Optomagnonics in Dispersive Media: Magnon-Photon Coupling Enhancement at the Epsilon-near-Zero Frequency

V. A. S. V. Bittencourt, I. Liberal, S. Viola-Kusminskiy

Reaching strong light-matter coupling in solid-state systems has long been pursued for the implementation of scalable quantum devices. Here, we put forward a system based on a magnetized epsilon-near-zero (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 magneto-optical response. We adopt a phenomenological approach to quantize the electromagnetic field inside a dispersive magnetic medium in order to obtain the frequency-dependent coupling between magnons and photons. We predict that, in the epsilon-near-zero regime, the single-magnon single-photon coupling can be comparable to the magnon frequency for a small magnetic volume and perfect mode overlap. For state-of-the-art illustrative values, this would correspond to achieving the single-magnon 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 Viola-Kusminskiy

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 frequency-tunable 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 non-resonant 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 de-excite 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 magnon-photon coupling in optically dispersive magnetic media

V. A. S. V. Bittencourt, I. Liberal, S. Viola-Kusminskiy

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 Viola-Kusminskiy, arXiv:2110.02984) that strong single-particle coupling between magnons and light can be realized in a magnetized epsilon-near-zero (ENZ) medium, in which magneto-optical effects are enhanced. Here we present a detailed derivation of the magnon-photon 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 plane-wave 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 ENZ-based optomagnonic systems.

Roadmap on Spin-Wave Computing

A. V. Chumak, P. Kabos, M. Wu, C. Abert, C. Adelmann, A. Adeyeye, J. Åkerman, F. G. Aliev, A. Anane, et al.

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 GHz-to-THz 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 proof-of-concept prototypes have already been realized in laboratories. This roadmap is a product of the collective work of many authors that covers versatile spin-wave 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 magnon-based quantum computing. The article is organized as a collection of sub-sections grouped into seven large thematic sections. Each sub-section 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 Viola-Kusminskiy, 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 optical-spring effect. In certain magnetic materials, mechanical vibrations can interact with magnetic excitations (magnons) via the magnetostrictive interaction, resulting in an analogous magnon-induced dynamical backaction. In this article, we directly observe the impact of magnon-induced 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.

All-Optical Generation of Antiferromagnetic Magnon Currents via the Magnon Circular Photogalvanic Effect

Emil Viñas Boström, Tahereh S. Parvini, James W. McIver, Angel Rubio, Silvia Viola-Kusminskiy, Michael A. Sentef

We introduce the magnon circular photogalvanic effect enabled by two-magnon Raman scattering. This provides an all-optical 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 spin-mechanics of a levitated magnetic microparticle

Vanessa Wachter, Victor A. S. V. Bittencourt, Shangran Xie, Sanchar Sharma, Nicolas Joly, Philip Russell, Florian Marquardt, Silvia Viola-Kusminskiy

We propose a platform that combines the fields of cavity optomagnonics and levitated optome- chanics in order to control and probe the coupled spin-mechanics of magnetic dielectric particles. We theoretically study the dynamics of a levitated Faraday-active 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 Viola-Kusminskiy, James A. Haigh, Koji Usami, Dany Lachance-Quirion, Yasunobu Nakamura, Can-Ming 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 magnon-photon coupling and the easily-reached 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 photon-mediated coupling of a magnon mode to a superconducting qubit enables measurements in the single magnon limit.

Design of an optomagnonic crystal: Towards optimal magnon-photon mode matching at the microscale

Jasmin Graf, Sanchar Sharma, Hans Hübl, Silvia Viola-Kusminskiy

We put forward the concept of an optomagnonic crystal: a periodically patterned structure at the microscale based on a magnetic dielectric, which can co-localize magnon and photon modes. The co-localization in small volumes can result in large values of the photon-magnon 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 one-dimensional 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 Viola-Kusminskiy

Generating nonclassical states in macroscopic systems is a long-standing 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.

Magnon-Phonon Quantum Correlation Thermometry

C. A. Potts, Victor A. S. V. Bittencourt, Silvia Viola-Kusminskiy, J. P. Davis

A large fraction of quantum science and technology requires low-temperature 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 cross-correlation measurement in which the spectrum of back-action 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 low-temperature 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 Viola-Kusminskiy

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 hard-axis 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 magnon-magnon interactions, including regions of magnon heating for a red-detuned driving laser. The multimode character of the system is evident in a substructure of the optomagnonically induced transparency window.

Cavity Optomagnonics

Silvia Viola-Kusminskiy

In the recent years a series of experimental and theoretical efforts have centered around a new topic: the coherent, cavity-enhanced 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 light-matter 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 Viola-Kusminskiy

In the emerging field of cavity optomagnonics, photons are coupled coherently to magnons in solid-state 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 magnon-heralding 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 magnon-photon 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 Bell-like states

Victor A. S. V. Bittencourt, Massimo Blasone

We describe in this paper the effects of Lorentz boost on the quantum entanglement encoded in two-particle Dirac bispinor Bell-like 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 Meyer-Wallach global measure of quantum entanglement due to the frame transformation and study its equivalence to the results obtained for the relativistic spin 1/2 Bell-like 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 ultra-relativistic states is solely due to an increasing of the entanglement associated with the spins subsystems. For such ultra-relativistic 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 particle-particle entanglement is invariant under boosts for any Bell-like state.

Quantum Magnetism, Spin Waves, and Optical Cavities

Silvia Viola-Kusminskiy

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.

