340
M. Svrˇ cek
that using the correct field, fully respecting the Goldstone theorem, the microscopic
theory for superconductors will yield true asymmetric ground states, which are geometrical in accordance with the J-T effect. It means, that superconductors also share
the common spontaneous symmetry breaking (SSB) with the J-T molecules. The
quantum chemist and expert on the J-T effect, Isaac Bersuker came exactly to the
same conclusion, writing in his book [112]: “Moreover, since the JTE has been shown
to be the only source of spontaneous distortion of high-symmetry configurations, we
come to the conclusion that the JTE is a unique mechanism of all the symmetry
breakings in condensed matter.” Bersuker further restated the prominence and role
of the J-T effect in connection with the discovery of high-Tc superconductivity [112]:
“The next significant resurgence of interest in the Jahn-Teller effect is related to the
late 1980s and is still continuing. It was triggered by one of the most important Nobel
Prize discoveries in physics of our times inspired by the Jahn-Teller effect: the hightemperature superconductivity. As explained by the authors of this discovery, “the
guiding idea in developing this concept was influenced by the Jahn-Teller polaron
model” (J.G. Bednorz and K.A. Müller, in Nobel Lectures: Physics, Ed. G. Ekspong,
World Scientific, Singapore, 1993, p. 424).”
Since the mechanism of SSB lies behind both the J-T effect and superconductivity,
it entails that both phenomena must be described by similar mathematical equations,
cf. the presentation given in the previous section. It is therefore somewhat surprising
that Bersuker ignored this fact accepting the Cooper pair based explanation for superconductors. In his book [112] he suggests further efforts to find a bridge between J-T
distortions and Cooper pairing citing: “However, the electron–phonon coupling is
not the only factor that influences the superconductivity, and it does not determine the
SC transition temperature directly. The path from local JT distortions to formation of
polarons via lattice dynamics, to formation of Cooper pairs, their density, stability,
and mobility, temperature dependence, to perfect diamagnetism, to structural phase
transition, and finally to SC, is very long and thorny, and therefore a comprehensive
JT theory of this important phenomenon has not yet been accomplished.”
In this connection it should be worth recalling Newton’s second antimetaphysical
rule [113]: „Hypoth. II. Ideoque effectuum naturalium ejusdem generis eædem sunt
causæ. Uti respirationis in Homine & in Bestia; descensus lapidum in Europa & in
America; Lucis in Igne culinari & in Sole; reflexionis lucis in Terra & in Planetis.”
It means that to the same natural effect the same causes must be assigned. Hence
J-T distortions are the common causes of both phenomena, the J-T effect and superconductivity, which are observed on systems with B-O degenerate ground states and
broken symmetries. Then it is not necessary to prompt the “very long and thorny
path” from J-T distortions to the formation of Cooper pairs. In order to improve the
understanding of the identity of these two phenomena, we will concentrate on their
common cause, i.e. the J-T distortions, and especially on their underlying intrinsic concepts, the B-O approximation and the SSB, which both need to be carefully
revised.
Starting first with the SSB and the problem of broken symmetries in the early
period of classical physics, it led to a theological controversy about the question of its
origin, between Newton and Leibniz. Hermann Weyl in his book [114], describes the
M. Svrˇ cek
that using the correct field, fully respecting the Goldstone theorem, the microscopic
theory for superconductors will yield true asymmetric ground states, which are geometrical in accordance with the J-T effect. It means, that superconductors also share
the common spontaneous symmetry breaking (SSB) with the J-T molecules. The
quantum chemist and expert on the J-T effect, Isaac Bersuker came exactly to the
same conclusion, writing in his book [112]: “Moreover, since the JTE has been shown
to be the only source of spontaneous distortion of high-symmetry configurations, we
come to the conclusion that the JTE is a unique mechanism of all the symmetry
breakings in condensed matter.” Bersuker further restated the prominence and role
of the J-T effect in connection with the discovery of high-Tc superconductivity [112]:
“The next significant resurgence of interest in the Jahn-Teller effect is related to the
late 1980s and is still continuing. It was triggered by one of the most important Nobel
Prize discoveries in physics of our times inspired by the Jahn-Teller effect: the hightemperature superconductivity. As explained by the authors of this discovery, “the
guiding idea in developing this concept was influenced by the Jahn-Teller polaron
model” (J.G. Bednorz and K.A. Müller, in Nobel Lectures: Physics, Ed. G. Ekspong,
World Scientific, Singapore, 1993, p. 424).”
Since the mechanism of SSB lies behind both the J-T effect and superconductivity,
it entails that both phenomena must be described by similar mathematical equations,
cf. the presentation given in the previous section. It is therefore somewhat surprising
that Bersuker ignored this fact accepting the Cooper pair based explanation for superconductors. In his book [112] he suggests further efforts to find a bridge between J-T
distortions and Cooper pairing citing: “However, the electron–phonon coupling is
not the only factor that influences the superconductivity, and it does not determine the
SC transition temperature directly. The path from local JT distortions to formation of
polarons via lattice dynamics, to formation of Cooper pairs, their density, stability,
and mobility, temperature dependence, to perfect diamagnetism, to structural phase
transition, and finally to SC, is very long and thorny, and therefore a comprehensive
JT theory of this important phenomenon has not yet been accomplished.”
In this connection it should be worth recalling Newton’s second antimetaphysical
rule [113]: „Hypoth. II. Ideoque effectuum naturalium ejusdem generis eædem sunt
causæ. Uti respirationis in Homine & in Bestia; descensus lapidum in Europa & in
America; Lucis in Igne culinari & in Sole; reflexionis lucis in Terra & in Planetis.”
It means that to the same natural effect the same causes must be assigned. Hence
J-T distortions are the common causes of both phenomena, the J-T effect and superconductivity, which are observed on systems with B-O degenerate ground states and
broken symmetries. Then it is not necessary to prompt the “very long and thorny
path” from J-T distortions to the formation of Cooper pairs. In order to improve the
understanding of the identity of these two phenomena, we will concentrate on their
common cause, i.e. the J-T distortions, and especially on their underlying intrinsic concepts, the B-O approximation and the SSB, which both need to be carefully
revised.
Starting first with the SSB and the problem of broken symmetries in the early
period of classical physics, it led to a theological controversy about the question of its
origin, between Newton and Leibniz. Hermann Weyl in his book [114], describes the