Summary of Superconductor Pb 10-x Cu x PO 4 6 O

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A new superconductor, LK-99?, has been created using the solid-state method and demonstrates levitation.

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Superconductivity and Levitation: Exploring LK-99?

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Introduction

• A superconductor called LK-99? has been synthesized using the solid-state method.

• The composition of LK-99? is (Pb 10-x Cu x (PO 4 ) 6 O).

• LK-99? exhibits the levitation phenomenon.

Enhanced Zero-Resistivity Region

• The zero-resistivity region of LK-99? is approximately three times larger than in low Tc superconductors.

• Phonon vibrations may contribute to the noise observed in this region.

Visual: Graph showing the zero-resistivity region comparison

Hexagonal Structure of Sample 1

• Sample 1 of LK-99? has a hexagonal structure.

• The lattice parameters are a=9.843 A and c=7.428 A.

Visual: Crystal structure diagram of LK-99?

Higher Tc Temperature

• Sample 1 of LK-99? exhibits a maximum Tc of 127?C.

• This indicates a higher Tc than previously observed.

Visual: Phase diagram showing the Tc temperature

Stabilizing Structure

• The superconductor's structure is stabilized by lone-pair electrons in Pb and bonds with Cu2+.

• This leads to a hole-driven insulator-to-metal transition.

Visual: Illustration of the stabilizing structure

Verifying Superconductivity

• Levitation phenomenon confirms the presence of superconductivity in LK-99?.

• Analysis of the material further supports its superconducting properties.

Visual: Image or video demonstrating levitation

Unveiling the Potential of LK-99?

• LK-99? is a promising superconductor with unique properties.

• Its enhanced zero-resistivity region and higher Tc temperature make it a valuable material for further exploration.

• Let's harness the potential of LK-99? for various applications in the field of superconductivity.

Key Points

A superconductor called LK-99? has been synthesized with the composition (Pb 10-x Cu x (PO 4 ) 6 O) using the solid-state method.
The superconductor exhibits the levitation phenomenon and has a higher zero-resistivity region compared to low Tc superconductors.
Sample 1 of the superconductor has a hexagonal structure with lattice parameters of a=9.843 A and c=7.428 A.
The superconductor has a maximum Tc of 127°C, indicating a higher Tc than that.
The structure of the superconductor is stabilized by the presence of lone-pair electrons in Pb and the formation of bonds with Cu2+.

Summaries

14 word summary

A new superconductor, LK-99?, has been synthesized using the solid-state method. It exhibits levitation.

32 word summary

A superconductor called LK-99?, with the composition (Pb 10-x Cu x (PO 4 ) 6 O), has been synthesized using the solid-state method. The material exhibits the levitation phenomenon of a supercon

227 word summary

A superconductor called LK-99?, with the composition (Pb 10-x Cu x (PO 4 ) 6 O), has been synthesized using the solid-state method. The material exhibits the levitation phenomenon of a supercon

The XRD analysis of sample 1 confirms that it has a hexagonal structure with lattice parameters of a=9.843 A and c=7.428 A. The volume of the sample shrinks by 0.48% due to the

The superconductor Pb10-xCuxPO46O exhibits a zero-resistivity region that is approximately three times larger than typical values observed in low Tc superconductors. The presence of noise in this region is attributed to phonon vibrations

Fig. 6(e) shows that sample 1 has a maximum Tc of 127°C, indicating that Tc is higher than that. Above Tc, the material exhibits the linear characteristic of a metal. The phase diagram in Fig.

The structure of the superconductor Pb10-xCuxPO46O is stabilized by the presence of lone-pair electrons in Pb and the formation of bonds with Cu2+. This leads to a hole-driven insulator-to-metal transition, resulting in

The MLA structure of the superconductor Pb10-xCuxPO46O exhibits both one-dimensional characteristics and a Tc above room temperature at atmospheric pressure. The presence of superconductivity was confirmed through observations of the levitation phenomenon and analysis of

In a study by Ishida et al., hidden structural and superconducting phases were observed in the antiperovskite arsenide SrPd3As. Crystal structures of lead oxide phosphates, including Pb4O(PO4)2

