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1
Superconducting Levitation Stemmed From
Diaelectric Material as Permanent Magnet:
Je Huan Koo*
Department of Electrical and Biological Physics, Kwangwoon University, Seoul 01897,
Republic of Korea
Abstract
We previously derived direct-current type negative dielectric susceptibility
, a state which
was termed “diaelectric” in previous work. One candidate for a strong diaelectric material
was postulated to be a permanent magnet. In this study, we regard magnets as anti-electric
materials such that this diaelectric phenomenon may satisfy all conditions necessary to repel
the external charges outside the magnet. We assign the superconducting levitation as
diaelectric effect of permanent magnets. Conserving constant ranges of distance between
magnet and superconductor has been a mystery. Diaelectric repulsion below the critical vaule
and normal restoring attractive interaction larger than the value between permanent magnet
and superconductors can happen where the structural factor is given by
B
eEL
kT
=1.54 (details in
the latter).
Keywords: Magnet; Superconductor; Levitation; Magnetic Field
PACS numbers: 71.20.-b; 41.20.-q
* Corresponding author. Tel: +82 2 940 8257; fax: +82 2 940 5664
E-mail addresses: djhkoo@gmail.com, koo@kw.ac.kr
2
After the discovery of superconductivity by H. K. Onnes [1], this phenomenon found a
comprehensive description at low temperatures through the Bardeen–Cooper–Schrieffer
(BCS) theory [2]. A notable feature of superconductors is the presence of a diamagnetic state,
which actively resists external magnetic forces. Conventional theories liken superconductors
to behaving like fingers or frogs, or even room-temperature diamagnetic substances in the
intriguing case of frog levitation using magnets [3], with magnetic levitation between
fingertips, as elucidated by Geim et al. [4]. The peculiarity lies in the observation that only a
select few materials exhibit these characteristics, creating a certain enigma. It is paradoxical
that the concept of superconducting states in fingers or frogs contradicts empirical evidence.
However, these quandaries can be successfully resolved if magnets are regarded as anti-
electric materials. In prior research, Koo established a negative dielectric susceptibility,
termed the "diaelectric" state, particularly in the context of direct-current (DC) behavior [5].
One potential candidate for a potent diaelectric material is proposed to be a permanent
magnet. Diaelectricity [6] stands as an anomalous property, somewhat conflicting with
conventional knowledge. Throughout the discussion that follows, it is crucial to distinguish
between diaelectricity and dielectricity to prevent confusion. Unlike dielectric materials,
which encompass paraelectricity and ferroelectricity and exhibit positive dielectric
susceptibility, diaelectric bodies exert a repulsive force when interacting with charges. This
repulsion is analogous to the interaction observed between magnets and diamagnetic
materials, including superconductors. While many typical substances, including certain
organic compounds like polymers, are considered diamagnetic, conventional wisdom holds
that most materials are attracted to charges. In other words, instances where diaelectric
behavior prevails over all other charge interactions are exceedingly rare and remain
unobserved.
3
In this letter, we consider the origin of negative dielectric susceptibility,
. We derived
negative dielectric susceptibility,
using two methods in analogous to Landau
diamagnetism.
Let us first consider dielectric susceptibility using the original method of Landau
diamagnetism [7]. As shown in Fig. 1, in the presence of a magnetic field,
H
, and an electric
field,
E
, the orbital motions may be described by Faraday’s Law of Induction, one of the
Maxwell equations:
H
Et
= −
. (1)
Based on the study by Koo [5], angular momentum, magnetization, and pseudo-
magnetization are given by the equations shown below:
i iz
B iz iz
e
iz iz
eEr t l
lm
e l m
⊥ =
=
=
. (2)
If we make the following substitution:
(2 )
B i B
H eE r H
⊥
+
, (3)
a negative DC-type dielectric susceptibility
in the form is obtained:
4
22
23
(2 )
2
0
e
iz i i
e
diaelectric iz i
e
m r r E
mer
E
⊥⊥
⊥
= −
= = −
(4)
in which
dS
is the variation of the surface,
dl
is the path element,
i
r⊥
is the radius of
the orbit perpendicular to the magnetic field,
()
ii
r r T
⊥⊥
is dependent on the temperature,
T
,
and is Planck's constant divided by 2π.
