Non-uniform magnetic fields for single-electron control.

Controlling single-electron states becomes increasingly important due to the wide-ranging advances in electron quantum optics. Single-electron control enables coherent manipulation of individual electrons and the ability to exploit the wave nature of electrons, which offers various opportunities for quantum information processing, sensing, and metrology. Here we explore non-uniform magnetic fields, which offer unique mechanisms for single-electron control. Considering the modeling perspective, conventional electron quantum transport theories are commonly based on gauge-dependent electromagnetic potentials. A direct formulation in terms of intuitive electromagnetic fields is thus not possible. In an effort to rectify this, a gauge-invariant formulation of the Wigner equation for general electromagnetic fields has been proposed [M. Nedjalkov et al., Phys. Rev. B, 2019, 99, 014423]. However, the complexity of this equation requires the derivation of a more convenient formulation for linear electromagnetic fields [M. Nedjalkov et al., Phys. Rev. A, 2022, 106, 052213]. This formulation directly includes the classical formulation of the Lorentz force and higher-order terms, depending on the magnetic field gradient, that are negligible for small variations of the magnetic field. In this work, we generalize this equation in order to include a general, non-uniform electric field and a linear, non-uniform magnetic field. The thus obtained formulation has been applied to investigate the capabilities of a linear, non-uniform magnetic field to control single-electron states in terms of trajectory, interference patterns, and dispersion. This has led to the exploration of a new type of transport inside electronic waveguides based on snake trajectories and the possibility of splitting wavepackets to realize edge states.

Gate-controlled electron quantum interference logic.

Inspired by using the wave nature of electrons for electron quantum optics, we propose a new type of electron quantum interference structure, where single-electron waves are coherently injected into a gate-controlled, two-dimensional waveguide and exit through one or more output channels. The gate-controlled interference effects lead to specific current levels in the output channels, which can be used to realize logic gate operations, e.g., NAND or NOR gates. The operating principle is shown by coherent, dynamic Wigner quantum electron transport simulations. A discussion of classical simulations (Boltzmann) allows to outline the underlying process of interference. Contrary to other electron control approaches used for advanced information processing, no magnetic or photonic mechanisms are involved.

A computational approach for investigating Coulomb interaction using Wigner-Poisson coupling.

Entangled quantum particles, in which operating on one particle instantaneously influences the state of the entangled particle, are attractive options for carrying quantum information at the nanoscale. However, fully-describing entanglement in traditional time-dependent quantum transport simulation approaches requires significant computational effort, bordering on being prohibitive. Considering electrons, one approach to analyzing their entanglement is through modeling the Coulomb interaction via the Wigner formalism. In this work, we reduce the computational complexity of the time evolution of two interacting electrons by resorting to reasonable approximations. In particular, we replace the Wigner potential of the electron-electron interaction by a local electrostatic field, which is introduced through the spectral decomposition of the potential. It is demonstrated that for some particular configurations of an electron-electron system, the introduced approximations are feasible. Purity, identified as the maximal coherence for a quantum state, is also analyzed and its corresponding analysis demonstrates that the entanglement due to the Coulomb interaction is well accounted for by the introduced local approximation.

Complex Systems in Phase Space.

The continued reduction of semiconductor device feature sizes towards the single-digit nanometer regime involves a variety of quantum effects. Modeling quantum effects in phase space in terms of the Wigner transport equation has evolved to be a very effective approach to describe such scaled down complex systems, accounting from full quantum processes to dissipation dominated transport regimes including transients. Here, we discuss the challanges, myths, and opportunities that arise in the study of these complex systems, and particularly the advantages of using phase space notions. The development of particle-based techniques for solving the transport equation and obtaining the Wigner function has led to efficient simulation approaches that couple well to the corresponding classical dynamics. One particular advantage is the ability to clearly illuminate the entanglement that can arise in the quantum system, thus allowing the direct observation of many quantum phenomena.

Simulation of the Impact of Ionized Impurity Scattering on the Total Mobility in Si Nanowire Transistors.

Nanowire transistors (NWTs) are being considered as possible candidates for replacing FinFETs, especially for CMOS scaling beyond the 5-nm node, due to their better electrostatic integrity. Hence, there is an urgent need to develop reliable simulation methods to provide deeper insight into NWTs' physics and operation, and unlock the devices' technological potential. One simulation approach that delivers reliable mobility values at low-field near-equilibrium conditions is the combination of the quantum confinement effects with the semi-classical Boltzmann transport equation, solved within the relaxation time approximation adopting the Kubo⁻Greenwood (KG) formalism, as implemented in this work. We consider the most relevant scattering mechanisms governing intraband and multi-subband transitions in NWTs, including phonon, surface roughness and ionized impurity scattering, whose rates have been calculated directly from the Fermi's Golden rule. In this paper, we couple multi-slice Poisson⁻Schrödinger solutions to the KG method to analyze the impact of various scattering mechanisms on the mobility of small diameter nanowire transistors. As demonstrated here, phonon and surface roughness scattering are strong mobility-limiting mechanisms in NWTs. However, scattering from ionized impurities has proved to be another important mobility-limiting mechanism, being mandatory for inclusion when simulating realistic and doped nanostructures, due to the short range Coulomb interaction with the carriers. We also illustrate the impact of the nanowire geometry, highlighting the advantage of using circular over square cross section shapes.

Electron evolution around a repulsive dopant in a quantum wire: coherence effects.

We present an analysis of the quantum processes involved in the electron evolution around a repulsive dopant in a quantum wire. The quantum electron behavior has been studied by using a Wigner function approach. The Wigner phase space description allows the treatment of both classical and quantum evolution in the same framework, enabling ease of highlighting the effects of coherence. While the former is governed by a force, which is the first derivative of the dopant potential, the latter accounts for the entire potential, namely all derivatives in the corresponding Taylor expansion take part in the interaction. This gives rise to processes of tunneling and non-locality of the action of the potential. The complicated interplay of these quantum effects with the boundary conditions associated with the wire affects the physical observables like electron and current densities and in particular can give rise to an increase of the total current.