arXiv subjects

Achim Rosch

Publications and source records attributed to Achim Rosch.

At least 55 records · Page 3Linked to original sources

arXiv2021

Universal principles of moiré band structures

Moiré materials provide a highly tunable environment for the realization of band structures with engineered physical properties. Specifically, moiré structures with Fermi surface flat bands - a synthetic environment for the realization of correlated phases - have moiré unit cells containing thousands of atoms and tantalizingly complex bands structures. In this paper we show that statistical principles go a long way in explaining universal physical properties of these systems. Our approach builds on three conceptual elements: the presence of quantum chaos caused by the effective irregularity of the atomic configurations on short length scales, Anderson localization in momentum space, and the presence of approximate crystalline symmetries. Which of these principles dominates depends on material parameters such as the extension of the Fermi surface or the strength of the moiré lattice potential. The phenomenological consequences of this competition are predictions for the characteristic group velocity of moiré bands, a primary indicator for their average flatness. In addition to these generic features, we identify structures outside the statistical context, notably almost flat bands close to the extrema of the unperturbed spectra, and the celebrated zero energy `magic angle' flat bands, where the latter require exceptionally fine tuned material parameters.

cond-mat.mes-hall↗

arXiv2020

Dicke transition in open many-body systems determined by fluctuation effects

In recent years, one important experimental achievement was the strong coupling of quantum matter and quantum light. Realizations reach from ultracold atomic gases in high-finesse optical resonators to electronic systems coupled to THz cavities. The dissipative nature of the quantum light field and the global coupling to the quantum matter leads to many exciting phenomena such as the occurrence of dissipative quantum phase transition to self-organized exotic phases. The theoretical treatment of these dissipative hybrid systems of matter coupled to a cavity field is very challenging. Previously, often mean-field approaches were applied which characterize the emergence of self-organized phases as a zero-temperature transition for the particles, a ground-state Dicke transition. Here we develop a new approach which combines a mean-field approach with a perturbative treatment of fluctuations beyond mean-field, which becomes exact in the thermodynamic limit. We argue that these fluctuations are crucial in order to determine the mixed state (finite temperature) character of the transition and to unravel universal properties of the self-organized states. We validate our results by comparing to time-dependent matrix-product-state calculations.

cond-mat.quant-gas↗

arXiv2020

Entropy production for quasi-adiabatic parameter changes dominated by hydrodynamics

A typical strategy of realizing an adiabatic change of a many-particle system is to vary parameters very slowly on a time scale $t_\text{r}$ much larger than intrinsic equilibration time scales. In the ideal case of adiabatic state preparation, $t_\text{r} \to \infty$, the entropy production vanishes. In systems with conservation laws, the approach to the adiabatic limit is hampered by hydrodynamic long-time tails, arising from the algebraically slow relaxation of hydrodynamic fluctuations. We argue that the entropy production $ΔS$ of a diffusive system at finite temperature in one or two dimensions is governed by hydrodynamic modes resulting in $ΔS \sim 1/\sqrt{t_\text{r}}$ in $d=1$ and $ΔS \sim \ln(t_\text{r})/t_\text{r}$ in $d=2$. In higher dimensions, entropy production is instead dominated by other high-energy modes with $ΔS \sim 1/t_\text{r}$. In order to verify the analytic prediction, we simulate the non-equilibrium dynamics of a classical two-component gas with point-like particles in one spatial dimension and examine the total entropy production as a function of $t_\text{r}$.

cond-mat.stat-mech↗

arXiv2020

Bistabilities and domain walls in weakly open quantum systems

Weakly pumped systems with approximate conservation laws can be efficiently described by a generalized Gibbs ensemble if the steady state of the system is unique. However, such a description can fail if there are multiple steady state solutions, for example, a bistability. In this case domains and domain walls may form. In one-dimensional (1D) systems any type of noise (thermal or non-thermal) will in general lead to a proliferation of such domains. We study this physics in a 1D spin chain with two approximate conservation laws, energy and the $z$-component of the total magnetization. A bistability in the magnetization is induced by the coupling to suitably chosen Lindblad operators. We analyze the theory for a weak coupling strength $ε$ to the non-equilibrium bath. In this limit, we argue that one can use hydrodynamic approximations which describe the system locally in terms of space- and time-dependent Lagrange parameters. Here noise terms enforce the creation of domains, where the typical width of a domain wall goes as $\sim 1/\sqrtε$ while the density of domain walls is exponentially small in $1/\sqrtε$. This is shown by numerical simulations of a simplified hydrodynamic equation in the presence of noise.

