Pulsed tunnel effect: new perspectives for controlling superconducting devices

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Quantum nature of electrical resistance

The quantum nature of electrical resistance can be described as follows.

1. Electrical resistance at the quantum level is caused by the scattering of electrons on various defects and inhomogeneities in the conductor:

• Scattering on phonons (vibrations of the crystal lattice);
• Scattering on impurities and defects in the crystal structure;
• Scattering on grain boundaries and surfaces.

2. Quantization of electronic states in the conductor leads to the discreteness of electrical resistance values. This is manifested in the quantum Hall effect and the Klitzing quantum resistance:

• Quantum Hall effect – quantization of Hall resistance in two-dimensional electron systems at low temperatures and strong magnetic fields;
• Klitzing quantum resistance – the fundamental resistance value of ℏ/e² ≈ 25.812 kΩ, observed in quantum point contacts.

3. Tunnel resistance at the boundaries of a super-conductor-normal metal (Josephson effect) also has a quantum nature, determined by the laws of quantum mechanics.
4. In nanostructures and molecular conductors, quan-tum size effects play a key role in the formation of electrical resistance.

Thus, the quantum nature of electrical resistance is manifested in the discreteness of electronic states, tunnel processes, and size effects that determine the transport properties of materials on micro- and nanoscales.

Quantum effects have a significant impact on the con-ductivity in nanostructures. The main mechanisms by which the quantum nature of materials manifests itself in electronic transport on the nanometer scale are.

1. Quantization of energy states. In nanostructures, the dimensions are comparable to the electron wavelength, leading to the quantization of energy states. This changes the density of electronic states and affects transport properties, such as electrical conductivity.
2. Ballistic transport. In very small structures, the electron mean free path can exceed the device size. This leads to a ballistic transport regime, where electrons move without scattering, significantly increasing the conductivity.
3. Tunnel effects. Quantum tunneling of electrons through potential barriers becomes possible in nanometer-scale structures. This effect is used, for example, in tunnel transistors, where the current is controlled by the tunnel barrier.
4. Coulomb blockade. In very small structures (quantum dots, single-electron transistors), adding or removing a single electron can significantly change the electrical properties. This is a mani-festation of the discreteness of electric charge on the nanometer scale.
5. Size effects. Reducing the size of structures down to the nanometer scale leads to the dominance of quantum size effects. This affects the density of electronic states, charge carrier mobility, and other transport characteristics.

Thus, quantum effects in nanostructures radically change their electrical properties and open up possibilities for the creation of new nanoelectronic devices.

From the modern perspective of quantum mechanics, an exciton can be characterized as follows.

1. Quasiparticle. An exciton is a quasiparticle con-sisting of a bound electron-hole pair, which is created as a result of photon absorption in a semiconductor or dielectric.
2. Electron-hole pair. The absorption of a photon leads to the excitation of an electron from the valence band to the conduction band, leaving behind a hole in the valence band. The electron and hole are bound by Coulomb attraction, forming an exciton.
3. Bound state. An exciton is a bound state of an electron and a hole, analogous to a hydrogen-like atom, where the electron and proton are bound by Coulomb interaction.
4. Energy levels. An exciton has discrete energy levels, similar to atomic levels, determined by its size and the masses of its constituent particles.
5. Exciton motion. An exciton can move through the crystal lattice of the material, preserving its bound state, similar to the motion of neutral particles.
6. Impact on optical properties. The formation of exci-tons affects the optical properties of the material, manifesting as excitonic absorption or emission peaks.
7. Applications. Excitons play an important role in the processes of light absorption and emission in semiconductors and dielectric materials used in optoelectronics and photonics.

Thus, from the perspective of modern quantum mechanics, an exciton is a bound state of an electron-hole pair, possessing quasiparticle properties and influencing the optical characteristics of materials.

However, it is important to note that an exciton is more of a theoretical model for describing certain processes, rather than a physically real particle. The main arguments in favor of this view are.

