Pseudospin Symmetry Research Articles

Transport through graphene nanoribbons: Suppression of transverse quantization by symmetry breaking

AbstractWe investigate transport through graphene nanoribbons in the presence of disorder scattering. We show that size quantization patterns are only present when pseudospin symmetry is preserved. Symmetry breaking disorder strongly suppresses signatures of transverse quantization due to the inherent entanglement of pseudospin and transverse quantum numbers in graphene. To quantitatively distinguish the influence of symmetry breaking and symmetry conserving disorder on transport, we consider weak localization: we observe a transition from weak antilocalization to weak localization as symmetry‐breaking disorder is introduced. We discuss implications for experimental observations of size quantization signatures.

Spin and pseudo-spin symmetries of fermionic particles with an energy-dependent potential in non-commutative phase space

In this paper, we consider the Dirac equation in two dimensions influenced by an energy-dependent potential within a non-commutative phase space (NCP) framework for which no clear and reasonable solution has been given until now. By using the Nikiforov–Uvarov method to solve our difficult equations we obtain all the allowed energy eigenvalues and wave functions for particles with fermionic statistics, such as heavy quark systems, individual leptons etc. for both pseudo-spin and spin symmetries in the presence and absence of an external magnetic field. Finally we analyze the behavior of the energy values achieved in the NCP space in terms of the system's mass and magnetic field for several n, l levels of the present work.

Relativistic Killingbeck energy states under external magnetic fields

We address the behavior of the Dirac equation with the Killingbeck radial potential including the external magnetic and Aharonov-Bohm (AB) flux fields. The spin and pseudo-spin symmetries are considered. The correct bound state spectra and their corresponding wave functions are obtained. We seek such a solution using the biconfluent Heun differential equation method. Further, we give some of our results at the end of this study. Our final results can be reduced to their non-relativistic forms by simply using some appropriate transformations. The spectra, in the spin and pseudo-spin symmetries, are very similar with a slight difference in energy spacing between different states.

Three-body model for an isoscalar spin-triplet neutron-proton pair inSb102

We discuss the isoscalar $T=0, S=1$ pairing correlation in the low-lying states of $^{102}{\rm Sb}={}^{100}{\rm Sn}+p+n$ nucleus. To this end, we employ ${\rm core}+p+n$ three-body model with the model space constructed by self-consistent mean-field calculations. The model is developed with both non-relativistic and relativistic effective interactions, the latter of which are found to be more realistic for the present case due to the pseudo-spin symmetry. It turns out that the $(L,S,T)=(0,1,0)$ pairing scheme is strongly hindered in $^{102}$Sb with the relativistic model because of the near degeneracy of the $g_{7/2}$ and $d_{5/2}$ orbitals in the valence space. This pair-breaking effect is clearly seen in the charge-exchange Gamow-Teller-type transitions rather than in the binding energies of $T=0$ and $T=1$ states.

Tensor coupling effect on relativistic symmetries

The similarity renormalization group is used to transform the Dirac Hamiltonian with tensor coupling into a diagonal form. The upper (lower) diagonal element becomes a Schr¨odinger-like operator with the tensor component separated from the original Hamiltonian. Based on the operator, the tensor effect of the relativistic symmetries is explored with a focus on the single-particle energy contributed by the tensor coupling. The results show that the tensor coupling destroying (improving) the spin (pseudospin) symmetry is mainly attributed to the coupling of the spin-orbit and the tensor term, which plays an opposite role in the single-particle energy for the (pseudo-) spin-aligned and spin-unaligned states and has an important influence on the shell structure and its evolution.

