Unambiguous Proof for Berry's Phase in the Sodium Trimer: Analysis of the Transition<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">A</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">E</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mi /><mml:mo>←</mml:mo><mml:mi /><mml:mrow><mml:

Büsch, H.; Dev, Vas; Eckel, H. A.; Kasahara, S.; Wang, J.; Demtröder, Wolfgang; Sebald, Peter; Meyer, Wilfried

doi:10.1103/physrevlett.81.4584

Cited by 102 publications

(94 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…(17), results from the redefinition r 0 − g/3K → r 0 of the size of the trimer, and the corresponding redefinition Q 1 + g/3K → Q 1 . The breathing mode frequency ω A in this model is K/M ; in Na 3 , multireference configuration interaction calculations give this to be about 17 meV [16], while experiment [17] suggests 16 meV, which implies K ≈ 1.5 eV/Å 2 . Unlike Eq.…”

Section: Quantized Vibrations Altered By Longuet-higgins Phasementioning

confidence: 73%

Quantum electrical dipole in triangular systems: A model for spontaneous polarity in metal clusters

2005

View full text Add to dashboard Cite

Triangular symmetric molecules with mirror symmetry perpendicular to the 3-fold axis are forbidden to have a fixed electrical dipole moment. However, if the ground state is orbitally degenerate and lacks inversion symmetry, then a "quantum" dipole moment does exist. The system of 3 electrons in D 3h symmetry is our example. This system is realized in triatomic molecules like Na3. Unlike the fixed dipole of a molecule like water, the quantum moment does not point in a fixed direction, but lies in the plane of the molecule and takes quantized values ±µ0 along any direction of measurement in the plane. An electric field F in the plane leads to a linear Stark splitting ±µ0| F |. We introduce a toy model to study the effect of Jahn-Teller distortions on the quantum dipole moment. We find that the quantum dipole property survives when the dynamic Jahn-Teller effect is included, if the distortion of the molecule is small. Linear Stark splittings are suppressed in low fields by molecular rotation, just as the linear Stark shift of water is suppressed, but will be revealed in moderately large applied fields and low temperatures. Coulomb correlations also give a partial suppression.

show abstract

Section: Quantized Vibrations Altered By Longuet-higgins Phasementioning

confidence: 73%

Quantum electrical dipole in triangular systems: A model for spontaneous polarity in metal clusters

2005

View full text Add to dashboard Cite

show abstract

“…In order to overcome this problem, we prepare the basis with required multi-valuedness in the following manner. This is a tight-binding model variant of the method employed to deal with the Longuet-Higgins sign-change in molecular problems [36][37][38].…”

Section: The Appearance Of Stable ∇χ Statesmentioning

confidence: 99%

Spin-vortex Superconductivity

Koizumi

2011

J Supercond Nov Magn

View full text Add to dashboard Cite

We present a theory of superconductivity based on the theoretical prediction that a macroscopic persistent current is generated by spin-vortices. It explains the origin of the phase variable θ that is canonical conjugate to the superfluid density as a Berry phase arising from the spin-vortex formation. This superconductivity does not require Cooperpairs as charge carriers, thus, is not directly related to the standard theory based on the BCS one; however, it exhibits the flux quantization in the unit Φ 0 = hc/2|e|, where h is Planck's constant, c the speed of light, and e the electron charge; and the AC Josephson frequency, f J = 2|e|V /h, where V is the voltage of the battery connected to the superconductor-insulator-superconductor junction. In due course, it is found that the standard derivation of the AC Josephson frequency misses a term arising from the flow of particles through the leads connected to the junction. If this contribution is included, the observed f J indicates that the phase θ is a variable conjugate to the number density of charge e carriers instead of the currently accepted charge 2e carriers. We propose an experiment that discriminates whether it is e or 2e. If the above claim is verified, it means that the BCS theory cannot predict whether a particular compound is a superconductor or not since it does not explain the origin of θ . A connection between the present mechanism and the BCS mechanism is discussed; the fact that the BCS theory gives an excellent estimate of T c is attributed to the fact that it predicts the temperature at which spin-vortices become long-lived due to the energy gap formation; since the stabilization by the electron-pair formation is compatible with the present mechanism, asymmetries observed in the H. Koizumi ( ) Institute of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan e-mail: koizumi@ims.tsukuba.ac.jp even and odd number of electron systems are preserved. The most notable difference is that the persistent current generation is formulated in a strictly particle-number-conserving manner. Thus, it does not violate the superselection rule for the total charge.

show abstract

“…The electronic wave function chosen this way is therefore a double-valued function of the nuclear coordinates. The sign change, known as the Longuet-Higgins phase [1,2], is a special case of the Berry phase [3,4], and its effects are observable in the vibrational spectroscopy of pseudorotating molecules [5,6] and electron paramagnetic resonance [7][8][9][10][11] and optical [12,13] spectroscopy of transition metal impurities in bulk crystals. Evidence for the dynamical Jahn-Teller effect in the excited states of the nitrogen-vacancy center in diamond has been reported [14][15][16][17][18], making the Longuet-Higgins phase rele- * Electronic address: rrequist@mpi-halle.mpg.de vant to its optical properties.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic analysis of the Berry curvature in theE⊗eJahn-Teller model

2017

View full text Add to dashboard Cite

The effective Hamiltonian for the linear E ⊗ e Jahn-Teller model describes the coupling between two electronic states and two vibrational modes in molecules or bulk crystal impurities. While in the Born-Oppenheimer approximation the Berry curvature has a delta function singularity at the conical intersection of the potential energy surfaces, the exact Berry curvature is a smooth peaked function. Numerical calculations revealed that the characteristic width of the peak is K 1/2 /gM 1/2 , where M is the mass associated with the relevant nuclear coordinates, K is the effective internuclear spring constant and g is the electronic-vibrational coupling. This result is confirmed here by an asymptotic analysis of the M → ∞ limit, an interesting outcome of which is the emergence of a separation of length scales. Being based on the exact electron-nuclear factorization, our analysis does not make any reference to adiabatic potential energy surfaces or nonadiabatic couplings. It is also shown that the Ham reduction factors for the model can be derived from the exact geometric phase.

show abstract

Unambiguous Proof for Berry's Phase in the Sodium Trimer: Analysis of the TransitionA2E′′←

Cited by 102 publications

References 19 publications

Quantum electrical dipole in triangular systems: A model for spontaneous polarity in metal clusters

Quantum electrical dipole in triangular systems: A model for spontaneous polarity in metal clusters

Spin-vortex Superconductivity

Asymptotic analysis of the Berry curvature in theE⊗eJahn-Teller model

Contact Info

Product

Resources

About