Nonequilibrium Occupation Research Articles

Floquet engineering of anomalous Hall effects in monolayer MoS2

Light-matter interactions have emerged as a new research focus recently offering promises of unveiling novel physics and leading to applications under nonequilibrium conditions. The quantized Hall conductivities predicted by Floquet theory assuming a Fermi-Dirac distribution however deviate from experimental observations. To resolve these puzzles, we consider the effect of nonequilibrium electron occupation to study the anomalous, valley, and spin Hall effects of a prototype monolayer transition metal dichalcogenide MoS2. We find that spin Hall conductivity can be effectively suppressed approaching zero value by linearly polarized light under near resonant excitations. In contrast, it is substantially enhanced by circularly polarized light, originating from optical selection rules and topological phase transitions. Besides, the quantized anomalous Hall conductivity is much reduced if nonequilibrium occupations of Floquet bands are considered. Our study provides a novel avenue for engineering various Hall effects in two-dimensional materials using light, holding great promises for future device applications.

Electrically detected single-spin resonance with quantum spin Hall edge states

Detection is most often the main impediment to reduce the number of spins in paramagnetic resonance experiments. Here we propose a new route to carry out electrically-detected spin resonance of an individual spin, placed at the edge of a quantum spin Hall insulator (QSHI). The edges of a QSHI host a one dimensional electron gas with perfect spin-momentum locking. Therefore, the spin relaxation induced by emission of an electron-hole pair at the edge state of the QSHI can generate current. Here we demonstrate that driving the system with an $AC$ signal, a nonequilibrium occupation can be induced in the absence of applied bias voltage, resulting in a $DC$ measurable current. We compute the $DC$ current as a function of the Rabi frequency $\Omega$, the spin relaxation and decoherence times, $T_1$ and we discuss the feasibility of this experiment with state-of-the-art instrumentation.

Quantum transport in driven systems with vibrations: Floquet nonequilibrium Green's functions and the self-consistent Born approximation

We investigate the effects of alternating voltage on nonequilibrium quantum systems with localized phonon modes. Nonequilibrium Green's functions are utilized, with electron-phonon coupling being considered with the $GD$ approximation (self-consistent Born approximation). Using a Floquet approach, we assume periodicity of the dynamics. This approach allows us to investigate the influence of the driven electronic component on the nonequilibrium occupation of the vibrations. It was found that signatures of inelastic transport gained photon-assisted peaks. A simplistic model was proposed and found to be in good agreement with the full model in certain parameter ranges. Moreover, it was found that driving the alternating current at resonance with vibrational frequencies caused an increase in phonon occupation.

In-plane optical phonon modes of current-carrying graphene

In this work, we study the in-plane optical phonon modes of current-carrying single-layer graphene whose coupling to the $\pi$ electron gas is strong. Such modes are expected to undergo a frequency shift compared to the non-current-carrying state due to the non-equilibrium occupation of the Dirac cone electronic eigen-states with the flowing $\pi$ electron gas. Large electron-phonon coupling (EPC) can be identified by an abrupt change in the slope of the phonon mode dispersion known as the Kohn anomaly, which mainly occurs for (i) the in-plane longitudinal/transverse optical (LO/TO) modes at the Brillouin zone (BZ) center ($\Gamma$ point), and (ii) the TO modes at the BZ corners ($K$ points). We show that the breaking of the rotational symmetry by the DC current results in different frequency shifts to the $\Gamma$-TO and $\Gamma$-LO modes. More specifically, the DC current breaks the TO-LO mode degeneracy at the $\Gamma$ point which ideally would be manifested as the splitting of the Raman G peak.

Nonequilibrium band occupation and optical response of gold after ultrafast XUV excitation

Free electron lasers offer unique properties to study matter in states far from equilibrium as they combine short pulses with a large range of photon energies. In particular, the possibility to excite core states drives new relaxation pathways that, in turn, also change the properties of the optically and chemically active electrons. Here, we present a theoretical model for the dynamics of the nonequilibrium occupation of the different energy bands in solid gold driven by exciting deep core states. The resulting optical response is in excellent agreement with recent measurements and, combined with our model, provides a quantitative benchmark for the description of electron–phonon coupling in strongly driven gold. Focusing on sub-picosecond time scales, we find essential differences between the dynamics induced by XUV and visible light.

