Twofold symmetry of c-axis resistivity in topological kagome superconductor CsV3Sb5 with in-plane rotating magnetic field

In transition metal compounds, due to the interplay of charge, spin, lattice and orbital degrees of freedom, many intertwined orders exist with close energies. One of the commonly observed states is the so-called nematic electron state, which breaks the in-plane rotational symmetry. This nematic state appears in cuprates, iron-based superconductor, etc. Nematicity may coexist, affect, cooperate or compete with other orders. Here we show the anisotropic in-plane electronic state and superconductivity in a recently discovered kagome metal CsV3Sb5 by measuring c-axis resistivity with the in-plane rotation of magnetic field. We observe a twofold symmetry of superconductivity in the superconducting state and a unique in-plane nematic electronic state in normal state when rotating the in-plane magnetic field. Interestingly these two orders are orthogonal to each other in terms of the field direction of the minimum resistivity. Our results shed new light in understanding non-trivial physical properties of CsV3Sb5.

Eigenvalues of energy in j (l + 1/2, l ‐ 1/2) electron state in the hydrogen atom derived from the relativistically modified Schrödinger equation

In the hydrogen atom, the eigenvalues of energy in j (l + 1/2, l ‐ 1/2) electron state cannot be correctly evaluated from the nonrelativistic Schrödinger equation. In order to express the relativistic properties of the wave equation for a particle with 1/2 spin, the Schrödinger equation is relativistically modified. The modified Schrödinger equation is solved for consistency with the eigenvalues of electron's energy derived from the Dirac equation. Based on the consistency of their eigenvalues, the different electron state is expressed. The microwave emission (e.g., 21 cm radio wave) by the hydrogen atom was thus predicted from this state.

Optical coherence transfer mediated by free electrons

We theoretically investigate the quantum-coherence properties of the cathodoluminescence (CL) emission produced by a temporally modulated electron beam. Specifically, we consider the quantum-optical correlations of CL produced by electrons that are previously shaped by a laser field. Our main prediction is the presence of phase correlations between the emitted CL field and the electron-modulating laser, even though the emission intensity and spectral profile are independent of the electron state. In addition, the coherence of the CL field extends to harmonics of the laser frequency. Since electron beams can be focused to below 1 Å, their ability to transfer optical coherence could enable the ultra-precise excitation, manipulation, and spectrally resolved probing of nanoscale quantum systems.

Phase Transformations, Magnetic Susceptibility and NEXAFS-Spectra of Cobalt-Doped Solid Solutions of Bismuth Orthoniobate

The electron state and the nature of the exchange interactions of cobalt atoms in BiNb1-xСoxO4-δ solid solutions of triclinic and orthorhombic modifications were studied using the magnetic susceptibility and NEXAFS-spectroscopy. In order to determine the electronic state of cobalt atoms, the solid solutions and oxides of cobalt CoO, Co3O4 were studied by NEXAFS-spectroscopy. The X-ray spectroscopy and the study of the magnetic susceptibility of the solid solutions revealed the presence of the monomers and exchange-related clusters of cobalt with the Co(II) and Co(III) charge states characterized mostly by the antiferromagnetic type of exchange. The cobalt containing solid solutions allowed us to confirm the reversibility of the α↔β-BiNbO4 phase transformation