First-principles methodology for quantum transport in multiterminal junctions

We present a generalized approach for computing electron conductance and I-V characteristics in multiterminal junctions from first-principles. Within the framework of Keldysh theory, electron transmission is evaluated employing an O(N) method for electronic-structure calculations. The nonequilibrium Green function for the nonequilibrium electron density of the multiterminal junction is computed self-consistently by solving Poisson equation after applying a realistic bias. We illustrate the suitability of the method on two examples of four-terminal systems, a radialene molecule connected to carbon chains and two crossed carbon chains brought together closer and closer. We describe charge density, potential profile, and transmission of electrons between any two terminals. Finally, we discuss the applicability of this technique to study complex electronic devices.Comment: Will be coming out in JCP soo

Magnetoresistance and negative differential resistance in Ni/Graphene/Ni vertical heterostructures driven by finite bias voltage: A first-principles study

Using the nonequilibrium Green function formalism combined with density functional theory, we study finite-bias quantum transport in Ni/Gr_n/Ni vertical heterostructures where $n$ graphene layers are sandwiched between two semi-infinite Ni(111) electrodes. We find that recently predicted "pessimistic" magnetoresistance of 100% for $n \ge 5$ junctions at zero bias voltage $V_b \rightarrow 0$, persists up to $V_b \simeq 0.4$ V, which makes such devices promising for spin-torque-based device applications. In addition, for parallel orientations of the Ni magnetizations, the $n=5$ junction exhibits a pronounced negative differential resistance as the bias voltage is increased from $V_b=0$ V to $V_b \simeq 0.5$ V. We confirm that both of these nonequilibrium effects hold for different types of bonding of Gr on the Ni(111) surface while maintaining Bernal stacking between individual Gr layers.Comment: 6 pages, 5 figures, PDFLaTeX; Figure labels correcte

Multiterminal single-molecule--graphene-nanoribbon thermoelectric devices with gate-voltage tunable figure of merit ZT

We study thermoelectric devices where a single 18-annulene molecule is connected to metallic zigzag graphene nanoribbons (ZGNR) via highly transparent contacts that allow for injection of evanescent wave functions from ZGNRs into the molecular ring. Their overlap generates a peak in the electronic transmission, while ZGNRs additionally suppress hole-like contributions to the thermopower. Thus optimized thermopower, together with suppression of phonon transport through ZGNR-molecule-ZGNR structure, yield the thermoelectric figure of merit ZT ~ 0.5 at room temperature and 0.5 < ZT < 2.5 below liquid nitrogen temperature. Using the nonequilibrium Green function formalism combined with density functional theory, recently extended to multiterminal devices, we show how the transmission resonance can also be manipulated by the voltage applied to a third ZGNR electrode, acting as the top gate covering molecular ring, to tune the value of ZT.Comment: 5 pages, 4 figures, PDFLaTe

Quantum-interference-controlled three-terminal molecular transistors based on a single ring-shaped-molecule connected to graphene nanoribbon electrodes

We study all-carbon-hydrogen molecular transistors where zigzag graphene nanoribbons play the role of three metallic electrodes connected to a ring-shaped 18-annulene molecule. Using the nonequilibrium Green function formalism combined with density functional theory, recently extended to multiterminal devices, we show that the proposed nanostructures exhibit exponentially small transmission when the source and drain electrodes are attached in a configuration that ensures destructive interference of electron paths around the ring. The third electrode, functioning either as an attached infinite-impedance voltage probe or as an "air-bridge" top gate covering half of molecular ring, introduces dephasing that brings the transistor into the "on" state with its transmission in the latter case approaching the maximum limit for a single conducting channel device. The current through the latter device can also be controlled in the far-from-equilibrium regime by applying a gate voltage.Comment: 5 pages, 4 color figures, PDFLaTeX, slightly expanded version of the published PRL articl

Optical properties of perovskite alkaline earth titanates : a formulation

In this communication we suggest a formulation of the optical conductivity as a convolution of an energy resolved joint density of states and an energy-frequency labelled transition rate. Our final aim is to develop a scheme based on the augmented space recursion for random systems. In order to gain confidence in our formulation, we apply the formulation to three alkaline earth titanates CaTiO_3, SrTiO_3 and BaTiO_3 and compare our results with available data on optical properties of these systems.Comment: 19 pages, 9 figures, Submitted to Journal of Physics: Condensed Matte

Advanced Quantum Poisson Solver in the NISQ era

The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to the linear systems through the finite difference method, we adopt the Harrow-Hassidim-Lloyd (HHL) algorithm as the basic framework. Particularly, in this work we present an advanced circuit that ensures the accuracy of the solution by implementing non-truncated eigenvalues through eigenvalue amplification as well as by increasing the accuracy of the controlled rotation angular coefficients, which are the critical factors in the HHL algorithm. We show that our algorithm not only increases the accuracy of the solutions, but also composes more practical and scalable circuits by dynamically controlling problem size in the NISQ devices. We present both simulated and experimental solutions, and conclude that overall results on the quantum hardware are dominated by the error in the CNOT gates.Comment: Quantum Week QCE 2022, poster pape

Advancing Algorithm to Scale and Accurately Solve Quantum Poisson Equation on Near-term Quantum Hardware

The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far either suffer from lack of accuracy and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to a linear system through the finite difference method, we adopt the HHL algorithm as the basic framework. Particularly, in this work we present an advanced circuit that ensures the accuracy of the solution by implementing non-truncated eigenvalues through eigenvalue amplification, as well as by increasing the accuracy of the controlled rotation angular coefficients, which are the critical factors in the HHL algorithm. Consequently, we are able to drastically reduce the relative error in the solution while achieving higher success probability as the amplification level is increased. We show that our algorithm not only increases the accuracy of the solutions but also composes more practical and scalable circuits by dynamically controlling problem size in NISQ devices. We present both simulated and experimental results and discuss the sources of errors. Finally, we conclude that though overall results on the existing NISQ hardware are dominated by the error in the CNOT gates, this work opens a path to realizing a multidimensional Poisson solver on near-term quantum hardware.Comment: 13 pages, 11 figures, 1 tabl