Cavity optomagnonics with magnetic textures: coupling a magnetic vortex to light
Jasmin Graf, Hannes Pfeifer, Florian Marquardt, Silvia ViolaKusminskiy
Physical Review B
98(24)
241406
(2018)

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Optomagnonic systems, where light couples coherently to collective excitations in magnetically ordered solids, are currently of high interest due to their potential for quantum information processing platforms at the nanoscale. Efforts so far, both at the experimental and theoretical level, have focused on systems with a homogeneous magnetic background. A unique feature in optomagnonics is however the possibility of coupling light to spin excitations on top of magnetic textures. We propose a cavityoptomagnonic system with a non homogeneous magnetic ground state, namely a vortex in a magnetic microdisk. In particular we study the coupling between optical whispering gallery modes to magnon modes localized at the vortex. We show that the optomagnonic coupling has a rich spatial structure and that it can be tuned by an externally applied magnetic field. Our results predict cooperativities at maximum photon density of the order of C≈10−2 by proper engineering of these structures.
Interacting adiabatic quantum motor
Anton Bruch, Silvia ViolaKusminskiy, Gil Refael, Felix von Oppen
PHYSICAL REVIEW B
97(19)
195411
(2018)

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We present a field theoretic treatment of an adiabatic quantum motor. We explicitly discuss a motor termed Thouless motor which is based on a Thouless pump operating in reverse. When a sliding periodic potential is considered as the motor degree of freedom, a bias voltage applied to the electron channel sets the motor in motion. We investigate a Thouless motor whose electron channel is modeled as a Luttinger liquid. Interactions increase the gap opened by the periodic potential. For an infinite Luttinger liquid the coupling induced friction is enhanced by electronelectron interactions. When the LL is ultimately coupled to Fermi liquid reservoirs, the dissipation reduces to its value for a noninteracting electron system for a constant motor velocity. Our results can also be applied to a motor based on a nanomagnet coupled to a quantum spin Hall edge.
Effect of interactions on quantumlimited detectors
Gleb Skorobagatko, Anton Bruch, Silvia ViolaKusminskiy, Alessandro Romito
We consider the effect of electronelectron interactions on a voltage biased quantum point contact in the tunneling regime used as a detector of a nearby qubit. We model the leads of the quantum point contact as Luttinger liquids, incorporate the effects of finite temperature and analyze the detectioninduced decoherence rate and the detector efficiency, Q. We find that interactions generically reduce the induced decoherence along with the detector's efficiency, and strongly affect the relative strength of the decoherence induced by tunneling and that induced by interactions with the local density. With increasing interaction strength, the regime of quantumlimited detection (Q > 1) is shifted to increasingly lower temperatures or higher bias voltages respectively. For small to moderate interaction strengths, Q is a monotonously decreasing function of temperature as in the noninteracting case. Surprisingly, for sufficiently strong interactions we identify an intermediate temperature regime where the efficiency of the detector increases with rising temperature.
Tuning the Pseudospin Polarization of Graphene by a Pseudomagnetic Field
Alexander Georgi, Peter NemesIncze, Ramon CarrilloBastos, Daiara Faria, Silvia ViolaKusminskiy, Dawei Zhai, Martin Schneider, Dinesh Subramaniam, Torge Mashoff, Nils M. Freitag, et al.
One of the intriguing characteristics of honeycomb lattices is the appearance of a pseudomagnetic field as a result of mechanical deformation. In the case of graphene, the Landau quantization resulting from this pseudomagnetic field has been measured using scanning tunneling microscopy. Here we show that a signature of the pseudomagnetic field is a local sublattice symmetry breaking observable as a redistribution of the local density of states. This can be interpreted as a polarization of graphene's pseudospin due to a strain induced pseudomagnetic field, in analogy to the alignment of a real spin in a magnetic field. We reveal this sublattice symmetry breaking by tunably straining graphene using the tip of a scanning tunneling microscope. The tip locally lifts the graphene membrane from a SiO2 support, as visible by an increased slope of the I(z) curves. The amount of lifting is consistent with molecular dynamics calculations, which reveal a deformed graphene area under the tip in the shape of a Gaussian. The pseudomagnetic field induced by the deformation becomes visible as a sublattice symmetry breaking which scales with the lifting height of the strained deformation and therefore with the pseudomagnetic field strength. Its magnitude is quantitatively reproduced by analytic and tightbinding models, revealing fields of 1000 T. These results might be the starting point for an effective THz valley filter, as a basic element of valleytronics.
