On a new type of massless Dirac fermions in crystalline topological insulators

A new type of massless Dirac fermions in crystalline three-dimensional topological insulators (three-dimensional → two-dimensional situation) has been predicted. The spectrum has fourfold degeneracy at the top of the two-dimensional Brillouin zone (M point) and twofold degeneracy near the M point. Crystal symmetry along with the time reversal invariance in three-dimensional topological insulators allows fourfold degenerate Dirac cones, which are absent in the classification of topological features in R.-J. Slager et al., Nat. Phys. 9, 98 (2013). The Hamiltonian in the cited work does not contain Dirac singularities with more than twofold degeneracy. For this reason, the corresponding topological classification is incomplete. The longitudinal magnetic field in the spinless case holds the massless dispersion law of fermions and does not lift fourfold degeneracy. In the spinor case, the magnetic field lifts fourfold degeneracy, holding only twofold degeneracy, and results in the appearance of a band gap in the spectrum of fermions.     

Landau levels in deformed bilayer graphene at low magnetic fields

We review the effect of uniaxial strain on the low-energy electronic dispersion and Landau level structure of bilayer graphene. Based on the tight-binding approach, we derive a strain-induced term in the low-energy Hamiltonian and show how strain affects the low-energy electronic band structure. Depending on the magnitude and direction of applied strain, we identify three regimes of qualitatively different electronic dispersions. We also show that in a weak magnetic field, sufficient strain results in the filling factor ν=±4 being the most stable in the quantum Hall effect measurement, instead of ν=±8 in unperturbed bilayer at a weak magnetic field. To mention, in one of the strain regimes, the activation gap at ν=±4 is, down to very low fields, weakly dependent on the strength of the magnetic field.     

Quantum modulation effect in a graphene-based magnetic tunnel junction

The electronic (quantum) transport in a NG/F_B/FG tunnel junction (where NG, F_B and FG are a normal graphene layer, a ferromagnetic barrier connected to a gate and a ferromagnetic graphene layer, respectively) is investigated. The motions of the electrons in the graphene layers are taken to be governed by the Dirac Equation. Parallel (P) and antiparallel alignment (AP) of the magnetizations in the barrier and in the ferromagnetic graphene are considered. Our work focuses on the oscillation of the electrical conductance (Gq), of the spin conductance (Gs) and of the tunneling magneto resistance (TMR) of this magnetic tunnel junction. We find that, the quantum modulation due to the effect of the exchange field in F_B will be seen in the plots the conductance and of the TMR as functions of the thickness of ferromagnetic barrier (L). The period of two multiplied sinusoidal terms of the modulation are seen to be controlled by varying the gate potential and the exchange field of the F_B layer. The phenomenon, a quantum beating, is built up with two oscillating spin conductance components which have different periods of oscillation related to the splitting of Dirac's energies in the F_B region. The amplitudes of oscillations of Gq, Gs and TMR are not seen to decrease as the thickness increases. The decaying behaviors seen in the conventional transport through an insulator do not appear.     

Universality of the ratio of the critical amplitudes of the magnetic susceptibility in a two-dimensional ising model with nonmagnetic impurities

The behavior of the magnetic susceptibility of a two-dimensional Ising model with nonmagnetic impurities is investigated numerically. A new method for determining the critical amplitudes and critical temperature is developed. The results of a numerical investigation of the ratio of the critical amplitudes of the magnetic susceptibility are presented. It is shown that the ratio of the critical amplitudes is universal right up to impurity concentrations q ≤ 0.25 (the percolation point of a square lattice is q _c = 0.407254). The behavior of the effective critical exponent γ(q) of the magnetic susceptibility is discussed. Apparently, a transition from Ising-type universal behavior to percolation behavior should occur in a quite narrow concentration range near the percolation point of the lattice.     