1. Holes are not physical particles. As mentioned, holes do not move as real particles, but rather represent the absence of an electron in the valence band, which creates the appearance of its motion.
2. Electron-hole pair. The exciton is described as a bound electron-hole pair, but in reality, this is simply a description of the redistribution of electrons upon excitation, not a real particle.
3. Quasiparticle. The exciton, like other quasiparticles (phonons, polarons, etc.), is a conceptual model for the convenient description of collective excitations, but not a physical particle.
4. Energy levels. Although the exciton has discrete energy levels, like an atom, this is more a conse-quence of the quantization of energy in the crystal lattice, rather than a property of a real particle.

Thus, the exciton is a useful theoretical model for de-scribing optical and electronic processes in semiconductors and dielectrics, but not a physical reality in the literal sense. The motion of holes is simply a convenient concept for explaining the observed phenomena.

In bismuth superconductors, excitons may play an important role in the mechanism of superconductivity, although their exact role is still being actively studied and is the subject of scientific debate. Here is how excitons can be described in this context.

1. Exciton generation. When bismuth compounds are cooled to superconducting temperatures, the ex-citation of electrons in the conducting bands leads to the formation of bound electron-hole pairs, i.e. excitons.
2. Exciton condensation. It is hypothesized that these excitons can condense into a coherent quantum state, similar to the Bose-Einstein condensate. This state of exciton condensation may contribute to the emergence of superconductivity.
3. Role in electron pairing. The interaction between excitons and electrons can lead to an effective attraction between electrons, which facilitates the formation of Cooper pairs – the basis of the superconducting state.
4. Effect on the energy spectrum. The presence of ex-citons can modify the energy spectrum of electrons near the Fermi level, creating conditions favorable for superconductivity.
5. Coupling with other collective excitations. Excitons can interact with other quasiparticles such as phonons, and these complex interactions may also play a role in the mechanism of superconductivity. Thus, although the exact role of excitons in the su-perconductivity of bismuth compounds is not completely clear, they are considered an important element that can contribute to the formation and stabilization of the superconducting state in these materials. Further studies will help to clarify their specific mechanism of action.

The interaction of excitons and phonons plays an important role in the mechanism of superconductivity in bismuth compounds.

1. Interaction of excitons and phonons. Excitons can interact with the vibrations of the crystal lattice, that is, with phonons. This interaction can lead to the scattering of excitons by phonons and to changes in the energy spectrum of excitons. Such interaction of excitons and phonons can contribute to the formation of Cooper pairs – the basis of the superconducting state.
2. Phonons with optimal energy. To achieve the maxi-mum temperature of the superconducting transition in bismuth compounds, the most effective pho-nons are those with energies corresponding to the cha-racteristic vibrational energies of the crystal lattice. In bismuth superconductors, these characteristic phonon energies lie in the range of ~10 to ~30 meV, which corresponds to de Broglie wavelengths of phonons of approximately 0.2 to 0.6 nanometers. It is precisely the phonons in this energy range that can most effectively interact with excitons and contribute to the formation of Cooper pairs, thereby providing the maximum temperature of the superconducting transition.

Thus, the interaction of excitons with phonons having energies on the order of 10–30 meV (de Broglie wavelengths of about 0.2–0.6 nm) is an important factor influencing the mechanism of high-temperature superconductivity in bismuth compounds. This type of interaction promotes the effective formation of Cooper pairs and the stabilization of the superconducting state.

There is a series of experiments that confirm the important role of excitons in the mechanism of superconductivity in bismuth compounds.