cond-mat.stat-mech↗

arXiv2020

Skyrmion and Tetarton Lattices in Twisted Bilayer Graphene

Recent experiments on twisted bilayer graphene show an anomalous quantum Hall (AQH) effect at filling of $3$ electrons per moirè unit cell. The AQH effect arises in an insulating state with both valley- and ferromagnetic order. We argue, that weak doping of such a system leads to the formation of a novel topological spin texture, a `double-tetarton lattice'. The building block of this lattice, the `double-tetarton', is a spin configuration which covers $1/4$ of the unit-sphere twice. In contrast to skyrmion lattices, the net magnetization of this magnetic texture vanishes. Only at large magnetic fields more conventional skyrmion lattices are recovered. But even for large fields the addition of a single charge to the ferromagnetic AQH state flips hundreds of spins. Our analysis is based on the investigation of an effective non-linear sigma model which includes the effects of long-ranged Coulomb interactions.

cond-mat.str-el↗

arXiv2020

Critical behavior near the many-body localization transition in driven open systems

Coupling a many-body localized system to a thermal bath breaks local conservation laws and washes out signatures of localization. When the bath is non-thermal or when the system is also weakly driven, local conserved quantities acquire a highly non-thermal stationary value. We demonstrate how this property can be used to study the many-body localization phase transition in weakly open systems. Here, the strength of the coupling to the non-thermal baths plays a similar role as a finite temperature in a $T=0$ quantum phase transition. By tuning this parameter, we can detect key features of the MBL transition: the divergence of the dynamical exponent due to Griffiths effects in one dimension and the critical disorder strength. We apply these ideas to study the MBL critical point numerically. The possibility to observe critical signatures of the MBL transition in an open system allows for new numerical approaches that overcome the limitations of exact diagonalization studies. Here we propose a scalable numerical scheme to study the MBL critical point using matrix-product operator solution to the Lindblad equation.

cond-mat.str-el↗

arXiv2020

Band Bending and Valence Band Quantization at Line Defects in MoS$_2$

The variation of the electronic structure normal to 1D defects in quasi-freestanding MoS$_2$, grown by molecular beam epitaxy, is investigated through high resolution scanning tunneling spectroscopy at $5$K. Strong upwards bending of valence and conduction bands towards the line defects is found for the 4|4E mirror twin boundary and island edges, but not for the 4|4P mirror twin boundary. Quantized energy levels in the valence band are observed wherever upwards band bending takes place. Focusing on the common 4|4E mirror twin boundary, density functional theory calculations give an estimate of its charging, which agrees well with electrostatic modeling. We show that the line charge can also be assessed from the filling of the boundary-localized electronic band, whereby we provide a measurement of the theoretically predicted quantized polarization charge at MoS$_2$ mirror twin boundaries. These calculations elucidate the origin of band bending and charging at these 1D defects in MoS$_2$. The 4|4E mirror twin boundary not only impairs charge transport of electrons and holes due to band bending, but holes are additionally subject to a potential barrier, which is inferred from the independence of the quantized energy landscape on either side of the boundary.

cond-mat.mes-hall↗

arXiv2020

Competition between Kondo and Kitaev Physics in Kitaev clusters coupled to a fermionic bath

Geometrically frustrated quantum impurities coupled to metallic leads have been shown to exhibit rich behavior with a quantum phase transition separating Kondo screened and local moment phases. Frustration in the quantum impurity can alternatively be introduced via Kitaev-couplings between different spins of the impurity cluster. We use the Numerical Renormalization Group (NRG) to study a range of systems where the quantum impurity comprising a Kitaev cluster is coupled to a bath of non-interacting fermions. The models exhibits a competition between Kitaev and Kondo dominated physics depending on whether the Kitaev couplings are greater or less than the Kondo temperature. We characterize the ground state properties of the system and determine the temperature dependence of the crossover scale for the emergence of fractionalized degrees of freedom in the model. We also demonstrate qualitatively as well as quantitatively that in the Kondo limit, the complex impurity can be mapped to an effective two-impurity system, where the emergent spin $1/2$ comprises of both Majorana and flux degrees of freedom. For a tetrahedral-shaped Kitaev cluster, an extra orbital degree of freedom closely related to a flux degree of freedom remains unscreened even in the presence of both Heisenberg and Kondo interactions.

