Fast nuclear spin relaxation rates in tilted cone Weyl semimetals: redshift factors from Korringa relation.

Spin lattice relaxation rate is investigated for 3D tilted cone Weyl semimetals (TCWSMs). The nuclear spin relaxation rate is presented as a function of temperature and tilt parameter. We find that the relaxation rate behaves as(1-ζ2)-αwithα≈ 9 where 0 ⩽ζ< 1 is the tilt parameter. We demonstrate that such a strong enhancement forζ≲ 1 that gives rise to very fast relaxation rates, is contributed by a new hyperfine interactions arising from the tilt itself. This can be attributed to the combination of anisotropy of the Fermi surface and an additional part related to the structure of the spacetime: extracting an effective density of states (DOS)ρ̃from the Korringa relation, we show that it is related to the DOSρof the tilted cone dispersion by the 'redshift factor' asρ̃=ρ/1-ζ2. We interpret this relation as NMR manifestation of an emergent underlying spacetime structure in TCWSMs.

Optical conductivity of triple point fermions.

As a low-energy effective theory on non-symmorphic lattices, we consider a generic triple point fermion Hamiltonian, which is parameterized by an angular parameterλ. We find strongλdependence in both Drude and interband optical absorption of these systems. The deviation of theT2coefficient of the Drude weight from Dirac/Weyl fermions can be used as a quick way to optically distinguish the triple point degeneracies from the Dirac/Weyl degeneracies. At the particularλ=π/6 point, we find that the 'helicity' reversal optical transition matrix element is identically zero. Nevertheless, deviating from this point, the helicity reversal emerges as an absorption channel.

Topological phase diagram of the disordered 2XY model in presence of generalized Dzyaloshinskii-Moriya interaction.

The topological index of a system determines its edge physics. However, in situations such as strong disorder where due to level repulsion the spectral gap closes, the topological indices are not well-defined. In this paper, we show that the localization length of zero modes determined by the transfer matrix method reveals much more information than the topological index. The localization length can provide not only information about the topological index of the Hamiltonian itself, but it can also provide information about the topological indices of the 'relative' Hamiltonians. As a case study, we study a generalized XY model (2XY model) further augmented by a generalized Dziyaloshinskii-Moriya-like (DM) interaction parameterized by [Formula: see text] that after fermionization breaks the time-reversal invariance. The parent Hamiltonian at [Formula: see text] which belongs to the BDI class is indexed by an integer winding number while the [Formula: see text] daughter Hamiltonian which belongs to class D is specified by a Z 2 index [Formula: see text]. We show that the localization length, in addition to determining Z 2, can count the number of Majorana zero modes leftover at the boundary of the daughter Hamiltonian-which are not protected by the winding number anymore. Therefore the localization length outperforms the standard topological indices in two respects: (i) it is much faster and more accurate to calculate and (ii) it can count the winding number of the parent Hamiltonian by looking into the edges of the daughter Hamiltonian.

NMR diagnosis of pseudo-scalar superconductivity in 3D Dirac materials.

Recently observed 4π periodic Andreev bound states in 3D Dirac materials are attributed to conventional superconducting pairing. Our alternative explanation in terms of a novel form of parity breaking pseudo-scalar superconducting order can be sharply diagnosed by nuclear magnetic resonance relaxation rate. The left-right symmetry breaking of the pseudo-scalar superconductivity can be directly probed as an anti-peak structure below T C in sharp contrast to the conventional Hebel-Slichter peak.

Semiconductor of spinons: from Ising band insulator to orthogonal band insulator.