Cavity optomagnonics with magnetic textures: coupling a magnetic vortex to light

Jasmin Graf, Hannes Pfeifer, Florian Marquardt, Silvia Viola-Kusminskiy

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 cavity-optomagnonic 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 Viola-Kusminskiy, Gil Refael, Felix von Oppen

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 electron-electron 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 quantum-limited detectors

Gleb Skorobagatko, Anton Bruch, Silvia Viola-Kusminskiy, Alessandro Romito

We consider the effect of electron-electron 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 detection-induced 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 quantum-limited 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 Nemes-Incze, Ramon Carrillo-Bastos, Daiara Faria, Silvia Viola-Kusminskiy, 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 tight-binding 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 Viola-Kusminskiy, Felix von Oppen, Abraham Nitzan

We present a consistent thermodynamic theory for the resonant level model in the wide-band limit, whose level energy is driven slowly by an external force. The problem of defining "system" and "bath" in the strong-coupling 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 weak-coupling limit of stochastic thermodynamics.

Coupled spin-light dynamics in cavity optomagnonics

Silvia Viola-Kusminskiy, Hong X. Tang, Florian Marquardt

Experiments during the past 2 years have shown strong resonant photon-magnon 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 solid-state systems by optical means. In this work we derive the microscopic optomagnonic Hamiltonian. In the linear regime the system reduces to the well-known optomechanical case, with remarkably large coupling. Going beyond that, we study the optically induced nonlinear classical dynamics of a macrospin. In the fast-cavity 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 self-sustained 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 Viola-Kusminskiy

The dynamics of a classical heavy particle moving in a quantum environment is determined by a Langevin equation which encapsulates the effect of the environment-induced reaction forces on the particle. For an open quantum system, these include a Born-Oppenheimer 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 time-dependent 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 Viola-Kusminskiy, N. Sandler

We calculate the local density of states (LDOS) for an infinite graphene sheet with a single centrosymmetric out-of-plane deformation, in order to investigate measurable strain signatures on graphene. We focus on the regime of small deformations and show that the strain-induced pseudomagnetic field induces an imbalance of the LDOS between the two triangular graphene sublattices in the region of the deformation. Real-space imaging reveals a characteristic sixfold symmetry pattern where the sublattice symmetry is broken within each fold, consistent with experimental and tight-binding 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.

Real-space tailoring of the electron-phonon coupling in ultraclean nanotube mechanical resonators

A. Benyamini, A. Hamo, Silvia Viola-Kusminskiy, 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 electron-phonon 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 electron-phonon 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 quantum-coherent electron-phonon systems.

Materials Design from Nonequilibrium Steady States: Driven Graphene as a Tunable Semiconductor with Topological Properties

Thomas Iadecola, David Campbell, Claudio Chamon, Chang-Yu Hou, Roman Jackiw, So-Young Pi, Silvia Viola-Kusminskiy

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 out-of-equilibrium quantum environments

Mark Thomas, Torsten Karzig, Silvia Viola-Kusminskiy, Gergely Zarand, Felix von Oppen

The Landauer-Buttiker 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 quantum-mechanical scattering system, extending previous work on adiabatic reaction forces for closed quantum systems.

Current-induced forces in mesoscopic systems: A scattering-matrix approach

Niels Bode, Silvia Viola-Kusminskiy, Reinhold Egger, Felix von Oppen

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 scattering-matrix 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 Landauer-Buttiker 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 scattering-matrix expressions for the current-induced 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 time-reversal-invariant 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 current-induced forces. Specifically, we find that in out-of-equilibrium situations the current-induced forces can destabilize the mechanical vibrations and cause limit-cycle dynamics.

Scattering Theory of Current-Induced Forces in Mesoscopic Systems

Niels Bode, Silvia Viola-Kusminskiy, Reinhold Egger, Felix von Oppen

We develop a scattering theory of current-induced forces exerted by the conduction electrons of a general mesoscopic conductor on slow "mechanical" degrees of freedom. Our theory describes the current-induced forces both in and out of equilibrium in terms of the scattering matrix of the phase-coherent conductor. Under general nonequilibrium conditions, the resulting mechanical Langevin dynamics is subject to both nonconservative and velocity-dependent Lorentz-like forces, in addition to (possibly negative) friction. We illustrate our results with a two-mode model inspired by hydrogen molecules in a break junction which exhibits limit-cycle dynamics of the mechanical modes.

Pinning of a two-dimensional membrane on top of a patterned substrate: The case of graphene

Silvia Viola-Kusminskiy, D. K. Campbell, A. H. Castro Neto, F. Guinea

We study the pinning of a two-dimensional membrane to a patterned substrate within elastic theory both in the bending rigidity and in the strain-dominated regimes. We find that both the in-plane strains and the bending rigidity can lead to depinning. We show from energetic arguments that the system experiences a first-order 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 Viola-Kusminskiy, 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 free-standing 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 Viola-Kusminskiy, 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 bond-bending 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.

Electron-electron interactions in graphene bilayers

Silvia Viola-Kusminskiy, D. K. Campbell, A. H. Castro Neto

We study the effect of electron-electron interactions in the quasiparticle dispersion of a graphene bilayer within the Hartree-Fock-Thomas-Fermi theory by using a four-bands model. We find that the electronic fluid can be described by a non-interacting-like 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 Viola-Kusminskiy, Johan Nilsson, D. K. Campbell, A. H. Castro Neto

We calculate the electronic compressibility arising from electron-electron interactions for a graphene bilayer within the Hartree-Fock 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 two-dimensional 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.

Mean-field study of the heavy-fermion metamagnetic transition

S. Viola-Kusminskiy, K. S. D. Beach, A. H. Castro Neto, D. K. Campbell

We investigate the evolution of the heavy-fermion ground state under application of a strong external magnetic field. We present a richer version of the usual hybridization mean-field theory that allows for hybridization in both the singlet and triplet channels and incorporates a self-consistent Weiss field. We show that for a magnetic field strength B*, a filling-dependent fraction of the zero-field 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 first-order 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.