Reaching strong lightmatter coupling in solidstate systems has long been pursued for the implementation of scalable quantum devices. Here, we put forward a system based on a magnetized epsilonnearzero (ENZ) medium, and we show that strong coupling between magnetic excitations (magnons) and light can be achieved close to the ENZ frequency due to a drastic enhancement of the magnetooptical response. We adopt a phenomenological approach to quantize the electromagnetic field inside a dispersive magnetic medium in order to obtain the frequencydependent coupling between magnons and photons. We predict that, in the epsilonnearzero regime, the singlemagnon singlephoton coupling can be comparable to the magnon frequency for a small magnetic volume and perfect mode overlap. For stateoftheart illustrative values, this would correspond to achieving the singlemagnon strong coupling regime, where the coupling rate is larger than all the decay rates. Finally, we show that the nonlinear energy spectrum intrinsic to this coupling regime can be probed via the characteristic multiple magnon sidebands in the photon power spectrum.
Protocol for generating an arbitrary quantum state of the magnetization in cavity magnonics
Sanchar Sharma, Victor A. S. V. Bittencourt, Silvia ViolaKusminskiy
arXiv:2201.10170
2201.10170
(2022)
We propose and numerically evaluate a protocol to generate an arbitrary quantum state of the magnetization in a magnet. The protocol involves repeatedly exciting a frequencytunable superconducting transmon and transferring the excitations to the magnet via a microwave cavity. To avoid decay, the protocol must be much shorter than magnon lifetime. Speeding up the protocol by simply shortening the pulses leads to nonresonant leakage of excitations to higher levels of the transmon accompanied by higher decoherence. We discuss how to correct for such leakages by applying counter pulses to deexcite these higher levels. In our protocol, states with a maximum magnon occupation of up to ∼9 and average magnon number up to ∼4 can be generated with fidelity >0.75.
Light propagation and magnonphoton coupling in optically dispersive magnetic media
V. A. S. V. Bittencourt, I. Liberal, S. ViolaKusminskiy
Achieving strong coupling between light and matter excitations in hybrid systems is a benchmark for the implementation of quantum technologies. We recently proposed (Bittencourt, Liberal, and ViolaKusminskiy, arXiv:2110.02984) that strong singleparticle coupling between magnons and light can be realized in a magnetized epsilonnearzero (ENZ) medium, in which magnetooptical effects are enhanced. Here we present a detailed derivation of the magnonphoton coupling Hamiltonian in dispersive media both for degenerate and nondegenerate optical modes, and show the enhancement of the coupling near the ENZ frequency. Moreover, we show that the coupling of magnons to planewave nondegenerate Voigt modes vanishes at specific frequencies due to polarization selection rules tuned by dispersion. Finally, we present specific results using a Lorentz dispersion model. Our results pave the way for the design of dispersive optomagnonic systems, providing a general theoretical framework for describing and engineering ENZbased optomagnonic systems.
2021
Roadmap on SpinWave Computing
A. V. Chumak, P. Kabos, M. Wu, C. Abert, C. Adelmann, A. Adeyeye, J. Åkerman, F. G. Aliev, A. Anane, et al.
arXiv:2111.00365
2111.00365
(2021)
Magnonics is a field of science that addresses the physical properties of spin waves and utilizes them for data processing. Scalability down to atomic dimensions, operations in the GHztoTHz frequency range, utilization of nonlinear and nonreciprocal phenomena, and compatibility with CMOS are just a few of many advantages offered by magnons. Although magnonics is still primarily positioned in the academic domain, the scientific and technological challenges of the field are being extensively investigated, and many proofofconcept prototypes have already been realized in laboratories. This roadmap is a product of the collective work of many authors that covers versatile spinwave computing approaches, conceptual building blocks, and underlying physical phenomena. In particular, the roadmap discusses the computation operations with Boolean digital data, unconventional approaches like neuromorphic computing, and the progress towards magnonbased quantum computing. The article is organized as a collection of subsections grouped into seven large thematic sections. Each subsection is prepared by one or a group of authors and concludes with a brief description of the current challenges and the outlook of the further development of the research directions.
Dynamical Backaction Magnomechanics
Clinton A. Potts, Emil Varga, Victor A. S. V. Bittencourt, Silvia ViolaKusminskiy, John P. Davis
Dynamical backaction resulting from radiation pressure forces in optomechanical systems has proven to be a versatile tool for manipulating mechanical vibrations. Notably, dynamical backaction has resulted in the cooling of a mechanical resonator to its ground state, driving phonon lasing, the generation of entangled states, and observation of the opticalspring effect. In certain magnetic materials, mechanical vibrations can interact with magnetic excitations (magnons) via the magnetostrictive interaction, resulting in an analogous magnoninduced dynamical backaction. In this article, we directly observe the impact of magnoninduced dynamical backaction on a spherical magnetic sample’s mechanical vibrations. Moreover, dynamical backaction effects play a crucial role in many recent theoretical proposals; thus, our work provides the foundation for future experimental work pursuing many of these theoretical proposals.
AllOptical Generation of Antiferromagnetic Magnon Currents via the Magnon Circular Photogalvanic Effect
Emil Viñas Boström, Tahereh S. Parvini, James W. McIver, Angel Rubio, Silvia ViolaKusminskiy, Michael A. Sentef
Physical Review B
104(10)
L100404
(2021)