Optical properties of MgxZn1−xO nanowire photonic crystals

We investigate the optical properties of two-dimensional periodic arrays of well-aligned Mg_xZn_1−xO nanowires, i.e., Mg_xZn_1−xO nanowire photonic crystals. The nanowire photonic crystal can exhibit a photonic band gap in the visible range. As the mole fraction of Mg, x, increases, the edge frequencies of the band gap increase and the band gap size decreases. The characteristics of relative band gap and vacant point defect mode are also studied with varying x. From the finite-difference time-domain simulations, we show that the light extraction from nanowires can be controlled by varying the distance between optically excited nanowires and a waveguide, and the mole fraction of Mg. Controlling the light extraction from nanostructures can be useful in the implementation of nanoscale light emitting devices.     

The Dirac particle in a one-dimensional “hydrogen atom”

Specific features of the behavior of the spectrum of steady states of the Dirac particle in a regularized ??Coulomb?? potential V??(z) = ?q/(|z| + ??) as a function of the cutting parameter of ?? in 1 + 1 D are investigated. It is shown that in such a one-dimensional relativistic ??hydrogen atom?? at ?? ? 1, the discrete spectrum becomes a quasi-periodic function of ??; this effect depends on the bonding constant analytically and has no nonrelativistic analog. This property of the Dirac spectral problem clearly demonstrates the presence of a physically containable energy spectrum at arbitrary small ?? > 0 and simultaneously the absence of the regular limiting transition to ?? ?? 0. Thus, the necessity of extension of a definition for the Dirac Hamiltonian with irregularized potential in 1 + 1 D is confirmed at all nonzero values of the bonding constant q. It is also noted that the three-dimensional Coulomb problem possesses a similar property at q = Z?? > 1, i.e., when the selfconsistent extension is required for the Dirac Hamiltonian with an irregularized potential.     

Anomalous influence of an external magnetic field on spin fluctuations in magnetic semiconductors with strong p-d hybridization and the colossal magnetoresistance effect

The colossal magnetoresistance effect in magnetic semiconductors based on lanthanum manganites has been investigated in terms of the model allowing for the effects of p-d hybridization and electronelectron Coulomb correlations. The influence of an external magnetic field on spin fluctuations has been considered under the conditions where the chemical potential is in a narrow heavy-fermion band formed in the hybridization gap. It has been shown that, in the vicinity of the Curie point T _C, the strong spin anharmonicity leads to an anomalously strong suppression of spin fluctuations by the external magnetic field, a phenomenon contributing significantly to the formation of colossal negative magnetoresistance.     

The chiral magnetic effect and chiral symmetry breaking in <Emphasis Type="Italic">SU</Emphasis>(3) quenched lattice gauge theory

We study some properties of the non-Abelian vacuum induced by strong external magnetic field. We perform calculations in the quenched SU(3) lattice gauge theory with tadpole-improved Lüscher-Weisz action and chirally invariant lattice Dirac operator. The following results are obtained: The chiral symmetry breaking is enhanced by the magnetic field. The chiral condensate depends on the strength of the applied field as a power function with exponent ν = 1.6 ± 0.2. There is a paramagnetic polarization of the vacuum. The corresponding susceptibility and other magnetic properties are calculated and compared with the theoretical estimations. There are nonzero local fluctuations of the chirality and electromagnetic current, which grow with the magnetic field strength. These fluctuations can be a manifestation of the Chiral Magnetic Effect.     

Spin and charge order in Mott insulators and d-wave superconductors

We argue that aspects of the anomalous, low temperature, spin and charge dynamics of the high temperature superconductors can be understood by studying the corresponding physics of undoped Mott insulators. Such insulators display a quantum transition from a magnetically ordered Néel state to a confining paramagnet with a spin gap; the latter state has bond-centered charge order, a low energy S=1 spin exciton, confinement of S=1/2 spinons, and a free S=1/2 moment near non-magnetic impurities. We discuss how these characteristics, and the quantum phase transitions, evolve upon doping the insulator into a d-wave superconductor. This theoretical framework was used to make a number of predictions for STM measurements and for the phase diagram of the doped Mott insulator in an applied magnetic field.     

