András Pályi

A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions

This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological band insulators in one and two dimensions. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. We use noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the model is introduced first and then its properties are discussed and subsequently generalized. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.

Caustics due to a negative refractive index in circular graphene p-n junctions.

We show that the wave functions form caustics in circular graphene p-n junctions which in the framework of geometrical optics can be interpreted with a negative refractive index.

Spin-Orbit-Induced Strong Coupling of a Single Spin to a Nanomechanical Resonator

We theoretically investigate the deflection-induced coupling of an electron spin to vibrational motion due to spin-orbit coupling in suspended carbon nanotube quantum dots. Our estimates indicate that, with current capabilities, a quantum dot with an odd number of electrons can serve as a realization of the Jaynes-Cummings model of quantum electrodynamics in the strong-coupling regime. A quantized flexural mode of the suspended tube plays the role of the optical mode and we identify two distinct two-level subspaces, at small and large magnetic field, which can be used as qubits in this setup. The strong intrinsic spin-mechanical coupling allows for detection, as well as manipulation of the spin qubit, and may yield enhanced performance of nanotubes in sensing applications.

Disorder-mediated electron valley resonance in carbon nanotube quantum dots

We propose a scheme for coherent rotation of the valley isospin of a single electron confined in a carbon nanotube quantum dot. The scheme exploits the ubiquitous atomic disorder of the nanotube crystal lattice, which induces time-dependent valley mixing as the confined electron is pushed back and forth along the nanotube axis by an applied ac electric field. Using experimentally determined values for the disorder strength we estimate that valley Rabi oscillations with a period on the nanosecond time scale are feasible. The valley resonance effect can be detected in the electric current through a double quantum dot in the single-electron transport regime.

Spin-valley blockade in carbon nanotube double quantum dots

We present a theoretical study of the Pauli or spin-valley blockade for double quantum dots in semiconducting carbon nanotubes. In our model we take into account the following characteristic features of carbon nanotubes: (i) fourfold (spin and valley) degeneracy of the quantum dot levels, (ii) the intrinsic spin-orbit interaction which is enhanced by the tube curvature, and (iii) valley-mixing due to short-range disorder, i.e., substitutional atoms, adatoms, etc. We find that the spin-valley blockade can be lifted in the presence of short-range disorder, which induces two independent random (in magnitude and direction) valley-Zeeman-fields in the two dots, and hence acts similarly to hyperfine interaction in conventional semiconductor quantum dots. In the case of strong spin-orbit interaction, we identify a parameter regime where the current as the function of an applied axial magnetic field shows a zero-field dip with a width controlled by the interdot tunneling amplitude, in agreement with recent experiments.

Subharmonic transitions and Bloch-Siegert shift in electrically driven spin resonance

We theoretically study coherent subharmonic (multiphoton) transitions of a harmonically driven spin. We consider two cases: magnetic resonance (MR) with a misaligned, i.e., nontransversal, driving field, and electrically driven spin resonance (EDSR) of an electron confined in a one-dimensional, parabolic quantum dot, subject to Rashba spin-orbit interaction. In the EDSR case, we focus on the limit where the orbital level spacing of the quantum dot is the greatest energy scale. Then, we apply time-dependent Schrieffer-Wolff perturbation theory to derive a time-dependent effective two-level Hamiltonian, allowing us to describe both MR and EDSR using the Floquet theory of periodically driven two-level systems. In particular, we characterize the fundamental (singlephoton) and the half-harmonic (two-photon) spin transitions. We demonstrate the appearance of two-photon Rabi oscillations, and analytically calculate the fundamental and half-harmonic resonance frequencies and the corresponding Rabi frequencies. For EDSR, we find that both the fundamental and the half-harmonic resonance frequencies change upon increasing the strength of the driving electric field, which is an effect analogous to the Bloch-Siegert shift known from MR. Remarkably, the drive-strength-dependent correction to the fundamental EDSR resonance frequency has an anomalous, negative sign, in contrast to the corresponding Bloch-Siegert shift in MR which is always positive. Our analytical results are supported by numerical simulations, as well as by qualitative interpretations for simple limiting cases.

Electron flow in circular n-p junctions of bilayer graphene

We present a theoretical study of electron wave functions in ballistic circular

Valley relaxation in graphene due to charged impurities

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

junctions of bilayer graphene. Similarly to the case of a circular

Two-dimensional electron scattering in regions of nonuniform spin-orbit coupling

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