1. Optical spectroscopy. Experiments using optical spectroscopy show the presence of intense absorption and emission bands associated with the excitation of excitons in bismuth superconductors. These optical properties are directly related to the strong electron-hole interaction, leading to the formation of excitonic states.
2. Tunneling spectroscopy. Studies using tunneling spectroscopy reveal features of the electronic density of states characteristic of the excitonic mechanism of superconductivity. Peaks in the density of states are observed, corresponding to the binding energies of excitons.
3. Heat capacity measurements. Anomalies in the tem-perature dependence of the heat capacity near the transition temperature to the superconducting state indicate the important role of collective excitations, such as excitons. These heat capacity anomalies are associated with phase transitions caused by the condensation of excitons.
4. Anisotropy of superconducting properties. Strong anisotropy of the critical field and critical current in bismuth superconductors has been experimentally observed. Such anisotropy is consistent with the expected properties of a superconducting condensate consisting of excitonic pairs.

The combination of these experimental data suggests that excitonic states and their interaction with phonons play a key role in the mechanism of high-temperature superconductivity in bismuth compounds.

The interaction of excitons with phonons is an important mechanism that contributes to the formation of superconductivity in bismuth compounds. Let’s consider in more detail how this interaction occurs.

1. Generation of excitons by phonons:

• Thermal vibrations of the crystal lattice (phonons) can excite electronic transitions, leading to the formation of excitons;
• Phonons with the appropriate energy interact with electrons and holes, binding them into excitonic states.

2. Stabilization of excitons by phonons:

• The interaction of excitons with phonons helps to stabilize them, preventing the decay of exciton pairs;
• Phonons “dress” the excitons, forming quasiparticles known as polarons;
• Polarons are more stable against local fluctuations and destruction, increasing the likelihood of their condensation.

3. Exciton-phonon coupling:

• Strong electron-phonon interaction in bismuth compounds leads to the formation of bound states of excitons and phonons;
• These coupled exciton-phonon states promote efficient charge transport and provide a mechanism for superconducting pairing.

4. Condensation of exciton pairs:

• At sufficiently low temperatures, exciton pairs can condense into a coherent superconducting state;
• The presence of phonons modifies the energy spectrum of excitons and influences the conditions for their condensation.

Thus, the close interaction of excitons with phonons is a key aspect in the mechanism of high-temperature superconductivity in bismuth compounds. This interaction helps to stabilize excitonic states and creates favorable conditions for their condensation into a superconducting state.

Phonons play an important role in determining the critical temperature T_c of superconductivity in bismuth-based compounds. Here are the main mechanisms through which phonons influence the critical temperature.

1. Electron-phonon interaction. Strong electron-phonon coupling in bismuth-based compounds enhances the effective attraction between electrons. This effective attraction, mediated by phonons, promotes the formation of Cooper pairs and increases T_c.
2. Isotope effect. Substituting different isotopes of bismuth with varying masses leads to changes in the frequency of phonon modes. Alterations in phonon frequencies influence the electron-phonon interaction and, consequently, T_c. A sig-nificant isotope effect has been observed in bismuth-based superconductors, confirming the importance of phonons.
3. Anisotropy of phonon modes. The crystal structure of bismuth-based compounds results in a strong anisotropy in the phonon spectra. Certain phonon modes, especially in specific directions, may have anomalously high frequencies. This phonon anisotropy affects the effective density of states available for Cooper pair formation, and hence T_c.
4. Pressure effects. External pressure can modify phonon frequencies and the strength of the electron-phonon interaction. This can lead to a strong dependence of T_c on the applied pressure in bismuth-based superconductors.

Overall, the intimate connection between the electronic structure and phononic excitations in bismuth-based compounds makes phonons a key factor in determining the high critical temperatures of superconductivity in these materials.