Broadband Nonlinear Optical Absorption Induced by Bandgap Renormalization in CVD-Grown Monolayer MoSe2.

Optical modulation on ultrashort time scales is both of central importance and an essential operation for applications in photonics and optoelectronics. Here, with a giant bandgap renormalization due to a high density of carrier injected by a femtosecond pulse, we realize an expected broadband saturable absorption in chemical vapor deposition grown monolayer transition-metal dichalcogenide MoSe2. Our findings reveal the band edge shift from ∼1.53 to ∼0.52 eV under the pump excitation of 0.80 eV, which is induced by the nonequilibrium occupation of electron-hole states after a Mott transition as well as the increase of carrier temperature.

Atomistic Band-Structure Computation for Investigating Coulomb Dephasing and Impurity Scattering Rates of Electrons in Graphene.

In this paper, by introducing a generalized quantum-kinetic model which is coupled self-consistently with Maxwell and Boltzmann transport equations, we elucidate the significance of using input from first-principles band-structure computations for an accurate description of ultra-fast dephasing and scattering dynamics of electrons in graphene. In particular, we start with the tight-binding model (TBM) for calculating band structures of solid covalent crystals based on localized Wannier orbital functions, where the employed hopping integrals in TBM have been parameterized for various covalent bonds. After that, the general TBM formalism has been applied to graphene to obtain both band structures and wave functions of electrons beyond the regime of effective low-energy theory. As a specific example, these calculated eigenvalues and eigen vectors have been further utilized to compute the Bloch-function form factors and intrinsic Coulomb diagonal-dephasing rates for induced optical coherence of electron-hole pairs in spectral and polarization functions, as well as the energy-relaxation time from extrinsic impurity scattering of electrons for non-equilibrium occupation in band transport.

Transport through vertical graphene contacts under intense laser fields

We theoretically study the electronic and transport properties of two graphene layers vertically coupled by an insulating layer under the influence of a time-periodic external light field. The non-adiabatic driving induces excitations of electrons and a redistribution of the occupied states which is manifested in the opening of gaps in the quasienergy spectrum of graphene. When a voltage is applied between the top and bottom graphene layers, the photo-induced nonequilibrium occupation modifies the transport properties of the contact. We investigate the electronic and transport properties of the contact by using the nonequilibrium Green's function formalism. To illustrate the behavior of the differential conductance of the vertical contact under the light illumination, we consider two cases. First, we assume that both the bottom and top layers consist of graphene and second we consider a finite mass term in the bottom layer. We obtain that the differential conductance is strongly suppressed due to the opening of gaps in the quasienergy spectrum in graphene. Additionally, the conductance shows features corresponding to the tunneling of photoexcited electrons at energies of the van Hove singularity for both the top and bottom layers. In the case of a finite mass term in the bottom layer, the differential conductance can be directly related to the tunneling of photoexcited electrons.

Quantum Interference and Nonequilibrium Josephson Currents in Molecular Andreev Interferometers.

We study the quantum interference (QI) effects in three-terminal Andreev interferometers based on polyaromatic hydrocarbons (PAHs) under non-equilibrium conditions. The Andreev interferometer consists of a PAH coupled to two superconducting and one normal conducting terminals. We calculate the current measured in the normal lead as well as the current between the superconducting terminals under non-equilibrium conditions. We show that both the QI arising in the PAH cores and the bias voltage applied to a normal contact have a fundamental effect on the charge distribution associated with the Andreev Bound States (ABSs). QI can lead to a peculiar dependence of the normal current on the superconducting phase difference that was not observed in earlier studies of mesoscopic Andreev interferometers. We explain our results by an induced asymmetry in the spatial distribution of the electron- and hole-like quasiparticles. The non-equilibrium charge occupation induced in the central PAH core can result in a transition in the current-phase relation of the supercurrent for large enough applied bias voltage on the normal lead. The asymmetry in the spatial distribution of the electron- and hole-like quasiparticles might be used to split Cooper pairs and hence to produce entangled electrons in four terminal setups.

Magneto-Oscillations of the Charge of a Field-Effect Transistor That Are due to a Microwave-Induced Nonequilibrium Electron Energy Distribution

The observation of microwave-induced changes in the charge of a field effect transistor with a channel formed by a bilayer electron system has confirmed that microwave radiation induces a nonequilibrium electron energy distribution function, which generates magneto-oscillations of the resistance of two-dimensional electron systems. The observed periodicity and beating of magneto-oscillations of the charge have been explained by the redistribution of electrons between the layers, which occurs because of the corresponding nonequilibrium occupation of electronic states.

