Magnetic resonance of collective paramagnets with gapped excitations spectrum
V. N. Glazkov
备注：
This text is an expanded author-translated version of the review prepared for the memorial issue of Journal of Experimental and Theoretical Physics dedicated to 100-year anniversary of A.S.~Borovik-Romanov (full memorial volume is available as JETP 131 No.1 (2020) [ZhETF 158 No.1 (2020)])
Some magnets due to particular geometry of the exchange bonds do not undergo transition to the conventional magnetically ordered state despite of the presence of significant exchange couplings. Instead, a collective paramagnetic state is formed. The later state can remain stable down to $T=0$ if the ground state of this magnet turns out to be nonmagnetic singlet separated from the excited triplet states by an energy gap. Low-temperature spin dynamics of the collective paramagnets with gapped excitations spectrum (or spin-gap magnets) can be described in terms of a dilute gas of the triplet excitations. Applied magnetic field can suppress the energy gap, resulting in the formation of the gapless spin-liquid state or even leading to the unusual phenomenon of field-induced antiferromagnetic order. Introduction of defects in the crystallographic structure of the spin-gap magnet can result either in the formation of multi-spin paramagnetic center or in the formation of randomly distributed modified exchange bonds in the crystal. This review includes results of electron spin resonance (ESR) spectroscopy study of several representative quantum paramagnets with gapped excitations spectrum: quasy-two-dimensional magnet \phcc{}, quasy-one-dimensional magnets of "spin-tube" type \sul{} and "spin-ladder" type \dimpy{}. We will demonstrate that ESR absorption spectra reveal common features of these systems: ESR spectroscopy allows to observe and characterize fine structure if the triplet energy levels, to identify many-particles relaxation processes in the gas of triplet excitations and to observe collective spin-wave oscillations in the field induced antiferromagnetically ordered state, as well as to observe some individual features of the studied systems.
AKLT state (or Haldane phase) in a spin-1 chain represents a large class of gapped topological paramagnets, which hosts symmetry-protected gapless excitations on the boundary. In this work we show how to realize this type of featureless spin-1 states on a generic two-dimensional lattice. These states have a gapped spectrum in the bulk but supports gapless edge states protected by spin rotational symmetry along a certain direction, and are featured by spin quantum Hall effect. Using fermion representation of integer-spins we show a concrete example of such spin-1 topological paramagnets on kago…
We report unexpected behaviour in a family of Cu spin- 1/2 systems, in which an apparent gap in the low energy magneto-optical absorption spectrum opens at low temperature. This previously unreported collective phenomenon arises at temperatures where the energy of the dominant exchange interaction exceeds the thermal energy. Simulations of the observed shifts in electron paramagnetic resonance spectral weight, which include spin anisotropy, reproduce this behavior yielding the magnitude of the spin anisotropy in these compounds.
We implement the coupled cluster method to very high orders of approximation to study the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$ Heisenberg model on a cross-striped square lattice. Every nearest-neighbour pair of sites on the square lattice has an isotropic antiferromagnetic exchange bond of strength $J_{1}>0$, while the basic square plaquettes in alternate columns have either both or neither next-nearest-neighbour (diagonal) pairs of sites connected by an equivalent frustrating bond of strength $J_{2} \equiv αJ_{1} > 0$. By studying the magnetic order parameter (i.e., the average local on-site m…
We predict the formation and superfluidity of polaritons in an optical microcavity formed by excitons in gapped graphene embedded there and microcavity photons. The Rabi splitting related to the creation of an exciton in a graphene layer in the presence of the band gap is obtained. The analysis of collective excitations as well as the sound velocity is presented. We show that the superfluid density and temperature of the Kosterlitz-Thouless phase transition are decreasing functions of the energy gap.
