Recent scanning tunneling spectroscopy experiments [V. W. Brar et. al., Appl. Phys. Lett. 91, 122102 (2007), Y. Zhang et. al., arXiv:0802.4315 (2008)] on graphene reported an unexpected gap of about $\pm 60$meV around the Fermi level. Here, we give a theoretical investigation explaining the experimentally observed spectra and confirming the phonon mediated tunneling as the reason for the gap: We study the real space properties of the wave functions involved in the tunneling process by means of ab-initio theory and present a model for the electron-phonon interaction, which couples the graphene's Dirac electrons with quasi free electron states at the Brillouin zone center. The self-energy associated with this electron-phonon interaction is calculated and its effects on tunneling into graphene are discussed. In particular, good agreement of the tunneling density of states within our model and the experimental[V. W. Brar et. al., Appl. Phys. Lett. 91, 122102 (2007), Y. Zhang et. al., arXiv:0802.4315 (2008)] dI/dU spectra is found.
We investigate tunneling in metal-insulator-metal junctions employing few atomic layers of hexagonal boron nitride (hBN) as the insulating barrier. While the low-bias tunnel resistance increases nearly exponentially with barrier thickness, subtle features are seen in the current-voltage curves, indicating marked influence of the intrinsic defects present in the hBN insulator on the tunneling transport. In particular, single electron charging events are observed, which are more evident in thicker-barrier devices where direct tunneling is substantially low. Furthermore, we find that annealing th…
Local electronic structures of nanometer-sized patches of epitaxial graphene and its interface layer with SiC(0001) have been studied by atomically resolved scanning tunneling microscopy and spectroscopy. Localized states belonging to the interface layer of a graphene/SiC system show to have an essential influence on the electronic structure of graphene. Giant enhancement of inelastic tunneling, reaching 50% of the total tunneling current, has been observed at the localized states on a nanometer-sized graphene monolayer surrounded by defects.
A quantum-kinetic theory of direct and phonon mediated indirect optical transitions is developed within the framework of the non-equilibrium Green's function formalism. After validation against the standard Fermi-Golden-Rule approach in the bulk case, it is used in the simulation of photocurrent generation in ultra-thin crystalline silicon p-i-n-junction devices.
Phonons, the fundamental vibrational modes of a crystal lattice, play a crucial role in determining electronic properties of materials through electron-phonon interaction. However, it has proved difficult to directly probe the phonon modes of materials in electrical measurements. Here, we report the observation of giant quantized phonon peaks of the K and K out-of-plane phonon in graphene monolayer in magnetic fields via tunneling spectra, which are usually used to measure local electronic properties of materials. A perpendicular magnetic field quantizes massless Dirac fermions in graphene int…
We report a computational theoretical investigation of electron spin-flip scattering induced by the electron-phonon interaction in the transition-metal ferromagnets bcc Fe, fcc Co and fcc Ni. The Elliott-Yafet electron-phonon spin-flip scattering is computed from first-principles, employing a generalized spin-flip Eliashberg function as well as ab initio computed phonon dispersions. Aiming at investigating the amount of electron-phonon mediated demagnetization in femtosecond laser-excited ferromagnets, the formalism is extended to treat laser-created thermalized as well as nonequilibrium, nont…
A composite material is considered which consists of conducting nanoparticles separated by tunneling dielectric barriers. The influence of the phonon thermal conductivity of dielectric matrix on the thermoelectric figure of merit of this composite material is theoretically in-vestigated. The range of values and barrier parameters that can lead to the thermoelectric figure of merit greater than unity is estimated. The influence of space charge and nonlinearity of current-voltage relations of tunneling barrier are also discussed.
We measure magnetization changes in a single crystal of the single-molecule magnet Fe8 when exposed to intense, short (<20 $μ$s) pulses of microwave radiation resonant with the m = 10 to 9 transition. We find that radiation induces a phonon bottleneck in the system with a time scale of ~5 $μ$s. The phonon bottleneck, in turn, drives the spin dynamics, allowing observation of thermally assisted resonant tunneling between spin states at the 100-ns time scale. Detailed numerical simulations quantitatively reproduce the data and yield a spin-phonon relaxation time of T1 ~ 40 ns.
