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

Limits to two-spin-qubit gate fidelity from thermal and vacuum fluctuations

High-fidelity quantum gate operations are essential for achieving scalable quantum circuits. In spin qubit quantum computing systems, metallic gates and antennas which are necessary for qubit operation, initialization, and readout, also cause detriments by enhancing fluctuations of electromagnetic fields. Therefore evanescent wave Johnson noise (EWJN) caused by thermal and vacuum fluctuations becomes an important unmitigated noise, which induces the decay of spin qubits and limits the quantum gate operation fidelity. Here, we first develop a quantum electrodynamics theory of EWJN. Then we propose a numerical technique based on volume integral equations to quantify EWJN strength in the vicinity of nanofabricated metallic gates with arbitrary geometry. We study the limits to two spin-qubit gate fidelity from EWJN-induced relaxation processes in two experimentally relevant quantum computing platforms: (a) silicon quantum dot system and (b) NV centers in diamond. Finally, we introduce the Lindbladian engineering method to optimize the control pulse sequence design and show its enhanced performance over Hamiltonian engineering in mitigating the influence of thermal and vacuum fluctuations. Our work leverages advances in computational electromagnetics, fluctuational electrodynamics and open quantum systems to suppress the effects of thermal and vacuum fluctuations and reach the limits of two-spin-qubit gate fidelity.Comment: 16 pages, 8 figure

Non-Asymptotic Quantum Scattering Theory for Low-Dimensional Materials

Over the past few decades, solid-state devices have steered the field of nanoelectronics. The advancement in semiconductor technology has led to the development of classical integrated circuits, which follows the trend defined by Moore’s law. However, in order to achieve the next generation of computing circuits, one requires to go beyond the limits of Moore’s law. This has led to a revolution in the development of new quantum materials, and harnessing their physical properties. This new class of quantum materials constitutes low-dimensional systems such as semiconductor heterostructures and atomically thin two-dimensional (2D) materials. Tunability of the physical properties offered by these structures, makes them ideal candidates to host high performance nanoelectronic circuits and quantum information platforms. In this thesis, we develop a scalable first-principles informed quantum transport theory to investigate the carrier transport properties of low-dimensional materials, and reveal their novel electronic and thermoelectric properties. While first-principles calculations effectively determine the atomistic potentials associated with defects and impurities, they are ineffective for direct modeling of carrier transport properties at length scales relevant for device applications. Traditionally, scattering properties are obtained by applying the asymptotic boundary conditions. However, these boundary conditions do not account for the decaying evanescent mode contributions, that are crucial while determining the transport properties of low-dimensional systems. Here, we develop a novel non-asymptotic quantum scattering theory to obtain the transport properties in proximity to the scattering centers, for confined as well as open domain in one-, two- and three-dimensional systems. We then bridge this scattering theory and the k.p perturbation theory, with inputs from ab-initio electronic structure calculations, to construct a versatile multiscale formalism. The continuum nature of the formalism enables us to model realistic meso- and nano-scale devices. The given formalism is applied to study electron scattering in quantum waveguides. Several interesting phenomena are revealed through our analysis. The Fano resonance profile for the transmission spectrum of both propagating and evanescent modes is observed. An enhancement of power factor far beyond the earlier proposed limits is obtained by embedding attractive impurities within the waveguide. A current rectification device is simulated, which is expected to find applications in quantum transport. We further apply this formalism to reveal the novel electronic and thermoelectric properties of monolayer lateral transition-metal dichalcogenide (TMDC) heterostructures. We show that material inclusions in such heterostructures leads to enhancement of electron mobility by an order of magnitude larger than pristine TMDCs. The band alignment between the materials also enhances the thermoelectric figure-of-mertit (ZT) and power factor far beyond the pristine TMDCs. Our study opens new avenues for constructing ultra-efficient in-plane thermoelectric devices using lateral TMDC heterostructures

Pico-photonics: Anomalous Atomistic Waves in Silicon

The concept of photonic frequency $(\omega)$ - momentum $(q)$ dispersion has been extensively studied in artificial dielectric structures such as photonic crystals and metamaterials. However, the $\omega-q$ dispersion of electrodynamic excitations hosted in natural materials at the atomistic level is far less explored. Here, we develop a Maxwell Hamiltonian theory of matter combined with the quantum theory of atomistic polarization to obtain the electrodynamic dispersion of natural materials interacting with the photon field. We apply this theory to silicon and discover the existence of anomalous atomistic waves. These waves occur in the spectral region where propagating waves are conventionally forbidden in a macroscopic theory. Our findings demonstrate that natural media can host a variety of yet to be discovered waves with sub-nano-meter effective wavelengths in the pico-photonics regime

Optical N-insulators: Topological obstructions to optical Wannier functions in the atomistic susceptibility tensor

A powerful result of topological band theory is that nontrivial phases manifest obstructions to constructing localized Wannier functions. In Chern insulators, it is impossible to construct Wannier functions that respect translational symmetry in both directions. Similarly, Wannier functions that respect time-reversal symmetry cannot be formed in quantum spin Hall insulators. This molecular orbital interpretation of topology has been enlightening and was recently extended to topological crystalline insulators which include obstructions tied to space-group symmetries. In this paper, we introduce a class of two-dimensional topological materials known as optical N-insulators that possess obstructions to constructing localized molecular polarizabilities. The optical N-invariant N∈Z is the winding number of the atomistic susceptibility tensor χ and counts the number of singularities in the electromagnetic linear response theory. We decipher these singularities by analyzing the optical band structure of the material—the eigenvectors of the susceptibility tensor—which constitutes the collection of optical Bloch functions. The localized basis of these eigenvectors are optical Wannier functions which characterize the molecular polarizabilities at different lattice sites. We prove that in a nontrivial optical phase N≠0, such a localized polarization basis is impossible to construct. Utilizing the mathematical machinery of K theory, these optical N-phases are refined further to account for the underlying crystalline symmetries of the material, generating a complete classification of the topological electromagnetic phase of matter