Journal
We introduce the magnon circular photogalvanic effect enabled by twomagnon Raman scattering. This provides an alloptical pathway to the generation of directed magnon currents with circularly polarized light in honeycomb antiferromagnetic insulators. The effect is the leading order contribution to magnon photocurrent generation via optical fields. Control of the magnon current by the polarization and angle of incidence of the laser is demonstrated. Experimental detection by sizable inverse spin Hall voltages in platinum contacts is proposed.
Optical signatures of the coupled spinmechanics of a levitated magnetic microparticle
Vanessa Wachter, Victor A. S. V. Bittencourt, Shangran Xie, Sanchar Sharma, Nicolas Joly, Philip Russell, Florian Marquardt, Silvia ViolaKusminskiy
Journal of the Optical Society of America BOptical Physics
38(12)

Journal

PDF
We propose a platform that combines the fields of cavity optomagnonics and levitated optome
chanics in order to control and probe the coupled spinmechanics of magnetic dielectric particles. We theoretically study the dynamics of a levitated Faradayactive dielectric microsphere serving as an optomagnonic cavity, placed in an external magnetic field and driven by an external laser. We find that the optically driven magnetization dynamics induces angular oscillations of the particle with low associated damping. Further, we show that the magnetization and angular motion dynamics
can be probed via the power spectrum of the outgoing light. Namely, the characteristic frequencies attributed to the angular oscillations and the spin dynamics are imprinted in the light spectrum by two main resonance peaks. Additionally, we demonstrate that a ferromagnetic resonance setup with an oscillatory perpendicular magnetic field can enhance the resonance peak corresponding to
the spin oscillations and induce fast rotations of the particle around its anisotropy axis.
Cavity Magnonics
Babak Zare Rameshti, Silvia ViolaKusminskiy, James A. Haigh, Koji Usami, Dany LachanceQuirion, Yasunobu Nakamura, CanMing Hu, Hong X. Tang, Gerrit E. W. Bauer, et al.
Cavity magnonics deals with the interaction of magnons  elementary excitations in magnetic materials  and confined electromagnetic fields. We introduce the basic physics and review the experimental and theoretical progress of this young field that is gearing up for integration in future quantum technologies. Much of its appeal is derived from the strong magnonphoton coupling and the easilyreached nonlinear regime in microwave cavities. The interaction of magnons with light as detected by Brillouin light scattering is enhanced in magnetic optical resonators, which can be employed to manipulate magnon distributions. The cavity photonmediated coupling of a magnon mode to a superconducting qubit enables measurements in the single magnon limit.
Design of an optomagnonic crystal: Towards optimal magnonphoton mode matching at the microscale
Jasmin Graf, Sanchar Sharma, Hans Hübl, Silvia ViolaKusminskiy
Physical Review Research
3(1)
013277
(2021)