Several experimental studies have been carried out on bismuth-based superconductors that confirm the important role of phonons in determining the critical temperature T_c of superconductivity:

1. Isotope effect. Replacing some bismuth isotopes with others changes the atomic mass, affecting the frequencies of phonon modes. Experiments have shown a significant isotopic shift of Tc in bismuth-based superconductors, indicating the important role of phonons.
2. Inelastic neutron scattering spectroscopy. This method allows direct measurement of phonon spectra in bismuth compounds. Experiments have revealed strong anisotropy of phonon modes, which is consistent with theoretical predictions. Anomalously high frequencies of some phonon modes explain the high Tc in these materials.
3. Angle-resolved photoemission spectroscopy (ARPES). ARPES allows mapping of the electronic structure and investigation of the electron-phonon interaction. ARPES experiments have revealed strong electron-phonon coupling in bismuth-based superconductors. The observed kinks in the disper-sion of electronic states are direct evidence of the ro-le of phonons.
4. Heat capacity measurements. Anomalies in the tem-perature dependence of heat capacity near T_c reflect the contribution of phonons to the formation of Cooper pairs. Experiments show that the phonon contribution to heat capacity is dominant in bismuth-based superconductors.

The totality of these experimental results convincingly confirms the key role of phonons in the formation of high critical temperatures of superconductivity in bismuth compounds.

Phonon mechanisms play a key role in determining the critical temperature of superconductors. Here are the main ways in which phonons affect T_c.

1. Electron-phonon interaction. In conventional BCS superconductors, such as elementary metals, electrons interact with crystal lattice vibrations (phonons), leading to the formation of Cooper pairs and superconductivity. The strength of the electron-phonon interaction determines the magnitude of the energy gap in the excitation spectrum and, consequently, affects T_c.
2. Isotope effect. Changing the mass of ions (e.g., by substituting isotopes) affects the frequency of phonon modes, which in turn affects T_c. The experimentally observed dependence of T_c on the isotope mass is evidence of the importance of phonon mechanisms.
3. Structural changes and phase transitions. Modifications to the crystal lattice structure, caused by doping or pressure, can change the frequencies of phonon modes and, consequently, the critical temperature. Phase transitions accompanied by structural changes can also affect the T_c of su-perconductors.
4. Phonon mode fluctuations. In some materials, especially in high-temperature superconductors, phonon mode fluctuations play an important role and can contribute to superconducting pairing.

Thus, a detailed understanding of the role of phonons is critical for explaining and predicting the critical temperatures of superconductors. Intensive research in this area continues to this day.

There are several examples of materials with anomalously high critical superconducting transition tem-peratures in which phonon mechanisms play a significant role.

1. Cuprate superconductors. For example, YBa₂Cu₃O₇ with a T_c around 92 K. In these mate-rials, strong electron-phonon interactions related to the vibrations of the copper-oxygen planes are observed. The role of phonons includes participation in the formation of Cooper pairs and modification of the electronic structure.
2. Iron-based superconductors. For example, compounds of the type LaFeAsO_{1 – x}F_x with T_c up to 55 K. Here, electron-phonon inter-actions, particularly those associated with the vibrations of the iron-arsenic layers, are also important. It is suggested that the enhancement of spin fluctuations by phonons plays a role in the superconducting mechanism.
3. Hydrogen-containing compounds under pressure. For example, the compound H₃S under a pressure of 155 GPa has a T_c around 203 K. In this case, the critical temperature is very high due to strong electron-phonon interactions with phonons associated with the vibrations of hydrogen atoms.
4. Magnesium diboride (MgB₂). T_c around 39 K. The superconductivity in this material is explained by two separate superconducting gaps, associated with different phonon modes.

Thus, in materials with high T_c, phonon vibrations and electron-phonon interactions play a key role, determining the superconducting properties. A detailed understanding of the role of phonons is an important task for the further development of superconducting electronics.

The Pulsed Tunnel Effect (PTE) can have a significant impact on the resistance and conductance in nanostructures.

1. Negative differential resistance. In the case of PTE, there can be situations where an increase in voltage leads to a decrease in current, which manifests as negative differential resistance. This occurs within certain voltage/current ranges, when electron tunneling becomes more probable. Regions with negative differential resistance can be used to create electronic switches, oscillators, and other nonlinear devices.
2. Current oscillations. Quantum effects in PTE can lead to periodic changes in current with a smooth change in voltage. This is related to the modulation of electron transmission through the tunnel barrier as the potential profile changes. Such current oscillations can be observed, for example, in resonant-tunneling diodes.
3. Impact on resistance. The presence of tunnel barriers in nanostructures significantly increases the device resistance. Under certain conditions, PTE can reduce the resistance, for instance, due to resonant tunneling. Thus, PTE allows for the dynamic control of the resistance in nanostructures.