Refined comparison theorems for the Dirac equation with spin and pseudo-spin symmetry in d dimensions

The classic comparison theorem of quantum mechanics states that if two potentials are ordered then the corresponding energy eigenvalues are similarly ordered, that is to say if $ V_{a}\le V_{b}$ , then $ E_{a}\le E_{b}$ . Such theorems have recently been established for relativistic problems even though the discrete spectra are not easily characterized variationally. In this paper we improve on the basic comparison theorem for the Dirac equation with spin and pseudo-spin symmetry in $ d\ge 1$ dimensions. The graphs of two comparison potentials may now cross each other in a prescribed manner implying that the energy values are still ordered. The refined comparison theorems are valid for the ground state in one dimension and for the bottom of an angular momentum subspace in $ d>1$ dimensions. For instance in a simplest case in one dimension, the condition $ V_{a}\le V_{b}$ is replaced by $ U_{a}\le U_{b}$ , where $ U_{i}(x)=\int_{0}^{x} V_{i}(t)dt$ , $ x\in[0,\infty)$ , and $i=a$ or b.

Fermions in a mixed vector-scalar double-step potential via continuous chiral transformation

The behaviour of fermions in the background of a double-step potential is analyzed with a general mixing of scalar and vector couplings via continuous chiral-conjugation transformation. Provided the vector coupling does not exceed the scalar coupling, a Sturm-Liouville approach for the double-step potential shows that the transmission coefficient exhibits oscillations and that a finite set of intrinsically relativistic bound-state solutions might appear as poles of the transmission amplitude in a strong coupling regime. An isolated bound-state solution resulting from coupled first-order equations might also come into sight. It is also shown that all those possible bound solutions disappear asymptotically as one approaches the conditions for the realization of the so-called spin and pseudospin symmetries in a four-dimensional space-time. Furthermore, we show that due to the additional mass acquired by the fermion from the scalar background the high localization of the fermion in an extreme relativistic regime does not violate the Heisenberg uncertainty principle.

Simple way to extract solutions and features of the Dirac equation for a noncentral potentials

The main purpose of the present study is to explore the classes of the Schrödinger-like wave equations derived from Dirac equation, for which the similarity transformation and asymptotic iteration algorithms can assist in generating second-order differential equation that admit general exact solutions in the presence of nonsymmetrical potential terms. For illustration purposes, we extract the exact bound-state solutions of the Dirac equation with the noncentral Hartmann potential for the cases of exact [Formula: see text] spin and pseudospin symmetries. Also, we have shown that both Dirac-radial and Dirac-polar parts are sensitive to the variation of the involved parameters.

Pseudospin Symmetry as a Bridge between Hadrons and Nuclei

Atomic nuclei exhibit approximate pseudospin symmetry. We review the arguments that this symmetry is a relativistic symmetry. The condition for this symmetry is that the sum of the vector and scalar potentials in the Dirac Hamiltonian is a constant. We give the generators of pseudospin symmetry. We review some of the predictions that follow from the insight that pseudospin symmetry has relativistic origins . We show that approximate pseudospin symmetry in nuclei predicts approximate spin symmetry in anti-nucleon scattering from nuclei. Since QCD sum rules predict that the sum of the scalar and vector potentials is small, we discuss the quark origins of pseudospin symmetry in nuclei and spin symmetry in hadrons.

Reprint of : Kondo effect in a carbon nanotube with spin–orbit interaction and valley mixing: A DM-NRG study

We investigate the effects of spin–orbit interaction (SOI) and valley mixing on the transport and dynamical properties of a carbon nanotube (CNT) quantum dot in the Kondo regime. As these perturbations break the pseudo-spin symmetry in the CNT spectrum but preserve time-reversal symmetry, they induce a finite splitting Δ between formerly degenerate Kramers pairs. Correspondingly, a crossover from the SU(4) to the SU(2)-Kondo effect occurs as the strength of these symmetry breaking parameters is varied. Clear signatures of the crossover are discussed both at the level of the spectral function as well as of the conductance. In particular, we demonstrate numerically and support with scaling arguments that the Kondo temperature scales inversely with the splitting Δ in the crossover regime. In presence of a finite magnetic field, time reversal symmetry is also broken. We investigate the effects of both parallel and perpendicular fields (with respect to the tube's axis) and discuss the conditions under which Kondo revivals may be achieved.

