A remarkable reduction in electronic conductivity in the core region rather than on the surface of secondary particles is proposed as a capacity-fading mechanism of a Ni-rich cathode. This result is confirmed by analyzing the electronic conductivity of the secondary particles of Li[Ni 0.98 Co 0.01 Mn 0.01 ]-O 2 using the scanning spreading resistance microscopy (SSRM) mode of atomic force microscopy. SSRM analysis reveals that a much thicker rocksalt phase, which is transformed from the original layered structure, on the surface of the primary particles in the core region electronically insulates the entire volume of the primary particles from the neighboring particles. Li intercalation−deintercalation is not achievable in the electronically insulated primary particles. Thus, visualization of the local electronic conductivity in the secondary particles confirms that the loss of electronic conductivity in the core region of the secondary particle is a key factor in the capacity fading of a Ni-rich cathode for lithium ion batteries.

We show that we can realize the surface state together with the bulk state of various types of topological matters in holographic context, by considering various types of Lorentz symmetry breaking. The fermion spectral functions in the presence of order show features like the gap, pseudo-gap, flat disk bands and the Fermi-arc connecting the two Dirac cones, which are familiar in Weyl and Dirac materials or Kondo lattice. Many of above features are associated with the zero modes whose presence is tied with a discrete symmetry of the interaction and these zero modes are associated with the surface states. Some of the order parameters in the bulk theory do not have an interpretation of symmetry breaking in terms of the boundary space, which opens the possibility of ‘an order without symmetry breaking’. We also pointed out that the spectrum of the symmetry broken phase mimics that of weakly interacting theory, although their critical version describe the strongly interacting system.

We discuss quantum phase transition by a solvable model in the dual gravity setup. By considering the effect of the scalar condensation on the fermion spectrum near the quantum critical point(QCP), we find that there is a topologically protected fermion zero mode associated with the metal to insulator transition. Unlike the topological insulator, our zero mode is for the bulk of the material, not the edge. We also show that the strange metal phase with T-linear resistivity emerges at high enough temperature as far as a horizon exists. The phase boundaries calculated according to the density of states allow us understanding the structures of the phase diagram near the QCP.

When a magnetic moment is embedded in a metal, it captures nearby itinerant electrons to form a so-called Kondo cloud. When magnetic impurities are sufficiently dense that their individual clouds overlap with each other they are expected to form a correlated electronic ground state. This is known as Kondo condensation and can be considered a magnetic version of Bardeen–Cooper–Schrieffer pair formation. Here, we examine this phenomenon by performing electrical transport and high-precision tunnelling density-of-states spectroscopy measurements in a highly P-doped crystalline silicon metal in which disorder-induced localized magnetic moments exist. We detect the Kondo effect in the resistivity of the Si metal at temperatures below 2 K and an unusual pseudogap in the density of states with gap edge peaks below 100 mK. The pseudogap and peaks are tuned by applying an external magnetic field and transformed into a metallic Altshuler–Aronov gap associated with a paramagnetic disordered Fermi liquid phase. We interpret these observations as evidence of Kondo condensation followed by a transition to a disordered Fermi liquid.

A flat band can be studied an infinitely strong coupling, realized in a simple system. Therefore, its holographic realization should be interesting. Laia and Tong gave a realization of the flat band over the entire momentum region by introducing a particular boundary term. Here, we give a model with a flat band over a finite region of momentum space using a bulk interaction term instead of the boundary term. We find that the spectrum of our model is precisely analogous to that of the ABC stacked multilayer graphene. In the presence of the chemical potential, the flat band is bent in our holographic model, which is very close to the band deformation due to the spin-orbit