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1. Weyl Fermions and broken symmetry phases of laterally confined 3 He films

   https://doi.org/10.1088/1361-648X/acf42b  

   Wu, Hao ; Sauls, J. A. ( September 2023 , Journal of Physics: Condensed Matter)

   Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D)³He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum,$L_z=(N/2)\hslash$, for$N/2$Cooper pairs. The power law suppression of the angular momentum,$L_z(T)\simeq (N/2)\hslash [1-\frac{2}{3}(\pi T/\mathrm{\Delta }{)}^2]$for$0⩽T\ll T_c$, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid³He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry at$D_{c2}\sim 16{\xi }_0$. The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement length$D\to D_{c_2}$. The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral ‘polar phase’ at$D_{c1}\sim 9{\xi }_0$, in which a single p-wave orbital state of Cooper pairs is aligned along the channel.

    

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2. Optical spectral weight, phase stiffness, and T c bounds for trivial and topological flat band superconductors

   https://doi.org/10.1073/pnas.2106744118  

   Verma, Nishchhal ; Hazra, Tamaghna ; Randeria, Mohit ( August 2021 , Proceedings of the National Academy of Sciences)

   We present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat-band superconductors that lead to upper bounds for the superfluid stiffness and the two-dimensional (2D)$T_c$. We focus on on-site attraction$\left|U\right|$on the Lieb lattice with trivial flat bands and on the π-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weight${\tilde{D}}_{\text{low}}\le \tilde{n}\left|U\right|\mathrm{\Omega }/2$with$\tilde{n}=min\left(n,2-n\right)$, where n is the flat-band density and Ω is the Marzari–Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound for${\tilde{D}}_{low}$linear in$\left|U\right|$. We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte Carlo results.

    

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3. Effects of incipient pairing on nonequilibrium quasiparticle transport in Fermi liquids

   https://doi.org/10.1093/ptep/ptac027  

   Lin, Wei-Ting ; Sauls, J. A. ( February 2022 , Progress of Theoretical and Experimental Physics)

   The low-temperature properties of a wide range of many-fermion systems spanning metals, quantum gases and liquids to nuclear matter are well understood within the framework of Landau’s theory of Fermi liquids. The low-energy physics of these systems is governed by interacting fermionic quasiparticles with momenta and energies near a Fermi surface in momentum space. Nonequilibrium properties are described by a kinetic equation for the distribution function for quasiparticles proposed by Landau. Quasiparticle interactions with other quasiparticles, phonons, or impurities lead to internal forces acting on a distribution of nonequilibrium quasiparticles, as well as collision processes that ultimately limit the transport of mass, heat, charge, and magnetization, as well as limiting the coherence times of quasiparticles. For Fermi liquids that are close to a second-order phase transition, e.g., Fermi liquids that undergo a superfluid transition, incipient Cooper pairs—long-lived fluctuations of the ordered phase—provide a new channel for scattering quasiparticles, as well as corrections to internal forces acting on the distribution of nonequilibrium quasiparticles. We develop the theory of quasiparticle transport for Fermi liquids in the vicinity of a BCS-type superfluid transition starting from Keldysh’s field theory for nonequilibrium, strongly interacting fermions. The leading corrections to Fermi-liquid theory for nonequilibrium quasiparticle transport near a Cooper instability arise from the virtual emission and absorption of incipient Cooper pairs. Our theory is applicable to quasiparticle transport in superconductors, nuclear matter, and the low-temperature phases of liquid 3He. As an implementation of the theory we calculate the pairing-fluctuation corrections to the attenuation of zero sound in liquid 3He near the superfluid transition and demonstrate quantitative agreement with experimental results.

    

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4. Topological Nanomaterials

   https://doi.org/doi.org/10.1038/s41578-019-0113-4  

   Liu, Pengzi ; Williams, James ; Cha, Judy ( January 2019 , Nature reviews. Materials)

   The past decade has witnessed the emergence of a new frontier in condensed matter physics: topological materials with an electronic band structure belonging to a different topological class from that of ordinary insulators and metals. This non-trivial band topology gives rise to robust, spin-polarized electronic states with linear energy–momentum dispersion at the edge or surface of the materials. For topological materials to be useful in electronic devices, precise control and accurate detection of the topological states must be achieved in nanostructures, which can enhance the topological states because of their large surface-to-volume ratios. In this Review, we discuss notable synthesis and electron transport results of topological nanomaterials, from topological insulator nanoribbons and plates to topological crystalline insulator nanowires and Weyl and Dirac semimetal nanobelts. We also survey superconductivity in topological nanowires, a nanostructure platform that might enable the controlled creation of Majorana bound states for robust quantum computations. Two material systems that can host Majorana bound states are compared: spin–orbit coupled semiconducting nanowires and topological insulating nanowires, a focus of this Review. Finally, we consider the materials and measurement challenges that must be overcome before topological nanomaterials can be used in next-generation electronic devices. 

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5. Two superconducting states with broken time-reversal symmetry in FeSe 1−x S x

   https://doi.org/10.1073/pnas.2208276120  

   Matsuura, Kohei ; Roppongi, Masaki ; Qiu, Mingwei ; Sheng, Qi ; Cai, Yipeng ; Yamakawa, Kohtaro ; Guguchia, Zurab ; Day, Ryan P. ; Kojima, Kenji M. ; Damascelli, Andrea ; et al ( May 2023 , Proceedings of the National Academy of Sciences)

   Iron-chalcogenide superconductors FeSe_1−xS_xpossess unique electronic properties such as nonmagnetic nematic order and its quantum critical point. The nature of superconductivity with such nematicity is important for understanding the mechanism of unconventional superconductivity. A recent theory suggested the possible emergence of a fundamentally new class of superconductivity with the so-called Bogoliubov Fermi surfaces (BFSs) in this system. However, such an ultranodal pair state requires broken time-reversal symmetry (TRS) in the superconducting state, which has not been observed experimentally. Here, we report muon spin relaxation (μSR) measurements in FeSe_1−xS_xsuperconductors for0≤x≤0.22covering both orthorhombic (nematic) and tetragonal phases. We find that the zero-field muon relaxation rate is enhanced below the superconducting transition temperatureT_cfor all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transverse-fieldμSR measurements reveal that the superfluid density shows an unexpected and substantial reduction in the tetragonal phase (x>0.17). This implies that a significant fraction of electrons remain unpaired in the zero-temperature limit, which cannot be explained by the known unconventional superconducting states with point or line nodes. The TRS breaking and the suppressed superfluid density in the tetragonal phase, together with the reported enhanced zero-energy excitations, are consistent with the ultranodal pair state with BFSs. The present results reveal two different superconducting states with broken TRS separated by the nematic critical point in FeSe_1−xS_x, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity.

    

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