The honeycomb lattice of graphene is a unique two-dimensional (2D) system where the quantum mechanics of electrons is equivalent to that of relativistic Dirac fermions. Novel nanometer-scale behavior in this material, including electronic scattering, spin-based phenomena, and collective excitations, is predicted to be sensitive to charge carrier density. In order to probe local, carrier-density dependent properties in graphene we have performed atomically-resolved scanning tunneling spectroscopy measurements on mechanically cleaved graphene flake devices equipped with tunable back-gate electro…
The acoustic phonon-mediated drag-contribution to the drag current created in the ballistic transport regime in a one-dimensional nanowire by phonons generated by a current-carrying ballistic channel in a nearby nanowire is calculated. The threshold of the phonon-mediated drag current with respect to bias or gate voltage is predicted.
Electronic transport in diatomic molecules (two-level systems) connected to metallic contacts is analyzed in the presence of competing electron-electron and electron-phonon interactions. We show that phonon emission and absorption processes are strongly modified when a Coulomb energy $U$ is included, as the phonons open channels that can result in destructive or constructive interference effects. Resonance conditions for these processes produce dramatic effects both in the density of states at the molecular sites, as well as in the conductance through the system. We find in particular an enhan…
We present electronic transport measurements of GaAs nanowires grown by catalyst-free metal-organic chemical vapor deposition. Despite the nanowires being doped with a relatively high concentration of substitutional impurities, we find them inordinately resistive. By measuring sufficiently high aspect-ratio nanowires individually in situ, we decouple the role of the contacts and show that this semi-insulating electrical behavior is the result of trap-mediated carrier transport. We observe Poole-Frenkel transport that crosses over to phonon-assisted tunneling at higher fields, with a tunneling …
We analyze generation of phonons in tunneling structures with two electron states coupled by electron-phonon interaction. The conditions of strong vibration excitations are determined and dependence of non-equilibrium phonon occupation numbers on the applied bias is found. For high vibration excitation levels self consistent theory for the tunneling transport is presented.
Based on the dielectric continuum model, we calculated the phonon assisted tunneling (PAT) current of general double barrier resonant tunneling structures (DBRTSs) including both symmetric and antisymmetric ones. The results indicate that the four higher frequency interface phonon modes (especially the one which peaks at either interface of the emitter barrier) dominate the PAT processes, which increase the valley current and decrease the PVR of the DBRTSs. We show that an asymmetric structure can lead to improved performance.
We investigated the tunneling anisotropic magnetoresistance (TAMR) in thick hcp Co films at cryogenic temperatures using scanning tunneling microscopy. At around -350 mV, a strong TAMR up to 30\% is found with a characteristic voltage dependence and a reversal of sign. With the help of \textit{ab initio} calculations the TAMR can be traced back to a spin-polarized occupied surface states that experience a strong spin-orbit interaction leading to a magnetization direction depending hybridization with bulk states.
We study the effect of electron-phonon interaction on current and zero-frequency shot noise in resonant tunneling through a series triple-quantum-dot coupling to a local phonon mode by means of a nonperturbative mapping technique along with the Green function formulation. By fixing the energy difference between the first two quantum dots to be equal to phonon frequency and sweeping the level of the third quantum dot, we find a largely enhanced current spectrum due to phonon effect, and in particular we predict current peaks corresponding to phonon-absorption and -emission assisted resonant tun…
We explore phonon-mediated quantum transport through electronic noise characterization of a commercial CMOS transistor. The device behaves as a single electron transistor thanks to a single impurity atom in the channel. A low noise cryogenic CMOS transimpedance amplifier is exploited to perform low-frequency noise characterization down to the single electron, single donor and single phonon regime simultaneously, not otherwise visible through standard stability diagrams. Single electron tunneling as well as phonon-mediated features emerges in rms-noise measurements. Phonons are emitted at high …
We have studied magnetodrag between spatially separated two dimensional electron systems due to the virtual phonon exchange with and without taking into account the screening effects. The drag rate as a function of magnetic field, temperature, and interlayer spacing is calculated.
