Pseudospin Symmetry Research Articles

Interacting multi-channel topological boundary modes in a quantum Hall valley system

Symmetry and topology are central to understanding quantum Hall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneously broken spin or pseudospin symmetry whose wavefunctions also have topological properties1,2. Domain walls between distinct broken-symmetry QHFM phases are predicted to host gapless one-dimensional modes-that is, quantum channels that emerge because of a topological change in the underlying electronic wavefunctions at such interfaces. Although various QHFMs have been identified in different materials3-8, interacting electronic modes at these domain walls have not been probed. Here we use a scanning tunnelling microscope to directly visualize the spontaneous formation of boundary modes at domain walls between QHFM phases with different valley polarization (that is, the occupation of equal-energy but quantum mechanically distinct valleys in the electronic structure) on the surface of bismuth. Spectroscopy shows that these modes occur within a topological energy gap, which closes and reopens as the valley polarization switches across the domain wall. By changing the valley flavour and the number of modes at the domain wall, we can realize different regimes in which the valley-polarized channels are either metallic or develop a spectroscopic gap. This behaviour is a consequence of Coulomb interactions constrained by the valley flavour, which determines whether electrons in the topological modes can backscatter, making these channels a unique class of interacting one-dimensional quantum wires.QHFM domain walls can be realized in different classes of two-dimensional materials, providing the opportunity to explore a rich phase space of interactions in these quantum wires.

Probing Resonances and Pseudospin Symmetry of the Eckart Potential by the Complex Scaling Method within the Relativistic Framework

Abstract The complex scaling method is applied to probe the resonances of a Dirac particle in the Eckart potential, along with the corresponding energies and widths obtained. Then, the dependence of the resonant energies and widths on the parameters of the potential is checked. The results indicate that the energy and width of the pseudospin doublets preserve a good pseudospin symmetry. Furthermore, the quality of pseudospin symmetry is correlated with the parameters of the Eckart potential.

Bound-state solutions of the Dirac equation for the Kratzer potential with pseudoscalar-Coulomb term

We present exact analytical solutions of the Dirac equation in (1 + 1) dimensions for the generalized Kratzer potential by taking the pseudoscalar interaction term as an attractive Coulomb potential. We study the problem for a particular (spin) symmetry of the Dirac Hamiltonian. After a qualitative analyse, we study the results for some special cases, such as the Dirac-Coulomb problem in the presence of pseudoscalar interaction, and the “pure” Coulomb problem by discussing some points about pseudospin and spin symmetries in one dimension. We also plot some figures representing the dependence of the energy on the quantum number, and potential parameters.

Approximate solutions of the Dirac equation with Coulomb-Hulthén-like tensor interaction

Abstract The solutions of spin and pseudospin symmetries with Trigonometric scarf potential are obtained in the presence of a new tensor interaction which breaks down the energy degeneracies in both symmetries leading to atomic stability. The nonrelativistic equation is obtained by taking the nonrelativistic limit of the spin symmetry. A simplified condition for energy equation for Formula method for special case is also given. Finally, we calculated Fisher information for both position and momentum spaces which can be used to determine the accuracy of predicting the localization of a particle.

Pseudospin Symmetry and Microscopic Origin of Shape Coexistence in the ^{78}Ni Region: A Hint from Lifetime Measurements.

Lifetime measurements of excited states of the light N=52 isotones ^{88}Kr, ^{86}Se, and ^{84}Ge have been performed, using the recoil distance Doppler shift method and VAMOS and AGATA spectrometers for particle identification and gamma spectroscopy, respectively. The reduced electric quadrupole transition probabilities B(E2;2^{+}→0^{+}) and B(E2;4^{+}→2^{+}) were obtained for the first time for the hard-to-reach ^{84}Ge. While the B(E2;2^{+}→0^{+}) values of ^{88}Kr, ^{86}Se saturate the maximum quadrupole collectivity offered by the natural valence (3s, 2d, 1g_{7/2}, 1h_{11/2}) space of an inert ^{78}Ni core, the value obtained for ^{84}Ge largely exceeds it, suggesting that shape coexistence phenomena, previously reported at N≲49, extend beyond N=50. The onset of collectivity at Z=32 is understood as due to a pseudo-SU(3) organization of the proton single-particle sequence reflecting a clear manifestation of pseudospin symmetry. It is realized that the latter provides actually reliable guidance for understanding the observed proton and neutron single particle structure in the whole medium-mass region, from Ni to Sn, pointing towards the important role of the isovector-vector ρ field in shell-structure evolution.

