arXiv subjects

Bernd Rosenow

Publications and source records attributed to Bernd Rosenow.

At least 55 records · Page 3Linked to original sources

arXiv2021

Equivalence of Spatial and Particle Entanglement Growth After a Quantum Quench

We analyze fermions after an interaction quantum quench in one spatial dimension and study the growth of the steady state entanglement entropy density under either a spatial mode or particle bipartition. For integrable lattice models, we find excellent agreement between the increase of spatial and particle entanglement entropy, and for chaotic models, an examination of two further neighbor interaction strengths suggests similar correspondence. This result highlights the generality of the dynamical conversion of entanglement to thermodynamic entropy under time evolution that underlies our current framework of quantum statistical mechanics.

cond-mat.stat-mech↗

arXiv2021

Tunable topological states hosted by unconventional superconductors with adatoms

Chains of magnetic atoms, placed on the surface of s-wave superconductors, have been established as a laboratory for the study of Majorana bound states. In such systems, the breaking of time reversal due to magnetic moments gives rise to the formation of in-gap states, which hybridize to form one-dimensional topological superconductors. However, in unconventional superconductors even non-magnetic impurities induce in-gap states since scattering of Cooper pairs changes their momentum but not their phase. Here, we propose a path for creating topological superconductivity, which is based on an unconventional superconductor with a chain of non-magnetic adatoms on its surface. The topological phase can be reached by tuning the magnitude and direction of a Zeeman field, such that Majorana zero modes at its boundary can be generated, moved and fused. To demonstrate the feasibility of this platform, we develop a general mapping of films with adatom chains to one-dimensional lattice Hamiltonians. This allows us to study unconventional superconductors such as Sr$_2$RuO$_4$ exhibiting multiple bands and an anisotropic order parameter.

cond-mat.supr-con↗

arXiv2021

Soft Mode in the Dynamics of Over-realizable On-line Learning for Soft Committee Machines

Over-parametrized deep neural networks trained by stochastic gradient descent are successful in performing many tasks of practical relevance. One aspect of over-parametrization is the possibility that the student network has a larger expressivity than the data generating process. In the context of a student-teacher scenario, this corresponds to the so-called over-realizable case, where the student network has a larger number of hidden units than the teacher. For on-line learning of a two-layer soft committee machine in the over-realizable case, we find that the approach to perfect learning occurs in a power-law fashion rather than exponentially as in the realizable case. All student nodes learn and replicate one of the teacher nodes if teacher and student outputs are suitably rescaled.

cond-mat.dis-nn↗

arXiv2021

Observation of quantum Hall interferometer phase jumps due to changing quasiparticle number

We measure the magneto-conductance through a micron-sized quantum dot hosting about 500 electrons in the quantum Hall regime. In the Coulomb blockade, when the island is weakly coupled to source and drain contacts, edge reconstruction at filling factors between one and two in the dot leads to the formation of two compressible regions tunnel coupled via an incompressible region of filling factor $ν=1$. We interpret the resulting conductance pattern in terms of a phase diagram of stable charge in the two compressible regions. Increasing the coupling of the dot to source and drain, we realize a Fabry-Pérot quantum Hall interferometer, which shows an interference pattern strikingly similar to the phase diagram in the Coulomb blockade regime. We interpret this experimental finding using an empirical model adapted from the Coulomb blockaded to the interferometer case. The model allows us to relate the observed abrupt jumps of the Fabry-Pérot interferometer phase to a change in the number of bulk quasiparticles. This opens up an avenue for the investigation of phase shifts due to (fractional) charge redistributions in future experiments on similar devices.

cond-mat.mes-hall↗

arXiv2021

Symmetry-related transport on a fractional quantum Hall edge

Low-energy transport in quantum Hall states is carried through edge modes, and is dictated by bulk topological invariants and possibly microscopic Boltzmann kinetics at the edge. Here we show how the presence or breaking of symmetries of the edge Hamiltonian underlie transport properties, specifically d.c. conductance and noise. We demonstrate this through the analysis of hole-conjugate states of the quantum Hall effect, specifically the $ν=2/3$ case in a quantum point-contact (QPC) geometry. We identify two symmetries, a continuous $SU(3)$ and a discrete $Z_3$, whose presence or absence (different symmetry scenarios) dictate qualitatively different types of behavior of conductance and shot noise. While recent measurements are consistent with one of these symmetry scenarios, others can be realized in future experiments.