Raw indexed text (33,846 chars / 5,575 words / 440 lines)

https://arxiv.org/abs/2307.12037

Superconductor Pb 10-x Cu x (PO 4 ) 6 O showing levitation at room temperature and

atmospheric pressure and mechanism

Sukbae Lee, 1,a) Jihoon Kim, 1 Hyun-Tak Kim, 2,3,b) Sungyeon Im, 1 SooMin An, 1 and Keun Ho Auh 1,4

Quantum Energy Research Centre, Inc., Seoul 05822, South Korea

ICT Basic Research Lab. ETRI, Daejeon 34129, South Korea

Department of Physics, College of William & Mary, Williamsburg, VA 23185, USA

Hanyang University, Seoul 04763, South Korea

a)Author to whom correspondence should be addressed : [email protected]

b)Author to whom correspondence should be addressed : [email protected], [email protected]

Abstract

A material called LK-99®, a modified-lead apatite crystal structure with the composition (Pb 10-x Cu x (PO 4 ) 6 O

(0.9

characteristic of Pb(6s1) above its superconducting critical temperature, T c , and the levitation phenomenon

as Meissner effect of a superconductor at room temperature and atmospheric pressure below T c . A LK-99®

sample shows T c above 126.85℃ (400K). We analyze that the possibility of room-temperature

superconductivity in this material is attributed to two factors: the first being the volume contraction resulting

from an insulator-metal transition achieved by substituting Pb with Cu, and the second being on-site

repulsive Coulomb interaction enhanced by the structural deformation in the one-dimensional(D) chain

(Pb2−O 1/2 −Pb2 along the c-axis) structure owing to superconducting condensation at T c . The mechanism of

the room-temperature T c is discussed by 1-D BR-BCS theory.

I. INTRODUCTION

For over 110 years since Onnes's 1911 discovery of superconductivity, scientists have searched for

room-temperature superconductors, materials that exhibit zero resistance to electrical current.

Superconductors have been discovered in various metal elements and compound crystals. In 1986,

a cuprate superconductor with a superconducting critical temperature, T c , over 40 K was found. 1,2

In 2015, a hydride of H 2 S was shown to demonstrate T c  203 K at a pressure of 155 GPa. 3 In

2023, a T c of 294 K at 10 kbar was measured on a nitrogen-doped lutetium hydride; 4 moreover, a

superconductor [LK-99 ® ] of over T c =300K was successfully synthesized (language: Korean). 5

1https://arxiv.org/abs/2307.12037

BCS(Bardeen-Cooper-Schrieffer) theory, which provides a microscopic explanation of

superconductivity, was introduced in 1957. 6 The Brinkman-Rice(BR)-BCS theory accounting for

T c of over room temperature was discovered in 2021. 7 Moreover, in 2021, a theory was published

that predicts T c as approximately 10% of Fermi temperature. 8 In addition, whether the pairing

symmetry of the superconducting energy gap in cuprate superconductors is d-wave or s-wave has

been debated for over 30 years; recent studies suggest that it may lean towards s-wave

symmetry. 9,10,11

To discover a room-temperature superconductor, observing the emergence of a metallic phase

through an insulator-to-metal transition (IMT) at temperatures higher than room temperature is

crucial. 12,13 Moreover, to explain this phenomenon, the discovery of a new material that exhibits

room-temperature superconductivity at atmospheric pressure, along with a comprehensive

mechanism, is required.

In this paper, we present a synthesis method for a Cu-doped lead apatite (LA) superconductor with

a Tc exceeding room temperature. We conduct levitation experiments and analyze the zero

resistance properties of the material. Moreover, we unveil the mechanism by which the metal phase

is formed through an insulator-to-metal transition (IMT) without undergoing a structural phase

transition in LA. Furthermore, we provide a phase diagram for the superconductor. Finally, we

briefly discuss the mechanism of room-temperature superconductivity based on the BR-BCS

theory 7 .

II. RESULTS and DISCUSSIONS

A. LK-99 ® : Synthesis

For sample manufacture, we synthesized Pb 10-x Cu x (PO 4 ) 6 O (0.9

the solid-state method. The raw materials used in the synthesis were PbO (Junsei, GR), PbSO 4

(Kanto, GR), Cu (Daejung, EP), and P (Junsei, EP). 5 The solid-state method is explained in Fig. 1.