Cubic helimagnets in magnetic field and at pressure

Cubic helimagnets with B20 structure display several unusual properties such as anisotropy of the spin-wave spectrum al small momenta q, rotation of the helix vector k in magnetic field and quantum phase transition at pressure. We demonstrate that first two phenomena are a result of umklapp processes mixing excitations with momenta q, q+k and q−k. At very low magnetic field perpendicular to k the helical structure remains stable due to spin-wave gap Δ. Its square is sum of two parts. The first one is a result of the magnon interaction and the second negative part stems from magneto-elastic interaction. It is suggested that competition between these parts leads to the quantum phase transition observed in MnSi and FeGe. For MnSi from rough estimations at ambient pressure was shown that both parts are comparable with the experimentally observed gap. The magneto-elastic interaction is also responsible for 2k modulation of the lattice and contributes to the magnetic anisotropy. Experimental observation by X-ray and neutron scattering of this lattice modulation allows to determine the strength of the magneto-elastic interaction responsible for above phenomena and the lattice helicity.     

The enigma of the quantum Hall effect in graphene

We apply Laughlin’s gauge argument to analyze the ν=0 quantum Hall effect observed in graphene when the Fermi energy lies near the Dirac point, and conclude that this necessarily leads to divergent bulk longitudinal resistivity in the zero temperature thermodynamic limit. We further predict that in a Corbino geometry measurement, where edge transport and other mesoscopic effects are unimportant, one should find the longitudinal conductivity vanishing in all graphene samples which have an underlying ν=0 quantized Hall effect. We argue that this ν=0 graphene quantum Hall state is qualitatively similar to the high field insulating phase (also known as the Hall insulator) in the lowest Landau level of ordinary semiconductor two-dimensional electron systems. We establish the necessity of having a high magnetic field and high mobility samples for the observation of the divergent resistivity as arising from the existence of disorder-induced density inhomogeneity at the graphene Dirac point.     

First principles study of half-metallic ferromagnetism in Cr-doped CdTe

We report a systematic study of the structural, electronic and magnetic properties of Cr-doped CdTe for various Cr concentrations x (=0.25, 0.5, 0.75 and 1.0) using first principles calculations based on the density functional theory (DFT). The electronic band structure of the alloy has been calculated using the Wu-Cohen (WC) as well as the Angel-Vosko (EV) generalized gradient approximation (GGA) for the exchange-correlation potential. The analysis of the density of states (DOS) curves shows the half-metallic ferromagnetic character with half-metallic gap more than 0.52 eV. While the origin of half-metallic ferromagnetism is explained, the band structure calculations are used to determine s (p)-d exchange constants N₀α (conduction band) and N₀β (valence band) that agree with typical magneto-optical experiment. It is found that the p-d hybridization reduces the magnetic moment of Cr from its free space charge value and produces small magnetic moments on the Cd and Te sites. Lastly, we discuss the robustness of half-metallicity with respect to the variation of lattice constants of the Cr_xCd_1−xTe alloys.     

Electronic structure calculations of lead chalcogenides PbS, PbSe, PbTe

In this work, we have extended our study of the mechanical properties and the electronic structure of PbTe to include other Pb chalcogenide compounds (PbSe, PbS). The calculations were performed self-consistently using the scalar-relativistic full-potential linearized augmented plane wave method. Both the local density approximation (LDA) and the generalized gradient approximation (GGA) to density-functional theory were applied.The equilibrium lattice constants and the bulk modulus of a number of structures (NaCl, CsCl, ZnS) were calculated as well as the elastic constants for the structures (NaCl, CsCl). The NaCl structure is found to be the most stable one among all the three phases considered. We have found that the GGA predicts the elastic constants in good agreement with experimental data.Both the LDA and GGA were successful in predicting the location of the band gap at the L point of the Brillouin zone but they are inconclusive regarding the value of the band-gap width. To resolve the issue of the gap, we performed Slater-Koster (SK) tight-binding calculations, including the spin-orbit coupling in the SK Hamiltonian. The SK results that are based on our GGA calculations give the best agreement with experiment.Results are reported for the pressure dependence of the energy gap of these compounds in the NaCl structure. The pressure variation of the energy gap indicates a transition to a metallic phase at high pressure. Band structure calculations in the CsCl structure show a metallic state for all compounds. The electronic band structure in the ZnS phase shows an indirect band gap at the W and X point of the Brillouin zone.     