cond-mat.str-el↗

arXiv2019

Thermally Condensing Photons into a Coherently Split State of Light

Techniques to control the quantum state of light play a crucial role in a wide range of fields, from quantum information science to precision measurements. While for electrons in solid state materials complex quantum states can be created by mere cooling, in the field of optics manipulation and control currently builds on non-thermodynamic methods. Using an optical dye microcavity, we have split photon wavepackets by thermalization within a potential with two minima subject to tunnel coupling. Even at room temperature, photons condense into a quantum-coherent bifurcated ground state. Fringe signals upon recombination show the relative coherence between the two wells, demonstrating a working interferometer with the non-unitary thermodynamic beamsplitter. This energetically driven optical state preparation opens up an avenue for exploring novel correlated and entangled optical manybody states.

cond-mat.quant-gas↗

arXiv2019

Universality of annihilation barriers of large magnetic skyrmions in chiral and frustrated magnets

Magnetic skyrmions are whirls in the magnetization whose topological winding number promises stability against thermal fluctuations and defects. They can only decay via singular spin configurations. We analyze the corresponding energy barriers of skyrmions in a magnetic monolayer for two distinct stabilization mechanisms, i.e., Dzyaloshinskii-Moriya interaction (DMI) and competing interactions. Based on our numerically calculated collapse paths on an atomic lattice, we derive analytic expressions for the saddle point textures and energy barriers of large skyrmions. The sign of the spin stiffness and the sign of 4th-order derivative terms in the classical field theory determines the nature of the saddle point and thus the height of the energy barrier. In the most common case for DMI-stabilized skyrmions, positive stiffness and negative 4th-order term, the saddle point energy approaches a universal upper limit described by an effective continuum theory. For skyrmions stabilized by frustrating interactions, the stiffness is negative and the energy barrier arises mainly from the core of a singular vortex configuration.

cond-mat.str-el↗

arXiv2019

Quantum confinement of the Dirac surface states in topological-insulator nanowires

The non-trivial topology of the three-dimensional (3D) topological insulator (TI) dictates the appearance of gapless Dirac surface states. Intriguingly, when a 3D TI is made into a nanowire, a gap opens at the Dirac point due to the quantum confinement, leading to a peculiar Dirac sub-band structure. This gap is useful for, e.g., future Majorana qubits based on TIs. Furthermore, these Dirac sub-bands can be manipulated by a magnetic flux and are an ideal platform for generating stable Majorana zero modes (MZMs), which play a key role in topological quantum computing. However, direct evidence for the Dirac sub-bands in TI nanowires has not been reported so far. Here we show that by growing very thin ($\sim$40-nm diameter) nanowires of the bulk-insulating topological insulator (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$ and by tuning its chemical potential across the Dirac point with gating, one can unambiguously identify the Dirac sub-band structure. Specifically, the resistance measured on gate-tunable four-terminal devices was found to present non-equidistant peaks as a function of the gate voltage, which we theoretically show to be the unique signature of the quantum-confined Dirac surface states. These TI nanowires open the way to address the topological mesoscopic physics, and eventually the Majorana physics when proximitised by an $s$-wave superconductor.

cond-mat.mes-hall↗

arXiv2019

Quantum skyrmions in frustrated ferromagnets

We develop a quantum theory of magnetic skyrmions and antiskyrmions in a spin-1/2 Heisenberg magnet with frustrating next-nearest neighbor interactions. Using exact diagonalization we show numerically that a quantum skyrmion exists as a stable many-magnon bound state and investigate its quantum numbers. We then derive a phenomenological Schrödinger equation for the quantum skyrmion and its internal degrees of freedom. We find that quantum skyrmions have highly unusual properties. Their bandwidth is exponentially small and arises from tunneling processes between skyrmion and antiskyrmion. The bandstructure changes both qualitatively and quantitatively when a single spin is added or removed from the quantum skyrmion, reflecting a locking of angular momentum and spin quantum numbers characteristic for skyrmions. Additionally, while for weak forces the quantum skyrmion is accelerated parallel to the force, it moves in a perpendicular direction for stronger fields.

cond-mat.str-el↗

arXiv2019

Tomonaga-Luttinger liquid in a box: electrons confined within MoS$_2$ mirror twin boundaries

Two- or three-dimensional metals are usually well described by weakly interacting, fermionic quasiparticles. This concept breaks down in one dimension due to strong Coulomb interactions. There, low-energy electronic excitations are expected to be bosonic collective modes, which fractionalize into independent spin and charge density waves. Experimental research on one-dimensional metals is still hampered by their difficult realization, their limited accessibility to measurements, and by competing or obscuring effects such as Peierls distortions or zero bias anomalies. Here we overcome these difficulties by constructing a well-isolated, one-dimensional metal of finite length present in MoS$_2$ mirror twin boundaries. Using scanning tunneling spectroscopy we measure the single-particle density of the interacting electron system as a function of energy and position in the 1D box. Comparison to theoretical modeling provides unambiguous evidence that we are observing spin-charge separation in real space.

