Spin-singlet Phase Research Articles

Dimer Crystallization Induced by Elemental Substitution in the Honeycomb Lattice of Ru1−xOsxCl3

Substitution effects of Os for Ru in {\alpha}-RuCl3 are investigated in a wide composition range of 0 =< x =< 0.67 in Ru1-xOsxCl3 by X-ray and electron diffraction, magnetic susceptibility, heat capacity, and Raman spectroscopy measurements. Apart from the Kitaev physics with antiferromagnetic interactions increasing with x, a rich phase diagram is obtained, which includes an antiferromagnetic long-range order below 12 K for x =< 0.15, a dome-shaped spin-singlet dimer phase below 130 K for 0.15 =< x =< 0.40, and a magnetic short-range order for x > 0.40. A dimerization as similarly observed in {\alpha}-RuCl3 under high pressure occurs in the spin-singlet phase. It is suggested that Ru-Os pairs in the solid solutions tend to form dimers with short bonds and trigger the first-order transition in the presence of pseudo-threefold rotational symmetry for dimerization around a substituted Os atom only at low substitutions. This is a rare example of molecular orbital crystallization induced by elemental substitution in a highly disordered system. The short-range order at high substitutions may be related to a random-singlet state stabilized by bond disorder in the honeycomb net.

Twisted bilayer graphene. VI. An exact diagonalization study at nonzero integer filling

Using exact diagonalization, we study the projected Hamiltonian with Coulomb interaction in the 8 flat bands of first magic angle twisted bilayer graphene. Employing the U(4) (U(4)$\times$U(4)) symmetries in the nonchiral (chiral) flat band limit, we reduced the Hilbert space to an extent which allows for study around $\nu=\pm 3,\pm2,\pm1$ fillings. In the first chiral limit $w_0/w_1=0$ where $w_0$ ($w_1$) is the $AA$ ($AB$) stacking hopping, we find that the ground-states at these fillings are extremely well-described by Slater determinants in a so-called Chern basis, and the exactly solvable charge $\pm1$ excitations found in [arXiv:2009.14200] are the lowest charge excitations up to system sizes $8\times8$ (for restricted Hilbert space) in the chiral-flat limit. We also find that the Flat Metric Condition (FMC) used in [arXiv:2009.11301,2009.11872,2009.12376,2009.13530,2009.14200] for obtaining a series of exact ground-states and excitations holds in a large parameter space. For $\nu=-3$, the ground state is the spin and valley polarized Chern insulator with $\nu_C=\pm1$ at $w_0/w_1\lesssim0.9$ (0.3) with (without) FMC. At $\nu=-2$, we can only numerically access the valley polarized sector, and we find a spin ferromagnetic phase when $w_0/w_1\gtrsim0.5t$ where $t\in[0,1]$ is the factor of rescaling of the actual TBG bandwidth, and a spin singlet phase otherwise, confirming the perturbative calculation [arXiv:2009.13530]. The analytic FMC ground state is, however, predicted in the intervalley coherent sector which we cannot access [arXiv:2009.13530]. For $\nu=-3$ with/without FMC, when $w_0/w_1$ is large, the finite-size gap $\Delta$ to the neutral excitations vanishes, leading to phase transitions. Further analysis of the ground state momentum sectors at $\nu=-3$ suggests a competition among (nematic) metal, momentum $M_M$ ($\pi$) stripe and $K_M$-CDW orders at large $w_0/w_1$.

