Gábor Széchenyi

Uniform tiling with electrical resistors

The electric resistance between two arbitrary nodes on any infinite lattice structure of resistors that is a periodic tiling of space is obtained. Our general approach is based on the lattice Greens function of the Laplacian matrix associated with the network. We present several non-trivial examples to show how efficient our method is. Deriving explicit resistance formulas it is shown that the Kagome, diced and decorated lattice can be mapped to the triangular and square lattice of resistors. Our work can be extended to the random walk problem or to electron dynamics in condensed matter physics.

Control of valley dynamics in silicon quantum dots in the presence of an interface step

Recent experiments on silicon nanostructures have seen breakthroughs toward scalable, long-lived quantum information processing. The valley degree of freedom plays a fundamental role in these devices, and the two lowest-energy electronic states of a silicon quantum dot can form a valley qubit. In this paper, we show that a single-atom high step at the silicon/barrier interface induces a strong interaction of the qubit and in-plane electric fields and that the strength of this interaction can be controlled by varying the relative position of the electron and the step. We analyze the consequences of this enhanced interaction on the dynamics of the qubit. The charge densities of the qubit states are deformed differently by the interface step, allowing nondemolition qubit readout via valley-to-charge conversion. A gate-induced in-plane electric field together with the interface step enables fast control of the valley qubit via electrically driven valley resonance. We calculate single- and two-qubit gate times, as well as relaxation and dephasing times, and present predictions for the parameter range where the gate times can be much shorter than the relaxation time and dephasing is reduced.

Valley-enhanced fast relaxation of gate-controlled donor qubits in silicon

Gate control of donor electrons near interfaces is a generic ingredient of donor-based quantum computing. Here, we address the question: how is the phonon-assisted qubit relaxation time T 1 affected as the electron is shuttled between the donor and the interface? We focus on the example of the flip-flop qubit (Tosi et al arXiv:1509.08538v1), defined as a combination of the nuclear and electronic states of a phosphorus donor in silicon, promising fast electrical control and long dephasing times when the electron is halfway between the donor and the interface. We theoretically describe orbital relaxation, flip-flop relaxation, and electron spin relaxation. We estimate that the flip-flop qubit relaxation time can be of the order of 100 μs, 8 orders of magnitude shorter than the value for an on-donor electron in bulk silicon, and a few orders of magnitude shorter (longer) than the predicted inhomogeneous dephasing time (gate times). All three relaxation processes are boosted by (i) the nontrivial valley structure of the electron-phonon interaction, and (ii) the different valley compositions of the involved electronic states.

Electron-electron attraction in an engineered electromechanical system

Two electrons in a quantum dot repel each other: their interaction can be characterized by a positive interaction energy. From the theory of superconductivity, we also know that mechanical vibrations of the crystal lattice can make the electron-electron interaction attractive. Analogously, if a quantum dot interacts with a mechanical degree of freedom, the effective interaction energy can be negative; that is, the electron-electron interaction might be attractive. In this work, we propose and theoretically study an engineered electromechanical system that exhibits electron-electron attraction: a quantum dot suspended on a nonlinear mechanical resonator, tuned by a bottom and a top gate electrode. We focus on the example of a dot embedded in a suspended graphene ribbon, for which we identify conditions for electron-electron attraction. Our results suggest the possibility of electronic transport via tunneling of packets of multiple electrons in such devices, similar to that in superconducting nanostructures, but without the use of any superconducting elements.

Transfer matrix approach for the Kerr and Faraday rotation in layered nanostructures

To study the optical rotation of the polarization of light incident on multilayer systems consisting of atomically thin conductors and dielectric multilayers we present a general method based on transfer matrices. The transfer matrix of the atomically thin conducting layer is obtained using the Maxwell equations. We derive expressions for the Kerr (Faraday) rotation angle and for the ellipticity of the reflected (transmitted) light as a function of the incident angle and polarization of the light. The method is demonstrated by calculating the Kerr (Faraday) angle for bilayer graphene in the quantum anomalous Hall state placed on the top of dielectric multilayers. The optical conductivity of the bilayer graphene is calculated in the framework of a four-band model.

Maximal Rabi frequency of an electrically driven spin in a disordered magnetic field

We present a theoretical study of the spin dynamics of a single electron confined in a quantum dot. Spin dynamics is induced by the interplay of electrical driving and the presence of a spatially disordered magnetic field, the latter being transverse to a homogeneous magnetic field. We focus on the case of strong driving, i.e., when the oscillation amplitude

Impurity-assisted electric control of spin-valley qubits in monolayer MoS2

A

Coulomb-blockade and Pauli-blockade magnetometry

of the electrons wave packet is comparable to the quantum dot length

Shape-sensitive Pauli blockade in a bent carbon nanotube

L

Current hot spot in the spin-valley blockade in carbon nanotubes

. We show that electrically driven spin resonance can be induced in this system by subharmonic driving, i.e., if the excitation frequency is an integer fraction (1/2, 1/3, etc) of the Larmor frequency. At strong driving we find that (i) the Rabi frequencies at the subharmonic resonances are comparable to the Rabi frequency at the fundamental resonance, and (ii) at each subharmonic resonance, the Rabi frequency can be maximized by setting the drive strength to an optimal, finite value. Our simple model is applied to describe electrical control of a spin-valley qubit in a weakly disordered carbon nanotube.