Quantum thermodynamics of the driven resonant level model
Anton Bruch, Mark Thomas, Silvia ViolaKusminskiy, Felix von Oppen, Abraham Nitzan
We present a consistent thermodynamic theory for the resonant level model in the wideband limit, whose level energy is driven slowly by an external force. The problem of defining "system" and "bath" in the strongcoupling regime is circumvented by considering as the system everything that is influenced by the externally driven level. The thermodynamic functions that are obtained to first order beyond the quasistatic limit fulfill the first and second law with a positive entropy production, successfully connect to the forces experienced by the external driving, and reproduce the correct weakcoupling limit of stochastic thermodynamics.
Coupled spinlight dynamics in cavity optomagnonics
Silvia ViolaKusminskiy, Hong X. Tang, Florian Marquardt
PHYSICAL REVIEW A
94(3)
033821
(2016)

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Experiments during the past 2 years have shown strong resonant photonmagnon coupling in microwave cavities, while coupling in the optical regime was demonstrated very recently for the first time. Unlike with microwaves, the coupling in optical cavities is parametric, akin to optomechanical systems. This line of research promises to evolve into a new field of optomagnonics, aimed at the coherent manipulation of elementary magnetic excitations in solidstate systems by optical means. In this work we derive the microscopic optomagnonic Hamiltonian. In the linear regime the system reduces to the wellknown optomechanical case, with remarkably large coupling. Going beyond that, we study the optically induced nonlinear classical dynamics of a macrospin. In the fastcavity regime we obtain an effective equation of motion for the spin and show that the light field induces a dissipative term reminiscent of Gilbert damping. The induced dissipation coefficient, however, can change sign on the Bloch sphere, giving rise to selfsustained oscillations. When the full dynamics of the system is considered, the system can enter a chaotic regime by successive period doubling of the oscillations.
Langevin dynamics of a heavy particle and orthogonality effects
Mark Thomas, Torsten Karzig, Silvia ViolaKusminskiy
The dynamics of a classical heavy particle moving in a quantum environment is determined by a Langevin equation which encapsulates the effect of the environmentinduced reaction forces on the particle. For an open quantum system, these include a BornOppenheimer force, a dissipative force, and a stochastic force due to shot and thermal noise. Recently, it was shown that these forces can be expressed in terms of the scattering matrix of the system by considering the classical heavy particle as a timedependent scattering center, allowing to demonstrate interesting features of these forces when the system is driven out of equilibrium. At the same time, it is well known that small changes in a scattering potential can have a profound impact on a fermionic system due to the Anderson orthogonality catastrophe. In this work, by calculating the Loschmidt echo, we relate Anderson orthogonality effects with the mesoscopic reaction forces for an environment that can be taken out of equilibrium. In particular, we show how the decay of the Loschmidt echo is characterized by fluctuations and dissipation in the system and discuss different quench protocols.
Local sublattice symmetry breaking for graphene with a centrosymmetric
deformation
M. Schneider, D. Faria, Silvia ViolaKusminskiy, N. Sandler
We calculate the local density of states (LDOS) for an infinite graphene sheet with a single centrosymmetric outofplane deformation, in order to investigate measurable strain signatures on graphene. We focus on the regime of small deformations and show that the straininduced pseudomagnetic field induces an imbalance of the LDOS between the two triangular graphene sublattices in the region of the deformation. Realspace imaging reveals a characteristic sixfold symmetry pattern where the sublattice symmetry is broken within each fold, consistent with experimental and tightbinding observations. The open geometry we study allows us to make use of the usual continuum model of graphene and to obtain results independent of boundary conditions. We provide an analytic perturbative expression for the contrast between the LDOS of each sublattice, showing a scaling law as a function of the amplitude and width of the deformation. We confirm our results by a numerically exact iterative scattering matrix method.