Chern bands of twisted bilayer graphene: Fractional Chern insulators and spin phase transition

When one of the graphene layers of Magic Angle Twisted Bilayer Graphene is nearly aligned with its hexagonal boron nitride substrate (a configuration dubbed TBG/hBN), the active electronic bands are nearly flat, and have a Chern number $C=\pm1$. Recent experiments demonstrated a quantum anomalous Hall effect and spontaneous valley polarization at integer filling $\nu_T=3$ of the conduction band in this system. Motivated by this discovery, we ask whether fractional quantum anomalous Hall states (FQAH) could also emerge in TBG/hBN. We focus on the range of filling fractions where valley ferromagnetism was observed experimentally. Using exact diagonalization, we find that the ground states at $\nu_T = \frac{10}{3}$ and $\nu_T=\frac{17}{5}$ are fractional Chern insulator states in the flat band limit (in the hole picture, these are the fractional quantum Hall fractions $\frac{2}{3}$ and $\frac{3}{5}$). The ground state is either spin polarized or a spin singlet depending sensitively on band parameters. For nominally realistic band parameters, spin polarization is favored. Flattening the Berry curvature by changing a band parameter gives way to the spin singlet phase. Our estimation of the charge gap in the flat band limit shows that the FQAH state may be seen at accessible temperatures in experiments. We also study the effect of a non-zero bandwidth and show that there is a reasonable range of parameters in which the FQAH state is the ground state.

Spin nematics next to spin singlets

We provide a route to generate nematic order in a spin-1/2 system. Unlike the well-known magnon-binding mechanism, our spin nematics requires neigher the frustration effect nor a spin polarization in a high field or in the vicinity of a ferromagnet, but instead appears next to the spin singlet phase. We start from a state consisting of a quantum spin-1/2 singlet dimer placed on each site of a triangular lattice, and show that inter-dimer ring exchange interactions efficiently dope the SU(2) triplets that itinerate and interact, easily driving a stable singlet state to either Bose Einstein condensates or a triplet crystal, some hosting a spin nematic order. A variety of roles the ring exchange serves include the generation of a bilinear-biquadratic interaction between nearby triplets, which is responsible for the emergent nematic order separated from the singlet phase by a first order transition.

Goldstone Modes in Bilayer Quantum Hall Systems at ν = 2

At the filling factor ν=2, the bilayer quantum Hall system has three phases, the spin-ferromagnet phase, the spin singlet phase and the canted antiferromagnet (CAF) phase, depending on the relative strength between the Zeeman energy and interlayer tunneling energy. We present a systematic method to derive the effective Hamiltonian for the Goldstone modes in these three phases. We then investigate the dispersion relations and the coherence lengths of the Goldstone modes. To explore a possible emergence of the interlayer phase coherence, we analyze the dispersion relations in the limit of zero tunneling energy. We find one gapless mode with the linear dispersion relation in the CAF phase.

The study of Goldstone modes in ν = 2 bilayer quantum Hall systems

At the filling factor $\nu$=2, the bilayer quantum Hall system has three phases, the spin-ferromagnet phase, the spin singlet phase and the canted antiferromagnet (CAF) phase, depending on the relative strength between the Zeeman energy and interlayer tunneling energy. We present a systematic method to derive the effective Hamiltonian for the Goldstone modes in these three phases. We then investigate the dispersion relations and the coherence lengths of the Goldstone modes. To explore a possible emergence of the interlayer phase coherence, we analyze the dispersion relations in the zero tunneling energy limit. We find one gapless mode with the linear dispersion relation in the CAF phase.

Ground-state properties, excitation spectra, and phase transitions in theS=12andS=32bilayer Heisenberg models on the honeycomb lattice

Motivated by the observation of a disordered spin ground state in the $S=3/2$ material Bi$_3$Mn$_4$O$_{12}$NO$_3$, we study the ground state properties and excitation spectra of the $S=3/2$ (and for comparison $S=1/2$) bilayer Heisenberg model on the honeycomb lattice, with and without frustrating further neighbor interactions. We use series expansions around the N\'eel state to calculate properties of the magnetically ordered phase. Furthermore, series expansions in $1/\lambda=J_1/J_{\perp}$, where $J_1$ is an in-plane exchange constant and $J_\perp$ is the exchange constant between the layers are used to study properties of the spin singlet phase. For the unfrustrated case, our results for the phase transitions are in very good agreement with recent Quantum Monte Carlo studies. We also obtain the excitation spectra in the disordered phase and study the change in the critical $\lambda$ when frustrating exchange interactions are added to the $S=3/2$ system and find a rapid suppression of the ordered phase with frustration. Implications for the material Bi$_3$Mn$_4$O$_{12}$NO$_3$ are discussed.