The process of sample synthesis comprises three steps. Step 1: To obtain Lanarkite Pb 2 (SO 4 )O =

PbO + Pb(SO 4 ), PbO and Pb(SO 4 ) powders were uniformly mixed in a ceramic crucible with a

rate of 50% each. The mixed powder was heated in a furnace at 725°C for 24 hours in the presence

of air [Fig. 1(b)]. During the heating process, the mixed materials underwent a chemical reaction,

2https://arxiv.org/abs/2307.12037

yielding lanarkite. Step 2: To synthesize Cu 3 P, Cu and P powders were mixed in a crucible as per

each component rate. The mixed powder was sealed in a crystal tube of 20 cm per gram with a

vacuum of 10 -3 torr [Fig. 1(a)]. The sealed tube containing the mixed materials was heated in a

furnace at 550°C for 48 hours [Fig. 1(c)]. During this process, the mixed materials underwent a

transformation and formed Cu 3 P crystals. Step 3: The Lanarkite and the Cu 3 P crystals were ground

to make powder and mixed in a crucible. Then, the mixed powders were sealed in a crystal tube of

a vacuum of 10 -3 torr [Fig. 1(a)]. The sealed tube containing the mixed powder was heated in a

furnace at 925°C for 5-20 hours [Fig. 1(d)]. During this process, the mixed powder reacted and

transformed into the final material of Pb 10-x Cu x (PO 4 ) 6 O. The sulfur element present in PbSO 4 was

evaporated during the reaction. The various shapes observed during the process are depicted in

photos [Figs. 1(e-i)].

FIG.1. (a) Layout of sealed vacuum crystal tube with mixed power. (b), (c), (d) Heat treatment conditions

of Lanarkite, Cu 3 P, Pb 10-x Cu x (PO 4 )O (0.9

reaction, appearing white to light gray. (f) Picture of the sealed sample after the reaction, (g) Sample

removal procedure from the furnace, (h) A shape of the sample of the sealed quartz tube, (i) A sample shape

in each process.

3https://arxiv.org/abs/2307.12037

B. LK-99 ® : Analysis of crystal structure

The manufactured powder’s crystallinity and structure were analyzed by X-ray diffraction (XRD)

measurements and data fitting. Fig. 2(a) shows a comparison of XRD data measured with LK-99 ®

sample 1 (over-doped material) and COD (Crystallography Open Database) data of the pure lead-

apatite supported by QualX software. The XRD analysis of the sample showed multiple black

peaks [Fig. 2(a)], indicating that it is a polycrystalline material. The XRD pattern of sample 1

closely matches that of modified-lead apatite (MLA) with slight peak shifts. However, the peak

indicated by symbol A in sample 1 is shifted to a larger angle, and a new peak, indicated by symbol

B, appears, suggesting a change in the lattice structure of sample 1, [Fig. 2(b)]. The shifts indicate

a decrease of lattice constant, which is interpreted as evidence of volume contraction. Comparing

the XRD pattern of sample 1 with MLA in the VESTA program confirms that sample 1 exhibits

an MLA structure, [Fig. 2(c)]. Specifically, an LA structure is formed as A 10 (BO 4 )C, one of the

frameworks of the hexagonal structure of element A. 14,15

4https://arxiv.org/abs/2307.12037

FIG. 2. (a) Comparison of XRD pattern measured with sample 1 and lead apatite data in Crystallography

Open Database. (b) Magnified pattern shows a peak shift and a new peak. (c) The XRD pattern is compared

with the modified apatite pattern obtained from BESTA program. It is closely fitted.

The XRD analysis reveals that sample 1 has a hexagonal structure of (P63/m, 176) with cell lattice

parameters of a=9.843 Å and c=7.428 Å [Figs. 3(a) and 3(b)], while the LA’s parameters are

a=9.865 Å and c=7.431 Å. The volume of sample 1 shrinks by 0.48%, resulting from substituting

Pb(M2) with Cu(M1). The phenomenon of shrinkage has already been studied in previous research

on apatite materials. 16 Although it is classified as an LA structure, Pb 10 (PO 4 ) 6 O, is an insulator;

conversely, Cu-doped LA, Pb 10-x Cu x (PO 4 ) 6 O, is a superconductor at room temperature and a metal

above T c . Moreover, it is structurally condensed by substituting M1 2+ (corresponding to Pb1 2+ , at

Pb(1) position in LA atomic classification in crystallography information file, cif.) at the black-

colored position in Figs. 3(a) and 3(b) by Cu 2+ ion (M2 2+ , one reddish-brown-colored among four

5https://arxiv.org/abs/2307.12037

Pb(1) positions in Fig. 3(a)). Owing to the shrinkage, it becomes a superconductor. 7 Further details

will be explained in a following section.

