This analysis provides an in-depth evaluation of theoretical and experimental pathways to achieving room-temperature superconductivity (RTS). Our focus is on leveraging physical methods to enhance the superconducting transition temperature (Tc) in high-temperature superconductors (HTSC). Drawing upon the Bose condensate framework and the translational-invariant (TI) bipolaron theory, we explore mechanisms underpinning the superconducting state and its dynamics. Detailed derivations, expanded calculations, and theoretical discussions highlight the path forward for practical applications of RTS.

Superconductivity, characterised by zero electrical resistance and the expulsion of magnetic fields (Meissner effect), has immense potential for revolutionising energy transmission, quantum computing, and material science. The current challenge lies in achieving room-temperature superconductivity. Traditionally, Tc improvements have relied on chemical modifications of materials. This report delves into physical mechanisms for enhancing Tc, focusing on Bose-Einstein condensates (BEC) of TI bipolarons. By reanalysing existing theoretical models, we identify pathways for elevating Tc through the dynamic behaviour of superconducting phases under specific external conditions.

Theoretical Framework

Superfluidity and Superconductivity

In 1941, L.D. Landau proposed the two-fluid model to describe superfluidity in helium II, presenting an alternative to earlier theories by F. London and L. Tisza. London and Tisza associated superfluidity with Bose-Einstein condensation (BEC). N.N. Bogoliubov subsequently bridged these perspectives by describing a weakly interacting Bose gas, reproducing the phonon-roton spectrum of Landau’s model. Bogoliubov demonstrated that the superfluid component arises as a condensate of Bose particles.

For superconductivity, however, the scenario differed. The Bardeen-Cooper-Schrieffer (BCS) theory established that electron pairs (Cooper pairs) are responsible for superconducting currents in conventional metals. Unlike the Bose particles in superfluidity, Cooper pairs in metals exhibit significant overlap, making them unsuitable as classical Bose particles.

The breakthrough in high-temperature superconductivity (HTSC) reshaped this understanding. In HTSC materials, the correlation length of paired states is much smaller, aligning more closely with the properties of Bose particles. This realisation reinforced the notion that superfluidity and superconductivity are related phenomena.

TI Bipolaron Spectrum (Bose Condensate of TI Bipolarons)

The translational-invariant (TI) bipolaron theory posits that bipolarons, formed by the coupling of electrons via phonon interactions, act as the fundamental bosons responsible for HTSC. Their energy spectrum is defined as and characterised by:

• : Bipolaron wave vector,

• : Effective mass of a bipolaron, derived from the band electron mass ,

• : Optical phonon frequency.

The ground state energy corresponds to, yielding . This spectrum mirrors the roton spectrum observed in superfluid helium II, underscoring the conceptual overlap between superfluidity and HTSC.

We adopt the TI bipolaron spectrum to describe the fundamental boson responsible for HTSC.

At present, two primary theories attempt to explain the pairing mechanism responsible for HTSC:

1. Electron-Phonon Interaction (BCS-like Mechanism): This theory extends the BCS framework, suggesting that electron-phonon interactions induce pairing in HTSC materials.

2. Magnetic Fluctuations: An alternative theory posits that pairing in HTSC arises from magnetic interactions, rather than phonons.

Without delving into the debate between these viewpoints, we adopt the translation-invariant (TI) bipolaron theory to describe the fundamental bosons responsible for HTSC.

Translation-Invariant Bipolaron Theory

The TI bipolaron model provides a framework for understanding HTSC. In this model, bipolarons\u2014pairs of electrons coupled via phonon interactions\u2014serve as the primary bosons. The spectrum of these TI bipolarons is described by the following equation:

E(k) =2.718 K k^2/2M + ^hw0,

where:

• k: Wave vector of the bipolaron,

• M = 2m : Effective mass of the bipolaron, derived from the band electron mass m ,

• ^hw0 [\hbar\omega_0] : Optical phonon frequency.

In this context, the ground state of the TI bipolaron corresponds to k = 0, yielding ^E(0) = ^hw0. This spectrum aligns closely with the roton spectrum in superfluid helium II, reinforcing the parallels between superfluidity and superconductivity.

Implications for Room-Temperature Superconductivity

By leveraging the TI bipolaron framework, it becomes possible to enhance T_c through physical activation of the Bose condensate. Specifically:

1. Subsurface Layer Motion: The superconducting phase involves a dynamic Bose condensate in the subsurface layer. This motion can be influenced by external magnetic fields or alternating currents, potentially increasing T_c in this region.

2. Bulk Condensate Activation: The bulk condensate, which remains motionless under standard conditions, represents a significant untapped potential. Activating this condensate\u2014for example, through alternating magnetic fields or thermal gradients\u2014could dramatically enhance T_c , possibly achieving room-temperature superconductivity.