Structural investigation of the spin-singlet phase in (TMTTF)2I

To elucidate the electronic state that exists in the boundary region between the spin-singlet phase and the high-pressure side antiferromagnetic phase in the modified generalized phase diagram, we carried out x-ray diffraction, electron spin resonance, and nuclear magnetic resonance measurements of the tetramethyl-tetrathia-fulvalene (TMTTF) family salt, (TMTTF)${}_{2}$I. The unit-cell volume of (TMTTF)${}_{2}$I is between that of (TMTTF)${}_{2}$Br and (TMTTF)${}_{2}$PF${}_{6}$. We found that (TMTTF)${}_{2}$I undergoes a spin-singlet phase transition at 21 K without involving paramagnetic charge-ordering phase. Therefore, the charge-ordering transition is not necessary for the spin-singlet transition of TMTTF salts as seen in other conventional spin-singlet salts. Finally, we discuss possible mechanisms of the spin-singlet phase transition.

Kondo effect in a side-coupled double quantum dot system embedded in a mesoscopic ring

We study the finite size effect of the Kondo screening cloud in a double-quantum-dot setup via a large-N slave-boson mean-field theory. In this setup, one of the dots is embedded in a close metallic ring with a finite size $L$ and the other dot is side-coupled to the embedded dot via an anti-ferromagnetic spin-spin exchange coupling with the strength K. The antiferromagnetic coupling favors the local spin-singlet and suppresses the Kondo screening. The effective Kondo temperature T_k (proptotional to the inverse of the Kondo screening cloud size) shows the Kosterlitz--Thouless (KT) scaling at finite sizes, indicating the quantum transition of the KT type between the Kondo screened phase for K < K_c and the local spin-singlet phase for K > K_c in the thermodynamic limit with K_c being the critical value. The mean-field phase diagram as a function of 1/L and K shows a crossover between Kondo and local spin-singlet ground states for K < K_c (L=4n, 4n+1, 4n+3) and for K>K_c (L=4n+2). To look into the crossover region more closely, the local density of states on the quantum dot and the persistent current at finite sizes with different values of $K$ are also calculated.

Manifestation of helical edge states as zero bias magneto-tunneling-conductance peaks innoncentrosymmetric superconductors

Helical edge states exist in the mixed spin singlet and triplet phase of a noncentrosymmetricsuperconductor (NCSS) when the pair amplitude (PA) in the negative helicity band,Δ−, is smaller than the PA in the positive helicity band,Δ+, i.e., when the PA in the triplet component is more than the same in the singletcomponent. We numerically determine energies of these edge states as a function ofγ = Δ−/Δ+. The presence of these edge states is reflected in the tunnelingprocess from a normal metal to an NCSS across a bias energyeV. (i) Angle resolved spin conductance (SC) obeying the symmetrygs(ϕ) = −gs(−ϕ) shows peaks when the bias energy equals the available quasiparticle edge state energyprovided . (ii) The total SC, Gs, iszero but modulates with eV for finite magnetic field H.(iii) The zero bias peaks of Gs and total charge conductance, Gc, at finite H splitinto two at finite eV for moderate H.(iv) At zero bias, Gc and Gs increasewith H andshow peaks at |H|∼γH0, where H0 is a characteristic field.

