Many Electrons Strongly Avoiding Each Other: Strange Goings On

Mark P. Silverman

Jian-Huang She, A. R. Bishop, Alexander V. Balatsky

Our current understanding of strongly correlated electron systems is based on a homogeneous framework. Here we take a step going beyond this paradigm by incorporating inhomogeneity from the beginning. Specifying to systems near the Mott metal-insulator transition, we propose a real-space picture of itinerant electrons functioning in the fluctuating geometries bounded by interfaces between metallic and insulating regions. In 2+1 dimensions, the interfaces are closed bosonic strings, and we have a system of strings coupled to itinerant electrons. When the interface tension vanishes, the geometric fluctuations become critical, which gives rise to non-Fermi-liquid behavior for the itinerant electrons. In particular, the poles of the fermion Green's function can be converted to zeros, indicating the absence of propagating quasiparticles. Furthermore, the quantum geometric fluctuations mediate Cooper pairing among the itinerant electrons, indicating the intrinsic instability of electronic systems near the Mott transition.

Eduardo C. Marino

Antonio Puccini

Abstract—One of the most interesting and peculiar phenomena of Quantum Mechanics is the interference (I) induced by the electrons. Strangely enough, though the electrons are real particles, they often behave just like waves. From the point of view of the classical mechanics the I induced by the electrons is unexplainable, however it is solved mathematically using the formalism of quantum mechanics and applying Schrödinger’s equation. The quantum solution of the problem is clear and elegant, especially from a mathematical point of view, however it still leaves some perplexities as to understand how exactly the phenomenon happens. We will make a hypothesis trying to understand the undulation phenomenon of the electron: it is really a strange and mysterious phenomenon. Maybe if we consider that the electron, just as the baryons and the mesons, might be made of smaller particles (saving the integrity of the unity of the negative electrical charge and the other Laws of Conservation), we could understand more easily how a single electron can go through two close holes at the same time. Analogously we could better understand another very particular quantum phenomenon carried out mainly by electrons, that is the tunnel effect. In this case, though the particle does not have enough energy to go through the potential barrier, though it does not have any material possibility to pass through a layer which does not have any hole, after several “attempts ” the particle will manage to pass through the barrier anyway, as it had dug a tunnel, or as it had managed to find a “breach ” in the wall. In this phenomenon too, though we can explain it from a mathematical point of view, using the equations of the quantum mechanics, it is still not clear how actually the electron manages to have an undulation behaviour.

Serhii Kryhin, Subir Sachdev A, Pavel A. Volkov

We show that nonlinear transport responses in strange metals are strong, larger by a factor of E_{F}/T than in Fermi liquids. Within the two-dimensional Yukawa-Sachdev-Ye-Kitaev model of a Fermi surface with a spatially random coupling to a critical scalar, the third order conductivity is found to diverge as 1/T at low T, indicating the existence of a voltage-temperature scaling regime in the conductance. Its frequency and orientation dependence contains information on relaxation times of heat and electron distribution deformations, providing a new set of tools to characterize strange metals.

Peter J. W. Debye