This analysis highlights the potential for physical methods to achieve room-temperature superconductivity in HTSC materials. By activating motionless Bose condensates and leveraging the TI bipolaron model, researchers can unlock new pathways for enhancing T_c . These insights provide a theoretical foundation for experimental efforts aimed at realising superconductivity at ambient conditions, heralding a new era in material science and technology.

nonZero Temperature

Now let us consider the case of a nonzero temperature T < T c, where Tc is the temperature of the superconducting transition. In this case some bipolarons are in the excited state. Being in the excited state, a bipolaron can interact with other excitations and defects of the crystal. As a result of such an interaction, the gas of excited states, being in equilibrium with the lattice rests as a whole relative to the lattice. At the same time the excitation gas cannot restrain the condensate part since it cannot exchange momentum with it. As a result, the distribution function of all TI bipolarons in the system of motionless Bose-condensate will have the form: m(k) = N0△(k)+[exp(𝜀(k)+ku)/T)-1]^-1,

Where 𝜀(k) is the spectrum of excited states of a TI bipolaron. The formula (4) takes into account that in the reference system in question concerned with the Bose condensate, the excitation gas moves relative to it together with the lattice at a velocity of: -u . Substitution of (1), (4) into (2) yields the following value of the total momentum P’ of excitations in the system of motionless condensate:

P = - M u N ; N / V = (MT / 2πh^2)^3/2 F3/2 (ധ0 / T), ; F3/2 (α) = 2/√π f x/e^x+α - 1 dx ; ധ0 = ധ0 - Mu^2 / 2,

Where V is the crystal volume, N’ = N - N0. Hence, the total momentum of all the TI bipolarons in the laboratory reference system, i.e. in the system related to the crystal lattice will be equal to: P = (N - N’)Mbpu = N0Mbpu.

Expressions (6)-(8) suggest that there is a limiting velocity of the motion of Bose condensate u<uc, uc = √2ധ/M. It follows that the temperature of the superconducting transition Tc (which results from (6) for: N’ = N) depends on the motion velocity of the Bose condensate and reaches maximum for u = 0. As the condensate velocity increases, Tc decreases and reaches its minimum: Tc = 3,31 n^2/3 h^2 / M , for u = uc.

What will happen if the motion velocity of the Bose condensate exceeds its critical velocity, i.e. the inequality u >uc is satisfied? The integral in (7) in this case does not exist and the steady-state motion appears to be impossible. For P>Pc = N0 Mbp uc the momentum of excitations starts to be transferred to the condensate restraining it till the condensate velocity becomes equal to uc.

Now let us consider the case when the sample is placed in a magnetic field. In view of Meissner effect, the magnetic field sets in motion the Bose condensate at the subsurface layer of the sample whose thickness is of the order of London penetration depth. Hence, the velocity u in a sample in a magnetic field appears to be distributed heterogeneously. Since the magnetic field does not penetrate into the sample, the main mass of the Bose condensate occurring in the sample will be motionless, playing the role of a kind of a ‘dark matter’. It follows that Tc in the subsurface layer differs greatly from that in the bulk of the sample. It follows that Tc in the subsurface layer differs greatly from that in the bulk of the sample. Thus, for example, for the bipolaron concentration nbp ≈ 2 . 10^20 cm^-3, m = m0 - electron mass in vacuum; ധ0 = 50 mev, according to (6)-(8), the critical temperature in the bulk of the sample (corresponding to ധ0(u = 0) = 50 mev) as compared to its surface value (corresponding to ധ0(u = uc) = 0) turns out to be nearly three-fold higher. For superconductors with Tc ≈ 100 K, involvement of the bulk part of the Bose condensate into the motion can three-fold enhance Tc, i.e. exceed the room temperature. This phenomenon was probably realised by S.C. Pais10. With this aim Pais used an alternating magnetic field which deteriorates the surface superconductor layer and an alternating current which sets the bulk Bose condensate in motion.

At temperatures below the superconducting transition temperature , some bipolarons occupy excited states. These excited bipolarons interact with crystal defects and phonons, forming an equilibrium excitation gas that remains stationary relative to the lattice. Importantly, the excitation gas does not impede the motion of the condensate, which continues independently.

Critical Velocity and Temperature Dependence

The motion of a Bose condensate is characterised by a critical velocity (u_c), beyond which superconductivity cannot be maintained. This critical velocity is defined as: uc = √2hw0 / m, where M is the bipolaron mass, and \omega_0 is the optical phonon frequency.

The superconducting transition temperature (Tc) depends on the velocity of the condensate (u}). When u = 0, ^Tc reaches its maximum value. As u increases, Tc decreases steadily, eventually reaching a point of divergence at uc. Beyond this critical velocity, momentum transfer causes instability in the condensate, making steady-state superconductivity unattainable. The critical temperature T_c is related to the bipolaron density (n) as follows: Tc = 3h^2 / kB (π^2 n / M)^2/3.

For a typical bipolaron density of πbp ≈ 2 x 10^20 cm ^-3, and an optical phonon frequency hw0 = 50 meV, the bulk condensate can be activated using alternating magnetic fields, leading to a threefold increase in Tc. This enhancement can potentially push the critical temperature beyond room temperature, a significant milestone for practical superconductivity.

Effects of Magnetic Fields

When exposed to a magnetic field, the Meissner effect drives motion in the subsurface layer of the Bose condensate. The velocity within this layer is distributed heterogeneously, while the bulk of the condensate remains motionless. This immobile bulk acts as a "dark matter" component, playing a critical role in the system’s overall superconducting properties.

The differences in velocity between the subsurface and bulk layers lead to significant variations in their respective critical temperatures. For instance, in a system where Tc ≈ 100K, activating the bulk condensate via alternating magnetic fields or currents can elevate Tc well beyond room temperature. By overcoming limitations of the surface layer, this activation unlocks the bulk condensate’s latent potential, significantly enhancing the overall superconducting performance.

Conclusion

The behaviour of translation-invariant (TI) bipolarons in a Bose condensate provides valuable insights into the mechanisms underlying high-temperature superconductivity (HTSC). Through the strategic activation of bulk condensates using external fields, researchers can achieve substantial increases in the critical temperature (T_c), potentially reaching room-temperature superconductivity. This study offers a foundational framework for advancing experimental techniques and unlocking new practical applications for superconducting materials.

References

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