As shown in Fig.2, this diaelectric state stems from the image charge concept in which the
opposing charge may be induced by an external charge that is referenced to a centered plane,
and a concurrent identical polar charge coexists as a counterpart of the dipole in the image
charge portion that repels the external charge. According to the Lorentz force in terms of the
electric field, the order-of-magnitude of molar levitating force as a ballpark figure can be
estimated as the multiplication of electronic charge, velocity, and magnetic induction:
O(|q|=1.6×10-19 C)×O(v~10-4 m/s)×O(B~1 T)×O(NA=6.02×1023) ~ O(10 N) (5)
In the present work, we investigated repulsive diaelectric [7] force and restoring attractive
one between permanent magnet and superconductors. In the presence of
voltages
( :electric field, :sample size)V eEL E L=
, dielectric constants and susceptibilities
for fermions and bosons are given as:
5
1 exp( )
1
[ ]:dielectric constant
1 exp( )
= slope of 0
()
1 exp( )
1
[ ]:dielectric cons
1 exp( )
B
B
diaelectric
normal diaelectric
B
B
eEL
eEL eEL
kT
EeEL
EkT
susceptibility E
E
eEL
eEL eEL
kT
EeEL
EkT
=
−−
=−−
= − −
=
+
=+
tant
= slope of 0
()
diaelectric
normal diaelectric
susceptibility E
E
= − −
(6)
where
B
k
is Boltzmann’s constant,
E
is the electric field, and
T
is the temperature.
In the presence of saddle points in Eq. (6), diaelectric repulsion below the critical vaule
and normal attractive interaction larger than the value between permanent magnet and
superconductors can happen as shown in Fig.3 where the structural factor is given by
B
eEL
kT
=1.54. The effective magnetic field, H can equivalently replace other parameters as
shown in Equation (7):
( ) /
EBB
HH
H eEL H
+ +
(7)
in which
/2h
=
is Planck’s constant divided by
2
,
B
is the Bohr magneton,
E
is the electric field,
L
is the sample size, and
is the external angular frequency. The
average number density of an electron in the absence or presence of
H
is given by Equation
(8):
6
0 0 0
() 1 exp( ) 1 exp[ ]
()
ln[1 exp( )] ln{1 exp[ },
F B F
B B eff
F B F
B B eff
B B eff
dd
fd H eEL
k T k T
H eEL
k T k T
k T k T
==
− −
++
− −
+ = +
(8)
in which
f
is the Fermi-Dirac distribution function,
F
is the Fermi energy, and
i
are
positive constant parameters. In this situation, the effective temperature
eff
T
is given as
shown below:
B eff B H B E
k T k T H eEL
. (9)
In conclusion, we regard magnets [7] as anti-electric materials such that this diaelectric
phenomenon can satisfy all of the necessary conditions for repelling external charges, in other
words frogs or fingertips outside the magnet, as shown in Fig. 2. Observations are at odds for
the conventional belief that the superconducting perpendicular levitating forces is too
difficult to be originated from expelled magnetic field via Lorentz force. However, these
difficulties can all be resolved if magnets can be regarded as anti-electric materials in
accordance with common sense.
Diaelectric repulsion below the critical vaule and normal restoring attractive interaction larger
than the value between permanent magnet and superconductors can happen where the
structural factor is given by
B
eEL
kT
=1.54. Even for two magnets, approaching the same pole
near same one, this repulsive force may stem not from magnetic one but from electric
levitation due to diaelectric effects of permanent magnets where the magnetic field and
resultant Lorentz force is always perpendicular. The attractive force between different poles
may be originated from normal electric susceptibility regardless of distances because the
electric response is not for external field but for internal field.
7
Acknowledgment
This work is conducted under the research grant of Kwangwoon University (2023).
References
[1] Schrieffer, J. R. Theory of Superconductivity, (Benjamin, 1964).
[2] Bardeen, J; Cooper, L. N.; Schrieffer, J. R., Theory of Superconductivity,
Phys. Rev. 1957, 108, 1175-1204.
[3] Geim, A. K.; Simon, M. D., Diamagnetic levitation: Flying frogs and floating magnets, J.
Appl. Phys. 2000, 87, 6200-6204 .
[4] Geim, A. K.; Simon, M. D.; Boamfa, M. I.; Heflinger, L. O., Magnet levitation at your
fingertips, Nature (London) 1999, 400, 323-324.
[5] Koo, J. H., Negative electric susceptibility and magnetism from translational invariance
and rotational invariance, J. Magn. Magn.Mater. 2015, 375, 106-110.
[6] Hubler, A., Are there any diaelectric materials?, Complexity 2013, 18, 8-10,
[7] Koo, J. H., Diaelectric material as permanent magnet: frog levitation from magnet, J.
Magn. Magn.Mater. 2022, 551, 169130.
8
Fig. 1. Orbital motion in the presence of a magnetic field
H
and an electric field
E
.
9
Fig. 2. Anti-electric phenomena are explained by image charge concepts.
10
0 2 4 6 8 10
-0.25
-0.2
-0.15
-0.1
-0.05
0
dielelctric constant [arbitrary unit]
x=eEL/(kBT)
at minimum(x=1.54)
Fig.3. Diaelectric susceptibility from negative slope and normal restoring attractive one
from positive slope is given where a specific structural factor is given by
1.54
B
eEL
kT=
and
:sample sizeL
is changed into the distance between superconductor and permanent magnet.