Theoretical study of the cubic Rashba effect at theSrTiO3(001) surfaces

The origin of Rashba spin splitting in the two-dimensional electron gas at the (001) surface of ${\mathrm{SrTiO}}_{3}$ is studied using first-principles calculations and tight-binding model. Calculations of oxygen vacancies under virtual crystal approximation reveal a two-dimensional electron-gas subband structure similar to polar materials, consistent with observations on ${\mathrm{SrTiO}}_{3}$. Our studies also confirm that $k$ dependence of the spin splitting is predominantly cubic in the surface $\mathrm{Ti}\ensuremath{-}{t}_{2g}$ states, even though structural relaxations diminish the effect in ${d}_{xy}$ bands. A tight-binding model, explicitly including $\mathrm{Ti}\ensuremath{-}d$ and $\mathrm{O}\ensuremath{-}p$ states as well as next-nearest-neighbor interactions, is derived to understand the first-principles results. Effective Rashba Hamiltonians for the surface bands are derived using quasidegenerate perturbation theory and scenarios in which linear $k$ contribution may be suppressed are discussed. However, the cubic terms in the Hamiltonian are found to be different from the model derived using $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ theory, leading to different pseudospin symmetry in the Brillouin zone.

Tridiagonal representation with pseudospin symmetry for a noncentral electric dipole and a ring-shaped anharmonic oscillator potential

The concepts of pseudospin symmetry in atomic nuclei and spin symmetry in anti-nucleon are reviewed. The exploration for understanding the origin of pseudospin symmetry and its breaking mechanism, and the empirical data supporting the pseudospin symmetry are introduced. A noncentral anharmonic oscillatory potential model is proposed, in which a noncentral electric dipole and a double ring-shaped component are included. The pseudospin symmetry for this potential model is investigated by working on a complete square integrable basis that supports a tridiagonal matrix representation of the Dirac wave operator. Then, solving the Dirac equation is translated into finding solutions of the recursion relation for the expansion coefficients of the wavefunction. The angular/radial wavefunction is written in terms of the Jacobi/Laguerre polynomials. The discrete spectrum of the bound states is obtained by diagonalization of the radial recursion relation, and the property of energy equation is discussed for showing the exact pseudospin symmetry. Several particular cases obtained by setting the parameters of the potential model to appropriate values are analyzed, and the energy equations are reduced to that of the anharmonic oscillator and that of the ring-shaped non-spherical harmonic oscillator, respectively. Finally, it is pointed out that the exact spin symmetry exists also in this potential model.

The Effect of Tensor Interaction in Splitting the Energy Levels of Relativistic Systems

We solve approximately Dirac equation for Eckart plus Hulthen potentials with Coulomb-like and Yukawa-like tensor interaction in the presence of spin and pseudospin symmetry fork≠0. The formula method is used to obtain the energy eigenvalues and wave functions. We also discuss the energy eigenvalues and the Dirac spinors for Eckart plus Hulthen potentials with formula method. To show the accuracy of the present model, some numerical results are shown in both pseudospin and spin symmetry limits.

General spin and pseudospin symmetries of the Dirac equation

In the 70's Smith and Tassie, and Bell and Ruegg independently found SU(2) symmetries of the Dirac equation with scalar and vector potentials. These symmetries, known as pseudospin and spin symmetries, have been extensively researched and applied to several physical systems. Twenty years after, in 1997, the pseudospin symmetry has been revealed by Ginocchio as a relativistic symmetry of the atomic nuclei when it is described by relativistic mean field hadronic models. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schr\"odinger-like equations, i.e, without a matrix structure. In this paper we propose a generalization of these SU(2) symmetries for potentials in the Dirac equation with several Lorentz structures, which also allow for the suppression of the matrix structure of second-order equation equation of either the upper or lower components of the Dirac spinor. We derive the general properties of those potentials and list some possible candidates, which include the usual spin-pseudospin potentials, and also 2- and 1-dimensional potentials. An application for a particular physical system in two dimensions, electrons in graphene, is suggested.

