arXiv subjects

Achim Rosch

Publications and source records attributed to Achim Rosch.

At least 73 records · Page 4Linked to original sources

arXiv2018

Time-dependent generalized Gibbs ensembles in open quantum systems

Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here we demonstrate numerically, that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which both break integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time-evolution on long time-scales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.

cond-mat.str-el↗

arXiv2017

Magnetic skyrmions and skyrmion clusters in the helical phase of Cu$_2$OSeO$_3$

Skyrmions are nanometric spin whirls that can be stabilized in magnets lacking inversion symmetry. The properties of isolated skyrmions embedded in a ferromagnetic background have been intensively studied. We show that single skyrmions and clusters of skyrmions can also form in the helical phase and investigate theoretically their energetics and dynamics. The helical background provides natural one-dimensional channels along which a skyrmion can move rapidly. In contrast to skyrmions in ferromagnets, the skymion-skyrmion interaction has a strong attractive component and thus skyrmions tend to form clusters with characteristic shapes. These clusters are directly observed in transmission electron microscopy measurements in thin films of Cu$_2$OSeO$_3$. Topological quantization, high mobility and the confinement of skyrmions in channels provided by the helical background may be useful for future spintronics devices.

cond-mat.str-el↗

arXiv2017

Pumping approximately integrable systems

Weak perturbations can drive an interacting many-particle system far from its initial equilibrium state if one is able to pump into degrees of freedom approximately protected by conservation laws. This concept has for example been used to realize Bose-Einstein condensates of photons, magnons, and excitons. Integrable quantum systems, like the one-dimensional Heisenberg model, are characterized by an infinite set of conservation laws. Here we develop a theory of weakly driven integrable systems and show that pumping can induce large spin or heat currents even in the presence of integrability breaking perturbations, since it activates local and quasi-local approximate conserved quantities. The resulting steady state is qualitatively captured by a truncated generalized Gibbs ensemble with Lagrange parameters that depend on the structure but not on the overall amplitude of perturbations nor the initial state. We suggest to use spin-chain materials driven by terahertz radiation to realize integrability-based spin and heat pumps.

cond-mat.str-el↗

arXiv2017

Gigantic negative magnetoresistance in a disordered topological insulator

With the recent discovery of Weyl semimetals, the phenomenon of negative magnetoresistance (MR) is attracting renewed interest. While small negative MR can occur due to the suppression of spin scattering or weak localization, large negative MR is rare in materials, and when it happens, it is usually related to magnetism. The large negative MR in Weyl semimetals is peculiar in that it is unrelated to magnetism and comes from chiral anomaly. Here we report that there is a new mechanism for large negative MR which is not related to magnetism but is related to disorder. In the newly-synthesized bulk-insulating topological insulator TlBi$_{0.15}$Sb$_{0.85}$Te$_2$, we observed gigantic negative MR reaching 98% in 14 T at 10 K, which is unprecedented in a nonmagnetic system. Supported by numerical simulations, we argue that this phenomenon is likely due to the Zeeman effect on a barely percolating current path formed in the disordered bulk. Since disorder can also lead to non-saturating linear MR in Ag$_{2+δ}$Se, the present finding suggests that disorder engineering in narrow-gap systems is useful for realizing gigantic MR in both positive and negative directions.

cond-mat.mes-hall↗

arXiv2017

Planar Hall effect from the surface of topological insulators

A prominent feature of topological insulators (TIs) is the surface states comprising of spin-nondegenerate massless Dirac fermions. Recent technical advances have made it possible to address the surface transport properties of TI thin films while tuning the Fermi levels of both top and bottom surfaces across the Dirac point by electrostatic gating. This opened the window for studying the spin-nondegenerate Dirac physics peculiar to TIs. Here we report our discovery of a novel planar Hall effect (PHE) from the TI surface, which results from a hitherto-unknown resistivity anisotropy induced by an in-plane magnetic field. This effect is observed in dual-gated devices of bulk-insulating Bi$_{2-x}$Sb$_{x}$Te$_{3}$ thin films, in which both top and bottom surfaces are gated. The origin of PHE is the peculiar time-reversal-breaking effect of an in-plane magnetic field, which anisotropically lifts the protection of surface Dirac fermions from back-scattering. The key signature of the field-induced anisotropy is a strong dependence on the gate voltage with a characteristic two-peak structure near the Dirac point which is explained theoretically using a self-consistent T-matrix approximation. The observed PHE provides a new tool to analyze and manipulate the topological protection of the TI surface in future experiments.

