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1. Energy-scale considerations of unconventional superconductors—implications to condensation and pairing

   https://doi.org/10.1016/j.physc.2023.1354361  

   Uemura, Yasutomo J. (November 2023, Physica C: Superconductivity and its Applications)

   Keller, Hugo; Bussmann-Holder, Annette; Deutscher, Guy; Lorenzana, José; Malozemoff, Alexis P.; Mihailovic, Dragan; Chu, Ching W (Ed.)

   Part of Special Issue: Oxide superconductors and beyond - In memoriam of Professor Karl Alex Müller, Abstract: Discovery of high-Tc cuprate superconductors (HTSC) in 1986 by Bednorz and Muller, followed by synthesis of A3C60, iron-pnictides/chalcogenides and other exotic superconducting (SC) systems, introduced unconventional superconductors (UCSC) having their mechanisms of condensation and/or pairing distinctly different from those of simpler metals which can be explained by BCS theory. This article will show how one can demonstrate their new mechanisms by examining correlations among key energy-scale parameters, including the transition temperature Tc, the superfluid density ns/m*, the effective Fermi energy εF, the excitation energy of the magnetic resonance mode (MRM), the onset temperatures of Nernst effect and light-induced transient superconductivity, and the spin fluctuation energy scale ℏωsf, and by resorting to analogy / comparisons with superfluid 4He as a representative system undergoing Bose Einstein Condensation (BEC). We will propose a paring mechanism in HTSC based on resonance of spin (ℏωsf) and charge (εF) energy scales, and apply that concept for explaining unusual behaviors in the overdoped region. We will also discuss modifications of a simple BEC-BCS crossover picture to account for actual situations with additional effects of competing order and phase separation. 

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2. Vortex structure and spectrum of an atomic Fermi superfluid in a spherical bubble trap

   https://doi.org/10.1103/PhysRevA.108.053303  

   He, Yan; Chien, Chih-Chun (November 2023, Physical Review A)

   The structures of multiply quantized vortices (MQVs) of an equal-population atomic Fermi superfluid in a rotating spherical bubble trap approximated as a thin shell are analyzed by solving the Bogoliubov-de Gennes (BdG) equation throughout the BCS-Bose Einstein condensation (BEC) crossover. Consistent with the Poincare-Hopf theorem, a pair of vortices emerge at the poles of the rotation axis in the presence of azimuthal symmetry, and the compact geometry provides confinement for the MQVs. While the single-vorticity vortex structure is similar to that in a planar geometry, higher-vorticity vortices exhibit interesting phenomena at the vortex center, such as a density peak due to accumulation of a normal Fermi gas and reversed circulation of current due to in-gap states carrying angular momentum, in the BCS regime but not the BEC regime because of the subtle relations between the order parameter and density. The energy spectrum shows the number of the in-gap state branches corresponds to the vorticity of a vortex, and an explanation based on a topological correspondence is provided. 

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3. Structure and scaling of Kitaev chain across a quantum critical point in real space

   https://doi.org/10.1088/1361-648X/ad64a0  

   He, Yan; Chien, Chih-Chun (July 2024, Journal of Physics: Condensed Matter)

   Abstract The spatial Kibble–Zurek mechanism is applied to the Kitaev chain with inhomogeneous pairing interactions that vanish in half of the lattice and result in a quantum critical point separating the superfluid and normal-gas phases in real space. The weakly-interacting BCS theory predicts scaling behavior of the penetration of the pair wavefunction into the normal-gas region different from conventional power-law results due to the non-analytic dependence of the BCS order parameter on the interaction. The Bogoliubov–de Gennes (BdG) equation produces numerical results confirming the scaling behavior and hints complications in the strong-interaction regime. The limiting case of the step-function quench reveals the dominance of the BCS coherence length in absence of additional length scale. Furthermore, the energy spectrum and wavefunctions from the BdG equation show abundant in-gap states from the normal-gas region in addition to the topological edge states. 

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4. Bose polarons near quantum criticality

   https://doi.org/10.1126/science.aax5850  

   Yan, Zoe Z.; Ni, Yiqi; Robens, Carsten; Zwierlein, Martin W. (April 2020, Science)

   The emergence of quasiparticles in interacting matter represents one of the cornerstones of modern physics. However, in the vicinity of a quantum critical point, the existence of quasiparticles comes under question. Here, we created Bose polarons near quantum criticality by immersing atomic impurities in a Bose-Einstein condensate (BEC) with near-resonant interactions. Using radiofrequency spectroscopy, we probed the energy, spectral width, and short-range correlations of the impurities as a function of temperature. Far below the superfluid critical temperature, the impurities formed well-defined quasiparticles. Their inverse lifetime, given by their spectral width, increased linearly with temperature at the so-called Planckian scale, consistent with quantum critical behavior. Close to the BEC critical temperature, the spectral width exceeded the impurity’s binding energy, signaling a breakdown of the quasiparticle picture. 

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5. Fractionalized conductivity and emergent self-duality near topological phase transitions

   https://doi.org/10.1038/s41467-021-25707-z  

   Wang, Yan-Cheng; Cheng, Meng; Witczak-Krempa, William; Meng, Zi Yang (December 2021, Nature Communications)

   Abstract The experimental discovery of the fractional Hall conductivity in two-dimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange statistics. These anyons are usually studied deep inside an insulating topological phase. It is natural to ask whether such fractionalization can be detected more broadly, say near a phase transition from a conventional to a topological phase. To answer this question, we study a strongly correlated quantum phase transition between a topological state, called a $${{\mathbb{Z}}}_{2}$$ Z 2 quantum spin liquid, and a conventional superfluid using large-scale quantum Monte Carlo simulations. Our results show that the universal conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. Moreover, a dynamically self-dual optical conductivity emerges at low temperatures above the transition point, indicating the presence of the elusive vison particles. Our study opens the door for the experimental detection of anyons in a broader regime, and has ramifications in the study of quantum materials, programmable quantum simulators, and ultra-cold atomic gases. In the latter case, we discuss the feasibility of measurements in optical lattices using current techniques. 

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