arXiv subjects

Niclas Müller

Publications and source records attributed to Niclas Müller.

6 recordsLinked to original sources

arXiv2022

Universal properties of boundary and interface charges in multichannel one-dimensional continuum models

We generalize our recent results for the boundary and interface charges in one-dimensional single-channel continuum [Phys. Rev. B 104, 155409 (2021)] and multichannel tight-binding [Phys. Rev. B 104, 125447 (2021)] models to the realm of the multichannel continuum systems. Using the technique of boundary Green's functions, we give a rigorous proof that the change in boundary charge upon the shift of the system towards the boundary by the distance $x_φ\in[0, L]$ is given by a perfectly linear function of $x_φ$ plus an integer-valued topological invariant $I$ -- the so called boundary invariant. For systems with weak potential amplitudes, we additionally develop Green's function-based low-energy theory, allowing one to analytically access the physics of multichannel continuum systems in the low-energy approximation.

cond-mat.mes-hall↗

arXiv2021

Universal properties of boundary and interface charges in multichannel one-dimensional models without symmetry constraints

The boundary charge that accumulates at the edge of a one-dimensional single-channel insulator is known to possess the universal property, that its change under a lattice shift towards the edge by one site is given by the sum of the average bulk electronic density and a topologically invariant contribution, restricted to the values $0$ and $-1$ [Phys. Rev. B 101, 165304 (2020)]. This quantized contribution is associated with particle-hole duality, ensures charge conservation and fixes the mod(1) ambiguity appearing in the Modern Theory of Polarization. In the present work we generalize the above-mentioned single-channel results to the multichannel case by employing the technique of boundary Green's functions. We show that the topological invariant associated with the change in boundary charge under a lattice shift in multichannel models can be expressed as a winding number of a certain combination of components of bulk Green's functions as function of the complex frequency, as it encircles the section of the energy axis that corresponds to the occupied part of the spectrum. We observe that this winding number is restricted to values ranging from $-N_c$ to $0$, where $N_c$ is the number of channels (orbitals) per site. Furthermore, we consider translationally invariant one-dimensional multichannel models with an impurity and introduce topological indices which correspond to the quantized charge that accumulates around said impurity. These invariants are again given in terms of winding numbers of combinations of components of bulk Green's functions. Through this construction we provide a rigorous mathematical proof of the so called nearsightedness principle formulated by W. Kohn [Phys. Rev. Lett. 76, 3168 (1996)] for noninteracting multichannel lattice models.

cond-mat.mes-hall↗

arXiv2020

Quadrupole spin polarization as signature of second-order topological superconductors

We study theoretically second-order topological superconductors characterized by the presence of pairs of zero-energy Majorana corner states. We uncover a quadrupole spin polarization at the system edges that provides a striking signature to identify topological phases, thereby complementing standard approaches based on zero-bias conductance peaks due to Majorana corner states. We consider two different classes of second-order topological superconductors with broken time-reversal symmetry and show that both classes are characterized by a quadrupolar structure of the spin polarization that disappears as the system passes through the topological phase transition. This feature can be accessed experimentally using spin-polarized scanning tunneling microscopes. We study different models hosting second-order topological phases, both analytically and numerically, and using Keldysh techniques we provide numerical simulations of the spin-polarized currents probed by scanning tips.

cond-mat.mes-hall↗

arXiv2020

Chiral 1D Floquet topological insulators beyond rotating wave approximation

We study one-dimensional (1D) Floquet topological insulators with chiral symmetry going beyond the standard rotating wave approximation. The occurrence of many anticrossings between Floquet replicas leads to a dramatic extension of phase diagram regions with stable topological edge states (TESs). We present an explicit construction of all TESs in terms of a truncated Floquet Hamiltonian in frequency space, prove the bulk-boundary correspondence, and analyze the stability of the TESs in terms of their localization lengths. We propose experimental tests of our predictions in curved bilayer graphene.

cond-mat.mes-hall↗

arXiv2020

Electronic transport in one-dimensional Floquet topological insulators via topological and nontopological edge states

Based on probing electronic transport properties we propose an experimental test for the recently discovered rich topological phase diagram of one-dimensional Floquet topological insulators with Rashba spin-orbit interaction [Kennes \emph{et al.}, Phys. Rev. B {\bf 100}, 041103(R) (2019)]. Using the Keldysh-Floquet formalism we compute electronic transport properties of these nanowires, where we propose to couple the leads in such a way, as to primarily address electronic states with a large weight at one edge of the system. By tuning the Fermi energy of the leads to the center of the topological gap we are able to directly address the topological edge states, granting experimental access to the topological phase diagram. Surprisingly, when tuning the lead Fermi energy to special values in the bulk which coincide with extremal points of the dispersion relation, we find additional peaks of similar magnitude to those caused by the topological edge states. These peaks reveal the presence of continua of states centered around aforementioned extremal points whose wavefunctions are linear combinations of delocalized bulk states and exponentially localized edge states, where the ratio of edge- to bulk-state amplitude is maximal at the extremal point of the dispersion. We discuss the transport properties of these \emph{non-topological edge states}, explain their emergence in terms of an intuitive yet quantitative physical picture and discuss their relationship with Van Hove singularities in the bulk of the system. The mechanism giving rise to these states is not specific to the model we consider here, suggesting that they may be present in a wide class of one-dimensional systems.

cond-mat.mes-hall↗

arXiv2016

Photonic Kondo model

Here we introduce and study a photonic analogue of the Kondo model. The model is defined as a far detuned regime of photonic scattering off a three-level emitter in a $Λ$-type configuration coupled to a one-dimensional transmission line with linear dispersion. We characterize this system by studying the dynamics of a local system (emitter) driven by a coherent field pulse as well as the first- and second-order correlation functions of the scattered light. Various polarization-dependent correlation effects including entanglement between the emitter and transmitted photons are quantified by the purity of the emitter's state. We also show that statistical properties of the scattered light are very sensitive to the polarization of the incoming coherent pulse.

quant-ph↗