cond-mat.mes-hall↗

arXiv2017

Hyers-Ulam stability of elliptic Möbius difference equation

The linear fractional map $ f(z) = \frac{az+ b}{cz + d} $ on the Riemann sphere with complex coefficients $ ad-bc \neq 0 $ is called Möbius map. If $ f $ satisfies $ ad-bc=1 $ and $ -2<a+d<2 $, then $ f $ is called $\textit{elliptic}$ Möbius map. Let $ \{ b_n \}_{n \in \mathbb{N}_0} $ be the solution of the elliptic Möbius difference equation $ b_{n+1} = f(b_n) $ for every $ n \in \mathbb{N}_0 $. Then the sequence $ \{ b_n \}_{n \in \mathbb{N}_0} $ has no Hyers-Ulam stability.

math.CA↗

arXiv2017

Edge instabilities and skyrmion creation in magnetic layers

We study both analytically and numerically the edge of two-dimensional ferromagnets with Dzyaloshinskii-Moriya (DM) interactions, considering both chiral magnets and magnets with interface-induced DM interactions. We show that in the field-polarized ferromagnetic phase magnon states exist which are bound to the edge, and we calculate their spectra within a continuum field theory. Upon lowering an external magnetic field, these bound magnons condense at a finite momentum and the edge becomes locally unstable. Micromagnetic simulations demonstrate that this edge instability triggers the creation of a helical phase which penetrates the field-polarized state within the bulk. A subsequent increase of the magnetic field allows to create skyrmions close to the edge in a controlled manner.

cond-mat.str-el↗

arXiv2016

Real-space imaging of a topological protected edge state with ultracold atoms in an amplitude-chirped optical lattice

Topological states of matter, as quantum Hall systems or topological insulators, cannot be distinguished from ordinary matter by local measurements in the bulk of the material. Instead, global measurements are required, revealing topological invariants as the Chern number. At the heart of topological materials are topologically protected edge states that occur at the intersection between regions of different topological order. Ultracold atomic gases in optical lattices are promising new platforms for topological states of matter, though the observation of edge states has so far been restricted in these systems to the state space imposed by the internal atomic structure. Here we report on the observation of an edge state between two topological distinct phases of an atomic physics system in real space using optical microscopy. An interface between two spatial regions of different topological order is realized in a one-dimensional optical lattice of spatially chirped amplitude. To reach this, a magnetic field gradient causes a spatial variation of the Raman detuning in an atomic rubidium three- level system and a corresponding spatial variation of the coupling between momentum eigenstates. This novel experimental technique realizes a cold atom system described by a Dirac equation with an inhomogeneous mass term closely related to the SSH-model. The observed edge state is characterized by measuring the overlap to various initial states, revealing that this topological state has singlet nature in contrast to the other system eigenstates, which occur pairwise. We also determine the size of the energy gap to the adjacent eigenstate doublet. Our findings hold prospects for the spectroscopy of surface states in topological matter and for the quantum simulation of interacting Dirac systems.

cond-mat.quant-gas↗

arXiv2016

Quantum-optical magnets with competing short- and long-range interactions: Rydberg-dressed spin lattice in an optical cavity

The fields of quantum simulation with cold atoms [1] and quantum optics [2] are currently being merged. In a set of recent pathbreaking experiments with atoms in optical cavities [3,4] lattice quantum many-body systems with both, a short-range interaction and a strong interaction potential of infinite range -mediated by a quantized optical light field- were realized. A theoretical modelling of these systems faces considerable complexity at the interface of: (i) spontaneous symmetry-breaking and emergent phases of interacting many-body systems with a large number of atoms $N\rightarrow\infty$, (ii) quantum optics and the dynamics of fluctuating light fields, and (iii) non-equilibrium physics of driven, open quantum systems. Here we propose what is possibly the simplest, quantum-optical magnet with competing short- and long-range interactions, in which all three elements can be analyzed comprehensively: a Rydberg-dressed spin lattice [5] coherently coupled to a single photon mode. Solving a set of coupled even-odd sublattice Master equations for atomic spin and photon mean-field amplitudes, we find three key results. (R1): Superradiance and a coherent photon field can coexist with spontaneously broken magnetic translation symmetry. The latter is induced by the short-range nearest-neighbor interaction from weakly admixed Rydberg levels. (R2): This broken even-odd sublattice symmetry leaves its imprint in the light via a novel peak in the cavity spectrum beyond the conventional polariton modes. (R3): The combined effect of atomic spontaneous emission, drive, and interactions can lead to phases with anomalous photon number oscillations. Extensions of our work include nano-photonic crystals coupled to interacting atoms and multi-mode photon dynamics in Rydberg systems.