Finite-temperature phase diagram of nonmagnetic impurities in high-temperature superconductors using ad=3 tJmodel with quenched disorder

We study a quenched disordered $d=3\text{ }tJ$ Hamiltonian with static vacancies as a model of nonmagnetic impurities in high-${T}_{c}$ materials. Using a renormalization-group approach, we calculate the evolution of the finite-temperature phase diagram with impurity concentration $p$ and find several features with close experimental parallels: Away from half filling, we see the rapid destruction of a spin-singlet phase (analogous to the superconducting phase in cuprates) which is eliminated for $p\ensuremath{\gtrsim}0.05$; in the same region for these dilute impurity concentrations, we observe an enhancement of antiferromagnetism. The antiferromagnetic phase near half filling is robust against impurity addition and disappears only for $p\ensuremath{\gtrsim}0.40$.

Phase transitions in a few-electron quantum dot in a magnetic field: Wigner phases and broken-symmetry spin-singlet states

We develop a variational many-body approach within a second quantized formulation for a few-electron system in a parabolic two-dimensional quantum dot (QD). By way of application, the nature of the ground state of a two-electron system in a parabolic QD in a broad range of magnetic fields is theoretically investigated. Various phase transitions on the basis of the resulting analytical expressions for energy of the system have been investigated: First, the well-known transition from a maximum density droplet to a Wigner phase in a magnetic field is obtained, provided that the QD is in conditions of weak confinement. Furthermore, in the case of relatively strong QD confinement and weak magnetic fields, a rotationally symmetric spin-singlet state is the ground state of the system. However, in a strong magnetic field and for the same QD confinement, a broken-symmetry spin-singlet state appears to be energetically favored over the symmetric spin-singlet state. A first investigation of such a broken-symmetry spin-singlet phase in a QD in a magnetic field is shown to be an important application of the proposed technique.

Ginzburg-Landau theory of noncentrosymmetric superconductors

The data of temperature dependent superfluid density $n_s(T)$ in Li$_2$Pd$_3$B and Li$_2$Pt$_3$B [Yuan {\it et al.}, \phrl97, 017006 (2006)] show that a sudden change of the slope of $n_s (T)$ occur at slightly lower than the critical temperature. Motivated by this observation, we microscopically derive the Ginzburg-Landau (GL) equations for noncentrosymmetric superconductors with Rashba type spin orbit interaction. Cooper pairing is assumed to occur between electrons only in the same spin split band and pair scattering is allowed to occur between two spin split bands. The GL theory of such a system predicts two transition temperatures, the higher of which is the conventional critical temperature $T_c$ while the lower one $T^*$ corresponds to the cross-over from a mixed singlet-triplet phase at lower temperatures to only spin-singlet or spin-triplet (depending on the sign of the interband scattering potential) phase at higher temperatures. As a consequence, $n_s (T)$ shows a kink at this cross-over temperature. We attribute the temperature at which sudden change of slope occurs in the observed $n_s (T)$ to the temperature $T^*$. This may also be associated with the observed kink in the penetration depth data of CePt$_3$Si. We have also estimated critical field near critical temperature.

Competing broken-symmetry and rotationally symmetric spin-singlet states in a few-electron quantum dot in a magnetic field

On the basis of developed variational many-body approach, within a second quantized formulation, the nature of the ground state of a few-electron system in a parabolic two-dimensional (2D) quantum dot (QD) is theoretically investigated. The resulting analytical expressions lead to various phase transitions: spin singlet, maximum density droplet, Wigner phase, etc. in a broad range of magnetic fields and QD confinement potentials. A first investigation of a broken-symmetry spin-singlet phase in a QD in a magnetic field is shown to be an important application of the proposed technique.

Charge-Transfer Excitations in One-Dimensional Dimerized Mott Insulators

We investigate the optical properties of one-dimensional (1D) dimerized Mott insulators using the 1D dimerized extended Hubbard model. Numerical calculations and a perturbative analysis from the decoupled-dimer limit clarify that there are three relevant classes of charge-transfer (CT) states generated by photoexcitation: interdimer CT unbound states, interdimer CT exciton states, and intradimer CT exciton states. This classification is applied to understanding the optical properties of an organic molecular material, 1,3,5-trithia-2,4,6-triazapentalenyl (TTTA), which is known for its photoinduced transition from the dimerized spin-singlet phase to the regular paramagnetic phase. We conclude that the lowest photoexcited state of TTTA is the interdimer CT exciton state and the second lowest state is the intradimer CT exciton state.

