arXiv subjects

Christoph Groth

Publications and source records attributed to Christoph Groth.

11 recordsLinked to original sources

arXiv2024

Computational quantum transport: a scattering approach perspective

This review is devoted to the different techniques that have been developed to compute the phase-coherent transport properties of quantum nanoelectronic systems connected to electrodes. Beside a review of the different algorithms proposed in the literature, we provide a comprehensive and pedagogical derivation of the two formalisms on which these techniques are based: the scattering approach and the (nonequilibrium) Green's function approach. We show that the scattering problem can be formulated as a system of linear equations and that different existing algorithms for solving this scattering problem amount to different sequences of Gaussian elimination. We explicitly prove the equivalence of the two formalisms. We discuss the stability and numerical complexity of the existing methods. The review ends with a selection of a few applications where numerical calculations were instrumental in shaping our understanding of the physics.

cond-mat.mes-hall↗

arXiv2021

Tkwant: a software package for time-dependent quantum transport

Tkwant is a Python package for the simulation of quantum nanoelectronics devices to which external time-dependent perturbations are applied. Tkwant is an extension of the Kwant package (https://kwant-project.org/) and can handle the same types of systems: discrete tight-binding-like models that consist of an arbitrary central region connected to semi-infinite electrodes. The problem is genuinely many-body even in the absence of interactions and is treated within the non-equilibrium Keldysh formalism. Examples of Tkwant applications include the propagation of plasmons generated by voltage pulses, propagation of excitations in the quantum Hall regime, spectroscopy of Majorana fermions in semiconducting nanowires, current-induced skyrmion motion in spintronic devices, multiple Andreev reflection, Floquet topological insulators, thermoelectric effects, and more. The code has been designed to be easy to use and modular. Tkwant is free software distributed under a BSD license and can be found at https://tkwant.kwant-project.org/.

cond-mat.mes-hall↗

arXiv2019

Pushing the limit of quantum transport simulations

Simulations of quantum transport in coherent conductors have evolved into mature techniques that are used in fields of physics ranging from electrical engineering to quantum nanoelectronics and material science. The most efficient general-purpose algorithms have a computational cost that scales as $L^{6 \dots 7}$ in 3D, which on the one hand is a substantial improvement over older algorithms, but on the other hand still severely restricts the size of the simulation domain, limiting the usefulness of simulations through strong finite-size effects. Here, we present a novel class of algorithms that, for certain systems, allows to directly access the thermodynamic limit. Our approach, based on the Green's function formalism for discrete models, targets systems which are mostly invariant by translation, i.e. invariant by translation up to a finite number of orbitals and/or quasi-1D electrodes and/or the presence of edges or surfaces. Our approach is based on an automatic calculation of the poles and residues of series expansions of the Green's function in momentum space. This expansion allows to integrate analytically in one momentum variable. We illustrate our algorithms with several applications: devices with graphene electrodes that consist of half an infinite sheet; Friedel oscillation calculations of infinite 2D systems in presence of an impurity; quantum spin Hall physics in presence of an edge; the surface of a Weyl semi-metal in presence of impurities and electrodes connected to the surface. In this last example, we study the conduction through the Fermi arcs of the topological material and its resilience to the presence of disorder. Our approach provides a practical route for simulating 3D bulk systems or surfaces as well as other setups that have so far remained elusive.

cond-mat.mes-hall↗

arXiv2016

Control of the Oscillatory Interlayer Exchange Interaction with Terahertz Radiation

The oscillatory interlayer exchange interaction between two magnetic layers separated by a metallic spacer is one of the few coherent quantum phenomena that persist at room temperature. Here we show that this interaction can be controlled dynamically by illuminating the sample (e.g. a spin valve) with radiation in the 10-100 THz range. We predict that the exchange interaction can be changed from ferromagnetic to anti-ferromagnetic (and vice versa) by tuning the amplitude and/or the frequency of the radiation. Our chief theoretical result is an expression that relates the dynamical exchange interaction to the static one that has already been extensively measured.

cond-mat.mes-hall↗

arXiv2015

Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices

We present a simple, general purpose, quantum Monte-Carlo algorithm for out-of-equilibrium interacting nanoelectronics systems. It allows one to systematically compute the expansion of any physical observable (such as current or density) in powers of the electron-electron interaction coupling constant $U$. It is based on the out-of-equilibrium Keldysh Green's function formalism in real-time and corresponds to evaluating all the Feynman diagrams to a given order $U^n$ (up to $n=15$ in the present work). A key idea is to explicitly sum over the Keldysh indices in order to enforce the unitarity of the time evolution. The method can easily reach long time, stationary regimes, even at zero temperature. We then illustrate our approach with an application to the Anderson model, an archetype interacting mesoscopic system. We recover various results of the literature such as the spin susceptibility or the "Kondo ridge" in the current-voltage characteristics. In this case, we found the Monte-Carlo free of the sign problem even at zero temperature, in the stationary regime and in absence of particle-hole symmetry. The main limitation of the method is the lack of convergence of the expansion in $U$ for large $U$, i.e. a mathematical property of the model rather than a limitation of the Monte-Carlo algorithm. Standard extrapolation methods of divergent series can be used to evaluate the series in the strong correlation regime.