Journal
We put forward the concept of an optomagnonic crystal: a periodically patterned structure at the microscale based on a magnetic dielectric, which can colocalize magnon and photon modes. The colocalization in small volumes can result in large values of the photonmagnon coupling at the single quanta level, which opens perspectives for quantum information processing and quantum conversion schemes with these systems. We study theoretically a simple geometry consisting of a onedimensional array of holes with an abrupt defect, considering the ferrimagnet yttrium iron garnet (YIG) as the basis material. We show that both magnon and photon modes can be localized at the defect, and use symmetry arguments to select an optimal pair of modes in order to maximize the coupling. We show that an optomagnonic coupling in the kHz range is achievable in this geometry, and discuss possible optimization routes in order to improve both coupling strengths and optical losses.
Spin cat states in ferromagnetic insulators
Sanchar Sharma, V. A. S. V. Bittencourt, Alexy D. Karenowska, Silvia ViolaKusminskiy
Physical Review B
103(10)
L100403
(2021)

Journal
Generating nonclassical states in macroscopic systems is a longstanding challenge. A promising platform in the context of this quest are novel hybrid systems based on magnetic dielectrics, where photons can couple strongly and coherently to magnetic excitations, although a nonclassical state therein is yet to be observed. We propose a scheme to generate a magnetization cat state, i.e., a quantum superposition of two distinct magnetization directions, using a conventional setup of a macroscopic ferromagnet in a microwave cavity. Our scheme uses the ground state of an ellipsoid shaped magnet, which displays anisotropic quantum fluctuations akin to a squeezed vacuum. The magnetization collapses to a cat state by either a single photon or a parity measurement of the microwave cavity state. We find that a cat state with two components separated by ∼5ℏ is feasible and briefly discuss potential experimental setups that can achieve it.
2020
MagnonPhonon Quantum Correlation Thermometry
C. A. Potts, Victor A. S. V. Bittencourt, Silvia ViolaKusminskiy, J. P. Davis
Physical Review Applied
13 (6)
064001
(2020)
A large fraction of quantum science and technology requires lowtemperature environments such as those afforded by dilution refrigerators. In these cryogenic environments, accurate thermometry can be difficult to implement, expensive, and often requires calibration to an external reference. Here, we theoretically propose a primary thermometer based on measurement of a hybrid system consisting of phonons coupled via a magnetostrictive interaction to magnons. Thermometry is based on a crosscorrelation measurement in which the spectrum of backaction driven motion is used to scale the thermomechanical motion, providing a direct measurement of the phonon temperature independent of experimental parameters. Combined with a simple lowtemperature compatible microwave cavity readout, this primary thermometer is expected to become a promising alternative for thermometry below 1 K.
Antiferromagnetic cavity optomagnonics
Tahereh S. Parvini, Victor A. S. V. Bittencourt, Silvia ViolaKusminskiy
Physical Review Research
2(2)
022027(R)
(2020)