Realspace tailoring of the electronphonon coupling in ultraclean
nanotube mechanical resonators
A. Benyamini, A. Hamo, Silvia ViolaKusminskiy, F. von Oppen, S. Ilani
The coupling between electrons and phonons is at the heart of many fundamental phenomena in nature. Despite tremendous advances in controlling electrons or phonons in engineered nanosystems, control over their coupling is still widely lacking. Here we demonstrate the ability to fully tailor electronphonon interactions using a new class of suspended carbon nanotube devices, in which we can form highly tunable single and double quantum dots at arbitrary locations along a nanotube mechanical resonator. We find that electronphonon coupling can be turned on and off by controlling the position of a quantum dot along the resonator. Using double quantum dots we structure the interactions in real space to couple specific electronic and phononic modes. This tailored coupling allows measurement of the phonons' spatial parity and imaging of their mode shapes. Finally, we demonstrate coupling between phonons and internal electrons in an isolated system, decoupled from the random environment of the electronic leads, a crucial step towards fully engineered quantumcoherent electronphonon systems.
Materials Design from Nonequilibrium Steady States: Driven Graphene as a Tunable Semiconductor with Topological Properties
Thomas Iadecola, David Campbell, Claudio Chamon, ChangYu Hou, Roman Jackiw, SoYoung Pi, Silvia ViolaKusminskiy
Controlling the properties of materials by driving them out of equilibrium is an exciting prospect that has only recently begun to be explored. In this Letter we give a striking theoretical example of such materials design: a tunable gap in monolayer graphene is generated by exciting a particular optical phonon. We show that the system reaches a steady state whose transport properties are the same as if the system had a static electronic gap, controllable by the driving amplitude. Moreover, the steady state displays topological phenomena: there are chiral edge currents, which circulate a fractional charge e/2 per rotation cycle, with the frequency set by the optical phonon frequency. DOI: 10.1103/PhysRevLett.110.176603
Scattering theory of adiabatic reaction forces due to outofequilibrium quantum environments
Mark Thomas, Torsten Karzig, Silvia ViolaKusminskiy, Gergely Zarand, Felix von Oppen
The LandauerButtiker theory of mesoscopic conductors was recently extended to nanoelectromechanical systems. In this extension, the adiabatic reaction forces exerted by the electronic degrees of freedom on the mechanical modes were expressed in terms of the electronic S matrix and its first nonadiabatic correction, the A matrix. Here, we provide a more natural and efficient derivation of these results within the setting and solely with the methods of scattering theory. Our derivation is based on a generic model of a slow classical degree of freedom coupled to a quantummechanical scattering system, extending previous work on adiabatic reaction forces for closed quantum systems.
Currentinduced forces in mesoscopic systems: A scatteringmatrix approach
Niels Bode, Silvia ViolaKusminskiy, Reinhold Egger, Felix von Oppen
BEILSTEIN JOURNAL OF NANOTECHNOLOGY
3
144162
(2012)

Journal
Nanoelectromechanical systems are characterized by an intimate connection between electronic and mechanical degrees of freedom. Due to the nanoscopic scale, current flowing through the system noticeably impacts upons the vibrational dynamics of the device, complementing the effect of the vibrational modes on the electronic dynamics. We employ the scatteringmatrix approach to quantum transport in order to develop a unified theory of nanoelectromechanical systems out of equilibrium. For a slow mechanical mode the current can be obtained from the LandauerButtiker formula in the strictly adiabatic limit. The leading correction to the adiabatic limit reduces to Brouwer's formula for the current of a quantum pump in the absence of a bias voltage. The principal results of the present paper are the scatteringmatrix expressions for the currentinduced forces acting on the mechanical degrees of freedom. These forces control the Langevin dynamics of the mechanical modes. Specifically, we derive expressions for the (typically nonconservative) mean force, for the (possibly negative) damping force, an effective "Lorentz" force that exists even for timereversalinvariant systems, and the fluctuating Langevin force originating from Nyquist and shot noise of the current flow. We apply our general formalism to several simple models that illustrate the peculiar nature of the currentinduced forces. Specifically, we find that in outofequilibrium situations the currentinduced forces can destabilize the mechanical vibrations and cause limitcycle dynamics.
Scattering Theory of CurrentInduced Forces in Mesoscopic Systems
Niels Bode, Silvia ViolaKusminskiy, Reinhold Egger, Felix von Oppen
We develop a scattering theory of currentinduced forces exerted by the conduction electrons of a general mesoscopic conductor on slow "mechanical" degrees of freedom. Our theory describes the currentinduced forces both in and out of equilibrium in terms of the scattering matrix of the phasecoherent conductor. Under general nonequilibrium conditions, the resulting mechanical Langevin dynamics is subject to both nonconservative and velocitydependent Lorentzlike forces, in addition to (possibly negative) friction. We illustrate our results with a twomode model inspired by hydrogen molecules in a break junction which exhibits limitcycle dynamics of the mechanical modes.
