Interplay between Rashba interaction and electromagnetic field in the edge states of a 2D topological insulator

The effects of Rashba interaction and electromagnetic field on the edge states of a two-dimensional topological insulator are investigated in a non-perturbative way. We show that the electron dynamics is equivalent to a problem of massless Dirac fermions propagating with an inhomogeneous velocity, enhanced by the Rashba profile with respect to the bare Fermi value $v_F$. Despite the inelastic and time-reversal breaking processes induced by the electromagnetic field, no backscattering occurs without interaction. The photoexcited electron densities are explicitly obtained in terms of the electric field and the Rashba interaction, and are shown to fulfil generalised chiral anomaly equations. The case of a Gaussian electromagnetic pulse is analysed in detail. When the photoexcitation occurs far from the Rashba region, the latter effectively acts as a "superluminal gate" boosting the photoexcited wavepacket outside the light-cone determined by $v_F$. In contrast, for an electric pulse overlapping the Rashba region the emerging wavepackets are squeezed in a manner that depends on the overlap area. The electron-electron interaction effects are also discussed, for both intra-spin and inter-spin density-density coupling. The results suggest that Rashba interaction, often considered as an unwanted disorder effect, may be exploited to tailor the shape and the propagation time of photoexcited spin-polarised wave packets.Comment: 15 pages, 6 figure

Noise and current correlations in tunnel junctions of Quantum Spin Hall edge states

The edge channels of two-dimensional topological systems are protected from elastic reflection and are noiseless at low temperature. Yet, noise and cross-correlations can be induced when electron waves partly transmit to the opposite edge via tunneling through a constriction. In particular, in a quantum spin Hall (QSH) system tunnelling occurs via both spin-preserving ($p$) and spin-flipping ($f$) processes, each fulfilling time-reversal symmetry. We investigate the current correlations of a four-terminal QSH setup in the presence of a tunneling region, both at equilibrium and out-of-equilibrium. We find that, although $p$ and $f$ processes do not commute and the generic current correlation depends on both, under appropriate conditions a direct detection of two types of partition noise is possible. In particular, while the spin-preserving partitioning can be probed for any arbitrary tunnel junction with a specific configuration of terminal biases, the spin-flipping partitioning can be directly detected only under suitably designed setups and conditions. We describe two setups where these conditions can be fulfilled, and both types of partitioning can be detected and controlled.Comment: 11 pages, 4 figure

Tuning Excess Noise by Aharonov-Bohm Interferometry

A voltage bias applied to a conductor induces a change of the current noise with respect to the equilibrium noise known as excess noise. We analyze the excess noise of the electronic current flowing through a mesoscopic Aharonov-Bohm ring threaded by a magnetic flux, coupled to a side gate, and contacted by two metallic electrodes. It is shown that the excess noise can be controlled both magnetically and electrostatically, demonstrating the full tunability of the system. At zero frequency, the ratio of the noise strength to the current (Fano factor) can thereby be minimized. Remarkably, at finite frequency, regions of negative excess noise emerge.Comment: 6 pages, 5 figures, final version, corrected typos and updated reference

Effects of disorder on electron tunneling through helical edge states

A tunnel junction between helical edge states, realized via a constriction in a Quantum Spin Hall system, can be exploited to steer both charge and spin current into various terminals. We investigate the effects of disorder on the transmission coefficient $T_p$ of the junction, by modelling disorder with a randomly varying (complex) tunneling amplitude $\Gamma_p=|\Gamma_p| \exp[i \phi_p]$. We show that, while for a clean junction $T_p$ is only determined by the absolute value $|\Gamma_p|$ and is independent of the phase $\phi_p$, the situation can be quite different in the presence of disorder: phase fluctuations may dramatically affect the energy dependence of $T_p$ of any single sample. Furthermore, analysing three different models for phase disorder (including correlated ones), we show that not only the amount but also the way the phase $\phi_p$ fluctuates determines the localisation length $\xi_{loc}$ and the sample-averaged transmission. Finally, we discuss the physical conditions in which these three models suitably apply to realistic cases.Comment: 14 pages, 7 figure

Photoexcitation in two-dimensional topological insulators: Generating and controlling electron wavepackets in Quantum Spin Hall systems