Progress on relativistic symmetries by similarity renormalization group

In the paper, we have outlined some progress on the researches of relativistic symmetries using the similarity renormalization group method and presented the theoretical details for the spherical and axially deformed nuclei. The Dirac Hamiltonian obtained from covariant density functional theory is transformed into a diagonal form, where the upper (lower) diagonal element becomes an operator describing the Dirac (anti-) particle. Every diagonal operator is made up of these components, which respectively correspond to the nonrelativistic term, the dynamical term, the spin-orbit interactions, the relativistic modification of kinetic energy, and the Darwin term. By using the operator, we have explored the origin and the broken mechanism of relativistic symmetries for the spherical and axially deformed nuclei. The results show that the breaking of spin symmetry almost completely is attributed to the spin-orbit interactions, while the pseudospin symmetry is related to the nonrelativistic term, the dynamical term and the spin-orbit coupling term.

Selected milestones and hot topics in nuclear structure researches

Several important milestones and hot topics in nuclear physics researches are reviewed. The discoveries of the atomic nucleus and its components are introduced firstly, followed by the corresponding nuclear bulk properties, including the nuclear masses, and radii, and the establishment of the nuclear shell model based on these discoveries. By examining the spin-orbital potential leading to the nuclear shell model, the nuclear spin and pseudospin symmetries, are discussed. As one of the most important aspects in nuclear physics, the nuclear rotation excitation dated back to 1960s, is reviewed in detail. Finally the chances and challenges for nuclear physics in the twenty-first century are provided based on some selected hot topics and important issues in current nuclear physics frontiers.

Single particle states in the Fermi sea and Dirac sea in spherical nuclei

The Dirac equation sits in the center of nuclear covariant density functional theories. In this review, we will introduce briefly the numerical methods of solving the Dirac equation for spherical nuclei and discuss several relevant topics. We introduce the shooting method which is used in solving the radial Dirac equation in the coordinate space and the Woods-Saxon basis expansion approach including the Schr\odinger-Woods-Saxon basis and the Dirac-Woods-Saxon basis. For the Dirac-Woods-Saxon basis, the completeness of the basis requires that not only the positive energy states in the Fermi sea but also the negative energy states in the Dirac sea should be included in the basis. The pseudospin symmetry of those negative energy states, or equivalently, the spin symmetry in the anti-nucleon spectra are discussed.

Dirac Equation for Scalar, Vector and Tensor Generalized Cornell Interaction

We consider spin and pseudospin symmetry limits of Dirac equation in the presence of scalar, vector and tensor generalized Cornell interaction and report the solutions via the quasi-exact analytical ansatz approach.

Kondo effect in a carbon nanotube with spin–orbit interaction and valley mixing: A DM-NRG study

We investigate the effects of spin–orbit interaction (SOI) and valley mixing on the transport and dynamical properties of a carbon nanotube (CNT) quantum dot in the Kondo regime. As these perturbations break the pseudo-spin symmetry in the CNT spectrum but preserve time-reversal symmetry, they induce a finite splitting Δ between formerly degenerate Kramers pairs. Correspondingly, a crossover from the SU(4) to the SU(2)-Kondo effect occurs as the strength of these symmetry breaking parameters is varied. Clear signatures of the crossover are discussed both at the level of the spectral function as well as of the conductance. In particular, we demonstrate numerically and support with scaling arguments that the Kondo temperature scales inversely with the splitting Δ in the crossover regime. In presence of a finite magnetic field, time reversal symmetry is also broken. We investigate the effects of both parallel and perpendicular fields (with respect to the tube's axis) and discuss the conditions under which Kondo revivals may be achieved.

Spin and Pseudospin Symmetries of Hellmann Potential with Three Tensor Interactions Using Nikiforov–Uvarov Method

The Dirac equation with Hellmann potential is presented in the presence of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT), and Hulthen-type tensor (HLT) interactions by using Nikiforov–Uvarov method. The bound state energy spectra and the radial wave functions are obtained approximately within the framework of spin and pseudospin symmetries limit. We have also reported some numerical results and figures to show the effects of the tensor interactions. Special cases of the potential are also discussed.