We present a systematic theory of acoustic-phonon-mediated superconductivity, which incorporates Coulomb repulsion, explaining the recent experiment in Bernal bilayer graphene under a large displacement field. The acoustic-phonon mechanism predicts that $s$-wave spin-singlet and $f$-wave spin-triplet pairings are degenerate and dominant. Assuming a spin-polarized valley-unpolarized normal state, we obtain $f$-wave spin-triplet superconductivity with a $T_c\sim 20$ mK near $n_e=-0.6\times 10^{12}$ cm$^{-2}$ for hole doping, in approximate agreement with the experiment. We further predict the ex…
A quantum dot molecule doped with a single electron in the presence of diagonal and off-diagonal carrier-phonon couplings is studied by means of a non-perturbative quantum kinetic theory. The interaction with acoustic phonons by deformation potential and piezoelectric coupling is taken into account. We show that the phonon-mediated relaxation is fast on a picosecond timescale and is dominated by the usually neglected off-diagonal coupling to the lattice degrees of freedom leading to phonon-assisted electron tunneling. We show that in the parameter regime of current electrical and optical exper…
A theory is presented for the modification of bandgaps in atomically thin boron nitride (BN) by attractive interactions mediated through phonons in a polarizable substrate, or in the BN plane. Gap equations are solved, and gap enhancements are found to range up to 70% for dimensionless electron-phonon coupling λ=1, indicating that a proportion of the measured BN bandgap may have a phonon origin.
Phonon-assisted tunneling in a double barrier resonant tunneling device can be seen as a resonance in the electron-phonon Fock space which is tuned by the applied voltage. We show that the geometrical parameters can induce a symmetry condition in this space that can strongly enhance the emission of longitudinal optical phonons. For devices with thin emitter barriers this is achieved by a wider collector's barrier.
Phonon-mediated spin dynamics in a two-electron double quantum dot under a phonon temperature gradient
Institute of Industrial Science, The University of Tokyo（东京大学工业科学研究所）；Center for Emergent Materials Science (CEMS), RIKEN（理化学研究所新兴材料科学中心）；RIKEN Center for Quantum Computing (RQC), RIKEN（理化学研究所量子计算中心）；Pure and Applied Sciences, University of Tsukuba（筑波大学自然系统工学研究科）
We report on a study of the phonon-mediated frictional drag between two-dimensional electron layers at the Landau level filling factor $ν=1/2$ predicted by Chern-Simons composite-fermion theory. Frictional drag between widely spaced layers is dominated by the phonon-mediated interaction and is altered from its zero-field form because of the large composite-fermion effective mass and, less strongly, by magnetic local-field effects. We find that the reduced drag resistance $ρ(T)/T^2$ peaks at a larger temperature and has a different density dependence than at zero field. We compare these results…
A theoretical model for the phonon-mediated off-resonant coupling between a quantum dot and a cavity, under resonant excitation of the quantum dot, is presented. We show that the coupling is caused by electron-phonon interaction in the quantum dot and is enhanced by the cavity. We analyze recently observed resonant quantum dot spectroscopic data by our theoretical model.
We investigate the competition between acoustic-phonon-mediated superconductivity and the long-range Coulomb interaction in moiréless graphene multilayers, specifically, Bernal bilayer graphene, rhombohedral trilayer graphene, and ABCA-stacked tetralayer graphene. In these graphene multilayers, the acoustic phonons can realize, through electron-phonon coupling, both spin-singlet and spin-triplet pairings, and the intra-sublattice pairings ($s$-wave spin-singlet and $f$-wave spin-triplet) are the dominant channels. Our theory naturally explains the distinct recent experimental findings in Berna…
We perform the investigations of the resonant tunneling via impurities embedded in the AlAs barrier of a single GaAs/AlGaAs heterostructure. In the $I(V)$ characteristics measured at 30mK, the contribution of individual donors is resolved and the fingerprints of phonon assistance in the tunneling process are seen. The latter is confirmed by detailed analysis of the tunneling rates and the modeling of the resonant tunneling contribution to the current. Moreover, fluctuations of the local structure of the DOS (LDOS) and Fermi edge singularities are observed.
Electron transport through a double quantum dot system is studied with taking into account electron-phonon interaction. The Keldysh nonequilibrium Green function formalism is used to compute the current and transmission coefficient of the system. The influence of the electron-phonon interaction, interdot tunneling, and temperature on the density of states and current is analyzed. Results show that although the electron-phonon interaction results in the appearance of side peaks in the conductance at low temperatures, they are disappeared in high temperatures.