Particle-hole continuum (PHC) for massive Dirac fermions in presence of short range interactions, provides an unprecedented opportunity for formation of two collective split-off states, one in the singlet and the other in the triplet (spin-1) channel in undoped system. Both poles are close in energy and are separated from thec continuum of free particle-hole excitations by an energy scale of the order of gap parameter $Δ$. They both disperse linearly with two different velocities reminiscent of spin-charge separation in Luttinger liquids. When the strength of Hubbard interactions is stronger t…
The peculiar features of quantum magnetism sometimes forbid the existence of gapped `featureless' paramagnets which are fully symmetric and unfractionalized. The Lieb-Schultz-Mattis theorem is an example of such a constraint, but it is not known what the most general restriction might be. We focus on the existence of featureless paramagnets on the spin-1 square lattice and the spin-1 and spin-1/2 honeycomb lattice with spin rotation and space group symmetries in 2+1D. Although featureless paramagnet phases are not ruled out by any existing theorem, field theoretic arguments disfavor their exis…
We report on far- and mid-infrared reflectivity of NdMnO3 from 4 K to 300K. Two main features are distinguished in the infrared spectra: active phonons in agreement with the expected for orthorhombic D2h 16-Pbnm (Z=4) space group remaining constant down to 4 K and a well-defined collective excitation in the THz region due to eg electrons in a d-orbital fluctuating environment. We trace its origin to the NdMnO3 high temperature orbital disordered intermediate phase not being totally dynamically quenched at lower temperatures. This results in minute orbital misalignments that translate in random…
We discuss the universal theory of localized impurities in the paramagnetic state of 2D antiferromagnets where the spin gap is assumed to be significantly smaller than a typical exchange energy. We study the impurity spin susceptibility near the host quantum transition from a gapped paramagnet to a Neel state, and we compute the impurity-induced damping of the spin-1 mode of the gapped antiferromagnet. Under suitable conditions our results apply also to d-wave superconductors.
Motivated by the interest in topological quantum paramagnets in candidate spin-$1$ magnets, we investigate the diamond lattice compound NiRh$_2$O$_4$ using {\it ab initio} theory and model Hamiltonian approaches. Our density functional study, taking into account the unquenched orbital degrees of freedom, shows stabilization of $S=1$ and $L=1$ state. We highlight the importance of spin-orbit coupling, in addition to Coulomb correlations, in driving the insulating gap, and uncover frustrating large second-neighbor exchange mediated by Ni-Rh covalency. A single-site model Hamiltonian incorporatin…
An attractive proposal for the hidden order (HO) in the heavy electron compound URu2Si2 is an itinerant multipole order of high rank. It is due to the pairing of electrons and holes centered on zone center and boundary, respectively in states that have maximally different total angular momentum components. Due to the pairing with commensurate zone boundary ordering vector the translational symmetry is broken and a HO quasiparticle gap opens below the transition temperature T_HO. Inelastic neutron scattering (INS) has demonstrated that for T<T_HO the collective magnetic response is dominated by…
We present a bond-operator theory (BOT) suitable for description both magnetically ordered phases and paramagnetic phases with singlet ground states in spin-1/2 magnets. Proposed BOT provides a regular expansion of physical quantities in powers of 1/n, where n is the maximum number of bosons which can occupy a unit cell (physical results correspond to n=1). Two variants of BOT are suggested: for two and for four spins in the unit cell (two-spin and four-spin BOTs, respectively). We consider spin-1/2 Heisenberg antiferromagnet (HAF) on simple square lattice bilayer by the two-spin BOT. Ground-s…
We have mapped from the quantum to the classical limit the spin excitation spectrum of the antiferromagnetic spin-1 Heisenberg chain system CsNiCl3 in its paramagnetic phase from T=5 to 200K. Neutron scattering shows that the excitations are resonant and dispersive up to at least T=70K, but broaden considerably with increasing temperature. The dispersion flattens out with increasing temperature as the resonance energy Delta at the antiferromagnetic wave-vector increases and the maximum in the dispersion decreases. The correlation length xi between T=12 and 50K is in agreement with quantum Mont…
It is widely believed that magnetic excitations become increasingly incoherent as temperature is raised due to random collisions which limit their lifetime. This picture is based on spin-wave calculations for gapless magnets in 2 and 3 dimensions and is observed experimentally as a symmetric Lorentzian broadening in energy. Here, we investigate a three-dimensional dimer antiferromagnet and find unexpectedly that the broadening is asymmetric - indicating that far from thermal decoherence, the excitations behave collectively like a strongly correlated gas. This result suggests that a temperature…