Electronic properties close to Dirac cone in two-dimensional organic conductor α-(BEDT-TTF)<Subscript>2</Subscript>I<Subscript>3</Subscript>

A zero-gap state (ZGS) has been found in a bulk system of two-dimensional organic conductor, α-(BEDT-TTF)₂I₃ salt which consists of four sites of donor molecules in a unit cell. In the present paper, the characteristic of the ZGS is analyzed in detail and the electronic properties are examined in the vicinity of the Dirac point where the conduction and valence bands degenerate to form the zero-gap. The eigenvectors of the energy band have four components of respective sites, where two of them correspond to inequivalent sites and the other two correspond to equivalent sites. It is shown that the former exhibits an exotic momentum dependence around the contact point and the latter shows almost a constant dependence. The density of states of each site close to the Dirac point is calculated to demonstrate the temperature dependence of the local magnetic susceptibility and the local nuclear magnetic relaxation rate. Further, the robust property of the ZGS against the anion potential is also shown by using the second-order perturbation.     

Giant paramagnetism in Li-doped Mo-S nanostructures

Magnetic measurements of Li-doped MoS_2−y nanostructures show a peculiarly large T-independent paramagnetic signal, which cannot be understood in terms of either Curie- or Pauli paramagnetism, or—for that matter—in terms of any simple spin-correlated state, such as antiferromagnetism or superparamagnetic spin clustering. This behaviour appears to be a result of a near-ideal one-dimensional (1D) strongly correlated state, due to the extraordinarily weak inherent coupling between 1D subunits (nanotubes or nanowires), which is an order of magnitude weaker even than in carbon nanotube ropes. In spite of clear evidence for strong electronic correlations from a giant paramagnetic susceptibility, no transition to an ordered state is observed down to very low temperatures and the system appears to be stabilised in a paramagnetic state by fluctuations characteristic of 1D systems. Down to 2 K there is no evidence of a low-temperature quantum critical point.     

Oxygen vacancy doping effect on the electrical and magnetic behavior of Ba5−xLaxNb4−xTixO15

We report electric and magnetic properties of oxygen deficient Ba_5−xLa_xNb_4−xTi_xO_15−δ phases, which have been prepared by solid-state reaction method followed by a controlled reduction process under hydrogen atmosphere. The extra electrons added by the formation of the oxygen vacancies (δ) introduce localized spins and the magnetic susceptibility can be described by a temperature-independent contribution and a Curie-Weiss term associated to the Ti³⁺ ion formation. Besides, the experimental resistivity (ρ) data of these four reduced compounds are well described in a wide temperature range with the equation , which suggests the presence of small polarons in the system. Although, all samples present electrical insulating behavior, the electrical resistivity decreases four orders of magnitude for intermediate x values. We interpreted this fact as a consequence of the mix between the localized bands of the Nb and Ti ions, which favors the promotion of carriers due to reduction of the band gap.     

What does NMR tell us about the electronic state of high-T c superconductors?

An introduction to the models which are usually applied, when interpreting the NMR (nuclear magnetic resonance) parameter Knight shift (K _s) and spin-lattice relaxation rate 1/T ₁ in the normal and the superconducting state of high-temperature superconductors, is given. The different hyperfine interaction parameters involved, as well as the static and dynamic susceptibility χ(q,ω) will be discussed. I will point at those highlights as antiferromagnetic correlations, spin gap and vortex lattice dynamics which have emerged from the analysis of the NMR data.     