In contradictin to the common concept that acoustic phonons can only travel inside a material medium, they can in fact "tunnel" across a vacuum gap with the help of piezoelectricity, transmitting a significantly stronger heat flux than that of blackbody radiation. Here, we present a theoretical formulation for the heat flux of such piezoelectrically mediated heat transfer, applicable to any anisotropic piezoelectric crystals with an arbitrary orientation. A few numerical results are demonstrated and compared to heat transfer driven by other close-range mechanisms, including near-field radiativ…
Metal-intercalated graphene on Ir(111) exhibits phonon signatures in inelastic elec- tron tunneling spectroscopy with strengths that depend on the intercalant. Extraor- dinarily strong graphene phonon signals are observed for Cs intercalation. Li interca- lation likewise induces clearly discriminable phonon signatures, albeit less pronounced than observed for Cs. The signal can be finely tuned by the alkali metal coverage and gradually disappears upon increasing the junction conductance from tunneling to con- tact ranges. In contrast to Cs and Li, for Ni-intercalated graphene the phonon signal…
We present experimental results showing phonon-mediated coupling between two quantum dots embedded inside a photonic crystal microcavity. With only one of the dots being spectrally close to the cavity, we observe both frequency up-conversion and down-conversion of the pump light via a $\sim1.2$ THz phonon. We demonstrate this process for both weak and strong regimes of dot-cavity coupling, and provide a simple theoretical model explaining our observations.
We investigate the effect of exchange and correlation (xc) in low-density electron bilayers. Along with the direct Coulomb interaction, the effective electron-electron interaction mediated by the exchange of virtual polar optical (PO) phonons is considered. We find that the introduction of xc corrections results in a significant enhancement of the transresistivity and qualitative changes in its temperature dependence. The virtual PO-phonon contribution behaves similarly to the Coulomb drag and reduces noticeably the total drag thereby resulting in a better agreement with the recent experimenta…
We investigate decoherence in a triple quantum dot in ring configuration in which one dot is coupled to a damped phonon mode, while the other two dots are connected to source and drain, respectively. In the absence of decoherence, single electron transport may get blocked by an electron falling into a superposition decoupled from the drain and known as dark state. Phonon-mediated decoherence affects this superposition and leads to a finite current. We study the current and its shot noise numerically within a master equation approach for the electrons and the dissipative phonon mode. A polaron …
We study the influence of the phonon environment on the electron dynamics in a doped quantum dot molecule. A non-perturbative quantum kinetic theory based on correlation expansion is used in order to describe both diagonal and off-diagonal electron-phonon couplings representing real and virtual processes with relevant acoustic phonons. We show that the relaxation is dominated by phonon-assisted electron tunneling between constituent quantum dots and occurs on a picosecond time scale. The dependence of the time evolution of the quantum dot occupation probabilities on the energy mismatch between…
We report on electron transport through an artificial molecule formed by two tunnel coupled quantum dots, which are laterally confined in a two-dimensional electron system of an Al$_x$Ga$_{1-x}$As/GaAs heterostructure. Coherent molecular states in the coupled dots are probed by photon-assisted tunneling (PAT). Above 10 GHz, we observe clear PAT as a result of the resonance between the microwave photons and the molecular states. Below 8 GHz, a pronounced superposition of phonon- and photon-assisted tunneling is observed. Coherent superposition of molecular states persists under excitation of ac…
Electronic transport in a carbon nanotube (CNT) metal-oxide-semiconductor field effect transistor (MOSFET) is simulated using the non-equilibrium Green's functions method with the account of electron-phonon scattering. For MOSFETs, ambipolar conduction is explained via phonon-assisted band-to-band (Landau-Zener) tunneling. In comparison to the ballistic case, we show that the phonon scattering shifts the onset of ambipolar conduction to more positive gate voltage (thereby increasing the off current). It is found that the subthreshold swing in ambipolar conduction can be made as steep as 40mV/d…
Band-to-band tunneling (BTBT) devices have recently gained a lot of interest due to their potential for reducing power dissipation in integrated circuits. We have performed extensive simulations for the BTBT operation of carbon nanotube metal-oxide-semiconductor field-effect transistors (CNT-MOSFETs) using the non-equilibrium Green's functions formalism for both ballistic and dissipative quantum transport. In comparison with recently reported experimental data (Y. Lu et al, J. Am. Chem. Soc., v. 128, p. 3518-3519, 2006), we have obtained strong evidence that BTBT in CNT-MOSFETs is dominated by…
We report both photon- and phonon-assisted tunneling transitions in a linear array of three quantum dots, which can only be understood by considering the full three-dimensionality of the charge stability diagram. Such tunneling transitions potentially contribute to leakage of qubits defined in this system. A detailed understanding of these transitions is important as they become more abundant and complex to analyze as quantum dot arrays are scaled up.