In summary, the pulsed tunnel effect in nanostructures can induce nonlinear effects, such as negative diffe-rential resistance and current oscillations. This opens up opportunities for the creation of new types of nano-electronic devices with unique transport characteristics.

The Pulsed Tunnel Effect is indeed closely related to the large current spikes that occur when overcoming the accumulated energy barrier.

The role of phonons in PTE is very important.

1. Energy accumulation through polarization. Before tunneling, electrons accumulate potential energy, causing polarization of the structure. This occurs due to the interaction of electrons with lattice vibrations (phonons).
2. Initiation of tunneling. When the accumulated energy reaches a certain threshold, it can be released through a sudden tunneling of electrons through the barrier. The interaction of electrons with phonons plays a key role in this process, allowing electrons to overcome the barrier.
3. Role of phonons in oscillations. The periodic changes in current during PTE are also related to the dynamics of phonons. Fluctuations in the pho-non field modulate the potential profile, affecting the probability of tunneling.
4. Influence on resistance. Scattering of electrons on phonons contributes to the resistance of the de-vice. Changes in the phonon spectrum during PTE can lead to variations in resistance.

Thus, phonons play a crucial role in the accumulation of energy, the initiation of tunneling, as well as the formation of the dynamic characteristics of PTE, which affect the resistance. Understanding these mechanisms is crucial for the development of nanoelectronic devices utilizing the pulsed tunnel effect.

The pulsed tunnel effect has great potential for use in various fields of electronics and nanotechnology. Here are some of the most promising application areas of this phenomenon.

1. Nanoelectronics:

• High-speed and energy-efficient switches and logic elements;
• Pulse generators and ultra-fast clock signal generators;
• Microwave (RF) devices, such as oscillators and detectors.

2. Sensing:

• High-sensitivity sensors for magnetic field, pressure, acceleration;
• Detectors for single electrons and photons.

3. Quantum computing:

• Realization of qubits based on PTE structures;
• Fast and energy-efficient switches for quantum circuits.

4. Energy:

• Current sources based on the PTE effect;
• Energy converters at micro- and nanoscales.

5. Medical technology:

• Mini- and microimplants with low power con-sumption;
• Highly sensitive biosensors.

The key advantages of using PTE are high speed, low power consumption, scalability, and the ability to integrate with existing nanotechnology platforms. Active research and development of PTE-based devices are underway in many leading research centers around the world.

When implementing devices based on the Resonant Tunneling Effect (RTE), there are a number of significant technological challenges that need to be overcome.

1. Structural homogeneity control:

• Strict control of the nanostructure elements is critical to achieving stable and reproducible characteristics;
• Inhomogeneities in materials, defects, and impurities can significantly distort the potential barrier profile.

2. Precise parameter tuning:

• Effective utilization of RTE requires very precise tuning of geometric dimensions, barrier heights, and other parameters;
• Small variations in these parameters can lead to significant changes in performance cha-racteristics.

3. Scalability and integration:

• Developing arrays of RTE devices and integrating them with other circuit components is a complex technological challenge;
• High packing density and parameter uniformity across the integrated circuit scale must be ensured.

4. Ensuring stability:

• Reliability and longevity of RTE devices under the influence of the environment, temperature, electrical, and mechanical loads is a critical issue;
• Stabilization of characteristics requires careful design and materials engineering solutions.

5. Thermal effects management:

• The high current and power densities associated with RTE can lead to local overheating and thermal degradation;
• Effective heat dissipation methods and thermal management are of great importance.

Overcoming these technological barriers is a key task for the successful implementation of RTE devices in practical applications. Active efforts by scientists and engineers in the fields of nanoelectronics, materials science, and micro-/nanofabrication are directed at solving these challenges.

