Hiroyasu Koizumi

The Geometric Phase in Quantum Systems

1. Introduction.- 2. Quantal Phase Factors for Adiabatic Changes.- 3. Spinning Quantum System in an External Magnetic Field.- 4. Quantal Phases for General Cyclic Evolution.- 5. Fiber Bundles and Gauge Theories.- 6. Mathematical Structure of the Geometric Phase I: The Abelian Phase.- 7. Mathematical Structure of the Geometric Phase II: The Non-Abelian Phase.- 8. A Quantum Physical System in a Quantum Environment - The Gauge Theory of Molecular Physics.- 9. Crossing of Potential Energy Surfaces and the Molecular Aharonov-Bohm Effect.- 10. Experimental Detection of Geometric Phases I: Quantum Systems in Classical Environments.- 11. Experimental Detection of Geometric Phases II: Quantum Systems in Quantum Environments.- 12. Geometric Phase in Condensed Matter I: Bloch Bands.- 13. Geometric Phase in Condensed Matter II: The Quantum Hall Effect.- 14. Geometric Phase in Condensed Matter III: Many-Body Systems.- A. An Elementary Introduction to Manifolds and Lie Groups.- B. A Brief Review of Point Groups of Molecules with Application to Jahn-Teller Systems.- References.

Two-Copper-Atom Units Induce a Pseudo Jahn–Teller Polaron in Hole-Doped Cuprate Superconductors

Multiconfiguration molecular orbital cluster calculation results combined with experimental observations suggest that the local electronic state unit for a doped hole contains at least two Cu atoms in contrast to the Zhang–Rice singlet state that includes only one Cu atom. The cluster calculation shows that a doped hole in a two copper containing cluster induces a pseudo Jahn–Teller instability with stabilization energy that agrees with a peak in the photoinduced conductivity measurement, and the Cu–O bond length fluctuations that explain the EXAFS experiment; the charge-transfer energy gap observed in the optical conductivity measurement, and an excitation energy that corresponds to a peak in the energy loss function are also obtained from the calculation including two Cu atoms.

GEOMETRIC PHASE IN TWO KRAMERS DOUBLETS MOLECULAR SYSTEMS

The geometric phase in two Kramers doublets molecular systems is considered. We obtain the general formula for the gauge potential arising from the vibronic interaction and spin–orbit interaction between two Kramers doublet electronic levels. Simple models for the Jahn–Teller and Renner–Teller problems with spin–orbit coupling are considered. It is demonstrated that the energy spectra obtained by the Born–Oppenheimer approximation with the gauge potential agree quite well with the exact energy spectra in strong vibronic cases. It is also shown that the inclusion of the scalar gauge potential is important in order to obtain accurate zero point energy. As an application, vibronic levels of the X 2E’ state of Cu3 are reexamined including spin–orbit interaction.

Spin-Wave Excitations in Effectively Half-Filled Mott Insulators

We study spin-wave excitations in an effectively half-filled Hubbard model, where the effectively half-filled situation is realized when all holes doped in the exactly half-filled parent compound become self-trapped lattice polarons, and their hopping rate is much slower than the neutron scattering time of magnetic excitation measurements. It is further assumed that the doped holes become stabilizing centers of spin vortices; thus, the spin texture is not necessarily that of an antiferromagnet. We derive a new spin Hamiltonian that is suitable for this situation by extending the usual antiferromagnetic Heisenberg model. It is shown that two modes of spin-wave excitations exist in this new spin Hamiltonian: the first is the one exhibits antiferromagetic dispersion in high energy excitations; the other shows a sharp commensurate peak at the excitation energy maximum, and a broadened dispersion at energies below. It is shown that the sum of these two modes form an hourglass-shaped magnetic excitation spectru...