We use the ionic Hubbard model to study the effects of strong correlations on a two-dimensional semiconductor. The spectral gap in the limit where on-site interactions are zero is set by the staggered ionic potential, while in the strong interaction limit it is set by the Hubbard U. Combining mean field solutions of the slave spin and slave rotor methods, we propose two interesting gapped phases in between: (i) the insulating phase before the Mott phase can be viewed as gapping a non-Fermi liquid state of spinons by the staggered ionic potential. The quasi-particles of underlying spinons are orthogonal to physical electrons, giving rise to the 'ARPES-dark' state where the ARPES gap will be larger than the optical and thermal gap. (ii) The Ising insulator corresponding to ordered phase of the Ising variable is characterized by single-particle excitations whose dispersion is controlled by Ising-like temperature and field dependences. The temperature can be conveniently employed to drive a phase transition between these two insulating phases where Ising exponents become measurable by ARPES and cyclotron resonance. The rare earth monochalcogenide semiconductors where the magneto-resistance is anomalously large can be a candidate system for the Ising band insulator. We argue that the Ising and orthogonal insulating phases require strong enough ionic potential to survive the downward renormalization of the ionic potential caused by Hubbard U.

Sea of Majorana fermions from pseudo-scalar superconducting order in three dimensional Dirac materials.

We suggest that spin-singlet pseudo-scalar s-wave superconducting pairing creates a two dimensional sea of Majorana fermions on the surface of three dimensional Dirac superconductors (3DDS). This pseudo-scalar superconducting order parameter Δ5, in competition with scalar Dirac mass m, leads to a topological phase transition due to band inversion. We find that a perfect Andreev-Klein reflection is guaranteed by presence of anomalous Andreev reflection along with the conventional one. This effect manifests itself in a resonant peak of the differential conductance. Furthermore, Josephson current of the Δ5|m|Δ5 junction in the presence of anomalous Andreev reflection is fractional with 4π period. Our finding suggests another search area for condensed matter realization of Majorana fermions which are beyond the vortex-core of p-wave superconductors. The required Δ5 pairing can be extrinsically induced by a conventional s-wave superconductor into a three dimensional Dirac material (3DDM).

Exact phase boundaries and topological phase transitions of the XYZ spin chain.

Within the block spin renormalization group, we give a very simple derivation of the exact phase boundaries of the XYZ spin chain. First, we identify the Ising order along x[over ̂] or y[over ̂] as attractive renormalization group fixed points of the Kitaev chain. Then, in a global phase space composed of the anisotropy λ of the XY interaction and the coupling Δ of the Δσ^{z}σ^{z} interaction, we find that the above fixed points remain attractive in the two-dimesional parameter space. We therefore classify the gapped phases of the XYZ spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain, which in turn is characterized by winding number ±1, depending on whether the Ising order parameter is along x[over ̂] or y[over ̂] directions; or (2) attracted to the charge density wave (CDW) phases of the underlying Jordan-Wigner fermions, which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the XYZ model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the XYZ model justifies why our analytical solution of the three-site problem that is at the core of the present renormalization group treatment is able to produce the exact phase boundaries of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the CDW-Ising phase is entitled to host appropriate form of zero modes. We further observe that in the Kitaev-chain the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

Exactly solvable spin chain models corresponding to BDI class of topological superconductors.

We present an exactly solvable extension of the quantum XY chain with longer range multi-spin interactions. Topological phase transitions of the model are classified in terms of the number of Majorana zero modes, nM which are in turn related to an integer winding number, nW. The present class of exactly solvable models belong to the BDI class in the Altland-Zirnbauer classification of topological superconductors. We show that time reversal symmetry of the spin variables translates into a sliding particle-hole (PH) transformation in the language of Jordan-Wigner fermions - a PH transformation followed by a π shift in the wave vector which we call it the πPH. Presence of πPH symmetry restricts the nW (nM) of time-reversal symmetric extensions of XY to odd (even) integers. The πPH operator may serve in further detailed classification of topological superconductors in higher dimensions as well.

Stable local moments of vacancies, substitutional and hollow site impurities in graphene.