Pulsed Tunneling Effect can be used to improve characteristics and expand application areas of super-conducting devices. Here are several examples of such applications.

1. Superconducting switches and logic elements. PTE structures can be integrated into superconducting circuits to realize fast and energy-efficient switches. This will enable the creation of ultra-high-speed superconducting digital devices.
2. Superconducting generators and amplifiers. The combination of PTE and superconducting materials can lead to the creation of ultra-fast and low-noise generators, amplifiers, and pulse generators. Such devices will find applications in microwave electronics, radar, and quantum computing.
3. Superconducting sensors. PTE structures integrated into superconducting sensors can significantly improve their sensitivity and speed. This is relevant for sensors of magnetic fields, single particles, gravitational waves, and other physical quantities.
4. Cryogenic electronics. Using PTE in cryogenic conditions at ultra-low temperatures can provide additional advantages in the form of more stable parameters and higher switching speeds. Such developments are important for quantum computing and other cryogenic systems.

The key factor for successful application of PTE in superconducting devices is the joint optimization of materials, design, and manufacturing technology. Active research in this direction is being carried out in leading scientific centers around the world.

The ability of the Pulsed Tunneling Effect to accumulate energy through interaction with phonons is a key advantage for application in superconducting devices.

Here’s a more detailed overview of how this works.

1. Phonons in superconductors. In superconducting materials, especially at cryogenic temperatures, there is a significant amount of phonons – quasiparticles associated with crystal lattice vibrations. These phonons play an important role in the mechanism of superconductivity, binding electrons into Cooper pairs.
2. Accumulation of phonon energy in PTE. Due to the specifics of tunneling in PTE structures, the energy of phonons can be effectively accu-mulated in such systems. Upon resonant excitation of the PTE, the energy of phonons accumulates, creating a non-equilibrium phonon subsystem.
3. Application for superconducting devices. This accumulated phonon energy can be beneficially used to control and improve the efficiency of superconducting elements. For example, it can be used for dynamic tuning of the parameters of superconducting switches, amplifiers, or sensors. This will allow increasing the speed, sensitivity, and energy efficiency of such devices.

Thus, the ability of PTE to interact with the phonon subsystem is a key advantage that opens up wide opportunities for improving the characteristics of super-conducting electronics. Research in this direction is one of the important trends in the field of superconducting technologies.

In addition to the pulsed tunnel effect, there are several other mechanisms that can improve the efficiency and characteristics of superconducting devices.

1. Dynamic control of the superconducting transition. PTE can be used for dynamic tuning of the critical current and transition temperature between the su-perconducting and normal metal states. This will allow adaptive control of the operating modes of superconducting elements, increasing their speed and energy efficiency.
2. Utilization of the proximity effect. By combining superconducting and normal metals in hybrid structures, the proximity effect can be leveraged. This allows modifying the properties of super-conductors, for example, by reducing critical cur-rents or transition temperatures. In combination with PTE, this provides additional opportunities for controlling the characteristics of devices.
3. Quantum interference effects. Quantum interference phenomena, sensitive to external influen-ces, manifest in superconducting rings and interferometers. Using PTE, these quantum effects can be effectively controlled, which is important for sensor and logic superconducting circuits.
4. Interaction with magnetic materials. By combi-ning superconductors with ferromagnetic or anti-ferromagnetic materials, spintronic effects can be realized. Together with PTE, this will enable the creation of highly sensitive superconducting spintronic devices.

Thus, the comprehensive use of PTE combined with other physical mechanisms opens up broad possibilities for improving the efficiency, speed, and functionality of next-generation superconducting electronics.

About the authors

Rustam Kh. Rakhimov

Author for correspondence.
Email: rustam-shsul@yandex.com
ORCID iD: 0000-0001-6964-9260
SPIN-code: 3026-2619

Dr. Sci. (Eng.), Head, Laboratory No. 1

References

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