Shell correction study of fission of doubly charged silver clusters

Fission of doubly charged silver clusters is investigated by the method of shell corrections. The following fission events are considered: Ag222+ → Agn+ + Ag22 −n+, (n=11, 10, 9, 8); Ag212+ → Agn+ + Ag21 −n+, (n=10, 9, 8, 7); Ag182+ → Agn+ + Ag18 −n+, (n=9, 8, 7, 6). It is found that the shell correction energy is comparable to or larger than the deformation energy of the liquid drop. Threshold energies for the fission events are calculated and compared with the experimental abundance spectra obtained by Katakuse et al. (1990). Correspondence between the calculated threshold energies with the shell corrections and the experimental abundance is very good, showing products from lower threshold fission channels yield more abundance. The threshold energies without the shell corrections are almost constant irrespective of the fission channels and cannot explain the experimental abundance. Abundance of some products are too small to be accounted for only by the threshold energies. The low abundance of those products may be explained by the presence of competing fission channels that have similar minimal energy paths. It is found in fission of Ag182+ that the shell correction overwhelms the Coulomb energy and the fission channel to Ag8 + Ag102+ is preferred over the fission channel to Ag8+ + Ag10+.

Bloch Electrons in a Jahn-Teller Crystal and an Orbital-Density-Wave State due to the Berry Phase

The effect of the Berry phase is included explicitly in the wavefunction describing conduction electrons in a crystal composed of periodically arrayed Jahn-Teller centers that have conically intersecting potential energy surfaces. The Berry phase can make a drastic change in the band structure, leading generally to the formation of an orbital-density-wave state. We discuss implications of our theory and possible relations to the orbital ordering observed in the manganese perovskites.

Role of the Berry Phase in the Formation of Stripes in Manganese Oxides

In order to gain an insight into the formation of paired Jahn–Teller (JT) stripes, we have investigated the electronic and vibronic structures in the manganese oxides by paying due attention to the effect of the Berry phase associated with the JT distortions on the band motion of an eg electron. In terms of a band-insulator picture, we have succeeded in obtaining the JT stripes and the stabilization mechanism of the CE-type antiferromagnetism in agreement with experiment.

The geometric phase in two electronic level systems

The effects of the geometric phase on vibronic states associated with the lower potential surface of two electronic level Hamiltonians are examined. We obtain the general formula for the gauge potential arising from the vibronic interaction. It is shown that this gauge potential is split into a topological part and a magnetic part, where the topological part gives rise to the phase factor of +1 or −1 when it is integrated along a closed trajectory in the nuclear coordinate space, and the magnetic part gives rise to a contribution depending on the local character of the trajectory and exists only in systems without time‐reversal symmetry. For particular examples, we consider the E⊗e and E⊗(b1+b2) Jahn–Teller systems with strong vibronic interactions. It is demonstrated that the ground states have vibronic standing wave states whose nuclear probability density distributions are localized in one of the equivalent minima on the lower potential surface. We also consider Zeeman splittings of degenerate vibronic...

Persistent current generation by a Berry phase

We consider a persistent current generation by the fictitious magnetic field generated by spin-vortices in a solid with two-dimensional conduction layers. Each center of the spin-vortices is a singularity that imposes the sign-change boundary condition on the wavefunction for the conduction electron. We handle the sign-change boundary condition by introducing a fictitious magnetic field and show that loop currents are generated by it even in the ground state. Actually, a distribution of NV singularities causes the ground state to be -fold degenerate with different current patterns. When an external magnetic field is applied, this degeneracy is partly lifted and the one that expels the magnetic field is chosen. This response strongly resembles the Meissner effect seen in superconductors. The flux quantization also occurs with the unit h/2e as in superconductors.

Appearance of a Drude-Like Peak from Spin-Wave Excitations in the Effectively Half-Filled Mott Insulator

We calculate the optical conductivity of the effectively half-filled Mott insulator that has been put forward as a relevant state for cuprates. It is shown that a Drude-like peak appears from transitions to spin-wave excited states that emerge when spin vortices exist; thus, it is indicated that the Drude-like peak in underdoped cuprates may not be a sign of the coherent motion of doped holes, but actually a sign of the presence of spin vortices and small polarons. The amplitude of the Drude-like peak increases with an increase in the number of spin vortices. Therefore, the doping and temperature dependences of the optical conductivity of cuprates are explained by the doping and temperature variations in the number of spin vortices. The calculated effective carrier number is also shown to explain the experimental value.