The two-sublattice nature of graphene lattice in conjunction with three-fold rotational symmetry, allows for the p-wave hybridization of the impurity state with the Bloch states of carbon atoms. Such an opportunity is not available in normal metals where the wave function is scalar. The p-wave hybridization function V(→k) appears when dealing with vacancies, substitutional adatoms and the hollow site impurities while the s-wave mixing on graphene lattice pertains only to the top site impurities. In this work, we compare the local moment formation in these two cases and find that the local moments formed by p-wave mixing compared to the s-wave one are robust against the changes in the parameters of the model. Furthermore, we investigate the stability of the local moments in the above cases. We find that the quantum fluctuations can destroy the local moments in the case of s-wave hybridization, while the local moments formed by p-wave hybridization survive the quantum fluctuations. Based on these findings, we propose vacancies, substitutional adatoms, and hollow site adatoms as possible candidates to produce stable local moments in graphene.

Valence bond phases in S = 1/2 Kane-Mele-Heisenberg model.

The phase diagram of the Kane-Mele-Heisenberg model in a classical limit [47] contains disordered regions in the coupling space, as the result of competition between different terms in the Hamiltonian, leading to frustration in finding a unique ground state. In this work we explore the nature of these phases in the quantum limit, for a S = 1/2. Employing exact diagonalization in Sz and nearest neighbour valence bond bases, and bond and plaquette valence bond mean field theories, we show that the disordered regions are divided into ordered quantum states in the form of plaquette valence bond crystals and staggered dimerized phases.

Kondo resonance from p-wave hybridization in graphene.

The p-wave hybridization in graphene present a distinct class of Kondo problem in pseudogap Fermi systems with bath density of states (DOS) ρ0(ε) ∝ |ε|. The peculiar geometry of substitutional and hollow-site ad-atoms, and effectively the vacancies allow for a p-wave form of momentum dependence in the hybridization of the associated local orbital with the Dirac fermions of the graphene host which results in a different picture than the s-wave momentum independent hybridization. For the p-wave hybridization function, away from the Dirac point we find closed-form formulae for the Kondo temperature TK which in contrast to the s-wave case is non-zero for any value of hybridization strength V of the single impurity Anderson model (SIAM). At the Dirac point where the DOS vanishes, we find a conceivably small value of Vmin above which the Kondo screening takes place even in the presence of particle-hole symmetry. We also show that the non-Lorentzian line shape of the local spectrum arising from anomalous hybridization function leads to much larger TK in vacant graphene compared to a metallic host with similar bandwidth and SIAM parameters.

RKKY interaction in heavily vacant graphene.

Dirac electrons in clean graphene can mediate the interactions between two localized magnetic moments. The functional form of the RKKY interaction in pristine graphene is specified by two main features: (i) an atomic-scale oscillatory part determined by a wavevector Q connecting the two valleys; with doping another longer range oscillation appears which arises from the existence of an extended Fermi surface characterized by a momentum scale kF; (ii) an algebraic R(α) decay in large distances where the exponent α =- 3 is a distinct feature of undoped Dirac sea in two dimensions. In this work, we investigate the effect of a few per cent vacancies on the above properties. Depending on the doping level, if the chemical potential lies on the linear part of the density of states, the exponent α remains at -3 even in vacant graphene. Otherwise α reduces towards more negative values. Presence of vacancies washes out both atomic-scale and Friedel oscillations of the RKKY interaction. The absence of atomic-scale oscillations indicates the destruction of two-valley structure of the parent graphene material. However, the absence of Friedel oscillations upon 'alloying' with vacancies indicates that a quantum ground state of heavily vacant doped graphene is not given by a unique kF momentum scale.

Collective excitations and the nature of Mott transition in undoped gapped graphene.