Dirac Equation with a New Tensor Interaction under Spin and Pseudospin Symmetries

The approximate analytical solutions of the Dirac equation under spin and pseudospin symmetries are examined using a suitable approximation scheme in the framework of parametric Nikiforov-Uvarov method. Because a tensor interaction in the Dirac equation removes the energy degeneracy in the spin and pseudospin doublets that leads to atomic stability, we study the Dirac equation with a Hellmann-like tensor potential newly proposed in this study. The newly proposed tensor potential removes the degeneracy from both the spin symmetry and pseudospin symmetry completely. The proposed tensor potential seems better than the Coulomb and Yukawa-like tensor potentials.

Solutions to the Dirac Equation for Manning-Rosen Plus Shifted Deng-Fan Potential and Coulomb-Like Tensor Interaction Using Nikiforov-Uvarov Method

We solve the Dirac equation for the Manning-Rosen plus shifted Deng-Fan potential including a Coulomb-like tensor potential with arbitrary spin–orbit coupling quantum number κ. In the framework of the spin and pseudospin (pspin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions in closed form by using the Nikiforov–Uvarov method. Also Special cases of the potential as been considered and their energy eigen values as well as their corresponding eigen functions are obtained for both relativistic and non-relativistic scope.

An investigation of the bound-state solutions of the Klein-Gordon equation for the generalized Woods-Saxon potential in spin symmetry and pseudo-spin symmetry limits

Recently, scattering of a Klein-Gordon particle in the presence of mixed scalar-vector generalized symmetric Woods-Saxon potential was investigated for the spin symmetric and the pseudo-spin symmetric limits in one spatial dimension. In this manuscript, the bound state solutions of the Klein-Gordon equation with mixed scalar-vector generalized symmetric Woods-Saxon potential are examined analytically within the framework of spin and pseudo-spin symmetry limits. We prove that the occurrence of bound state energy spectrum exists only in the spin symmetric limit, while in the pseudo-spin symmetric limit, the bound state spectrum does not exist. Besides the theoretical proof, the Newton-Raphson numerical methods are used to calculate the bound state energy spectra of a neutral Kaon particle, confined in a generalized symmetric Woods-Saxon potential, energy well constituted with repulsive or attractive surface interactions, for the spin and pseudo-spin symmetric limits, respectively. Numerical results are consistent with the non-existence of the bound state energy spectrum in the pseudo-spin symmetric limit.

Dirac Equation with Unequal Scalar and Vector Potentials under Spin and Pseudospin Symmetry

An approximate solution of the Dirac equation in the D-dimensional space is obtained under spin and pseudospin symmetry limits for the scalar and vector inversely quadratic Yukawa potential within the framework of parametric Nikiforov-Uvarov method using a suitable approximation scheme to the spin-orbit centrifugal term. The two components spinor of the wave function and their energy equations are fully obtained. Some numerical results are obtained for the energy level with various dimensions (D), quantum number (n), vector potential V0 and scalar potential S0 . The results obtained under spin symmetry using either V0 or S0 are equal to the results obtained usingV S 0 0  . But under the pseudospin symmetry, the results obtained using V0 or S0 are not equal to the results obtained usingV S 0 0  .

