Electron transport in a graphene quantum well can be analogous to photon transmission in an optical fiber. In this work, we present a detailed theoretical analysis to study the transport characteristics of graphene waveguides under the influence of different edge orientations. The non-equilibrium Green's function approach in combination with the tight-binding Hamiltonian has been utilized to investigate the conductance properties of straight armchair and zigzag oriented graphene waveguides. Conductance plateaus at integer steps of $4e^2/h$ have been observed in both orientations while the zigzag oriented waveguides present a wider first quantized plateau compared to that in the armchair oriented ones. Using various geometric and physical parameters, including side-barrier and waveguide width, and the metallic properties of terminals, we investigate the conductance profile of waveguides. In addition to the observation of valley symmetry in both edge orientations, this article explores the critical influence of drain contacts on waveguide conductance. Furthermore, we extended our transport study to three different highly bent waveguide configurations, such as U-shape, L-shape, and split-shape waveguides, in order to explore their applications in graphene-based ballistic integrated circuit devices. In the end, we also calculated the conductance of larger graphene waveguides using the scalable tight-binding model, in order to compare the results obtained from the original model.

Over the last decade, quantum computing has experienced significant changes and captured worldwide attention. In particular, superconducting qubits have become the leading candidates for scalable quantum computers, and a number of cryogenic materials have scientifically demonstrated their potential uses in constructing qubit chips. However, because of insufficient coherence time, establishing a robust and scalable quantum platform is still a long-term goal. Another consideration is the control circuits essential to initializing, operating and measuring the qubits. To keep noise low, control circuits in close proximity to the qubits require superior reliability in the cryogenic environment. The realization of the quantum advantage demands qubits with appropriate circuitry designs to maintain long coherence times and entanglement. In this work, we briefly summarize the current status of cryogenic materials for qubits and discuss typical cryogenic circuitry designs and integration techniques for qubit chips. In the end, we provide an assessment of the prospects of quantum computers and some other promising cryogenic materials.

Achieving self-consistent convergence with the conventional effective-mass approach at ultra-low temperatures (below 4.2 K) is a challenging task, which mostly lies in the discontinuities in material properties (e.g. effective-mass, electron affinity, dielectric constant). In this article, we develop a novel self-consistent approach based on cell-centered finite-volume discretization of the Sturm–Liouville form of the effective-mass Schrödinger equation and generalized Poisson’s equation (FV-SP). We apply this approach to simulate the one-dimensional electron gas formed at the Si–SiO₂ interface via a top gate. We find excellent self-consistent convergence from high to extremely low (as low as 50 mK) temperatures. We further examine the solidity of FV-SP method by changing external variables such as the electrochemical potential and the accumulative top gate voltage. Our approach allows for counting electron–electron interactions. Our results demonstrate that FV-SP approach is a powerful tool to solve effective-mass Hamiltonians.

The non-equilibrium Green’s function (NEGF) approach offers a practical framework for simulating various phenomena in mesoscopic systems. As the dimension of electronic devices shrinks to just a few nanometers, the need for new effective-mass based 3D implementations of NEGF has become increasingly apparent. This work extends our previous finite-volume (FV) implementation—originally developed for the self-consistent solution of the Schrödinger and Poisson equations in 2D—into a full 3D NEGF framework. Our implementation begins with exploring a few problems with the common textbook Finite Difference implementations of NEGF. We then concisely demonstrate how FV discretization addresses few key implementation challenges. Importantly, we explain how this type of discretization enables evaluating the self-energies, which account for the effects of reservoirs. The potential applications of this new method are illustrated through two examples. We anticipate that this implementation will be broadly applicable to open quantum systems, especially in cases where a fully three-dimensional domain is essential.

Electron transport in a graphene quantum well can be analogous to photon transmission in an optical fiber. In this work, we present a detailed theoretical analysis to study the transport characteristics of graphene waveguides under the influence of different edge orientations. Non-equilibrium Green's function approach in combination with tight-binding Hamiltonian has been utilized to investigate the conductance properties of straight armchair and zigzag oriented graphene waveguides. Conductance plateaus at integer steps of $4e^2/h$ have been observed in both orientations while the zigzag oriented waveguides present a wider first quantized plateau compared to that in the armchair oriented ones. Using various geometric and physical parameters, including side-barrier and waveguide width, and the metallic properties of terminals, we investigate the conductance profile of waveguides. In addition to the observation of valley-symmetry in both edge orientations, this article explores the critical influence of drain contacts on waveguide conductance. Furthermore, we extended our transport study to three different highly bent waveguide configurations, such as U-shape, L-shape and split-shape waveguides, in order to explore their applications in graphene-based ballistic integrated circuit devices. In the end, we also calculated the conductance of larger graphene waveguides using the scalable tight-binding model, in order to compare the results obtained from the original model.