The particle-hole continuum (PHC) for massive Dirac fermions provides an unprecedented opportunity for the formation of two collective split-off states, one in the singlet and the other in the triplet (spin-1) channel, when the short-range interactions are added to the undoped system. Both states are close in energy and are separated from the continuum of free particle-hole excitations by an energy scale of the order of the 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 than a critical value, the velocity of singlet excitation, which we interpret as a charge composite boson, becomes zero and renders the system a Mott insulator. Beyond this critical point the low-energy sector is left with a linearly dispersing triplet mode-a characteristic of a Mott insulator. The velocity of the triplet mode at the Mott criticality is twice the velocity of the underlying Dirac fermions. The phase transition line in the space of U and Δ is in qualitative agreement with our previous dynamical mean field theory calculations.

Nonlinear optical response in gapped graphene.

We present a formulation for the nonlinear optical response in gapped graphene, where the low-energy single-particle spectrum is modeled by massive Dirac theory. As a representative example of the formulation presented here, we obtain a closed form formula for the third harmonic generation in gapped graphene. It turns out that the covariant form of the low-energy theory gives rise to peculiar logarithmic singularities in the nonlinear optical spectra. The universal functional dependence of the response function on dimensionless quantities indicates that the optical nonlinearity can be largely enhanced by tuning the gap to smaller values.

Equations-of-motion method for triplet excitation operators in graphene.

The particle-hole continuum in the Dirac sea of graphene has a unique window underneath, which in principle leaves room for bound state formation in the triplet particle-hole channel (Baskaran and Jafari 2002 Phys. Rev. Lett. 89 016402). In this work, we construct appropriate triplet particle-hole operators and, using a repulsive Hubbard-type effective interaction, we employ equations of motion to derive approximate eigenvalue equations for such triplet operators. While the secular equation for the spin density fluctuations gives rise to an equation which is second order in the strength of the short range interaction, the explicit construction of the triplet operators obtained here shows that, in terms of these operators, the second-order equation can be factorized to two first-order equations, one of which gives rise to a solution below the particle-hole continuum of Dirac electrons in undoped graphene.

Plaquette valence bond ordering in a J1-J2 Heisenberg antiferromagnet on a honeycomb lattice.

We study an S = 1/2 Heisenberg model on the honeycomb lattice with first and second neighbor antiferromagnetic exchange (J(1)-J(2) model), employing exact diagonalization in both the S(z) = 0 basis and nearest neighbor singlet valence bond (NNVB) basis. We find that for 0.2 < J(2)/J(1) < 0.3, the NNVB basis gives a proper description of the ground state in comparison with the exact results. By analyzing the dimer-dimer as well as the plaquette-plaquette correlations and also defining appropriate structure factors, we investigate possible symmetry breaking states as the candidates for the ground state in the frustrated region. We provide a body of evidence in favor of plaquette valence bond ordering for 0.2 < J(2)/J(1) < 0.3. By further increasing the ratio J(2)/J(1), this state undergoes a transition to the staggered dimerized state.

Anderson transition in disordered bilayer graphene.

Employing the kernel polynomial method (KPM), we study the electronic properties of the graphene bilayers with Bernal stacking in the presence of diagonal disorder, within the tight-binding approximation and nearest neighbor interactions. The KPM method enables us to calculate local density of states (LDOS) without the need to exactly diagonalize the Hamiltonian. We use the geometrical averaging of the LDOS at different lattice sites as a criterion to distinguish the localized states from extended ones. We find that this model undergoes an Anderson metal-insulator transition at a critical value of disorder strength.

Gapless spin-1 neutral collective mode branch for graphite.

Using the standard tight binding model of 2D graphite with short range electron repulsion, we predict a gapless spin-1, neutral collective mode branch below the particle-hole continuum with energy vanishing linearly with momenta at the Gamma and K points in the Brillouin zone. This spin-1 mode has a wide energy dispersion, 0 to approximately 2 eV, and is not Landau damped. The "Dirac cone spectrum" of electrons at the chemical potential of graphite generates our collective mode, so we call this "spin-1 zero sound" of the "Dirac sea." Epithermal neutron scattering experiments and spin polarized electron energy loss spectroscopy can be used to confirm and study our collective mode.