Energy Spectrum of the K-State Solutions of the Dirac Equation for Modified Eckart Plus Inverse Square Potential Model in the Presence of Spin and Pseudo-Spin Symmetry within the Framework of Nikifarov-Uvarov Method

Energy Spectrum of the K-State Solutions of the Dirac Equation for Modified Eckart Plus Inverse Square Potential Model in the Presence of Spin and Pseudo-Spin Symmetry within the Framework of Nikifarov-Uvarov Method

Tensor force effect on the evolution of single-particle energies in some isotopic chains in the relativistic Hartree–Fock approximation

Within a nonlinear relativistic Hartree–Fock approximation combined with the BCS method, we study the effect of the nucleon–nucleon tensor force of the π-exchange potential on the spin- and pseudospin–orbit doublets along the Ca and Sn isotopic chains.We show how the self-consistent tensor force effect modifies the splitting of both kinds of doublets in an interdependent form, leading, quite generally, to opposite effects in the accomplishment of the spin and pseudospin symmetries (the one is restored, the other one deteriorates and vice versa). The ordering of the single-particle energy levels is crucial to this respect.Also, we observe a mutual dependence on the evolution of the shell closure gap Z = 50 and the energy band outside the core, along the Sn chain, as due to the tensor force. In fact, when the shell gap is quenched the outside energy band is enlarged, and vice versa. A reduction of the strength of the pion tensor force with respect to its experimental value from the nucleon–nucleon scattering is needed to get results closer to the experiment. Pairing correlations act to some extent in the opposite direction of the tensor term of the one-pion-exchange force.

Relativistic effects in the study of weakly bound $${}^{17}$$17F and $${}^{11}$$11Be nuclei

Relativistic effects are employed to describe the weakly bound nuclei of $${}^{17}$$ F and $${}^{11}$$ Be. In order to calculate the energy levels of the ground state and the excited states of these nuclei, we solved the Dirac equation with pseudospin symmetry in the shell model by using the basic concept of supersymmetric shape invariance method. The results obtained from this approach are compared with a non-relativistic approach and experiment. It was then seen that the relativistic approach matches more with the experimental results.

Temperature effects on nuclear pseudospin symmetry in the Dirac-Hartree-Bogoliubov formalism

We present finite temperature Dirac-Hartree-Bogoliubov (FTDHB) calculations for the tin isotope chain to study the dependence of pseudospin on the nuclear temperature. In the FTDHB calculation, the density dependence of the self-consistent relativistic mean fields, the pairing, and the vapor phase that takes into account the unbound nucleon states are considered self-consistently. The mean field potentials obtained in the FTDHB calculations are fit by Woods-Saxon (WS) potentials to examine how the WS parameters are related to the energy splitting of the pseudospin pairs as the temperature increases. We find that the nuclear potential surface diffuseness is the main driver for the pseudospin splittings and that it increases as the temperature grows. We conclude that pseudospin symmetry is better realized when the nuclear temperature increases. The results confirm the findings of previous works using RMF theory at $T=0$, namely that the correlation between the pseudospin splitting and the parameters of the Woods-Saxon potentials implies that pseudospin symmetry is a dynamical symmetry in nuclei. We show that the dynamical nature of the pseudospin symmetry remains when the temperature is considered in a realistic calculation of the tin isotopes, such as that of the Dirac-Hartree-Bogoliubov formalism.

(Pseudo)spin symmetry in the single-neutron spectrum of Λ hypernuclei

Pseudospin and spin symmetries in the single-neutron spectra of Λ hypernuclei, and the effects of Λ impurity on these symmetries, are studied in the relativistic mean field model. It is found that the spin symmetry is violated while the pseudospin symmetry is approximately conserved, which is similar to the case in ordinary nuclei. As an impurity, the Λ hyperon makes the spin symmetry worse while making the pseudospin symmetry better, which arises from the decrease in the centrifugal barrier and the increase in the pseudo-centrifugal barrier in their competitions with the spin–orbit and pseudospin–orbit potentials, respectively. Further, our investigation extended to the Sn isotopes with , , and , and indicated that the effects of Λ impurity on pseudospin and spin symmetries are universal.