FIG. 3. (a) Top view of Cu-doped LA, Pb 10-x Cu x (PO 4 ) 6 O, to c-axis. Inside, hexagonal six M1s

corresponding to Pb2s (2 indicates the number of classifications of Pb(2) in cif.) are folded by two layers

composed of Pb 3 O 1/2 expressed as a triangle, [Fig. 3(b)]. (b) Side view of the Cu-doped LA. 1 unit cell is

also displayed. (c) In the superconducting state, layout to explain a one-dimensional superconducting chain

along the c-axis. The CDW is the charge-density-wave and V CDW <0 is the CDW potential. V Sup <0 is a

potential containing the superconducting carrier. 7 U c > 0 is the critical on-site repulsive Coulomb energy in

the BR picture. 17 This was re-drawn with Fig. 4 in Ref. 5.

C. LK-99 ® : Meissner effect

Figures 4(a) and 4(b) illustrate the temperature-dependent diamagnetic susceptibilities of zero-

6https://arxiv.org/abs/2307.12037

field cool (ZFC) and field cool (FC) in sample 2 (obtained in a quartz vessel with low doping of

lead apatite) and sample 3 (manufactured using higher-purity raw materials). The measurements

were conducted in a temperature range of -73.15℃(200K) to 126.85℃(400K) and involved the

observation of the Meissner effect, expelling the magnetic field. Fig. 4(c) shows the levitation

phenomenon measured at room temperature and atmospheric pressure for sample 4 (heat-treated

with sample 2), indicating the presence of a superconducting phase at room temperature and

atmospheric pressure, although the levitation is not perfect. Video of the levitation is attached as

Fig. 4(d). The susceptibilities were measured for samples 2 and 3 using MPMS-Evercool at Kaist

Analysis center for Research Advancement.

7https://arxiv.org/abs/2307.12037

FIG. 4. (a) Temperature dependence of diamagnetic susceptibilities measured in samples 2 (a) and 3 (b).

attached.

8https://arxiv.org/abs/2307.12037

D. LK-99 ® : Resistivity

Figure 5 shows the temperature dependence of the resistivity of sample 2 (4.8  10.1  1.2mm)

measured at 30 mA by the four-probe method. A jump in resistivity appears near T c =104.8℃

(377.95K). Above T c , the linear characteristic of metal originating from the IMT is displayed.

Below T c , three different behaviors are exhibited. In the first region below red-arrow C (near 60 o C),

equivalent to region F in the inset of Fig. 5, the resistivity with noise signals can be regarded as

zero. In the second region, indicated by the red arrows C and D (near 90 o C) and corresponding to

region G in the inset of Fig. 5, the resistivity of the sample monotonically increases with

temperature. This indicates the occurrence of resistance, suggesting a breakdown of the

superconducting energy gap as the temperature increases. At the third region between red-arrow

D and T c , corresponding to region H in the inset of Fig. 5, the resistivity does not transparently

change with increasing temperature; however, d  /dT fluctuates at the final stage of the breakdown

of the energy gap. In the first region, where signals resembling noise are observed, the zero-

resistivity region is approximately 88% (333K/378K) of T c under Kelvin units. This is

approximately three times larger than the typical value of about 30% observed in low T c

superconductors. The presence of noise in the zero-resistivity region is often attributed to phonon

vibrations at higher temperatures, as indicated by region F in inset 5; the signals like noise were

directly measured 5 . The presence of the zero-resistivity region is evidence of an s-wave

superconductor because a node-type superconductor with no-gap metal at node, such as d x 2 -y 2

pairing symmetry has no zero-resistivity region due to increase of metal resistivity with increasing

temperature. 10,11

9https://arxiv.org/abs/2307.12037

FIG. 5. Temperature dependence of resistivity. Inset shows d  /dT=d(1/resistivity)/dT, regarded as the

density of states (DOS). The temperature dependence of d  /dT is interpreted as that of DOS. Resistivity

figure was re-drawn with Fig. 6(a) in Ref. 5.