Journal
Currently there is a growing interest in studying the coherent interaction between magnetic systems and electromagnetic radiation in a cavity, prompted partly by possible applications in hybrid quantum systems. We propose a multimode cavity optomagnonic system based on antiferromagnetic insulators, where optical photons couple coherently to the two homogeneous magnon modes of the antiferromagnet. These have frequencies typically in the THz range, a regime so far mostly unexplored in the realm of coherent interactions, and which makes antiferromagnets attractive for quantum transduction from THz to optical frequencies. We derive the theoretical model for the coupled system, and show that it presents unique characteristics. In particular, if the antiferromagnet presents hardaxis magnetic anisotropy, the optomagnonic coupling can be tuned by a magnetic field applied along the easy axis. This allows us to bring a selected magnon mode into and out of a dark mode, providing an alternative for a quantum memory protocol. The dynamical features of the driven system present unusual behavior due to optically induced magnonmagnon interactions, including regions of magnon heating for a reddetuned driving laser. The multimode character of the system is evident in a substructure of the optomagnonically induced transparency window.
In the recent years a series of experimental and theoretical efforts have centered around a new topic: the coherent, cavityenhanced interaction between optical photons and solid state magnons. The resulting emerging field of Cavity
Optomagnonics is of interest both at a fundamental level, providing a new platform to study lightmatter interaction in confined structures, as well as for its possible relevance for hybrid quantum technologies. In this chapter I introduce the basic concepts of Cavity Optomagnonics and review some theoretical developments.
Magnon heralding in cavity optomagnonics
Victor A. S. V. Bittencourt, Verena Feulner, Silvia ViolaKusminskiy
In the emerging field of cavity optomagnonics, photons are coupled coherently to magnons in solidstate systems. These new systems are promising for implementing hybrid quantum technologies. Being able to prepare Fock states in such platforms is an essential step towards the implementation of quantum information schemes. We propose a magnonheralding protocol to generate a magnon Fock state by detecting an optical cavity photon. Due to the peculiarities of the optomagnonic coupling, the protocol involves two distinct cavity photon modes. Solving the quantum Langevin equations of the coupled system, we show that the temporal scale of the heralding is governed by the magnonphoton cooperativity and derive the requirements for generating high fidelity magnon Fock states. We show that the nonclassical character of the heralded state, which is imprinted in the autocorrelation of an optical “read” mode, is only limited by the magnon lifetime for small enough temperatures. We address the detrimental effects of nonvacuum initial states, showing that high fidelity Fock states can be achieved by actively cooling the system prior to the protocol.
Lorentz boosts of bispinor Belllike states
Victor A. S. V. Bittencourt, Massimo Blasone
Journal of Physics: Conference Series
1275
012026
(2019)

Journal
We describe in this paper the effects of Lorentz boost on the quantum entanglement encoded in twoparticle Dirac bispinor Belllike states. Each particle composing the system described in this formalism has three degrees of freedom: spin, chirality, and momentum, and the joint state can be interpreted as a 6 qubit state. Given the transformation law of bispinor under boosts, we compute the change of the MeyerWallach global measure of quantum entanglement due to the frame transformation and study its equivalence to the results obtained for the relativistic spin 1/2 Belllike states, constructed in the framework of the irreducible representations of the Lorentz group. We verify that the monotonic increase of the global entanglement under boosts for ultrarelativistic states is solely due to an increasing of the entanglement associated with the spins subsystems. For such ultrarelativistic states, the entanglement related to the chirality degrees of freedom is invariant, and the variation of the global entanglement of bispinor states is the same as the one calculated for relativistic spin 1/2 states. We also show that the particleparticle entanglement is invariant under boosts for any Belllike state.
Quantum Magnetism, Spin Waves, and Optical Cavities
This primer thoroughly covers the fundamentals needed to understand the interaction of light with magnetically ordered matter and it focuses on "cavity optomagnonics" which is a topic undergoing intense study in current research.
The book is unique in combining elements of electromagnetism, quantum magnetism, and quantum optics and it is intended for advanced undergraduate or graduate students.
2018
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)

Journal

PDF
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.
suggested by editors
Interacting adiabatic quantum motor
Anton Bruch, Silvia ViolaKusminskiy, Gil Refael, Felix von Oppen
PHYSICAL REVIEW B
97(19)
195411
(2018)

Journal

PDF
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.
before 2018
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, 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)

Journal

PDF
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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