-1 $K$-$\Gamma$ chain built of a Kitaev ($K$) interaction and an off-diagonal $\Gamma$ term. In the case of isotropic bond strength, a Haldane phase, which resembles the ground state of a spi...

The key to unraveling intriguing phenomena observed in various Kitaev materials lies in understanding the interplay of Kitaev (K) interaction and a symmetric off-diagonal Γ interaction. To provide insight into the challenging problems, we study the quantum phase diagram of a bond-alternating spin-12gx−gyK−Γ chain by density-matrix renormalization-g...

Ferromagnetism in two-dimensional CrI3 has generated a lot of excitement, and it was recently proposed that the spin-orbit coupling (SOC) in iodine may generate bond-dependent spin interactions leading to magnetic anisotropy. Here, we derive a microscopic spin model of S=3/2 on transition metals surrounded by heavy ligands in honeycomb Mott insulat...

Material realization of the non-Abelian Kitaev spin liquid phase—an example of Ising topological order (ITO)—has been the subject of intense research in recent years. The 4d honeycomb Mott insulator α−RuCl3 has emerged as a leading candidate, as it enters a field-induced magnetically disordered state where a half-integer quantized thermal Hall cond...

A minimal Kitaev-Gamma model has been recently investigated to understand various Kitaev systems. In the one-dimensional Kitaev-Gamma chain, an emergent SU(2)1 phase and a rank-1 spin ordered phase with Oh→D4 symmetry breaking were identified using non-Abelian bosonization and numerical techniques. However, puzzles near the antiferromagnetic Kitaev...

Material realizations of the bond-dependent Kitaev interactions with S=1/2 local moments have vitalized the research in quantum spin liquids. Recently, it has been proposed that higher-spin analogs of the Kitaev interactions may also occur in a number of materials with strong spin-orbit coupling. In contrast to the celebrated S=1/2 Kitaev model on...

We have used resonant inelastic x-ray scattering to reveal optical magnons in a honeycomb lattice iridate α−Li2IrO3. The spectrum in the energy region 20–25 meV exhibits momentum dependence, of which energy is highest at the location of the magnetic Bragg peak, (h,k)=(±0.32,0), and lowered toward (0,0) and (±1,0). We compare our data with a linear...

The bond-dependent Kitaev model on the honeycomb lattice with anyonic excitations has recently attracted considerable attention. However, in solid-state materials other spin interactions are present, and among such additional interactions, the off-diagonal symmetric Gamma interaction, another type of bond-dependent term, has been particularly chall...

We have used resonant inelastic x-ray scattering to reveal optical magnons in a honeycomb lattice iridate $\alpha$-Li$_{2}$IrO$_{3}$. The spectrum in the energy region 20-25 meV exhibits momentum dependence, of which energy is highest at the location of the magnetic Bragg peak, ($\textit{h}, \textit{k}$) = ($\pm$0.32, 0), and lowered toward (0, 0)...

Hund's coupling in multiorbital systems allows for the possibility of even-parity orbital-antisymmetric spin-triplet pairing, which can be stabilized by spin-orbit coupling (SOC). While this pairing expressed in the orbital basis is uniform and spin-triplet, it appears in the band basis as a pseudospin-singlet, with the momentum dependence determin...

The key to unraveling intriguing phenomena observed in various Kitaev materials lies in understanding the interplay of Kitaev ($K$) interaction and a symmetric off-diagonal $\Gamma$ interaction. To provide insight into the challenging problems, we study the quantum phase diagram of a bond-alternating spin-$1/2$ $g_x$-$g_y$ $K$-$\Gamma$ chain by den...

The observation of the highly unusual half-quantum vortex (HQV) in a single crystalline superconductor excludes unequivocally the spin-singlet symmetry of the superconducting order parameter. HQVs were observed previously in mesoscopic samples of Sr2RuO4 in cantilever torque magnetometry measurements, thus providing direct evidence for spin-triplet...

Frustrated magnets with highly degenerate ground states are at the heart of hunting exotic states of matter. Recent studies in spin-orbit coupled honeycomb magnets have generated immense interest in bond-dependent interactions, appreciating a symmetric off-diagonal $\Gamma$ interaction which exhibits a macroscopic degeneracy in the classical limit....

The appearance of nontrivial phases in Kitaev materials exposed to an external magnetic field has recently been a subject of intensive studies. Here, we elucidate the relation between the field-induced ground states of the classical and quantum spin models proposed for such materials, by using the infinite density matrix renormalization group (iDMR...

Hund's coupling in multi-orbital systems allows for the possibility of even-parity orbital-antisymmetric spin-triplet pairing which can be stabilized by spin-orbit coupling (SOC). While this pairing expressed in the orbital basis is uniform and spin-triplet, it appears at the Fermi surface (FS) as a pseudospin-singlet, with the momentum-dependence...

Ferromagnetism in the two-dimensional CrI$_3$ has generated a lot of excitement, and it was recently proposed that the spin-orbit coupling in Iodine may generate bond-dependent spin interactions leading to magnetic anisotropy. Here we derive a microscopic spin model of S=3/2 on transition metals surrounded by heavy ligands in honeycomb Mott insulat...

Shortly after the discovery of superconductivity in Sr2RuO4, spin-triplet pairing was proposed and further corroborated by a constant Knight shift (K) across the transition temperature (Tc). However, a recent experiment observed a drop in K at Tc which becomes larger under uniaxial strain, ruling out several spin-triplet scenarios. Here we show tha...

Effects of electron many-body interactions amplify in an electronic system with a narrow bandwidth opening a way to exotic physics. A narrow band in a two-dimensional (2D) honeycomb lattice is particularly intriguing as combined with Dirac bands and topological properties but the material realization of a strongly interacting honeycomb lattice desc...

The bond-dependent Kitaev model on the honeycomb lattice with anyonic excitations has recently attracted considerable attention. However, in solid state materials other spin interactions are present, and among such additional interactions, the off-diagonal symmetric Gamma interaction, another type of bond-dependent term, has been particularly chall...

Effects of electron many-body interactions amplify in an electronic system with a narrow bandwidth opening a way to exotic physics. A narrow band in a two-dimensional (2D) honeycomb lattice is particularly intriguing as combined with Dirac bands and topological properties but the material realization of a strongly interacting honeycomb lattice desc...

Recent proposals for spin-1 Kitaev materials, such as honeycomb Ni oxides with heavy elements of Bi and Sb, have shown that these compounds naturally give rise to antiferromagnetic (AFM) Kitaev couplings. Conceptual interest in such AFM Kitaev systems has been sparked by the observation of a transition to a gapless U(1) spin liquid at intermediate...

Material realization of the non-Abelian Kitaev spin liquid phase - an example of Ising topological order (ITO) - has been the subject of intense research in recent years. The $4d$ honeycomb Mott insulator $\alpha$-RuCl$_3$ has emerged as a leading candidate, as it enters a field-induced magnetically disordered state where a half-integer quantized t...