We use resonant inelastic x-ray scattering (RIXS) to probe the propagation of plasmons in the electron-doped cuprate superconductor Sr$_{0.9}$La$_{0.1}$CuO$_2$ (SLCO). We detect a plasmon gap of $\sim$~120 meV at the two-dimensional Brillouin zone center, indicating that low-energy plasmons in SLCO are not strictly acoustic. The plasmon dispersion, including the gap, is accurately captured by layered $t$-$J$-$V$ model calculations. A similar analysis performed on recent RIXS data from other cuprates suggests that the plasmon gap is generic and its size is related to the magnitude of the interl…
PSI Center for Scientific Computing, Theory and Data（瑞士保罗谢勒研究所科学计算、理论与数据中心）；Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理系）；Condensed Matter Theory, Department of Physics, TU Dortmund University（多特蒙德大学物理系凝聚态理论）
Using the conventional $T$-matrix approach, we discuss gapped phases in 1D, 2D, and 3D spin systems (both with and without a long range magnetic order) with bond disorder and with weakly interacting bosonic elementary excitations. This work is motivated by recent experimental and theoretical activity in spin-liquid-like systems with disorder and in the disordered interacting boson problem. In particular, we apply our theory to both paramagnetic low-field and fully polarized high-field phases in dimerized spin-$\frac12$ systems and in integer-spin magnets with large single-ion easy-plane anisot…
A three-dimensional Kitaev model on a hyperhoneycomb lattice is investigated numerically at finite temperature. The Kitaev model is one of the solvable quantum spin models, where the ground state is given by gapped and gapless spin liquids, depending on the anisotropy of the interactions. This model can be rewritten as a free Majorana fermion system coupled with $Z_2$ variables. The density of states of Majorana fermions shows an excitation gap in the gapped region, while it is semimetallic in the gapless region reflecting the Dirac node. Performing the Monte Carlo simulation, we calculate the…
We report spontaneous appearance of antiferromagnetic order in a model gapped quantum paramagnet Ni(Cl$_{1-x}$Br$_x$)$_2$$\cdot$4SC(NH$_2$)$_2$ induced by a change in bromine concentration x. This transition is qualitatively similar to a z = 1 magnetic quantum critical point. However, the observed critical scaling of thermodynamic and magnetic properties has rather unusual critical exponents.
In Mott insulators, the strong electron-electron Coulomb repulsion prevents metallicity and charge excitations are gapped. In dimensions greater than one, their spins are usually ordered antiferromagnetically at low temperatures. Geometrical frustrations can destroy this long-range order, leading to exotic quantum spin liquid (QSL) states. However, their magnetic ground states have been a long-standing mystery. Here we show that a QSL state in the organic Mott insulator EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ with two-dimensional triangular lattice has Pauli-paramagnetic-like low-energy excitations, whic…
Magnetic frustration can lead to peculiar magnetic orderings that break a discrete symmetry of the lattice in addition to the fundamental magnetic symmetries (i.e., spin rotation invariance and time-reversal symmetry). In this work, we focus on frustrated quantum magnets and study the nature of the quantum phase transition between a paramagnet and a magnetically ordered state with broken threefold ($Z_3$) crystal rotation symmetry. We predict the transition to happen in two stages, giving rise to an intermediate nematic phase in which rotation symmetry is broken but the system remains magnetic…
We review recent experimental and theoretical results on the interaction between single-particle excitations and collective spin excitations in the superconducting state of high-Tc cuprates. We concentrate on the traces, that sharp features in the magnetic excitation spectrum imprint in the spectra of single-particle excitations. The review gives in the first part an overview over the main corresponding experimental results obtained by inelastic neutron scattering, angle resolved photoemission spectroscopy and optical spectroscopy, concentrating on the so-called magnetic resonance mode and the…
We study the spin-$1/2$ ferromagnetic Heisenberg-Kitaev-$Γ$ model in the anisotropic (Toric code) limit to reveal the nature of the quantum phase transition between the gapped $Z_2$ quantum spin liquid and a spin ordered phase (driven by Heisenberg interactions) as well as a trivial paramagnet (driven by pseudo-dipolar interactions, $Γ$). The transitions are obtained by a simultaneous condensation of the Ising electric and magnetic charges-- the fractionalized excitations of the $Z_2$ quantum spin liquid. Both these transitions can be continuous and are examples of deconfined quantum critical …
We report the local probe investigation of a frustrated antiferromagnet Pr$_3$BWO$_9$ with the distorted kagome lattice. Absence of magnetic order or spin freezing is indicated by the spectral analysis down to 0.3 K and specific heat measurements down to 0.09 K. The Knight shifts show an upturn behavior with the sample cooling down, which is further suppressed by external field. For the spin dynamics, gapped spin excitation is observed from the temperature dependence of spin-lattice relaxation rates, with the gap size proportional to the applied magnetic field intensity. Comparatively, an unex…
