arXiv subjects

Tianran Chen

Publications and source records attributed to Tianran Chen.

51 records · Page 3Linked to original sources

arXiv2015

On the Network Topology Dependent Solution Count of the Algebraic Load Flow Equations

A large amount of research activity in power systems areas has focused on developing computational methods to solve load flow equations where a key question is the maximum number of isolated solutions.Though several concrete upper bounds exist, recent studies have hinted that much sharper upper bounds that depend the topology of underlying power networks may exist. This paper establishes such a topology dependent solution bound which is actually the best possible bound in the sense that it is always attainable. We also develop a geometric construction called adjacency polytope which accurately captures the topology of the underlying power network and is immensely useful in the computation of the solution bound. Finally we highlight the significant implications of the development of such solution bound in solving load flow equations.

math.OC↗

arXiv2015

An index-resolved fixed-point homotopy and potential energy landscapes

Stationary points (SPs) of the potential energy landscapes can be classified by their Morse index, i.e., the number of negative eigenvalues of the Hessian evaluated at the SPs. In understanding chemical clusters through their potential energy landscapes, only SPs of a particular Morse index are needed. We propose a modification of the "fixed-point homotopy" method which can be used to directly target stationary points of a specified Morse index. We demonstrate the effectiveness of our approach by applying it to the Lennard-Jones clusters.

cond-mat.soft↗

arXiv2015

Parallel degree computation for solution space of binomial systems with an application to the master space of $\mathcal{N}=1$ gauge theories

The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized techniques exist. For both theoretic and applied purposes, the degree of the solution set of a system of binomial equations often plays an important role in understanding the geometric structure of the solution set. Its computation, however, is computationally intensive. This paper proposes a specialized parallel algorithm for computing the degree on GPUs that takes advantage of the massively parallel nature of GPU devices. The preliminary implementation shows remarkable efficiency and scalability when compared to the closest CPU-based counterpart. Applied to the "master space problem of $\mathcal{N}=1$ gauge theories" the GPU-based implementation achieves nearly 30 fold speedup over its CPU-only counterpart enabling the discovery of previously unknown results. Equally important to note is the far superior scalability: with merely 3 GPU devices on a single workstation, the GPU-based implementation shows better performance, on certain problems, than a small cluster totaling 100 CPU cores.

math.AG↗

arXiv2014

Communication: Newton homotopies for sampling stationary points of potential energy landscapes

One of the most challenging and frequently arising problems in many areas of science is to find solutions of a system of multivariate nonlinear equations. There are several numerical methods that can find many (or all if the system is small enough) solutions but they each exhibit characteristic problems. Moreover, traditional methods can break down if the system contains singular solutions. Here, we propose an efficient implementation of Newton homotopies, which can sample a large number of the stationary points of complicated many-body potentials. We demonstrate how the procedure works by applying it to the nearest-neighbor $ϕ^4$ model and atomic clusters.

cond-mat.stat-mech↗

arXiv2014

Theory of a field effect transistor based on semiconductor nanocrystal array

We study the surface conductivity of a field-effect transistor (FET) made of periodic array of spherical semiconductor nanocrystals (NCs). We show that electrons introduced to NCs by the gate voltage occupy one or two layers of the array. Computer simulations and analytical theory are used to study the array screening and corresponding evolution of electron concentrations of the first and second layers with growing gate voltage. When first layer NCs have two electrons per NC the quantization energy gap between its 1S and 1P levels induces occupation of 1S levels of second layer NCs. Only at a larger gate voltage electrons start leaving 1S levels of second layer NCs and filling 1P levels of first layer NCs. By substantially larger gate voltage, all the electrons vacate the second layer and move to 1P levels of first layer NCs. As a result of this nontrivial evolution of the two layers concentrations, the surface conductivity of FET non-monotonically depends on the gate voltage. The same evolution of electron concentrations leads to non-monotonous behaviour of the differential capacitance.

cond-mat.mes-hall↗

arXiv2014

Photoluminescence in array of doped semiconductor nanocrystals

We study the dependence of the quantum yield of photoluminescence of a dense, periodic array of semiconductor nanocrystals (NCs) on the level of doping and NC size. Electrons introduced to NCs via doping quench photoluminescence by the Auger process, so that practically only NCs without electrons contribute to the photoluminescence. Computer simulation and analytical theory are used to find a fraction of such empty NCs as a function of the average number of donors per NC and NC size. For an array of small spherical NCs, the quantization gap between 1S and 1P levels leads to transfer of electrons from NCs with large number of donors to those without donors. As a result, empty NCs become extinct, and photoluminescence is quenched abruptly at an average number of donors per NC close to 1.8. The relative intensity of photoluminescence is shown to correlate with the type of hopping conductivity of an array of NCs.