cond-mat.quant-gas↗

arXiv2016

Switching of Charge-Current-Induced Spin Polarization in the Topological Insulator BiSbTeSe2

The charge-current-induced spin polarization is a key property of topological insulators for their applications in spintronics. However, topological surface states are expected to give rise to only one type of spin polarization for a given current direction, which has been a limiting factor for spin manipulations. Here we report that in devices based on the bulk-insulating topological insulator BiSbTeSe2, an unexpected switching of spin polarization was observed upon changing the chemical potential. The spin polarization expected from the topological surface states was detected in a heavily electron-doped device, whereas the opposite polarization was reproducibly observed in devices with low carrier densities. We propose that the latter type of spin polarization stems from topologically-trivial two-dimensional states with a large Rashba spin splitting, which are caused by a strong band bending at the surface of BiSbTeSe2 beneath the ferromagnetic electrode used as a spin detector. This finding paves the way for realizing the "spin transistor" operation in future topological spintronic devices.

cond-mat.mes-hall↗

arXiv2016

SU(4) Skyrmions in the $ν=\pm 1$ Quantum Hall State of Graphene

We explore different skyrmion types in the lowest Landau level of graphene at a filling factor $ν=\pm 1$. In addition to the formation of spin and valley pseudospin skyrmions, we show that another type of spin-valley entangled skyrmions can be stabilized in graphene due to an approximate SU(4) spin-valley symmetry that is affected by sublattice symmetry-breaking terms. These skyrmions have a clear signature in spin-resolved density measurements on the lattice scale, and we discuss the expected patterns for the different skyrmion types.

cond-mat.mes-hall↗

arXiv2015

The Floquet-Boltzmann equation

Periodically driven quantum systems can be used to realize quantum pumps, ratchets, artificial gauge fields and novel topological states of matter. Starting from the Keldysh approach, we develop a formalism, the Floquet-Boltzmann equation, to describe the dynamics and the scattering of quasiparticles in such systems. The theory builds on a separation of time-scales. Rapid, periodic oscillations occurring on a time scale $T_0=2 π/Ω$, are treated using the Floquet formalism and quasiparticles are defined as eigenstates of a non-interacting Floquet Hamiltonian. The dynamics on much longer time scales, however, is modelled by a Boltzmann equation which describes the semiclassical dynamics of the Floquet-quasiparticles and their scattering processes. As the energy is conserved only modulo $\hbar Ω$, the interacting system heats up in the long-time limit. As a first application of this approach, we compute the heating rate for a cold-atom system, where a periodical shaking of the lattice was used to realize the Haldane model.

cond-mat.quant-gas↗

arXiv2015

Critical elasticity at zero and finite temperature

Elastic phase transitions of crystals and phase transitions whose order parameter couples linearly to elastic degrees of freedom are reviewed with particular focus on instabilities at zero temperature. A characteristic feature of these transitions is the suppression of critical fluctuations by long-range shear forces. As a consequence, at an elastic crystal symmetry-breaking quantum phase transition the phonon velocity vanishes only along certain crystallographic directions giving rise to critical phonon thermodynamics described by a stable Gaussian fixed point. At an isostructural solid-solid quantum critical end point, on the other hand, the complete suppression of critical fluctuations results in true mean-field critical behavior without a diverging correlation length. Whenever an order parameter couples bilinearly to the strain tensor, the critical properties are eventually governed by critical crystal elasticity. This is, for example, the case for quantum critical metamagnetism but also for the classical critical Mott end point at finite $T$. We discuss and compare the solid-solid end points expected close to the Mott transition in V$_2$O$_3$ and $κ$-(BEDT-TTF)$_2 X$.

cond-mat.str-el↗

arXiv2015

Spin-Peierls Instability of Three-Dimensional Spin Liquids with Majorana Fermi Surfaces