We solve for the finite temperature collective mode dynamics in the Holstein-double exchange problem, using coupled Langevin equations for the phonon and spin variables. We present results in a strongly anharmonic regime, close to a polaronic instability. For our parameter choice the system transits from an `undistorted' ferromagnetic metal at low temperature to a structurally distorted paramagnetic insulator at high temperature, through a short range charge ordered (CO) phase near the ferromagnetic crossover at $T_{FM}$. The small amplitude harmonic phonons at low temperature cross over to la…
Quantum spin liquid is a disordered magnetic state with fractional spin excitations. Its clearest example is found in an exactly solved Kitaev honeycomb model where a spin flip fractionalizes into two types of anyons, quasiparticles that are neither fermions nor bosons: a pair of gauge fluxes and a Majorana fermion. Here we demonstrate this kind of fractionalization in the Kitaev paramagnetic state of the honeycomb magnet $α$-RuCl$_3$. The spin-excitation gap measured by nuclear magnetic resonance consists of the predicted Majorana fermion contribution following the cube of the applied magneti…
We investigate the equilibrium state and the collective modes of an excitonic insulator (EI) in a Fabry-Pérot cavity. In an EI, two bands of a semiconductor or semimetal spontaneously hybridize due to the Coulomb interaction between electrons and holes, leading to the opening of a gap. The coupling to the electromagnetic field reduces the symmetry of the system with respect to phase rotations of the excitonic order parameter from $U(1)$ to $Z_2$. While the reduction to a discrete symmetry would in general lead to a gapped phase mode and enhance the stability of the ordered phase, the coupling …
We have performed high-field magnetization and ESR measurements on Ba$_3$CoSb$_2$O$_9$ single crystals, as a representative two-dimensional spin-1/2 Heisenberg antiferromagnet on a uniform triangular lattice, and have determined all the magnetic parameters. For an applied magnetic field $H$ parallel to the $ab$-plane, the entire magnetization curve including the plateau at one-third of the saturation magnetization ($M_\mathrm{s}$) is in excellent agreement with the results of theoretical calculations except an anomaly near $(3/5)M_\mathrm{s}$, indicative of an additional field-induced transiti…
Correlation effects in CuO$_2$ layers give rise to a complicated landscape of collective excitations in high-T$_{\rm c}$ cuprates. Their description requires an accurate account for electronic fluctuations at a very broad energy range and remains a challenge for the theory. Particularly, there is no conventional explanation of the experimentally observed `resonant' antiferromagnetic mode, which is often considered to be a mediator of superconductivity. Here we model spin excitations of the hole-doped cuprates in the paramagnetic regime and show that this antiferromagnetic mode is associated wi…
We present a phenomenological, two-fluid approach to understanding the magnetic excitations in Fe pnictides, in which a paramagnetic fluid with gapless, incoherent particle-hole excitations coexists with an antiferromagnetic fluid with gapped, coherent spin wave excitations. We show that this two-fluid phenomenology provides an excellent quantitative description of NMR data for magnetic "122" pnictides, and argue that it finds a natural justification in LSDA and spin density wave calculations. We further use this phenomenology to estimate the maximum renormalisation of the ordered moment that …
We have investigated the dilute magnetic impurity effect on the magnetic properties of a quantum spin liquid candidate Ba3ZnRu2O9 and a spin gapped compound Ba3CaRu2O9. The magnetic ground state of each compound stands against 2% substitution of magnetic impurities for Zn or Ca. We have found that the magnetic response of these impurities, which behave as paramagnetic spins, depends on the host materials and the difference of the two manifests itself in the Weiss temperature, which can hardly be explained by the dilute magnetic impurities alone in the case of Ba3ZnRu2O9. We consider a contribu…
The ground-state phase diagram of a spin-1/2 XXZ chain with competing ferromagnetic nearest-neighbor (J_1<0) and antiferromagnetic second-neighbor (J_2>0) exchange couplings is studied by means of the infinite time evolving block decimation algorithm and effective field theories. For the SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the range -4<J_1/J_2<0 has a small but finite ferromagnetic dimer order. We argue that this spontaneous dimer order is associated with effective spin-1 degrees of freedom on dimerized bonds, which collectively form a valence bond solid st…
