Tianran Chen

Theory of volumetric capacitance of an electric double-layer supercapacitor.

Electric double-layer supercapacitors are a fast-rising class of high-power energy storage devices based on porous electrodes immersed in a concentrated electrolyte or ionic liquid. As yet there is no microscopic theory to describe their surprisingly large capacitance per unit volume (volumetric capacitance) of ~100 F/cm(3), nor is there a good understanding of the fundamental limits on volumetric capacitance. In this paper we present a non-mean-field theory of the volumetric capacitance of a supercapacitor that captures the discrete nature of the ions and the exponential screening of their repulsive interaction by the electrode. We consider analytically and via Monte Carlo simulations the case of an electrode made from a good metal and show that in this case the volumetric capacitance can reach the record values. We also study how the capacitance is reduced when the electrode is an imperfect metal characterized by some finite screening radius. Finally, we argue that a carbon electrode, despite its relatively large linear screening radius, can be approximated as a perfect metal because of its strong nonlinear screening. In this way the experimentally measured capacitance values of ~100 F/cm(3) may be understood.

Theory of hopping conduction in arrays of doped semiconductor nanocrystals

The resistivity of a dense crystalline array of semiconductor nanocrystals (NCs) depends in a sensitive way on the level of doping as well as on the NC size and spacing. The choice of these parameters determines whether electron conduction through the array will be characterized by activated nearest-neighbor hopping or variable-range hopping (VRH). Thus far, no general theory exists to explain how these different behaviors arise at different doping levels and for different types of NCs. In this paper, we examine a simple theoretical model of an array of doped semiconductor NCs that can explain the transition from activated transport to VRH. We show that in sufficiently small NCs, the fluctuations in donor number from one NC to another provide sufficient disorder to produce charging of some NCs, as electrons are driven to vacate higher shells of the quantum confinement energy spectrum. This confinement-driven charging produces a disordered Coulomb landscape throughout the array and leads to VRH at low temperature. We use a simple computer simulation to identify different regimes of conduction in the space of temperature, doping level, and NC diameter. We also discuss the implications of our results for large NCs with external impurity charges and for NCs that are gated electrochemically.

Surface roughness dominated pinning mechanism of magnetic vortices in soft ferromagnetic films

Although pinning of domain walls in ferromagnets is ubiquitous, the absence of an appropriate characterization tool has limited the ability to correlate the physical and magnetic microstructures of ferromagnetic films with specific pinning mechanisms. Here, we show that the pinning of a magnetic vortex, the simplest possible domain structure in soft ferromagnets, is strongly correlated with surface roughness, and we make a quantitative comparison of the pinning energy and spatial range in films of various thickness. The results demonstrate that thickness fluctuations on the lateral length scale of the vortex core diameter, i.e., an effective roughness at a specific length scale, provides the dominant pinning mechanism. We argue that this mechanism will be important in virtually any soft ferromagnetic film.

Anomalously small resistivity and thermopower of strongly compensated semiconductors and topological insulators

In the recent paper we explained why the maximum bulk resistivity of topological insulators (TIs)is so small [B. Skinner, T. Chen, and B. I. Shklovskii, Phys. Rev. Lett. 109, 176801 (2012)]. Using the model of completely compensated semiconductor we showed that when Fermi level is pinned in the middle of the gap the activation energy of resistivity

Effects of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators

\Delta =0.3 (E_g/2)

Electrostatic tuning of the properties of disordered indium-oxide films near the superconductor-insulator transition

, where

Photoluminescence in arrays of doped semiconductor nanocrystals

E_g

Cooperative charging in a nanocrystal assembly gated by ionic liquid

is the semiconductor gap. In this paper, we consider strongly compensated

Magnetic vortex dynamics in the presence of pinning

n

Phase diagram of magnetic vortex dynamics

-type semiconductor. We find position of the Fermi level