Anomalous conductivity, Hall factor, magnetoresistance, and thermopower of accumulation layer in SrTiO3\text{SrTiO}_3

We study the low temperature conductivity of the electron accumulation layer induced by the very strong electric field at the surface of $\text{SrTiO}_3$ sample. Due to the strongly nonlinear lattice dielectric response, the three-dimensional density of electrons $n(x)$ in such a layer decays with the distance from the surface $x$ very slowly as $n(x) \propto 1/x^{12/7}$. We show that when the mobility is limited by the surface scattering the contribution of such a tail to the conductivity diverges at large $x$ because of growing time electrons need to reach the surface. We explore truncation of this divergence by the finite sample width, by the bulk scattering rate, or by the crossover to the bulk linear dielectric response with the dielectric constant $\kappa$. As a result we arrive at the anomalously large mobility, which depends not only on the rate of the surface scattering, but also on the physics of truncation. Similar anomalous behavior is found for the Hall factor, the magnetoresistance, and the thermopower

Collapse of electrons to a donor cluster in SrTiO3_3

It is known that a nucleus with charge $Ze$ where $Z>170$ creates electron-positron pairs from the vacuum. These electrons collapse onto the nucleus resulting in a net charge $Z_n<Z$ while the positrons are emitted. This effect is due to the relativistic dispersion law. The same reason leads to the collapse of electrons to the charged impurity with a large charge number $Z$ in narrow-band gap semiconductors and Weyl semimetals as well as graphene. In this paper, a similar effect of electron collapse and charge renormalization is found for donor clusters in SrTiO$_3$ (STO), but with a very different origin. At low temperatures, STO has an enormously large dielectric constant. Because of this, the nonlinear dielectric response becomes dominant when the electric field is not too small. We show that this leads to the collapse of surrounding electrons into a charged spherical donor cluster with radius $R$ when its total charge number $Z$ exceeds a critical value $Z_c\simeq R/a$ where $a$ is the lattice constant. Using the Thomas-Fermi approach, we find that the net charge $Z_ne$ grows with $Z$ until $Z$ exceeds another value $Z^*\simeq(R/a)^{9/7}$. After this point, $Z_n$ remains $\sim Z^*$. We extend our results to the case of long cylindrical clusters. Our predictions can be tested by creating discs and stripes of charge on the STO surface

Classification of modules of the intermediate series over Ramond N=2 superconformal algebras

In this paper, we first discuss the structure of the Ramond N=2 superconformal algebras. Then we also classify the modules of the intermediate series over Ramond N=2 superconformal algebra.Comment: 17 Pages. LaTeX. We simplify some computations in Section 2, and correct some misprints in Section

Identification and characterization of the dominant thermal resistance in lithium-ion batteries using operando 3-omega sensors

Poor thermal transport within lithium-ion batteries fundamentally limits their performance, safety, and lifetime, in spite of external thermal management systems. All prior efforts to understand the origin of batteries' mysteriously high thermal resistance have been confined to ex situ measurements without understanding the impact of battery operation. Here, we develop a frequency-domain technique that employs sensors capable of measuring spatially resolved intrinsic thermal transport properties within a live battery while it is undergoing cycling. Our results reveal that the poor battery thermal transport is due to high thermal contact resistance between the separator and both electrode layers and worsens as a result of formation cycling, degrading total battery thermal transport by up to 70%. We develop a thermal model of these contact resistances to explain their origin. These contacts account for up to 65% of the total thermal resistance inside the battery, leading to far-reaching consequences for the thermal design of batteries. Our technique unlocks new thermal measurement capabilities for future battery research