We apply quantum continuum mechanics to the calculation of the excitation spectrum of a coupled electron-hole bilayer. The theory expresses excitation energies in terms of ground-state intra- and inter-layer pair correlation functions, which are available from Quantum Monte Carlo calculations. The final formulas for the collective modes deduced from this approach coincide with the formulas obtained in the "quasi-localized particle approximation" by Kalman et al., and likewise, the theory predicts the existence of gapped excitations in the charged channels, with the gap arising from electron-ho…
We present a dynamical mean-field study of dynamical susceptibilities in two-band Hubbard model. Varying the model parameters we analyze the two-particle excitations in the normal as well as in the ordered phase, an excitonic condensate. The two-particle DMFT spectra in the ordered phase reveal the gapless Goldstone modes arising from spontaneous breaking of continuous symmetries. We also observe gapped Higgs mode, characterized by vanishing of the gap at the phase boundary. Qualitative changes observed in the spin susceptibility can be used as an experimental probe to identify the excitonic c…
Graphene subject to a strong, tilted magnetic field exhibits an insulator-metal transition tunable by tilt-angle, attributed to the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk state at filling factor zero. We develop a theoretical description for the spin and valley edge textures in the two phases, and the implied evolution in the nature of edge modes through the transition. In particular, we show that the CAF has gapless neutral modes in the bulk, but supports gapped charged edge modes. At the transition to the FM state the charged edge modes become gapless a…
By using superconducting quantum interference device (SQUID) magnetometry we investigated anisotropic high-field (H < 7 T) low-temperature (10 K) magnetization response of inhomogeneous nanoisland FeNi films grown by rf sputtering deposition on Sitall (TiO2) glass substrates. In the grown FeNi films, the FeNi layer nominal thickness varied from 0.6 to 2.5 nm, across the percolation transition at the d_c=1.8 nm. We discovered that, beyond conventional spin-magnetism of Fe21Ni79 permalloy, the extracted out-of-plane magnetization response of the nanoisland FeNi films is not saturated in the rang…
Two B-site ordered double perovskites, La2LiMoO6 and Ba2YMoO6, based on the S = 1/2 ion, Mo5+, have been investigated in the context of geometric magnetic frustration. Powder neutron diffraction, heat capacity, susceptibility, muon spin relaxation(_SR), and 89Y NMR- including MAS NMR- data have been collected. La2LiMoO6 deviates strongly from simple Curie-Weiss paramagnetic behavior below 150K and zero-field cooled/ field cooled (ZFC/FC)irreversibility occurs below 20K with a weak, broad susceptibility maximum near 5K in the ZFC data. A Curie-Weiss fit shows a reduced mu_eff=1.42μ_B, (spin onl…
Quantum fluctuations become particularly relevant in highly frustrated quantum magnets and can lead to new states of matter. We provide a simple and robust scenario for inducing magnetic vortex crystals in frustrated Mott insulators. By considering a quantum paramagnet that has a gapped spectrum with six-fold degenerate low energy modes, we study the magnetic field induced condensation of these modes. We use a dilute gas approximation to demonstrate that a plethora of multi-$\mathbf{Q}$ condensates are stabilized for different combinations of exchange interactions. This rich quantum phase diag…
Collective plasma excitations in moiré flat bands display unique properties reflecting strong electron-electron interactions and unusual carrier dynamics in these systems. Unlike the conventional two-dimensional plasmon modes, dispersing as $\sqrt{k}$ at low frequencies and plunging into particle-hole continuum at higher frequencies, the moiré plasmons pierce through the flat-band continuum and acquire a strong over-the-band character. Due to the complex structure of the moiré superlattice unit cell, the over-the-band plasmons feature several distinct branches connected through zone folding in…
The manipulation of topological states in quantum matter is an essential pursuit of fundamental physics and next-generation quantum technology. Here we report the magnetic manipulation of Weyl fermions in the kagome spin-orbit semimetal Co$_3$Sn$_2$S$_2$, observed by high-resolution photoemission spectroscopy. We demonstrate the exchange collapse of spin-orbit-gapped ferromagnetic Weyl loops into paramagnetic Dirac loops under suppression of the magnetic order. We further observe that topological Fermi arcs disappear in the paramagnetic phase, suggesting the annihilation of exchange-split Weyl…
The recent discovery of topological Kondo insulating behaviour in strongly correlated electron systems has generated considerable interest in Kondo insulators both experimentally and theoretically. The Kondo semiconductors CeT2Al10 (T=Fe, Ru and Os) possessing a c-f hybridization gap have received considerable attention recently because of the unexpected high magnetic ordering temperature of CeRu2Al10 (TN=27 K) and CeOs2Al10 (TN=28.5 K) and the Kondo insulating behaviour observed in the valence fluctuating compound CeFe2Al10 with a paramagnetic ground state down to 50 mK. We are investigating …