Experiments studying phonon mediated drag in the double layer two dimensional electron gas system are reported. Detailed measurements of the dependence of drag on temperature, layer spacing, density ratio, and matched density are discussed. Comparisons are made to theoretical results [M. C. Bonsager et al., Phys. Rev. B 57, 7085 (1998)] which propose the existence of a new coupled electron-phonon collective mode. The layer spacing and density dependence at matched densities for samples with layer spacings below 2600 A do not support the existence of this mode, showing behavior expected for ind…
Tunneling two-level systems are ubiquitous in amorphous solids, and form a major source of noise in systems such as nano-mechanical oscillators, single electron transistors, and superconducting qubits. Occurance of defect tunneling despite their coupling to phonons is viewed as a hallmark of weak defect-phonon coupling. This is since strong coupling to phonons results in significant phonon dressing and suppresses tunneling in two-level tunneling defects effectively. Here we determine the dynamics of a crystalline tunnelling defect strongly coupled to phonons incorporating the full 3D geometry …
Conduction between graphene layers is suppressed by momentum conservation whenever the layer stacking has a rotation. Here we show that phonon scattering plays a crucial role in facilitating interlayer conduction. The resulting dependence on orientation is radically different than previously expected, and far more favorable for device applications. At low temperatures, we predict diode-like current-voltage characteristics due to a phonon bottleneck. Simple scaling relationships give a good description of the conductance as a function of temperature, doping, rotation angle, and bias voltage, re…
Motivated by a recent experiment on nonlinear tunneling in a suspended Carbon nanotube connected to two normal electrodes [S. Sapmaz, {\it et al}., Phys. Rev. Lett. {\bf 96}, 26801 (2006)], we investigate nonequilibrium vibration-mediated sequential tunneling through a molecular quantum dot with two electronic orbitals asymmetrically coupled to two electrodes and strongly interacting with an internal vibrational mode, which is itself weakly coupled to a dissipative phonon bath. For this purpose, we establish rate equations using a generic quantum Langevin equation approach. Based on these equa…
We present a TCAD compatible multiscale model of phonon-assisted band-to-band tunneling (BTBT) in semiconductors, that incorporates the non-parabolic nature of complex bands within the bandgap of the material. This model is shown capture the measured current-voltage data in silicon, for current transport along the $[100]$, $[110]$ and $[111]$ directions. Our model will be useful to predict band-to-band tunneling phenomena to quantify on and off currents in Tunnel FETs and in small geometry MOSFETs and FINFETs.
Current-voltage characteristics of suspended single-wall carbon nanotube quantum dots show a series of steps equally spaced in voltage. The energy scale of this harmonic, low-energy excitation spectrum is consistent with that of the longitudinal low-k phonon mode (stretching mode) in the nanotube. Agreement is found with a Franck-Condon-based model in which the phonon-assisted tunneling process is modeled as a coupling of electronic levels to underdamped quantum harmonic oscillators. Comparison with this model indicates a rather strong electron-phonon coupling factor of order unity.
Power dissipation has become a major obstacle in performance scaling of modern integrated circuits, and has spurred the search for devices operating at lower voltage swing. In this letter, we study p-i-n band-to-band tunneling field effect transistors (TFET) taking semiconducting carbon nanotubes as the channel material. The on-current of these devices is mainly limited by the tunneling barrier properties, and phonon scattering has only a moderate effect. We show, however, that the off-current is limited by phonon absorption assisted tunneling, and thus is strongly temperature-dependent. Subth…
We introduce an exactly solvable model to study decoherence of a central spin interacting with a spin bath where the coupling is mediated by phonons which we assume to be in a coherent state or thermal distribution. For the coherent state case, we find that the decoherence factor decays in a Gaussian fashion and it becomes independent of the phonon frequencies at short times. If the phonon energies are much larger than spin-phonon coupling or bath spins are fully polarized, decoherence time becomes independent of the initial phonon state. For the thermal state case, phonons play more important…
We show that the piezoelectric coupling to three-dimensional phonons in GaAs renormalizes the current-voltage exponent for tunneling of electrons into an incompressible quantum Hall edge. The leading correction is always negative, in agreement with experiments on the $ν= 1/3$ state and, depending on the precise value of the edge plasmon speed, can be as large as a few percent. We also discuss higher-order corrections, which determine the effect of the piezoelectric coupling in the extreme infrared limit.