cond-mat.mes-hall↗

arXiv2014

Classical and quantum spreading of a charge pulse

With the technical progress of radio-frequency setups, high frequency quantum transport experiments have moved from theory to the lab. So far the standard theoretical approach used to treat such problems numerically--known as Keldysh or NEGF (Non Equilibrium Green's Functions) formalism--has not been very successful mainly because of a prohibitive computational cost. We propose a reformulation of the non-equilibrium Green's function technique in terms of the electronic wave functions of the system in an energy-time representation. The numerical algorithm we obtain scales now linearly with the simulated time and the volume of the system, and makes simulation of systems with 10^5 - 10^6 atoms/sites feasible. We illustrate our method with the propagation and spreading of a charge pulse in the quantum Hall regime. We identify a classical and a quantum regime for the spreading, depending on the number of particles contained in the pulse. This numerical experiment is the condensed matter analogue to the spreading of a Gaussian wavepacket discussed in quantum mechanics textbooks.

cond-mat.mes-hall↗

arXiv2014

Theoretical, numerical, and experimental study of a flying qubit electronic interferometer

We discuss an electronic interferometer recently measured by Yamamoto et al. This "flying quantum bit" experiment showed quantum oscillations between electronic trajectories of two tunnel-coupled wires connected via an Aharanov-Bohm ring. We present a simple scattering model as well as a numerical microscopic model to describe this experiment. In addition, we present new experimental data to which we confront our numerical results. While our analytical model provides basic concepts for designing the flying qubit device, we find that our numerical simulations allow to reproduce detailed features of the transport measurements such as in-phase and anti-phase oscillations of the two output currents as well as a smooth phase shift when sweeping a side gate. Furthermore, we find remarkable resemblance for the magneto conductance oscillations in both conductance and visibility between simulations and experiments within a specific parameter range.

cond-mat.mes-hall↗

arXiv2014

Numerical simulations of time resolved quantum electronics

This paper discusses the technical aspects - mathematical and numerical - associated with the numerical simulations of a mesoscopic system in the time domain (i.e. beyond the single frequency AC limit). After a short review of the state of the art, we develop a theoretical framework for the calculation of time resolved observables in a general multiterminal system subject to an arbitrary time dependent perturbation (oscillating electrostatic gates, voltage pulses, time-vaying magnetic fields) The approach is mathematically equivalent to (i) the time dependent scattering formalism, (ii) the time resolved Non Equilibrium Green Function (NEGF) formalism and (iii) the partition-free approach. The central object of our theory is a wave function that obeys a simple Schrodinger equation with an additional source term that accounts for the electrons injected from the electrodes. The time resolved observables (current, density. . .) and the (inelastic) scattering matrix are simply expressed in term of this wave function. We use our approach to develop a numerical technique for simulating time resolved quantum transport. We find that the use of this wave function is advantageous for numerical simulations resulting in a speed up of many orders of magnitude with respect to the direct integration of NEGF equations. Our technique allows one to simulate realistic situations beyond simple models, a subject that was until now beyond the simulation capabilities of available approaches.

cond-mat.mes-hall↗

arXiv2012

Competing topological phases in few-layer graphene

We investigate the effect of spin-orbit coupling on the band structure of graphene-based two-dimensional Dirac fermion gases in the quantum Hall regime. Taking monolayer graphene as our first candidate, we show that a quantum phase transition between two distinct topological states -- the quantum Hall and the quantum spin Hall phases -- can be driven by simply tuning the Fermi level with a gate voltage. This transition is characterized by the existence of a chiral spin-polarized edge state propagating along the interface separating the two topological phases. We then apply our analysis to the more difficult case of bilayer graphene. Unlike in monolayer graphene, spin-orbit coupling by itself has indeed been predicted to be unsuccessful in driving bilayer graphene into a topological phase, due to the existence of an even number of pairs of spin-polarized edge states. While we show that this remains the case in the quantum Hall regime, we point out that by additionally breaking the layer inversion symmetry, a non-trivial quantum spin Hall phase can re-emerge in bilayer graphene at low energy. We consider two different symmetry-breaking mechanisms: inducing spin-orbit coupling only in the upper layer, and applying a perpendicular electric field. In both cases, the presence at low energy of an odd number of pairs of edge states can be driven by an exchange field. The related situation in trilayer graphene is also discussed.

cond-mat.mes-hall↗

arXiv2012

Graphene-based heterojunction between two topological insulators

Quantum Hall (QH) and quantum spin Hall (QSH) phases have very different edge states and, when going from one phase to the other, the direction of one edge state must be reversed. We study this phenomena in graphene in presence of a strong perpendicular magnetic field on top of a spin-orbit (SO) induced QSH phase. We show that, below the SO gap, the QSH phase is virtually unaffected by the presence of the magnetic field. Above the SO gap, the QH phase is restored. An electrostatic gate placed on top of the system allows to create a QSH-QH junction which is characterized by the existence of a spin-polarized chiral state, propagating along the topological interface. We find that such a setup naturally provides an extremely sensitive spin-polarized current switch.

cond-mat.mes-hall↗

arXiv2012

Tunable thermopower in a graphene-based topological insulator

Following the recent proposal by Weeks et al., which suggested that indium (or thallium) adatoms deposited on the surface of graphene should turn the latter into a quantum spin Hall (QSH) insulator characterized by a sizeable gap, we perform a systematic study of the transport properties of this system as a function of the density of randomly distributed adatoms. While the samples are, by construction, very disordered, we find that they exhibit an extremely stable QSH phase with no signature of the spatial inhomogeneities of the adatom configuration. We find that a simple rescaling of the spin-orbit coupling parameter allows us to account for the behaviour of the inhomogeneous system using a homogeneous model. This robustness opens the route to a much easier experimental realization of this topological insulator. We additionally find this material to be a very promising candidate for thermopower generation with a target temperature tunable from 1 to 80K and an efficiency ZT close to 1.

cond-mat.mes-hall↗