One of the most fascinating challenges in Physics is the realization of an electron-based counterpart of quantum optics, which requires the capability to generate and control single electron wave packets. The edge states of quantum spin Hall (QSH) systems, i.e. two-dimensional (2D) topological insulators realized in HgTe/CdTe and InAs/GaSb quantum wells, may turn the tide in the field, as they do not require the magnetic field that limits the implementations based on quantum Hall effect. Here we show that an electric pulse, localized in space and/or time and applied at a QSH edge, can photoexcite electron wavepackets by intra-branch electrical transitions, without invoking the bulk states or the Zeeman coupling. Such wavepackets are spin-polarised and propagate in opposite directions, with a density profile that is independent of the initial equilibrium temperature and that does not exhibit dispersion, as a result of the linearity of the spectrum and of the chiral anomaly characterising massless Dirac electrons. We also investigate the photoexcited energy distribution and show how, under appropriate circumstances, minimal excitations (Levitons) are generated. Furthermore, we show that the presence of a Rashba spin-orbit coupling can be exploited to tailor the shape of photoexcited wavepackets. Possible experimental realizations are also discussed.Comment: 17 pages, 3 Figure

Tunnel junction of helical edge states: Determining and controlling spin-preserving and spin-flipping processes through transconductance

When a constriction is realized in a 2D quantum spin Hall system, electron tunneling between helical edge states occurs via two types of channels allowed by time-reversal symmetry, namely spin-preserving ({p}) and spin-flipping ({f}) tunneling processes. Determining and controlling the effects of these two channels is crucial to the application of helical edge states in spintronics. We show that, despite the Hamiltonian terms describing these two processes do not commute, the scattering matrix entries of the related 4-terminal setup always factorize into products of p-terms and f-terms contributions. Such factorization provides an operative way to determine the transmission coefficient $T_p$ and $T_f$ related to each of the two processes, via transconductance measurements. Furthermore, these transmission coefficients are also found to be controlled independently by a suitable combination of two gate voltages applied across the junction. This result holds for an arbitrary profile of the tunneling amplitudes, including disorder in the tunnel region, enabling us to discuss the effect of the finite length of the tunnel junction, and the space modulation of both magnitude and phase of the tunneling amplitudes.Comment: 16 pages, 8 figures. Extended Discussion Section, updated reference lis

Full electrical control of Charge and Spin conductance through Interferometry of Edge States in Topological Insulators

We investigate electron interferometry of edge states in Topological Insulators. We show that, when inter-boundary coupling is induced at two quantum point contacts of a four terminal setup, both Fabry-P\'erot-like and Aharonov-Bohm-like loop processes arise. These underlying interference effects lead to a full electrically controllable system, where the magnitude of charge and spin linear conductances can be tuned by gate voltages, without applying magnetic fields. In particular we find that, under appropriate conditions, inter-boundary coupling can lead to negative values of the conductance. Furthermore, the setup also allows to selectively generate pure charge or pure spin currents, by choosing the voltage bias configuration.Comment: 12 pages, 5 figures (expanded discussion section, corrected typos

Dispersionless propagation of electron wavepackets in single-walled carbon nanotubes

We investigate the propagation of electron wavepackets in single-walled carbon nanotubes via a Lindblad-based density-matrix approach that enables us to account for both dissipation and decoherence effects induced by various phonon modes. We show that, while in semiconducting nanotubes the wavepacket experiences the typical dispersion of conventional materials, in metallic nanotubes its shape remains essentially unaltered, even in the presence of the electron-phonon coupling, up to micron distances at room temperature.Comment: 4 pages, 2 figures, accepted by Appl. Phys. Let

Evidence for Majorana bound states in transport properties of hybrid structures based on helical liquids

Majorana bound states can emerge as zero-energy modes at the edge of a two-dimensional topological insulator in proximity to an ordinary s-wave superconductor. The presence of an additional ferromagnetic domain close to the superconductor can lead to their localization. We consider both N-S and S-N-S junctions based on helical liquids and study their spectral properties for arbitrary ferromagnetic scatterers in the normal region. Thereby, we explicitly compute Andreev wave-functions at zero energy. We show under which conditions these states form localized Majorana bound states in N-S and S-N-S junctions. Interestingly, we can identify Majorana-specific signatures in the transport properties of N-S junctions and the Andreev bound levels of S-N-S junctions that are robust against external perturbations. We illustrate these findings with the example of a ferromagnetic double barrier (i.e. a quantum dot) close to the N-S boundaries.Comment: In v2, section IV about Josephson junctions has been partly rewritten in order to discuss the ABS spectrum in the presence of a double ferromagnetic barrier. The list of references has been update