E. LK-99 ® : I-V characteristics

Figure 6(a) shows the temperature dependence of an I-V curve measured in sample 1. Above T c ,

the linear characteristic of a metal is displayed. As the temperature increases, T c, current decreases.

Moreover, the magnitude of the jump of T c, current decreases with increasing current. In particular,

at 105 o C, the jump is very small. This indicates that the magnitude of the jump does not

monotonically decrease. This is known as exponential decrease in a gap-nogap transition

material. 18 We conducted a detailed analysis of the current-voltage (I-V) curve below T c, current ,

measured at 25°C, focusing on the logarithmic y-axis. The curve can be divided into several

regions: I, J, K, L, M, and N. In regions I, J, and K, we observe an increase in resistance, indicating

the breaking of the superconducting energy gap due to Joule heating when the current exceeds a

certain threshold. The curve is obvious, as indicated by red-arrow O in an I-V curve measured at

10https://arxiv.org/abs/2307.12037

45 o C. More high current of region L accelerates the breaking, which can be interpreted as an

avalanche region. At region M of much higher current, voltage does not almost change. This

indicates that the density of states (DOS)=dI/dV is constant near T c, current , suggesting that the

pairing symmetry is s-wave, [Figs. 6(b) and 6(c)]. If the superconducting gap has a node, dI/dV

near T c, current should increase. 오류 !

책갈피가 정의되어 있지 않습니다 .

After the jump, region N is a metal with

the linear Ohmic characteristic. The transition between the superconducting gap and the nogap

metal is the gap-nogap transition [Fig. 6(a)]. The transition is almost identical to the characteristic

of the IMT. 19,20 Moreover, the fluctuation of regions I, J, and K, [Fig. 6(c)], is owing to temperature

inhomogeneity caused by Joule heat generated by both current and heat applied by the temperature

controller. Fig. 6(d) shows the magnetic field dependence of sample 1. Above the jump of T c , the

I-V curve exhibits Ohmic characteristics, indicating a metallic behavior. As the magnetic field

increases, T c, current , decreases, exhibiting the typical characteristic of a superconductor. Fig. 6(e)

exhibits a maximum T c of 127 o C in heat-treated sample 1. Because the jump remains, we deduce

that T c exceeds 127 o C. Above T c , the linear characteristic of a metal is displayed. A summary of

the results is shown in the phase diagram [Fig. 7].

11https://arxiv.org/abs/2307.12037

FIG. 6. (a) The temperature dependence of an I-V y-axis log curve, obtained through a method measuring

voltage with applying current. (b) Differential curve of data at 25 o C. (c) DOS = d  /dI, the derivative curve

of conductance. dI=1mA is constant. Regions I, J, K and M present the characteristic of s-wave symmetry.

(d) Magnetic field dependence of I-V curves. (e) 127 o C is a temperature below a T c owing to temperature

limitation of the measurement system.

12https://arxiv.org/abs/2307.12037

FIG. 7. Phase diagram of Cu 2+ -doped LA Pb 10-x Cu x (PO 4 ) 6 O. IMT is the insulator-to-metal transition and

MIT is the metal-to-insulator transition. IMT and MIT follow the same concepts, indicating a gap-nogap

transition. IST is an insulator-superconductor transition (gap-gap transition), indicating a change of electric

characteristics in the same gap structure.

III. POSSIBLE MECHANISM OF SUPERCONDUCTIVITY

A . LK-99 ® : One-dimensional metal

The mother material of the LA structure, as shown in Fig. 3, is disassembled by the following

chemical formula,

Pb 10 (PO 4 ) 6 O  [Pb1 4 ] F [Pb2 6 ] T (PO 4 ) 6 O

= [Pb1 4 (PO 4 ) 8/3 ] F + [Pb2 6 (PO 4 ) 10/3 O] T ,

= [Pb1 4 (PO 4 ) 8/3 ] F + [Pb2 3 (PO 4 ) 5/3 O 1/2 + Pb2 3 (PO 4 ) 5/3 O 1/2 ] T ,

= [Pb1 4 (PO 4 ) (2+2/3) ] F + [Pb2 3 (PO 4 ) (1+2/3) O 1/2 + Pb2 3 (PO 4 ) (1+2/3) O 1/2 ] T , ---- (1)

where F names the frame part and T denotes a part of the tunnel along the c-axis. This highly stable

structure consists of two layers of frames with an interior region. 21 , 22 , 23 Formula (1) is

characterized by a one-dimensional bonding of Pb2 and O 1/2 in the T part. When parts of the Pb1