Magnetotransport study of the canted antiferromagnetic phase in bilayerν=2quantum Hall state

Magnetotransport properties are investigated in the bilayer quantum Hall state at the total filling factor $\nu=2$. We measured the activation energy elaborately as a function of the total electron density and the density difference between the two layers. Our experimental data demonstrate clearly the emergence of the canted antiferromagnetic (CAF) phase between the ferromagnetic phase and the spin-singlet phase. The stability of the CAF phase is discussed by the comparison between experimental results and theoretical calculations using a Hartree-Fock approximation and an exact diagonalization study. The data reveal also an intrinsic structure of the CAF phase divided into two regions according to the dominancy between the intralayer and interlayer correlations.

Valence-bond crystal in a pyrochlore antiferromagnet with orbital degeneracy.

We discuss the ground state of a pyrochlore lattice of threefold orbitally degenerate S=1/2 magnetic ions. We derive an effective spin-orbital Hamiltonian and show that the orbital degrees of freedom can modulate the spin exchange, removing the infinite spin-degeneracy characteristic of pyrochlore structures. The resulting state is a collection of spin-singlet dimers, with a residual degeneracy due to their relative orientation. This latter is lifted by a magnetoelastic interaction, induced in the spin-singlet phase space, that forces a tetragonal distortion. Such a theory provides an explanation for the helical spin-singlet pattern observed in the B spinel MgTi2O4.

Phase transition on (BEDO-TTF) (Cl2TCNQ): Spin dynamics observed by NMR measurements

13C NMR measurements were carried out to investigate the electronic state of Mixedstack organic charge-transfer complex (BEDO-TTF)(Cl 2 TCNQ). From the remarkable temperature dependence of the central shift and relaxation rate, we have confirmed that the transition at 110 K is from paramagnetic to nonmagnetic spin-singlet phase.

Spin-exchange interactions of spin-one bosons in optical lattices: Singlet, nematic, and dimerized phases

We consider insulating phases of cold spin-1 bosonic particles with antiferromagnetic interactions, such as {sup 23}Na, in optical lattices. We show that spin-exchange interactions give rise to several distinct phases, which differ in their spin correlations. In two- and three-dimensional lattices, insulating phases with an odd number of particles per site are always nematic. For insulating states with an even number of particles per site, there is always a spin-singlet phase, and there may also be a first-order transition into the nematic phase. The nematic phase breaks spin rotational symmetry but preserves time reversal symmetry, and has gapless spin-wave excitations. The spin-singlet phase does not break spin symmetry and has a gap to all excitations. In one-dimensional lattices, insulating phases with an odd number of particles per site always have a regime where translational symmetry is broken and the ground state is dimerized. We discuss signatures of various phases in Bragg scattering and time-of-flight measurements.

Grassmannian fields and doubly enhanced Skyrmions in the bilayer quantum Hall system at ν=2

At the filling factor $\nu=2$ the bilayer quantum Hall system has three phases, the ferromagnetic phase (spin phase), the spin singlet phase (ppin phase) and the canted antiferromagnetic phase. We analyze soft waves and quasiparticle excitations in the spin and ppin phases. It is shown that the dynamic field is the Grassmannian G$_{4,2}$ field carrying four complex degrees of freedom. In each phase there are four complex soft waves (pseudo-Goldstone modes) and one kind of skyrmion excitations (G$_{4,2}$ skyrmions) flipping either spins or pseudospins coherently. An intriguing property is that a quasiparticle is a G$_{4,2}$ skyrmion essentially consisting of two CP$^{3}$ skyrmions and thus possesses charge $2e$.