Pinning of a twodimensional membrane on top of a patterned substrate: The case of graphene
Silvia ViolaKusminskiy, D. K. Campbell, A. H. Castro Neto, F. Guinea
We study the pinning of a twodimensional membrane to a patterned substrate within elastic theory both in the bending rigidity and in the straindominated regimes. We find that both the inplane strains and the bending rigidity can lead to depinning. We show from energetic arguments that the system experiences a firstorder phase transition between the attached configuration to a partially detached one when the relevant parameters of the substrate are varied, and we construct a qualitative phase diagram. Our results are confirmed through analytical solutions for some simple geometries of the substrate's profile. We apply our model to the case of graphene on top of a SiO2 substrate and show that typical orders of magnitude for corrugations imply graphene will be partially detached from the substrate.
Biaxial Strain in Graphene Adhered to Shallow Depressions
Constanze Metzger, Sebastian Remi, Mengkun Liu, Silvia ViolaKusminskiy, Antonio H. Castro Neto, Anna K. Swan, Bennett B. Goldberg
Measurements on graphene exfoliated over a substrate prepatterned with shallow depressions demonstrate that graphene does not remain freestanding but instead adheres to the substrate despite the induced biaxial strain. The strain is homogeneous over the depression bottom as determined by Raman measurements. We find higher Raman shifts and Gruneisen parameters of the phonons underlying the G and 2D bands under biaxial strain than previously reported. Interference modeling is used to determine the vertical position of the graphene and to calculate the optimum dielectric substrate stack for maximum Raman signal.
Lenosky's energy and the phonon dispersion of graphene
Silvia ViolaKusminskiy, D. K. Campbell, A. H. Castro Neto
We calculate the phonon spectrum for a graphene sheet resulting from the model proposed by Lenosky et al. [Nature (London) 355, 333 (1992)] for the free energy of the lattice. This model takes into account not only the usual bondbending and stretching terms, but it also captures the possible misalignment of the p(z) orbitals. We compare our results with previous models used in the literature and with available experimental data. We show that while this model provides an excellent description of the flexural modes in graphene, an extra term in the energy is needed for it to be able to reproduce the full phonon dispersion correctly beyond the Gamma point.
Electronelectron interactions in graphene bilayers
Silvia ViolaKusminskiy, D. K. Campbell, A. H. Castro Neto
We study the effect of electronelectron interactions in the quasiparticle dispersion of a graphene bilayer within the HartreeFockThomasFermi theory by using a fourbands model. We find that the electronic fluid can be described by a noninteractinglike dispersion but with renormalized parameters. We compare our results with recent cyclotron resonance experiments in this system. Copyright (C) EPLA, 2009
Electronic compressibility of a graphene bilayer
Silvia ViolaKusminskiy, Johan Nilsson, D. K. Campbell, A. H. Castro Neto
We calculate the electronic compressibility arising from electronelectron interactions for a graphene bilayer within the HartreeFock approximation. We show that, due to the chiral nature of the particles in this system, the compressibility is rather different from those of either the twodimensional electron gas or ordinary semiconductors. We find that an inherent competition between the contributions coming from intraband exchange interactions (dominant at low densities) and interband interactions (dominant at moderate densities) leads to a nonmonotonic behavior of the compressibility as a function of carrier density.
Meanfield study of the heavyfermion metamagnetic transition
S. ViolaKusminskiy, K. S. D. Beach, A. H. Castro Neto, D. K. Campbell
We investigate the evolution of the heavyfermion ground state under application of a strong external magnetic field. We present a richer version of the usual hybridization meanfield theory that allows for hybridization in both the singlet and triplet channels and incorporates a selfconsistent Weiss field. We show that for a magnetic field strength B*, a fillingdependent fraction of the zerofield hybridization gap, the spin up quasiparticle band becomes fully polarized  an event marked by a sudden jump in the magnetic susceptibility. The system exhibits a kind of quantum rigidity in which the susceptibility (and several other physical observables) is insensitive to further increases in field strength. This behavior ends abruptly with the collapse of the hybridization order parameter in a firstorder transition to the normal metallic state. We argue that the feature at B* corresponds to the "metamagnetic transition" in YbRh2Si2. Our results are in good agreement with recent experimental measurements.
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