Exploration of The Duality Between Generalized Geometry and Extraordinary Magnetoresistance

We outline the duality between the extraordinary magnetoresistance (EMR), observed in semiconductor-metal hybrids, and non-symmetric gravity coupled to a diffusive $U(1)$ gauge field. The corresponding gravity theory may be interpreted as the generalized complex geometry of the semi-direct product of the symmetric metric and the antisymmetric Kalb-Ramond field: ($g_{\mu\nu}+\beta_{\mu\nu}$). We construct the four dimensional covariant field theory and compute the resulting equations of motion. The equations encode the most general form of EMR within a well defined variational principle, for specific lower dimensional embedded geometric scenarios. Our formalism also reveals the emergence of additional diffusive pseudo currents for a completely dynamic field theory of EMR. The proposed equations of motion now include terms that induce geometrical deformations in the device geometry in order to optimize the EMR. This bottom-up dual description between EMR and generalized geometry/gravity lends itself to a deeper insight into the EMR effect with the promise of potentially new physical phenomena and properties.Comment: 13 pages and 6 figures. Revised/edited for clarity and purpose. Several references added. Updated title based on suggestions and comments received. Version accepted for publication in Phys.Rev.

Lateral transition metal dichalcogenide heterostructures for high efficiency thermoelectric devices

Increasing demands for renewable sources of energy has been a major driving force for developing efficient thermoelectric materials. Two-dimensional (2D) transition-metal dichalcogenides (TMDC) have emerged as promising candidates for thermoelectric applications due to their large effective mass and low thermal conductivity. In this article, we study the thermoelectric performance of lateral TMDC heterostructures within a multiscale quantum transport framework. Both $n$-type and $p$-type lateral heterostructures are considered for all possible combinations of semiconducting TMDCs: MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$. The band alignment between these materials is found to play a crucial in enhancing the thermoelectric figure-of-merit ($ZT$) and power factor far beyond those of pristine TMDCs. In particular, we show that the room-temperature $ZT$ value of $n$-type WS$_2$ with WSe$_2$ triangular inclusions, is five times larger than the pristine WS$_2$ monolayer. $p$-type MoSe$_2$ with WSe$_2$ inclusions is also shown to have a room-temperature $ZT$ value about two times larger than the pristine MoSe$_2$ monolayer. The peak power factor values calculated here, are the highest reported amongst gapped 2D monolayers at room temperature. Hence, 2D lateral TMDC heterostructures open new avenues to develop ultra-efficient, planar thermoelectric devices

Tuning spatial entanglement in interacting few-electron quantum dots

Confined geometries such as semiconductor quantum dots are promising candidates for fabricating quantum computing devices. When several quantum dots are in proximity, spatial correlation between electrons in the system becomes significant. In this article, we develop a fully variational action integral formulation for calculating accurate few-electron wavefunctions in configuration space, irrespective of potential geometry. To evaluate the Coulomb integrals with high accuracy, a novel numerical integration method using multiple Gauss quadratures is proposed. Using this approach, we investigate the confinement of two electrons in double quantum dots, and evaluate the spatial entanglement. We investigate the dependence of spatial entanglement on various geometrical parameters. We derive the two-particle wavefunctions in the asymptotic limit of the separation distance between quantum dots, and obtain universal saturation values for the spatial entanglement. Resonances in the entanglement values due to avoided level-crossings of states are observed. We also demonstrate the formation of electron clusters, and show that the entanglement value is a good indicator for the formation of such clusters. Further, we show that a precise tuning of the entanglement values is feasible with applied external electric fields

Finite size scaling for quantum criticality using the finite-element method

Finite size scaling for the Schr\"{o}dinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite element method was shown to be a powerful numerical method for ab initio electronic structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, density functional theory under the local density approximation, and an "exact"' formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems.Comment: 15 pages, 19 figures, revision based on suggestions by referee, accepted in Phys. Rev.

Exploration of Near-Horizon CFT Duality and AdS2/CFT1AdS_2/CFT_1 in Conformal Weyl Gravity

We compute near horizon black hole entropy via the N\"other current method within the conformal Weyl gravity paradigm for vacuum and non-vacuum spacetimes. We do this, in the vacuum case, for the near horizon near extremal Kerr metric and for the non-vacuum case we couple the conformal Weyl gravity field equations to a near horizon (linear) $U(1)$ gauge potential and analyze the respective found solutions. We highlight the non-universality of black hole entropy between black hole solutions of varying symmetries, yet their congruence with Wald's entropy formula for the respective gravity theory. Finally, we implement an $AdS_2/CFT_1$ construction to compute the full asymptotic symmetry group of one of the non-vacuum conformal Weyl black holes. We do this by performing a Robinson-Wilczek two dimensional reduction, thus enabling the construction of an effective quantum theory of the remaining field content. The effective stress energy tensor generates an asymptotic Virasoro algebra, to $s$-wave approximation, whose center in conjunction with their proper regularized lowest Virasoro eigen-mode is implemented to compute black hole entropy via the statistical Cardy formula. We additionally implement quantum holomorphic fluxes (of the dual CFT) in the near horizon to compute the Hawking temperature of the respective black hole spacetime. We conclude with a discussion and outlook for future work.Comment: 20 pages, no figure

Infrared Nonlinear Optics

Contains report on one research project.U.S. Air Force - Office of Scientific Research (Contract F49620-84-C-0010

Quantum response of weakly chaotic systems

Chaotic systems, that have a small Lyapunov exponent, do not obey the common random matrix theory predictions within a wide "weak quantum chaos" regime. This leads to a novel prediction for the rate of heating for cold atoms in optical billiards with vibrating walls. The Hamiltonian matrix of the driven system does not look like one from a Gaussian ensemble, but rather it is very sparse. This sparsity can be characterized by parameters $s$ and $g$ that reflect the percentage of large elements, and their connectivity respectively. For $g$ we use a resistor network calculation that has direct relation to the semi-linear response characteristics of the system.Comment: 7 pages, 5 figures, expanded improved versio

Center-of-Mass Properties of the Exciton in Quantum Wells

We present high-quality numerical calculations of the exciton center-of-mass dispersion for GaAs/AlGaAs quantum wells of widths in the range 2-20 nm. The k.p-coupling of the heavy- and light-hole bands is fully taken into account. An optimized center-of-mass transformation enhances numerical convergence. We derive an easy-to-use semi-analytical expression for the exciton groundstate mass from an ansatz for the exciton wavefunction at finite momentum. It is checked against the numerical results and found to give very good results. We also show multiband calculations of the exciton groundstate dispersion using a finite-differences scheme in real space, which can be applied to rather general heterostructures.Comment: 19 pages, 12 figures included, to be published in Phys. Rev.