Patrik Recher

Single valley Dirac fermions in zero-gap HgTe quantum wells

Most of the notable properties of graphene are a result of the cone-like nature of the points in its electronic structure where its conduction and valance bands meet. Similar structures arise in 2D HgTe quantum wells, but without the spin- and valley-degeneracy of graphene; their properties are also likely to be easier to control.

Bound states and persistent currents in topological insulator rings

We analyze theoretically the bound state spectrum of an Aharonov Bohm (AB) ring in a two-dimensional topological insulator using the four-band model of HgTe-quantum wells as a concrete example. We calculate analytically the circular helical edge states and their spectrum as well as the bound states evolving out of the bulk spectrum as a function of the applied magnetic flux and dimension of the ring. We also analyze the spin-dependent persistent currents, which can be used to measure the spin of single electrons. We further take into account the Rashba spin-orbit interaction which mixes the spin states and derive its effect on the ring spectrum. The flux tunability of the ring states allows for coherent mixing of the edge- and the spin degrees of freedom of bound electrons which could be exploited for quantum information processing in topological insulator rings.

The Aharonov-Bohm effect in graphene rings

Abstract This is a review of electronic quantum interference in mesoscopic ring structures based on graphene, with a focus on the interplay between the Aharonov–Bohm effect and the peculiar electronic and transport properties of this material. We first present an overview on recent developments of this topic, both from the experimental as well as the theoretical side. We then review our recent work on signatures of two prominent graphene-specific features in the Aharonov–Bohm conductance oscillations, namely Klein tunneling and specular Andreev reflection. We close with an assessment of experimental and theoretical development in the field and highlight open questions as well as potential directions of the developments in future work.

Electric Field Control of Spin Rotation in Bilayer Graphene

The manipulation of the electron spin degree of freedom is at the core of the spintronics paradigm, which offers the perspective of reduced power consumption, enabled by the decoupling of information processing from net charge transfer. Spintronics also offers the possibility of devising hybrid devices able to perform logic, communication, and storage operations. Graphene, with its potentially long spin-coherence length, is a promising material for spin-encoded information transport. However, the small spin-orbit interaction is also a limitation for the design of conventional devices based on the canonical Datta-Das spin field-effect transistors. An alternative solution can be found in magnetic doping of graphene or, as discussed in the present work, in exploiting the proximity effect between graphene and ferromagnetic oxides (FOs). Graphene in proximity to FO experiences an exchange proximity interaction, that acts as an effective Zeeman field for electrons in graphene, inducing a spin precession around the magnetization axis of the FO. Here we show that in an appropriately designed double-gate field-effect transistor, with a bilayer graphene channel and FO used as a gate dielectric, spin-precession of carriers can be turned ON and OFF with the application of a differential voltage to the gates. This feature is directly probed in the spin-resolved conductance of the bilayer.

Renormalization group approach for the scattering off a single Rashba impurity in a helical liquid

The occurrence of two-particle inelastic backscattering has been conjectured in helical edge states of topological insulators and is expected to alter transport. Here, by using a renormalization group approach, we provide a microscopic derivation of this process, in the presence of a time-reversal invariant Rashba impurity potential. We are able to prove that such an effect only occurs in the presence of electron-electron interactions. Furthermore, we find that the linear conductance as a function of temperature exhibits a crossover between two scaling behaviors, T^4K for K>1/2 and T^(8K−2) for K<1/2, with K the Luttinger parameter

Electron transport in multiterminal networks of Majorana bound states

We investigate electron transport through multiterminal networks hosting Majorana bound states (MBS) in the framework of full counting statistics. In particular, we apply our general results to T-shaped junctions of two Majorana nanowires. When the wires are in the topologically nontrivial regime, three MBS are localized near the outer ends of the wires, while one MBS is localized near the crossing point, and when the lengths of the wires are finite adjacent MBS can overlap. We propose a combination of current and cross-correlation measurements to reveal the predicted coupling of four Majoranas in a topological T junction. Interestingly, we show that the elementary transport processes at the central lead are different compared to the outer leads, giving rise to characteristic nonlocal signatures in electronic transport. We find quantitative agreement between our analytical model and numerical simulations of a tight-binding model. Using the numerical simulations, we discuss the effect of weak disorder on the current and the cross-correlation functions.

Proposal for an all-electrical detection of crossed Andreev reflection in topological insulators.

Using a generalized wave matching method we solve the full scattering problem for quantum spin Hall insulator-superconductor (SC)-quantum spin Hall insulator junctions. We find that for systems narrow enough so that the bulk states in the SC part couple both edges, the crossed Andreev reflection (CAR) is significant and the electron cotunneling (T) and CAR become spatially separated. We study the effectiveness of this separation as a function of the system geometry and the level of doping in the SC. Moreover, we show that the spatial separation of both effects allows for an all-electrical measurement of CAR and T separately in a five-terminal setup or by using the spin selection of the quantum spin Hall effect in an H-bar structure.

Chiral Majorana edge states in HgTe quantum wells

HgTe-based quantum wells (QWs) recently attracted a lot of attention for the realization of a two-dimensional topological insulator with protected helical edge states. Another class of topological systems is topological superconductors (TSCs) with Majorana edge states. In this paper, we show how proximity induced s-wave superconductivity in the bulk of HgTe-QWs and in the presence of a Zeeman field can exhibit a TSC with chiral Majorana edge states. We calculate the topological invariants and the corresponding Majorana edge states explicitly within a four-band model accounting for inversion symmetry breaking terms due to the Rashba spin–orbit coupling and bulk inversion asymmetry present in these QWs.

How to distinguish between specular and retroconfigurations for Andreev reflection in graphene rings.

We numerically investigate Andreev reflection in a graphene ring with one normal conducting and one superconducting lead by solving the Bogoliubov-de Gennes equation within the Landauer-Büttiker formalism. By tuning chemical potential and bias voltage, it is possible to switch between regimes where electron and hole originate from the same band (retroconfiguration) or from different bands (specular configuration) of the graphene dispersion, respectively. We find that the dominant contributions to the Aharonov-Bohm conductance oscillations in the subgap transport are of period h/2e in retroconfiguration and of period h/e in specular configuration, confirming the predictions obtained from a qualitative analysis of interfering scattering paths. Because of the robustness against disorder and moderate changes to the system, this provides a clear signature to distinguish both types of Andreev reflection processes in graphene.

Tunable quantum spin Hall effect in double quantum wells

The field of topological insulators (TIs) is rapidly growing. Concerning possible applications, the search for materials with an easily controllable TI phase is a key issue. The quantum spin Hall effect, characterized by a single pair of helical edge modes protected by time-reversal symmetry, has been demonstrated in HgTe-based quantum wells (QWs) with an inverted bandgap. We analyze the topological properties of a generically coupled HgTe-based double QW (DQW) and show how in such a system a TI phase can be driven by an inter-layer bias voltage, even when the individual layers are non-inverted. We argue, that this system allows for similar (layer-)pseudospin based physics as in bilayer graphene but with the crucial absence of a valley degeneracy.