cond-mat.str-el↗

arXiv2019

Interplay of electronic and spin degrees in ferromagnetic SrRuO$_3$: anomalous softening of magnon gap and stiffness

The magnon dispersion of ferromagnetic SrRuO$_3$ was studied by inelastic neutron scattering experiments on single crystals as function of temperature. Even at low temperature the magnon modes exhibit substantial broadening pointing to strong interaction with charge carriers. We find an anomalous temperature dependence of both the magnon gap and the magnon stiffness, which soften upon cooling in the ferromagnetic phase. Both effects trace the temperature dependence of the anomalous Hall effect. We argue that these results show that Weyl points and the anomalous Hall effect can directly influence the spin dynamics in metallic ferromagnets.

cond-mat.str-el↗

arXiv2018

Activating many-body localization in solids by driving with light

Due to the presence of phonons, many body localization (MBL) does not occur in disordered solids, even if disorder is strong. Local conservation laws characterizing an underlying MBL phase decay due to the coupling to phonons. Here we show that this decay can be compensated when the system is driven out of equilibrium. The resulting variations of the local temperature provide characteristic fingerprints of an underlying MBL phase. We consider a one-dimensional disordered spin-chain which is weakly coupled to a phonon bath and weakly irradiated by white light. The irradiation has weak effects in the ergodic phase. However, if the system is in the MBL phase irradiation induces strong temperature variations of order 1 despite the coupling to phonons. Temperature variations can be used similar to an order parameter to detect MBL phases, the phase transition and an MBL correlation length.

cond-mat.str-el↗

arXiv2018

Approximately quantized thermal Hall effect of chiral liquids coupled to phonons

The recent observation of a half-integer quantized thermal Hall effect in $α$-RuCl$_3$ is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A similar quantized thermal Hall effect is expected in chiral topological superconductors. The unavoidable presence of gapless acoustic phonons, however, implies that, in contrast to the quantized electrical conductivity, the thermal Hall conductivity $κ_xy$ is never exactly quantized in real materials. Here, we investigate how phonons affect the quantization of the thermal conductivity focusing on the edge theory. As an example we consider a Kitaev spin liquid gapped by an external magnetic field coupled to acoustic phonons. The coupling to phonons destroys the ballistic thermal transport of the edge mode completely, as energy can leak into the bulk, thus drastically modifying the edge-picture of the thermal Hall effect. Nevertheless, the thermal Hall conductivity remains approximately quantized and we argue, that the coupling to phonons to the edge mode is a necessary condition for the observation of the quantized thermal Hall effect. The strength of this edge coupling does, however, not affect the conductivity. We argue that for sufficiently clean systems the leading correction to the quantized thermal Hall effect, $Δκ_{xy}/T \sim \text{sign(B)} \, T^2$, arises from a intrinsic anomalous Hall effect of the acoustic phonons due to Berry phases imprinted by the chiral (spin) liquid in the bulk. This correction depends on the sign but not the amplitude of the external magnetic field.

cond-mat.str-el↗

arXiv2018

Topological superconductivity in Kondo-Kitaev model

We investigate possible topological superconductivity in the Kondo-Kitaev model on the honeycomb lattice, where the Kitaev spin liquid is coupled to conduction electrons via the Kondo coupling. We use the self-consistent Abrikosov-fermion mean-field theory to map out the phase diagram. Upon increasing the Kondo coupling, a first order transition occurs from the decoupled phase of spin liquid and conduction electrons to a ferromagnetic topological superconductor of Class D with a single chiral Majorana edge mode. This is followed by a second order transition into a paramagnetic topological superconductor of Class DIII with a single helical Majorana edge mode. These findings offer a novel route to topological superconductivity in the Kondo lattice system. We discuss the connection between topological nature of the Kitaev spin liquid and topological superconductors obtained in this model.

cond-mat.str-el↗

arXiv2018

Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws

We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the system to a new steady state which can be approximately but efficiently described by a (generalized) Gibbs ensemble characterized by one Lagrange parameter for each conservation law. The value of those has to be determined from rate equations for conserved quantities. Remarkably, even weak perturbations can lead to large responses of conserved quantities. We present a perturbative expansion of the steady state density matrix; first we give the condition that fixes the zeroth order expression (Lagrange parameters) and then determine the higher order corrections via projections of the Liouvillian. The formalism can be applied to a wide range of problems including two-temperature models for electron-phonon systems, Bose condensates of excitons or photons or weakly perturbed integrable models. We test our formalism by studying interacting fermions coupled to non-thermal reservoirs, approximately described by a Boltzmann equation.

cond-mat.str-el↗