Three-dimensional (3D) variants of the Kitaev model can harbor gapless spin liquids with a Majorana Fermi surface on certain tricoordinated lattice structures such as the recently introduced hyperoctagon lattice. Here we investigate Fermi surface instabilities arising from additional spin exchange terms (such as a Heisenberg coupling) which introduce interactions between the emergent Majorana fermion degrees of freedom. We show that independent of the sign and structure of the interactions, the Majorana surface is always unstable. Generically the system spontaneously doubles its unit cell at exponentially small temperatures and forms a spin liquid with line nodes. Depending on the microscopics further symmetries of the system can be broken at this transition. These spin-Peierls instabilities of a 3D spin liquid are closely related to BCS instabilities of fermions.

cond-mat.str-el↗

arXiv2015

Equilibration and Approximate Conservation Laws: Dipole Oscillations and Perfect Drag of Ultracold Atoms in a Harmonic Trap

The presence of (approximate) conservation laws can prohibit the fast relaxation of interacting many-particle quantum systems. We investigate this physics by studying the center-of-mass oscillations of two species of fermionic ultracold atoms in a harmonic trap. If their trap frequencies are equal, a dynamical symmetry (spectrum generating algebra), closely related to Kohn's theorem, prohibits the relaxation of center-of-mass oscillations. A small detuning $δω$ of the trap frequencies for the two species breaks the dynamical symmetry and ultimately leads to a damping of dipole oscillations driven by inter-species interactions. Using memory-matrix methods, we calculate the relaxation as a function of frequency difference, particle number, temperature, and strength of inter-species interactions. When interactions dominate, there is almost perfect drag between the two species and the dynamical symmetry is approximately restored. The drag can either arise from Hartree potentials or from friction. In the latter case (hydrodynamic limit), the center-of-mass oscillations decay with a tiny rate, $1/τ\propto (δω)^2/Γ$, where $Γ$ is a single particle scattering rate.

cond-mat.quant-gas↗

arXiv2015

Inertia, diffusion and dynamics of a driven skyrmion

Skyrmions recently discovered in chiral magnets are a promising candidate for magnetic storage devices because of their topological stability, small size ($\sim 3-100$nm), and ultra-low threshold current density ($\sim 10^{6}$A/m$^2$) to drive their motion. However, the time-dependent dynamics has hitherto been largely unexplored. Here we show, by combining the numerical solution of the Landau-Lifshitz-Gilbert equation and the analysis of a generalized Thiele's equation, that inertial effects are almost completely absent in skyrmion dynamics driven by a time-dependent current. In contrast, the response to time-dependent magnetic forces and thermal fluctuations depends strongly on frequency and is described by a large effective mass and a (anti-) damping depending on the acceleration of the skyrmion. Thermal diffusion is strongly suppressed by the cyclotron motion and is proportional to the Gilbert damping coefficient $α$. This indicates that the skyrmion position is stable, and its motion responds to the time-dependent current without delay or retardation even if it is fast. These findings demonstrate the advantages of skyrmions as information carriers.

cond-mat.str-el↗

arXiv2014

Novel model for wine fermentation including the yeast dying phase

This paper presents a novel model for wine fermentation including a death phase for yeast and the influence of oxygen on the process. A model for the inclusion of the yeast dying phase is derived and compared to a model taken from the literature. The modeling ability of the several models is analyzed by comparing their simulation results.

q-bio.QM↗

arXiv2014

Capturing of a Magnetic Skyrmion with a Hole

Magnetic whirls in chiral magnets, so-called skyrmions, can be manipulated by ultrasmall current densities. Here we study both analytically and numerically the interactions of a single skyrmion in two dimensions with a small hole in the magnetic layer. Results from micromagnetic simulations are in good agreement with effective equations of motion obtained from a generalization of the Thiele approach. Skyrmion-defect interactions are described by an effective potential with both repulsive and attractive components. For small current densities a previously pinned skyrmion stays pinned whereas an unpinned skyrmion moves around the impurities and never gets captured. For higher current densities, j_c1 < j < j_c2, however, single holes are able to capture moving skyrmions. The maximal cross section is proportional to the skyrmion radius and to Sqrt(alpha), where alpha is the Gilbert damping. For j > j_c2 all skyrmions are depinned. Small changes of the magnetic field strongly change the pinning properties, one can even reach a regime without pinning, j_c2=0. We also show that a small density of holes can effectively accelerate the motion of the skyrmion and introduce a Hall effect for the skyrmion.

cond-mat.str-el↗