cond-mat.mes-hall↗

arXiv2020

Bulk-boundary correspondence for non-Hermitian Hamiltonians via Green functions

Genuinely non-Hermitian topological phases can be realized in open systems with sufficiently strong gain and loss; in such phases, the Hamiltonian cannot be deformed into a gapped Hermitian Hamiltonian without energy bands touching each other. Comparing Green functions for periodic and open boundary conditions we find that, in general, there is no correspondence between topological invariants computed for periodic boundary conditions, and boundary eigenstates observed for open boundary conditions. Instead, we find that the non-Hermitian winding number in one dimension signals a topological phase transition in the bulk: It implies spatial growth of the bulk Green function.

cond-mat.mes-hall↗

arXiv2020

Topological Magnetoelectric Effect: Nonlinear Time-Reversal-Symmetric Response, Witten Effect, and Half-Integer Quantum Hall Effect

Topological insulators (TIs) in three space dimensions can be characterized by a quantized magnetoelectric coefficient. However, this coupling does not have experimentally observable consequences in the presence of time-reversal symmetry, because the contributions of both bulk and surface states cancel each other. Instead, the characteristic response of a TI is a nonlinear magnetoelectric effect. Field theoretic aspects of the nonlinear magnetoelectric response and numerical calculations for experimentally relevant geometries are discussed. Distinct from this effect, the magnetoelectric coupling would bind a charge $\pm e/2$ in response to a monopole, which is referred to as Witten effect. If time reversal is broken explicitly, for instance, by a Zeeman field acting on the surface layer, the electromagnetic response of a TI can be described by a half-integer quantum Hall effect of surface electrons.

cond-mat.mes-hall↗

arXiv2020

Exponentially growing bulk Green functions as signature of nontrivial non-Hermitian winding number in one dimension

A nonzero non-Hermitian winding number indicates that a gapped system is in a nontrivial topological class due to the non-Hermiticity of its Hamiltonian. While for Hermitian systems nontrivial topological quantum numbers are reflected by the existence of edge states, a nonzero non-Hermitian winding number impacts a system's bulk response. To establish this relation, we introduce the bulk Green function, which describes the response of a gapped system to an external perturbation on timescales where the induced excitations have not propagated to the boundary yet, and show that it will grow in space if the non-Hermitian winding number is nonzero. Such spatial growth explains why the response of non-Hermitian systems on longer timescales, where excitations have been reflected at the boundary repeatedly, may be highly sensitive to boundary conditions. This exponential sensitivity to boundary conditions explains the breakdown of the bulk-boundary correspondence in non-Hermitian systems: topological invariants computed for periodic boundary conditions no longer predict the presence or absence of boundary states for open boundary conditions.

cond-mat.mes-hall↗

arXiv2020

Electron-pairing in the quantum Hall regime due to neutralon exchange

The behavior of electrons in condensed matter systems is mostly determined by the repulsive Coulomb interaction. However, under special circumstances the Coulomb interaction can be effectively attractive, giving rise to electron pairing in unconventional superconductors and specifically designed mesoscopic setups. In quantum Hall systems electron interactions can play a particularly important role due to the huge degeneracy of Landau levels, leading for instance to the emergence of quasi-particles with fractional charge and anyonic statistics. Quantum Hall Fabry-Pérot (FPI) interferometers have attracted increasing attention due to their ability to probe such exotic physics. In addition, such interferometers are affected by electron interactions themselves in interesting ways. Recently, experimental evidence for electron pairing in a quantum Hall FPI was found (H.K. Choi et al., Nat. Comm 6, 7435 (2015)) . Theoretically describing an FPI in the limit of strong backscattering and under the influence of a screened Coulomb interaction, we compute electron shot noise and indeed find a two-fold enhanced Fano factor for some parameters, indicative of electron pairing. This result is explained in terms of an electron interaction due to exchange of neutral inter-edge plasmons, so-called neutralons.