(meaning the Pb(1) site in LA cif.) and the Pb2 (meaning the Pb(2) position in LA cif.) sites are

13https://arxiv.org/abs/2307.12037

randomly substituted by Cu 2+ (3d 9 ) (one hole) elements, chemical formula of the Cu 2+ -doped LA

structure is expressed as follows:

Pb 10-x Cu x (PO 4 ) 6 O = [Pb 4-a Cu a (PO 4 ) 8/3 ] F + [Pb 6-b Cu b (PO 4 ) 10/3 O] T , where a+b=x

= [Pb 4-a Cu a (PO 4 ) 8/3 ] F + [Pb 3-c Cu c (PO 4 ) 5/3 O 1/2 + Pb 3-c Cu c (PO 4 ) 5/3 O 1/2 ] T , where c=b/2, a and b 0

= [Pb 4-a Cu a (PO 4 ) (2+2/3) ] F + [Pb 3-c Cu c (PO 4 ) (1+2/3) O 1/2 + Pb 3-c Cu c (PO 4 ) (1+2/3) O 1/2 ] T . ---- (2)

Hole doping quantities are determined as the outmost orbitals of -3a (=2(4-a)+(-1)a+(-3)(2+2/3))

in the frame part and -3c (=2(3-c)+(-1)c+(-3)(1+2/3)+(-2)(1/2)) in the T part. When IMT occurs

by Cu 2+ doping, IMT is generated at both the F and the T parts. Generally, because an insulator

has a larger volume than that of a metal, the IMT is accompanied by a volume contraction without

the structural phase transition. The substitutions at the Pb1 sites, as indicated by the reddish-brown

color in Fig. 3(a), induce a volume contraction(1 st ) in the frame through the IMT(1 st ). 16 Moreover,

substitutions at the Pb2 sites lead to an IMT(2 nd ) in the T part. The evidence of the volume

contraction is shown in Fig. 2(b). If the doping quantities of a and c in formula (2) differ, the extent

of the IMT and the magnitude of volume contraction may vary. If a>c, below a critical doping

level, the volume contraction(1 st ) in the frame may be larger than the volume contraction(2 nd ) in

the T part.

The outmost orbital of Pb is 6s 2 6p 2 . One electron in the 6p 2 orbital of Pb2 is coupled to the O of

PbO, whereas the other contributes to the bonding of tetrahedral phosphate, PO 4 , [formulas (1) and

(2)]. Consequently, the inside structure is stabilized. Lone-pair electrons of 6s 2 in Pb play an

important role on the phase transition; the 6s 2 electrons are spherically symmetric and displaced

structure relative to the position of Pb atoms and contributing to polar interaction,. 23 Moreover,

Cu 2+ can form a bond with one of lone-pair electrons of 6s 2 in Pb2, transforming the outmost

orbital of Pb2 to 6s 1 . Therefore, 𝑃𝑏 1−𝑥

𝐶𝑢 𝑥+2 O ([2 electrons of 6s 2 ] + [one hole of 3d 9 ] = 6s 1 after

combining of electron and hole as polar interaction) at a Pb2 site acquires the electronic structure

of metal of half filling, 6s 1 . This is referred to as the hole-driven insulator-to-metal transition

(IMT). 19,20,24 Hence, Pb 3 (O 1/2 = O 1/4 + O 1/4 ) structures are generated and the oxygen is located at

slightly higher or slightly lower position than Pb2, [blue balls in red dot box in Fig. 3(b)]. The

nearest two oxygens (blue balls) at the O 1/4 position in O 1/2 of 1-D channel, as shown in the red-

14https://arxiv.org/abs/2307.12037

dot box of unit cell of Fig. 3b, are generally repulsive. In metal case, when one oxygen of the O 1/4

vibrates (the distance between Pb2 and O 1/4 expands and contracts), the other anti-vibrates (the

distance contracts and expands, respectively). This indicates that oxygen breathes; the distance

between Pb2and O 1/4 is same. One unit cell has two Pb 3 O 1/2 structures [Fig. 3(b)]. In the metal

state, the Pb2(6s 1 ) carrier flows through the conduction band formed by Pb2−Pb2 and oxygens in

the Pb2 (in lower Pb 3 O 1/2 ) −> O 1/2 −> Pb2 (in higher Pb 3 O 1/2 ) structure breath along c-axis, [Fig.