Interactions between mesoscopic devices induced by interface acoustic phonons propagating in the plane of a two-dimensional electron system (2DES) are investigated by phonon-spectroscopy. In our experiments ballistic electrons injected from a biased quantum point contact emit phonons and a portion of them are reabsorbed exciting electrons in a nearby degenerate 2DES. We perform energy spectroscopy on these excited electrons employing a tunable electrostatic barrier in an electrically separate and unbiased detector circuit. The transferred energy is found to be bounded by a maximum value corres…
The role of optical-phonons in frictional drag between two adjacent but electrically isolated two-dimensional electron gases is investigated. Since the optical-phonons in III-V materials have a considerably larger coupling to electrons than acoustic phonons (which are the dominant drag mechanism at low T and large separations) it might be expected that the optical phonons will give a large effect high temperatures. The two key differences between optical and acoustic phonon mediated drag are: (1) the optical phonon mediated interlayer interaction is short-ranged due to their negligible group v…
In bilayer CrI3, experimental and theoretical studies suggest that the magnetic order is closely related to the layer staking configuration. In this work, we study the effect of dynamical lattice distortions, induced by non-linear phonon coupling, in the magnetic order of the bilayer system. We use density functional theory to determine the phonon properties and group theory to obtain the allowed phonon-phonon interactions. We find that the bilayer structure possesses low-frequency Raman modes that can be non-linearly activated upon the coherent photo-excitation of a suitable infrared phonon m…
When dressed particles (polarons) exchange quantum phonons, the resulting interactions are generally attractive. If the particles have hard-core statistics and the coupling to phonons is through the kinetic energy terms, phonon-mediated interactions are repulsive. Here, we show that such repulsive phonon-mediated interactions bind dressed particles into bipolarons with unique properties. These bipolaron states appear in the gap between phonon excitations, above the two-polaron continuum. While thermodynamically unstable, the bipolaron is protected by energy and momentum conservation and repres…
Phonon-assisted tunneling rates are evaluated for a well isolated double dot system defined in a GaAs semiconductor heterostructure of finite thickness. A separable model for the confining potential allows accurate determinations of doublet electron wavefunctions and energies. It is found that at small doublet energies the piezoelectric rates due to flexural modes give the dominant contribution. For small slab thicknesses the predicted rates are up to two orders of magnitude higher than for very thick slabs.
We derive an explicit expression for the quantum conductivity of a molecular wire containing a redox center, which is embedded in an electrochemical environment. The redox center interacts with the solvent, and the average over the solvent configurations is performed numerically. Explicit calculations have been performed for a chain of three atoms. When the redox center interacts strongly with neighboring electronic levels, the current-potential curves show interesting features like rectification, current plateaus and negative differential resistance. Electronic spectroscopy of intermediate st…
Topological phononic insulators are the counterpart of three-dimensional quantum spin Hall insulators in phononic systems and, as such, their topological surfaces are characterized by Dirac cone-shaped gapless edge states arising as a consequence of a bulk-boundary correspondence. We propose a theoretical framework for the possible superconducting phase in these materials, where the attractive interaction between electrons is mediated by topological phonons in nontrivial boundary modes. Within the BCS limit, we develop a self-consistent two-band gap equation, whose solutions show that the supe…
We present a tunnel spectroscopy study of single PbS Quantum Dots (QDs) as function of temperature and gate voltage. Three distinct signatures of strong electron-phonon coupling are observed in the Electron Tunneling Spectrum (ETS) of these QDs. In the shell-filling regime, the $8\times$ degeneracy of the electronic levels is lifted by the Coulomb interactions and allows the observation of phonon sub-bands that result from the emission of optical phonons. At low bias, a gap is observed in the ETS that cannot be closed with the gate voltage, which is a distinguishing feature of the Franck-Condo…