cond-mat.mes-hall↗

arXiv2020

Fractional Coulomb blockade for quasiparticle tunneling between edge channels

We study the magneto-conductance of a $1.4~\mathrm{μm}$-wide quantum dot in the fractional quantum Hall regime. For a filling factor $\approx 2/3$ and $\gtrsim 1/3$ in the quantum dot the observed Coulomb resonances show a periodic modulation in magnetic field. This indicates a non-trivial reconstruction of the 2/3 fractional quantum Hall state in the quantum dot. We present a model for the charge stability diagram of the system assuming two compressible regions separated by an incompressible stripe of filling factor $2/3$ and $1/3$, respectively. From the dependence of the magnetic field period on total magnetic field we construct the zero-field charge density distribution in the quantum dot. The tunneling between the two compressible regions exhibits fractional Coulomb blockade. For both filling factor regions, we extract a fractional charge $e^*/e = 0.32 \pm 0.03$ by comparing to measurements at filling factor 2. With their close relation to quantum Hall Fabry-Pérot interferometers, our investigations on quantum dots in the fractional quantum Hall regime extend and complement interference experiments investigating the nature of anyonic fractional quantum Hall quasiparticles.

cond-mat.mes-hall↗

arXiv2019

Flux superperiods and periodicity transitions in quantum Hall interferometers

For strongly screened Coulomb interactions, quantum Hall interferometers can operate in a novel regime: the intrinsic energy gap can be larger than the charging energy, and addition of flux quanta can occur without adding quasi-particles. We show that flux superperiods are possible, and reconcile their appearance with the Byers-Yang theorem. We explain that the observation of anyonic statistical phases is possible by tuning to the transition from a regime with constant chemical potential to a regime with constant particle density, where a flux superperiod changes to a periodicity with one flux quantum at a critical magnetic field strength.

cond-mat.mes-hall↗

arXiv2019

Partial Equilibration of the Anti-Pfaffian edge due to Majorana Disorder

We consider electrical and thermal equilibration of the edge modes of the Anti-Pfaffian quantum Hall state at $ν=5/2$ due to tunneling of the Majorana edge mode to trapped Majorana zero modes in the bulk. Such tunneling breaks translational invariance and allows scattering between Majorana and other edge modes in such a way that there is a parametric difference between the length scales for equilibration of charge and heat transport between integer and Bose mode on the one hand, and for thermal equilibration of the Majorana edge mode on the other hand. We discuss a parameter regime in which this mechanism could explain the recent observation of quantized heat transport [Banerjee et all, Nature 559, 7713 (2018)].

cond-mat.str-el↗

arXiv2018

Noise on complex quantum Hall edges: Chiral anomaly and heat diffusion

Electrical and thermal conductances of a quantum Hall bar reflect the topological structure of the incompressible bulk phase. Here we show that noise of electrical current carried through the edge evidences the interplay between these two topological observables. Transport through a structured edge is modeled by a voltage-biased line junction made up of two counter-propagating modes associated with respective filling factors. Specifically, we focus on the edge of a $ν=2/3$ fractional quantum Hall state. Noise is generated at a point distinctly separated from the hot spot (where most of the Ohmic dissipation takes place) and reflects the competition between ballistically carried downstream current and diffusively carried heat (which can propagate also upstream). We propose specific setups where our predictions can be measured.

cond-mat.mes-hall↗

arXiv2018

Evolution of the transmission phase through a Coulomb-blockaded Majorana wire

We present a study of the transmission of electrons through a semiconductor quantum wire with strong spin-orbit coupling in proximity to an s-wave superconductor, which is Coulomb-blockaded. Such a system supports Majorana zero modes in the presence of an external magnetic field. Without superconductivity, phase lapses are expected to occur in the transmission phase, and we find that they disappear when a topological superconducting phase is stabilized. We express tunneling through the nanowire with the help of effective matrix elements, which depend on both the fermion parity of the wire and the overlap with Bogoliubov-de-Gennes wave functions. Using a modified scattering matrix formalism, that allows for including electron-electron interactions, we study the transmission phase in different regimes.

