## Publications

#### 2016

##### Quantum time mirrors

**V. Krueckl**, M. Fink, K. Richter

arXiv:1603.07503

Both metaphysical and practical considerations related to time inversion have intrigued scientists for generations. Physicists have strived to devise and implement time-inversion protocols, in particular different forms of "time mirrors" for classical waves. Here we propose two conceptually different realisations of instantaneous time mirrors for quantum systems, i.e. controlled time discontinuities acting through pulses on wavefronts and leading to distinct wave function echoes with high fidelities. The first concept exploits up to now unrelated mechanisms of wavefront time inversion and population reversal in spatially extended two-level systems, the latter quintessential to spin echoes. It can be implemented in Dirac-like systems, such as (real or artificial) graphene. The second protocol is based on a non-linear mirror for a Bose-Einstein condensate whose dynamics is described by the non-linear Schr\"odinger equation, and is realisable in cold atom setups.

#### 2015

##### Two-dimensional topological insulator edge state backscattering by dephasing

**V. Krueckl**, K. Richter

Physical Review B

**92**, 205306

To understand the seemingly absent temperature dependence in the conductance of two-dimensional topological insulator edge states, we perform a numerical study which identifies the quantitative influence of the combined effect of dephasing and elastic scattering in charge puddles close to the edges. We show that this mechanism may be responsible for the experimental signatures in HgTe/CdTe quantum wells if the puddles in the samples are large and weakly coupled to the sample edges. We propose experiments on artificial puddles which allow to verify this hypothesis and to extract the real dephasing time scale using our predictions. In addition, we present a new method to include the effect of dephasing in wave-packet-time-evolution algorithms.

#### 2014

##### Fabry-Pérot interference in gapped bilayer graphene with broken anti-Klein tunneling

**V. Krueckl**, D. Bischoff, P. Simonet, K. Watanabe, T. Taniguchi, K. Richter, K. Ensslin, T. Ihn

*Physical Review Letters*

**113**, 116601 (2014)

We report the experimental observation of Fabry-Pérot (FP) interference in the conductance of a gate-defined cavity in a dual-gated bilayer graphene (BLG) device. The high quality of the BLG flake, combined with the device's electrical robustness provided by the encapsulation between two hexagonal boron nitride layers, allows us to observe ballistic phase-coherent transport through a 1µm-long cavity. We confirm the origin of the observed interference pattern by comparing to tight-binding calculations accounting for the gate-tunable bandgap. The good agreement between experiment and theory, free of tuning parameters, further verifies that a gap opens in our device. The gap is shown to destroy the perfect reflection for electrons traversing the barrier with normal incidence (anti-Klein tunneling). The broken anti-Klein tunneling implies that the Berry phase, which is found to vary with the gate voltages, is always involved in the FP oscillations regardless of the magnetic field, in sharp contrast with single-layer graphene.

##### Using Topological Insulator Proximity to Generate Perfectly Conducting Channels in Materials without Topological Protection

**V. Krueckl**, K. Richter

New Journal of Physics

**16**, 113058

We show that hybrid structures of topological insulators and materials without topological protection can be employed to create perfectly conducting channels hosted in the non-topological part. These states inherit the topological protection from the proximity of the topological insulator but are more fragile to time-reversal symmetry breaking because of their extended character. We explore their formation in the band structure of model hybrid systems as well as realistic heterostructures involving HgTe/CdTe-based two-dimensional topological insulators. Using numerical quantum transport calculations for the HgTe/CdTe material system we propose two experimental settings which allow for the detection of the induced perfectly conducting channels, both in the localized and diffusive regime, by means of magneto conductance and shot noise.

#### 2013

##### Wave packets in mesoscopic systems:

From time-dependent dynamics to transport phenomena in graphene and topological insulators

**V. Krueckl**

Dissertation,

*Univ.-Verl. Regensburg, ISBN 978-3-86845-097-2*

At the beginning of 21th century, the range of solid state materials was extended by crystals featuring charge excitations with a chiral spin or pseudo-spin texture close to the Fermi energy. Such exceptional electronic properties can be found in graphene or topological insulators, which both render a great potential for upcoming electronic devices.

In this thesis, mesoscopic systems of such solid state materials are investigated by a time-dependent scheme, which describes the electronic excitations by the propagation of wave packets. Based on the time evolution of initial states dynamical and static observables are studied and new electronic phenomena are revealed. For example, the motion of electrons in graphene or topological insulators exhibit time-dependent features like Bloch-Zener oscillations or wave-packet revivals, which are not present in conventional electron gases. Also static properties, like transport characteristics, are encoded in the time evolution. For instance, the switching features of a topological insulator constriction can be extracted from a single wave-packet injected into a lead. The underlying effect builds the foundation of a novel charge and spin-transistor, which is presented in this thesis alongside other proposals for novel experiments in graphene or topological insulators.

#### 2012

##### Probing the Band Topology of Mercury Telluride through Weak Localization and Antilocalization

**V. Krueckl**, und K. Richter

*Semicond. Sci. Technol. (special issue on "Topological Insulators")*

**27**, 124006 (2012)

We analyze the effect of weak localization (WL) and weak antilocalization (WAL) in the electronic transport through HgTe/CdTe quantum wells. We show that for increasing Fermi energy the magnetoconductance of a diffusive system with inverted band ordering features a transition from WL to WAL and back, if spin-orbit interactions from bulk and structure inversion asymmetry can be neglected. This, and an additional splitting in the magnetoconductance profile, is a signature of the Berry phase arising for inverted band ordering and not present in heterostructures with conventional ordering. In presence of spin-orbit interaction both band topologies exhibit WAL, which is distinctly energy dependent solely for quantum wells with inverted band ordering. This can be explained by an energy-dependent decomposition of the Hamiltonian into two blocks.