Spin glass like behavior in Cd0.42Mn0.58In2S4

The magnetic behavior of the diluted magnetic semiconductor Cd_0.42Mn_0.58In₂S₄ has been study by dc magnetization and ac susceptibility experiments. Zero field cooled and field cooled measurements reveal irreversibility below T_irr=2.60±0.15 K. Ac susceptibility data, performed as a function of the temperature and the frequency, confirm the spin-glass like behavior of the material with T_f=2.75±0.15 K. High temperature susceptibility data follow a typical Curie-Weiss law with θ=−74±1 K which suggests predominant antiferromagnetic interactions. The randomness of the magnetic ions, necessary to explain the magnetic behavior of the material, has been determined by X-ray powder diffraction experiments.     

Physical properties of the delafossite LaCuO2

High-quality LaCuO₂, elaborated by solid-state reaction in sealed tube, crystallizes in the delafossite structure. The thermal analysis under reducing atmosphere (H₂/N₂: 1/9) revealed a stoichiometric composition LaCuO_2.00. The oxide is a direct band-gap semiconductor with a forbidden band of 2.77 eV. The magnetic susceptibility follows a Curie-Weiss law from which a Cu²⁺ concentration of 1% has been determined. The oxygen insertion in the layered crystal lattice induces p-type conductivity. The electrical conduction occurs predominantly by small polaron hopping between mixed valences Cu^+/2+ with an activation energy of 0.28 eV and a hole mobility (μ_300 K=3.5×10⁻⁷ cm² V⁻¹ s⁻¹), thermally activated. Most holes are trapped in surface-polaron states upon gap excitation. The photoelectrochemical study, reported for the first time, confirms the p-type conduction. The flat band potential (V_fb=0.15 V_SCE) and the hole density (N_A=5.8×10¹⁷ cm⁻³) were determined, respectively, by extrapolating the curve C⁻² versus the potential to their intersection with C⁻²=0 and from the slope of the linear part in the Mott-Schottky plot. The valence band is made up of Cu-3d orbital, positioned at 4.9 eV below vacuum. An energy band diagram has been established predicting the possibility of the oxide to be used as hydrogen photocathode.     

Influence of quadrupole–quadrupole-type interaction on the chaotic dynamics of $$\alpha $$-helical proteins

We calculate the electronic band dispersion of graphene monolayer on a two-dimensional transition metal dichalcogenide substrate (GrTMD) around K and \(\mathbf{K}^{\prime }\) points by taking into account the interplay of the ferromagnetic impurities and the substrate-induced interactions. The latter are (strongly enhanced) intrinsic spin–orbit interaction (SOI), the extrinsic Rashba spin–orbit interaction (RSOI) and the one related to the transfer of the electronic charge from graphene to substrate. We introduce exchange field (M) in the Hamiltonian to take into account the deposition of magnetic impurities on the graphene surface. The cavalcade of the perturbations yield particle–hole symmetric band dispersion with an effective Zeeman field due to the interplay of the substrate-induced interactions with RSOI as the prime player. Our graphical analysis with extremely low-lying states strongly suggests the following: The GrTMDs, such as graphene on \(\hbox {WY}_{2}\), exhibit (direct) band-gap narrowing / widening (Moss–Burstein (MB) gap shift) including the increase in spin polarisation (P) at low temperature due to the increase in the exchange field (M) at the Dirac points. The polarisation is found to be electric field tunable as well. Finally, there is anticrossing of non-parabolic bands with opposite spins, the gap closing with same spins, etc. around the Dirac points. A direct electric field control of magnetism at the nanoscale is needed here. The magnetic multiferroics, like \(\hbox {BiFeO}_{3}\) (BFO), are useful for this purpose due to the coupling between the magnetic and electric order parameters.