3(c)]. In the superconducting state, carriers of Pb2(6s 1 )s at nearest neighbor sites form a bi-polaron

in a superconducting bound state (V Super potential = V CDW potential + U c, critical on-site Coulomb energy ), where

charge-density-wave state (CDW) has the structure of long and short distances in (Pb2-O 1/4 or Pb2-

O 1/2 ) between nearest neighbor Pb sites formed by breathing mode distortion (stopping breath)

between oxygens in the Pb 3 O 1/2 structures). Then, the distance between Pb2and O 1/4 differs, which

is the structural distortion and the on-site Coulomb interaction, U, between carriers in metal is

changed to U c . The formation of the superconducting bound state is facilitated by the enhanced

on-site Coulomb repulsive interaction, resulting from both the structural contraction (1st) at the

frame of the LA induced by Cu 2+ doping and the structural distortion accompanied by volume

contraction (2nd) owing to the temperature difference (∆T = T IMT - T c ) at T c . These factors

contribute to superconducting condensation, as depicted in the phase diagram shown in Fig. 7. 7

The bi-polaron is able to tunnel through a barrier between two Pb3O1/2 structures in a one-

dimensional chain along the c-axis, where the Pb2 in the lower Pb3O 1/2 is connected to O 1/2 and to

Pb2 in the higher Pb 3 O 1/2 (as shown in Figure 3(c)). Additionally, the first term of the frame part

in formula (2) can exhibit superconductivity owing to the IMT; however, because it is not one-

dimensional, its Tc will be much smaller compared to that of the T part in Formula (2). The

underlying reasons for this behavior will be further explained in the subsequent section.

B. LK-99 ® : Strong correlation

As for a room-temperature-T c mechanism, the MLA structure inducing the IMT is characterized

by volume contractions(1 st and 2 nd ) by substituting Pb with Cu. A known theory to explain room-

temperature superconductivity, including structural volume contraction, is BR-BCS, suggesting

that divergence of the DOS, caused by on-site Coulomb repulsive interaction U increased by

15https://arxiv.org/abs/2307.12037

volume contraction, increases superconducting T c over room temperature in the BR-BCS T c . 7,25

When dimensionality is considered, 1-dimension(D) DOS is proportional to (m * /E * ) 0.5 with the

divergence to  , where an effective mass of carrier, m*m/[1-(U/U c ) 2 ]=m/[1-  4  2 ], and kinetic

energy, E * E k (1-U/U c ) 2 =E k (1-  2  ) 2 , U/U c =  2  with percolation to increasing  as a function of

doping x and correlation strength   1(1) generating the maximum number of excited carriers, 17

band-filling factor 0<  1 are defined. 7 The effective 2D-DOS * =2D-DOS (non-interaction_BCS) /[1-  4  2 ]

with the divergence to  is given because of 2D-DOS *  m * . 3D-DOS *  (m * ) 1.5 (E * ) 0.5 has the

divergence to  . 1D-DOS * =1D-DOS (non-interaction_BCS) /[(1-  4  2 ) 0.5 (1-  2  )] where   1(1). 1D-

DOS * is larger than 2D-DOS * and 3D-DOS * in the same condition. When 1D-DOS * =N * (0) is

applied to electron-phonon coupling  *  N * (0)V=A  BCS in the BCS-T c formula, where A=1/[(1-

 4  2 ) 0.5 (1-  2  )] and V is the attractive electron-phonon potential and is known as about 0.2 eV 26 ,

T c will increase above room temperature when  approaches one, on the basis of the BR-BCS T c 7 .