cond-mat.mes-hall↗

arXiv2013

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

In the three-dimensional topological insulator (TI), the physics of doped semiconductors exists literally side-by-side with the physics of ultra-relativistic Dirac fermions. This unusual pairing creates a novel playground for studying the interplay between disorder and electronic transport. In this mini-review we focus on the disorder caused by the three-dimensionally distributed charged impurities that are ubiquitous in TIs, and we outline the effects it has on both the bulk and surface transport in TIs. We present self-consistent theories for Coulomb screening both in the bulk and at the surface, discuss the magnitude of the disorder potential in each case, and present results for the conductivity. In the bulk, where the band gap leads to thermally activated transport, we show how disorder leads to a smaller-than-expected activation energy that gives way to VRH at low temperatures. We confirm this enhanced conductivity with numerical simulations that also allow us to explore different degrees of impurity compensation. For the surface, where the TI has gapless Dirac modes, we present a theory of disorder and screening of deep impurities, and we calculate the corresponding zero-temperature conductivity. We also comment on the growth of the disorder potential as one moves from the surface of the TI into the bulk. Finally, we discuss how the presence of a gap at the Dirac point, introduced by some source of time-reversal symmetry breaking, affects the disorder potential at the surface and the mid-gap density of states.

cond-mat.mes-hall↗

arXiv2013

Electrostatic Tuning of the Properties of Disordered Indium Oxide Films near the Superconductor-Insulator Transition

The evolution with carrier concentration of the electrical properties of amorphous indium oxide (InO) thin films has been studied using electronic double layer transistor configurations. Carrier variations of up to 7 X 10^(14) carriers/cm^2 were achieved using an ionic liquid as a gate dielectric. The superconductor-insulator transition was traversed and the magnitude and position of the large magnetoresistance peak found in the insulating regime were modified. The systematic variation of the magnetoresistance peak with charge concentration was found to be qualitatively consistent with a simulation based on a model involving granularity.

cond-mat.supr-con↗

arXiv2013

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 $Δ=0.3 (E_g/2)$, where $E_g$ is the semiconductor gap. In this paper, we consider strongly compensated $n$-type semiconductor. We find position of the Fermi level $μ$ calculated from the bottom of the conduction band and the activation energy of the resistivity $Δ$ as a function of compensation $K$, and show that $Δ= 0.3 (E_c-μ) $ holds at any $1-K \ll 1$. At the same time Peltier energy (heat) $Π$ is even smaller: $Π\simeq 0.5Δ= 0.15(E_c - μ)$. We also show that at low temperatures the activated conductivity crosses over to variable range hopping (VRH) and find the characteristic temperature of VRH, $T_{ES}$, as a function of $1-K$.

cond-mat.str-el↗

arXiv2012

Why is the bulk resistivity of topological insulators so small?

As-grown topological insulators (TIs) are typically heavily-doped $n$-type crystals. Compensation by acceptors is used to move the Fermi level to the middle of the band gap, but even then TIs have a frustratingly small bulk resistivity. We show that this small resistivity is the result of band bending by poorly screened fluctuations in the random Coulomb potential. Using numerical simulations of a completely compensated TI, we find that the bulk resistivity has an activation energy of just 0.15 times the band gap, in good agreement with experimental data. At lower temperatures activated transport crosses over to variable range hopping with a relatively large localization length.

cond-mat.mes-hall↗

arXiv2012

Coulomb gap triptychs, $\sqrt{2}$ effective charge, and hopping transport in periodic arrays of superconductor grains

In granular superconductors, individual grains can contain bound Cooper pairs while the system as a whole is strongly insulating. In such cases the conductivity is determined by electron hopping between localized states in individual grains. Here we examine a model of hopping conductivity in such an insulating granular superconductor, where disorder is assumed to be provided by random charges embedded in the insulating gaps between grains. We use computer simulations to calculate the single-electron and electron pair density of states at different values of the superconducting gap $Δ$, and we identify "triptych" symmetries and scaling relations between them. At a particular critical value of $Δ$, one can define an effective charge $\sqrt{2}e$ that characterizes the density of states and the hopping transport. We discuss the implications of our results for magnetoresistance and tunneling experiments.

cond-mat.dis-nn↗

arXiv2012

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.

cond-mat.mes-hall↗

arXiv2012

Coulomb gap triptych in a periodic array of metal nanocrystals

The Coulomb gap in the single particle density of states (DOS) is a universal consequence of electron-electron interaction in disordered systems with localized electron states. Here we show that in arrays of monodisperse metallic nanocrystals, there is not one but three identical adjacent Coulomb gaps, which together form a structure that we call a "Coulomb gap triptych." We calculate the DOS and the conductivity in two- and three-dimensional arrays using a computer simulation. Unlike in the conventional Coulomb glass models, in nanocrystal arrays the DOS has a fixed width in the limit of large disorder. The Coulomb gap triptych can be studied via tunneling experiments.

cond-mat.mes-hall↗

arXiv2011

Cooperative Charging in a Nanocrystal Assembly Gated By Ionic Liquid

In order to make a densely packed assembly of undoped semiconductor nanocrystals conductive, it is usually gated by a room temperature ionic liquid. The ionic liquid enters the pores of the super-crystal assembly under the influence of an applied voltage. We study the capacitance of such a device as a function of the gate voltage. We show that, counter-intuitively, the capacitance of the system is the sum of delta-functions located at a sequence of critical gate voltages. At each critical voltage every nanocrystal acquires one additional electron.

cond-mat.mes-hall↗

arXiv2011

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 of 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.

cond-mat.mtrl-sci↗