Quantum gas microscopy of an attractive Fermi–Hubbard system

The attractive Fermi-Hubbard model is the simplest theoretical model for studying pairing and superconductivity of fermions on a lattice. Although its s-wave pairing symmetry excludes it as a microscopic model for high-temperature superconductivity, it exhibits much of the relevant phenomenology, including a short-coherence length at intermediate coupling and a pseudogap regime with anomalous properties. Here we study an experimental realization of this model using a two-dimensional (2D) atomic Fermi gas in an optical lattice. Our site-resolved measurements on the normal state reveal checkerboard charge-density-wave correlations close to half-filling. A "hidden" SU(2) pseudo-spin symmetry of the Hubbard model at half-filling guarantees superfluid correlations in our system, the first evidence for such correlations in a single-band Hubbard system of ultracold fermions. Compared to the paired atom fraction, we find the charge-density-wave correlations to be a much more sensitive thermometer, useful for optimizing cooling into superfluid phases in future experiments.

Spin and pseudospin symmetries in the single- Λ spectrum

We explore spin and pseudospin symmetries in the single-$\mathrm{\ensuremath{\Lambda}}$ spectrum within the framework of relativistic mean-field theory. We find that the spin symmetry of the single-$\mathrm{\ensuremath{\Lambda}}$ spectrum maintains, which is consistent with experimental results of small spin-orbit splitting, whereas the approximate pseudospin symmetry is quite similar to that of nucleons. More interestingly, the $\ensuremath{\omega}\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$ tensor coupling has opposite effects on these symmetries which makes the spin symmetry better but the pseudospin symmetry worse. This can be understood by the negative value of the $\ensuremath{\omega}\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$ tensor potential, which reduces the spin-orbit potential while increasing the pseudospin-orbit potential.

Analytic Spin and Pseudospin Solutions to the Dirac Equation for the Quadratic Exponential-Type Potential Plus Eckart Potential and Yukawa-Like Tensor Interaction

We solve the Dirac equation for the quadratic exponential-type potential plus Eckart potential including a Yukawa-like tensor potential with arbitrary spin–orbit coupling quantum number κ. In the framework of the spin and pseudospin (pspin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions in closed form by using the Nikiforov–Uvarov method. Also Special cases of the potential as been considered and their energy eigen values as well as their corresponding eigen functions are obtained for both relativistic and non-relativistic scope.

Approximate bound-states solution of the Dirac equation with some thermodynamic properties for the deformed Hylleraas plus deformed Woods-Saxon potential

The Pekeris approximate scheme is introduced to deal with the centrifugal term in a Dirac equation with the deformed Hylleraas plus Woods-Saxon (DHWS) potential model. The relativistic energy solutions for the spin and pseudospin symmetries are obtained via the Nikiforov-Uvarov (NU) method. In the non-relativistic limits we calculated the thermodynamics properties for some selected diatomic molecules.

Approximate bound and scattering solutions of Dirac equation for the modified deformed Hylleraas potential with a Yukawa-type tensor interaction

Analytical bound and scattering state solutions of Dirac equation are investigated for the modified deformed Hylleraas potential with a Yukawa-type tensor interaction. The energy equation, phase shifts and normalization constants of the pseudospin and spin symmetry limits are represented. Since the modified deformed Hylleraas potential reduces to the Poschl–Teller, Hulthen and deformed Hylleraas potential, we have obtained energy equation and scattering properties of the Dirac equation for these potentials within a Yukawa-type tensor interaction. We have also reported some numerical results to show the effect of tensor interaction.

Spin and pseudospin symmetries and their breaking mechanisms in antinucleon spectrum

We explore the origins and breaking mechanisms of the spin and pseudospin symmetries for the antinucleon spectrum by the use of the similarity renormalization group, which transforms the Dirac Hamiltonian into a diagonal form and decomposes it into several independent components. By comparing the contribution of every component to the spin and pseudospin splittings, it is found that the energy splitting of spin doublets is dominated by the spin-orbit coupling while the pseudospin breaking comes mainly from these contributions of the nonrelativistic term and the dynamical term. In addition, the dependencies of the spin and pseudospin symmetries on the shape of the potential and the quantum numbers of the doublets are clarified.