We study collective spin excitations of a magnetically ordered state in a multi-component system composed of both itinerant electrons and local moments. Here the induced spin-density-wave (SDW) ordering of itinerant electrons and the collinear antiferromangetic (AF) ordering of local moments are locked together via a Hund's rule coupling. We show that the Goldstone theorem still holds at the RPA level with the gapless spin wave protected inside the small SDW gap of itinerant electrons, which, however, is fragile in the presence of ion-anisotropy. A gapped out-of-phase spin mode extending over …
We study the Kitaev-Heisenberg-$Γ$ model with antiferromagnetic Kitaev exchanges in the strong anisotropic (toric code) limit to understand the phases and the intervening phase transitions between the gapped $Z_2$ quantum spin liquid and the spin-ordered (in the Heisenberg limit) as well as paramagnetic phases (in the pseudo-dipolar, $Γ$, limit). We find that the paramagnetic phase obtained in the large $Γ$ limit has no topological entanglement entropy and is proximate to a gapless critical point of a system described by an equal superposition of differently oriented stacked one-dimensional $Z…
We present thermodynamic phase diagrams showing magnetic analog of "three states of matter," namely, spin liquid, paramagnetic, and magnetically ordered phases, obtained by unbiased quantum Monte Carlo simulations. Our simulations are carried out for Kitaev's toric codes in two and three dimensions, i.e., the simplest realizations of gapped topological $Z_2$ spin liquids, extended by a nearest-neighbor ferromagnetic Ising coupling. We find that the ordered phase borders on the spin liquid by a discontinuous transition line in three dimensions, while it grows continuously from the quantum criti…
We predict the existence of an undamped collective spin excitation in doped graphene in the paramagnetic regime, referred to as paramagnons. Since the electrons and the holes involved in this collective mode reside in different valleys of the band structure, the momentum of these inter-valley paramagnons is given by the separation of the valleys in momentum space. The energy of the inter-valley paramagnons lies in the void region below the continuum of inter-band single-particle electron-hole excitations that appears when graphene is doped. The paramagnons are undamped due to the lack of elect…
We develop a theory of the excitonic phase recently proposed as the zero-field insulating state observed near charge neutrality in monolayer WTe$_2$. Using a Hartree-Fock approximation, we numerically identify two distinct gapped excitonic phases: a spin density wave state for weak non-zero interaction strength and spin spiral order at stronger interactions, separated by a narrow window of non-excitonic quantum spin Hall insulator. We introduce a simplified model capturing key features of the WTe$_2$ band structure, in which these phases appear as distinct valley ferromagnetic orders. We link …
We study the magnetic excitation spectra in the paramagnetic state of BaFe$_{2}$As$_{2}$ from the \textit{ab initio} perspective. The one-particle excitation spectrum is determined within the combination of the density functional theory and the dynamical mean-field theory method. The two-particle response function is extracted from the local two-particle vertex function, also computed by the dynamical mean field theory, and the polarization function. This method reproduces all the experimentally observed features in inelastic neutron scattering (INS), and relates them to both the one particle …
The microscopic modeling of spin-orbit entangled $j=1/2$ Mott insulators such as the layered hexagonal Iridates Na$_2$IrO$_3$ and Li$_2$IrO$_3$ has spurred an interest in the physics of Heisenberg-Kitaev models. Here we explore the effect of lattice distortions on the formation of the collective spin-orbital states which include not only conventionally ordered phases but also gapped and gapless spin-orbital liquids. In particular, we demonstrate that in the presence of spatial anisotropies of the exchange couplings conventionally ordered states are formed through an order-by-disorder selection…
The two-dimensional d-wave superconducting state of the high temperature superconductors has a number of different elementary excitations: the spin-singlet Cooper pairs, the spin S=1/2 fermionic quasiparticles, and a bosonic S=1 resonant collective mode, phi_{alpha}, at the antiferromagnetic wavevector. Although the phi_{alpha} quanta are strongly coupled to the gapped quasiparticles near the (pi,0), (0,pi) wavevectors (the "hot spots"), they are essentially decoupled from the low energy quasiparticles near the nodes of the superconducting gap. Consequently, distinct and independent low energy…
The electronic properties of twisted bilayer graphene (TBG) can be dramatically different from those of a single graphene layer, in particular when the two layers are rotated relative to each other by a small angle. TBG has recently attracted a great deal of interest, sparked by the discovery of correlated insulating and superconducting states, for twist angle $θ$ close to a so-called 'magic angle' $\approx 1.1°$. In this work, we unveil, via near-field optical microscopy, a collective plasmon mode in charge-neutral TBG near the magic angle, which is dramatically different from the ordinary si…