cond-mat.mes-hall↗

arXiv2018

Incoherent transport on the $ν=2/3$ quantum Hall edge

The nature of edge state transport in quantum Hall systems has been studied intensely ever since Halperin [1] noted its importance for the quantization of the Hall conductance. Since then, there have been many developments in the study of edge states in the quantum Hall effect, including the prediction of multiple counter-propagating modes in the fractional quantum Hall regime, the prediction of edge mode renormalization due to disorder, and studies of how the sample confining potential affects the edge state structure (edge reconstruction), among others. In this paper, we study edge transport for the $ν_{\text{bulk}}=2/3$ edge in the disordered, fully incoherent transport regime. To do so, we use a hydrodynamic approximation for the calculation of voltage and temperature profiles along the edge of the sample. Within this formalism, we study two different bare mode structures with tunneling: the original edge structure predicted by Wen [2] and MacDonald [3], and the more complicated edge structure proposed by Meir [4], whose renormalization and transport characteristics were discussed by Wang, Meir and Gefen (WMG) [5]. We find that in the fully incoherent regime, the topological characteristics of transport (quantized electrical and heat conductance) are intact, with finite size corrections which are determined by the extent of equilibration. In particular, our calculation of conductance for the WMG model in a double QPC geometry reproduce conductance results of a recent experiment by R. Sabo, et al. [17], which are inconsistent with the model of MacDonald. Our results can be explained in the charge/neutral mode picture, with incoherent analogues of the renormalization fixed points of Ref. [5]. Additionally, we find diffusive $(\sim1/L)$ conductivity corrections to the heat conductance in the fully incoherent regime for both models of the edge.

cond-mat.mes-hall↗

arXiv2017

Time-reversal-symmetric topological magnetoelectric effect in three-dimensional topological insulators

One of the hallmarks of time-reversal-symmetric topological insulators in three dimensions is the topological magnetoelectric effect (TME). So far, a time-reversal breaking variant of this effect has attracted much attention, in the sense that the induced electric charge changes sign when the direction of an externally applied magnetic field is reversed. Theoretically, this effect is described by the so-called axion term. Here, we discuss a time-reversal-symmetric TME, where the electric charge depends only on the magnitude of the magnetic field but is independent of its sign. We obtain this nonperturbative result by a combination of analytic and numerical arguments, and suggest a mesoscopic setup to demonstrate it experimentally.

cond-mat.mes-hall↗

arXiv2017

Subperiods and apparent pairing in integer quantum Hall interferometers

We analyze the magnetic field and gate voltage dependence of the longitudinal resistance in an integer quantum Hall Fabry-Pérot interferometer, taking into account the interactions between an interfering edge mode, a non-interfering edge mode and the bulk. For weak bulk-edge coupling and sufficiently strong inter-edge interaction, we obtain that the interferometer operates in the Aharonov-Bohm regime with a flux periodicity halved with respect to the usual expectation. Even in the regime of strong bulk-edge coupling, this behavior can be observed as a subperiodicity of the interference signal in the Coulomb dominated regime. We do not find evidence for a connection between a reduced flux period and electron pairing, though. Our results can reproduce some recent experimental findings.

cond-mat.mes-hall↗

arXiv2017

Dissipation in mesoscale superfluids

We investigate the maximum speed at which a driven superfluid can flow through a narrow constriction with a size on the order of the healing length. Considering dissipation via the thermal nucleation of quantized vortices, we calculate the critical velocity for superfluid $^4$He and ultracold atomtronic circuits, identify fundamental length and velocity scales, and are thus able to present results obtained in widely different temperature and density ranges in a universal framework. For ultra-narrow channels we predict a drastic reduction in the critical velocity as the energy barrier for flow reducing thermally activated phase slip fluctuations is suppressed.

cond-mat.mes-hall↗