##### Switching spin and charge between edge states in topological insulator constrictions: a transer matrix approach

**V. Krueckl**, und K. Richter

*Proc. SPIE 8461, Spintronics V*

**84610Z**(2012)

We show how the different spin polarized edge states of the two-dimensional topological insulator mercury telluride can be selectively switched within an elongated constriction. To this end, we derive an effective onedimensional Hamiltonian incorporating the confinement induced gap between right- and left-moving edge states, as well as an energy dependent effective spin-orbit interaction. By means of a transfer matrix approach, we study the transport properties based on this model Hamiltonian and reveal switching characteristics that can serve as the building block for a three state spin- and charge transistor based on a locally gated topological insulator constriction.

##### Bloch-Zener oscillations in graphene and topological insulators

**V. Krueckl**, und K. Richter

*Physical Review B*

**85**, 115433 (2012)

We show that superlattices based on zero-gap semiconductors such as graphene and mercury telluride exhibit characteristic Bloch-Zener oscillations that emerge from the coherent superposition of Bloch oscillations and multiple Zener tunneling between the electron and hole branch. We demonstrate this mechanism by means of wave-packet dynamics in various spatially periodically modulated nanoribbons subject to an external bias field. The associated Bloch frequencies exhibit a peculiar periodic bias dependence, which we explain within a two-band model. Supported by extensive numerical transport calculations, we show that this effect gives rise to distinct current oscillations observable in the I-V characteristics of graphene and mercury telluride superlattices.

#### 2011

##### Switching spin and charge between edge states in topological insulator constriction

**V. Krueckl**, und K. Richter

*Physical Review Letters*

**107**, 086803 (2011)

We show how the coupling between opposite edge states, which overlap in
a constriction made of the topological insulator mercury telluride (HgTe),
can be employed both for steering the charge flow into different
edge modes and for controlled spin switching.
Unlike in a conventional spin transistor, the switching does not rely on
a tunable Rashba spin-orbit interaction, but on the energy dependence
of the edge state wavefunctions.

Based on this mechanism, and supported by extensive numerical transport calculations,
we present two different ways to control
spin- and charge-currents, depending on the local gating of the constriction,
resulting in a high fidelity spin transistor.

##### Weak localization in mesoscopic hole transport: Berry phases and classical correlations

**V. Krueckl**, M. Wimmer, I. Adagideli, J. Kuipers, und K. Richter

*Physical Review Letters*

**106**, 146801 (2011)

We consider phase-coherent transport through ballistic and diffusive two-dimensional hole systems based on the Kohn-Luttinger Hamiltonian. We show that intrinsic heavy-hole–light-hole coupling gives rise to clear-cut signatures of an associated Berry phase in the weak localization which renders the magnetoconductance profile distinctly different from electron transport. Nonuniversal classical correlations determine the strength of these Berry phase effects and the effective symmetry class, leading even to antilocalization-type features for circular quantum dots and Aharonov-Bohm rings in the absence of additional spin-orbit interaction. Our semiclassical predictions are confirmed by numerical calculations.

#### 2010

##### Wave packet approach to transport in mesoscopic systems

**V. Krueckl**

*Physica Scripta*

**82**, 038101 (2010)

Wave packets provide a well established and versatile tool for studying time-dependent effects in molecular physics. Here, we demonstrate the application of wave packets to mesoscopic nanodevices at low temperatures. The electronic transport in the devices is expressed in terms of scattering and transmission coefficients, which are efficiently obtained by solving an initial value problem (IVP) using the time-dependent Schroedinger equation. The formulation as an IVP makes non-trivial device topologies accessible and by tuning the wave packet parameters one can extract the scattering properties for a large range of energies.

##### Self-consistent calculation of electric potentials in Hall devices

**V. Krueckl**, E. J. Heller, und R. E. Parrott

*Physical Review B*

**81**, 205306 (2010)

Using a first-principles classical many-body simulation of a Hall bar, we study the necessary conditions for the formation of the Hall potential: (i) Ohmic contacts with metallic reservoirs, (ii) electron-electron interactions, and (iii) confinement to a finite system. By propagating thousands of interacting electrons over million time-steps we capture the build-up of the self-consistent potential, which resembles results obtained by conformal-mapping methods. As shown by a microscopic model of the current injection, the Hall effect is linked to specific boundary conditions at the particle reservoirs.

##### Theory of the quantum Hall effect in finite graphene devices

**V. Krueckl**, E. J. Heller, R. E. Parrott, und C.-T. Liang

*Physical Review B*

**81**, 081410 (2010)

We study the quantum Hall effect (QHE) in graphene based on the current injection model. In our model, the presence of disorder, the edge-state picture, extended states and localized states, which are believed to be indispensable ingredients in describing the QHE, do not play an important role. Instead the boundary conditions during the injection into the graphene sheet, which are enforced by the presence of the Ohmic contacts, determine the current-voltage characteristics.

#### 2009

##### Revivals of quantum wave packets in graphene

**V. Krueckl**, und T. Kramer

*New Journal of Physics*

**11**, 093010 (2009)

We investigate the propagation of wave-packets on graphene in a perpendicular magnetic field and the appearance of collapses and revivals in the time-evolution of an initially localised wave-packet. The wave-packet evolution in graphene differs drastically from the one in an electron gas and shows a rich revival structure similar to the dynamics of highly excited Rydberg states. We present a novel numerical wave-packet propagation scheme in order to solve the effective single-particle Dirac-Hamiltonian of graphene and show how the collapse and revival dynamics is affected by the presence of disorder. Our effective numerical method is of general interest for the solution of the Dirac equation in the presence of potentials and magnetic fields.