The BR-BCS theory uses a bi-polaron strongly coupled by the attractive charge-density-wave

potential (short-range electron-phonon interaction), instead of the Cooper pair defined as coupling

of excited two electrons bound by the attractive screened long-range electron-phonon (atom)

interaction. 7,26 Moreover, the general mechanism of superconductivity in the Fermi system with

strong repulsive interaction explained in the 2D system that superconducting T c reaches about 10%

of Fermi temperature (if T Fermi  10,000 K is assumed), 8 although this mechanism is not involved

in volume contraction. The theory of hole superconductivity suggested much higher T c than that

proposed in BCS theory. 24 In addition, one-dimensional superconductivity and T c enhancement

were already disclosed. 27,28,29,30

IV. CONCLUSION

We have successfully developed a method for synthesizing a superconducting material with an

MLA structure, exhibiting both one-dimensional characteristics and a T c above room temperature

at atmospheric pressure. The presence of superconductivity was confirmed through observations

of the levitation phenomenon and analysis of zero resistivity. The unique features of the MLA

structure include volume contraction (1 st ) resulting from substituting Pb with Cu. On-site Coulomb

repulsive interaction increased by volume contractions(1 st and 2 nd ) may cause the superconducting

16https://arxiv.org/abs/2307.12037

phenomenon, as mentioned in the BR-BCS theory. Furthermore, the room-temperature

superconductor opens up possibilities for high-performance superconducting wires and magnets

operating at room temperature, with potential applications in energy transmission, transportation,

and scientific research.

ACKNOWLEDGEMENTS

We acknowledge late Prof. Chair Tong-seek for initiating research of a 1-dimensional superconductor of

over room temperature at atmospheric pressure. In particular, his enthusiasm on superconductor study

impressed many researchers. Moreover, we thank Mr. Ki Se-woong, Mr. Lee Byungkyu (CEO of ProCell

Therapeutics, Inc.), Mr. Yoon Sang-ok (Chairman of FINE Inc.) so much for financial supporting, and Bang

Jaekyu and Kim Gyeongcheol so much for wholeheartedly sharing the burdens and difficulties in this

investigation. This research was primarily supported by research-and-development funds from Quantum

Energy Research Centre Inc.. SQUID measurements were supported by the National Research Foundation

of Korea grant funded by the Korea government(MSIT) (No. 2019R111A1A01059675) and Korea

University Grant (Projects of an author, Young-Wan, Kwon taking charge of SQUID measurements). We

thank Prof. Mumtaz Qazilbash for valuable comments. An author, Hyun-Tak Kim (H. T. Kim),’s knowledge

on mechanisms of both superconductivity and the metal-insulator (gap-nogap) transition highly contributed

to writing the mechanism part. The knowledge was acquired over 20 years by processes of performing

national projects including project [Grant 2017-0-00830] funded by Institute for Information and

Communications Technology Promotion (IITP) in MSIT of Korea government in ETRI. H. T. Kim left

ETRI on Nov. of 2022.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Sukbae, Lee:

Conceptualization(lead); Data curation(equal); Funding acquisition(lead);

Investigation(equal);

Methodology(equal);

Project

administration(lead);

Resources(equal);

Software(equal); Supervision(lead); Validation(equal); Visualization(support); Writing – original

draft(equal); Writing – review & editing(equal), Ji-hoon, Kim: Conceptualization(equal); Data

curation(equal); Formal analysis(equal); Investigation(equal); Methodology(equal); Project

administration(equal); Software(equal); Supervision(equal); Validation(equal); Visualization(equal),

Sungyeon, Im: Data curation(support); Funding acquisition(equal); Resources(equal); Supervision(equal);

Validation(equal)

SooMin,

An:

Data

curation(support);

Funding

acquisition(support);

Investigation(support); Project administration(support); Resources(support); Validation(support); Writing

– original draft(support); Keun Ho, Auh: Funding acquisition(support); Methodology(equal); Project

administration(support); Supervision(equal); Writing – original draft(lead). Hyun-Tak Kim analyzed s-

wave symmetry, and made room-tem.-T c mechanism including metal-insulator transition and CDW

structural distortion through structure analysis, wrote this manuscript with authors.

17https://arxiv.org/abs/2307.12037

DATA AVAILABILITY

The data that support this study are available from the corresponding authors upon reasonable request.

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