Recent advances in the theory of superconductivity

James F. Annett, S. P. Kruchinin

Li-Wei He, Shun-Li Yu, Jianxin Li

Abstract The kagome lattice, with its unique geometric structure, has emerged as a leading platform for exploring quantum many-body physics, particularly in the study of quantum spin liquids (QSLs) and unconventional superconductivity. This review highlights recent advancements in the investigations of QSLs, fractional magnetization plateau phases in kagome antiferromagnets, and unconventional superconductivity in vanadium-based kagome superconductors. We begin by examining the classical ground-state properties of the nearest-neighbor kagome antiferromagnetic Heisenberg model and introducing recent experimental progress in the study of QSLs and fractional magnetization plateau phases. Next, we discuss the fermionic description of the QSL states, along with related gauge theory and the variational Monte Carlo (VMC) method. We then focus on discussing the VMC studies of QSLs and magnetization plateau phases in kagome antiferromagnets. For superconductivity in kagome systems, we first analyze the characteristics of the electronic structure and the possible associated electronic instabilities. Finally, we review recent experimental advances in unconventional superconductivity in AV 3 Sb 5 (A = K, Rb, Cs), with a particular focus on chiral superconductivity and pairing density waves.

P. Mikheenko

With the advance of superconducting quantum computing and the attempts of extending its operating range to higher temperatures, a special attention is paid to nanostructured quantum circuits. In particular, quasi one-dimensional quantum wires with phase slip centers are argued to be promising structures for the next generation of quantum computers. In its turn, this stimulates revisiting the question about the possibility of quantum processing of information in quasi one-dimensional structures in the nervous system, specifically the brain, in living organisms, especially in the light of recent findings that suggest robust room-temperature superconductivity in these structures. The early theories of superconductivity were in favor of its quasi one-dimensional nature, and the recent findings suggest that reducing dimensions of a system could be a good approach for increasing the critical temperature of a material. Here, based on experimental data, it is argued that both room-temperature superconductivity and quantum processing of information are possible in the microtubules that are abundant in the nervous system and form the scaffolding of every cell in advanced living organisms. The origin of superconductivity in microtubules, and the way in which quantum processing of information may take place in them, are discussed. The role of Josephson oscillations in processing and exchange of information is emphasized.

Alexandre M. Zagoskin

Subhojit Halder, Kinjal A. Chauhan, Muhamad Bagher Barfar +2 more

This chapter explores the foundational concepts underlying superconducting qubits, pivotal in modern quantum computing. It begins with the harmonic oscillator, fundamental to both classical and quantum mechanics. Section 2.1 introduces its classical and quantum descriptions, emphasizing energy quantization and assessing its potential as a qubit. Section 2.2 focuses on the quantum LC oscillator, integral to superconducting circuit theory. Starting with the classical dynamics of an LC circuit, we derive its Hamiltonian and transition to its quantum description using ladder operators. This section bridges classical circuit theory and quantum systems, paving the way to understanding superconducting qubits. Sections 2.3–2.5 examine key qubit types. Section 2.3 introduces phase, charge, and flux qubits, highlighting their operational principles and the physical parameters they encode, such as magnetic flux or electric charge. Section 2.4 delves into the transmon qubit, exploring its Hamiltonians and methods for control and measurement. Finally, Section 2.5 surveys recent advancements in superconducting qubit designs, offering insights into the evolution toward next-generation qubits. This chapter provides a comprehensive framework for understanding superconducting qubits, linking classical systems to quantum technologies, and contextualizing their role in advancing quantum computation.

Alexandre M. Zagoskin