Tracking the ultrafast nonequilibrium energy flow between electronic and lattice degrees of freedom in crystalline nickel

Femtosecond laser excitation of solid-state systems creates non-equilibrium hot electrons that cool down by transferring their energy to other degrees of freedom and ultimately to lattice vibrations of the solid. By combining ab initio calculations with ultrafast diffuse electron scattering we gain a detailed understanding of the complex non-equilibrium energy transfer between electrons and phonons in laser-excited Ni metal. Our experimental results show that the wavevector resolved population dynamics of phonon modes is distinctly different throughout the Brillouin zone and are in remarkable agreement with our theoretical results. We find that zone-boundary phonon modes become occupied first. As soon as the energy in these modes becomes larger than the average electron energy a backflow of energy from lattice to electronic degrees of freedom occurs. Subsequent excitation of lower-energy phonon modes drives the thermalization of the whole system on the picosecond timescale. We determine the evolving non-equilibrium phonon occupations which we find to deviate markedly from thermal occupations.

Local structure investigation of cobalt ferrite-based nanoparticles by synchrotron X-ray diffraction and absorption spectroscopy

In this work, the local structure of ferrite nanoparticles (CoFe2O4) composed of a cobalt ferrite core surrounded by a thin layer of maghemite (CoFe2O4@γ-Fe2O3) was investigated by crossing analyses of X-ray powder Diffraction (XRD), X-ray Absorption Spectroscopy (XANES/EXAFS) and Diffraction Anomalous Fine Structure (DAFS). The proportion of the core and the shell phases was carefully checked by chemical analysis. The whole of these multiple complementary techniques confirmed the non-equilibrium site occupancy in the cobalt ferrite core. The cation distribution was precisely determined showing that about 15% of cobalt ions are located at tetrahedral sites. The results of EXAFS spectra indicated interatomic distances very close to bulk values. The mean coordination number of both metallic cations was found to be lower than expected for bare nanoparticles and reflected the core-shell structure in CoFe2O4@γ-Fe2O3 ones. Finally, DAFS analyses were applied to enlighten the local structure around iron atoms in specific Bragg planes.

Strong pinning theory of thermal vortex creep in type-II superconductors

We study thermal effects on pinning and creep in type-II superconductors where vortices interact with a low density $n_p$ of strong point-like defects with pinning energy $e_p$ and extension $\xi$, the vortex core size. Defects are classified as strong if the interaction between a single pin and an individual vortex leads to the appearance of bistable solutions describing pinned and free vortex configurations. Extending the strong pinning theory to account for thermal fluctuations, we provide a quantitative analysis of vortex depinning and creep. We determine the thermally activated transitions between bistable states using Kramer's rate theory and find the non-equilibrium steady-state occupation of vortex states. The latter depends on the temperature $T$ and vortex velocity $v$ and determines the current--voltage (or force--velocity) characteristic of the superconductor at finite temperatures. We find that the $T=0$ linear excess-current characteristic $v \propto (j-j_c) \, \Theta(j-j_c)$ with its sharp transition at the critical current density $j_c$, keeps its overall shape but is modified in three ways due to thermal creep: a downward renormalization of $j_c$ to the thermal depinning current density $j_\mathrm{dp}(T) < j_c$, a smooth rounding of the characteristic around $j_\mathrm{dp}(T)$, and the appearance of thermally assisted flux flow (TAFF) ${v \propto j \exp(-U_0/k_{\rm \scriptscriptstyle B} T)}$ at small drive $j \ll j_c$, with the activation barrier $U_0$ defined through the energy landscape at the intersection of free and pinned branches. This characteristic emphasizes the persistence of pinning of creep at current densities beyond critical.

Role of defects on the magnetic behaviour of the geometrically frustrated spinel ZnFe2O4

Defective zinc ferrites ZnFe2O4-δ obtained by vacuum annealing bulk Zn-ferrite at different temperatures TAnn were investigated by using XANES at Zn-K, Fe-K and XMCD at Fe-L2,3 edges, static and dynamic magnetic measurements. The cation inversion that confers to the starting ferrite a weak ferromagnetic response is progressively lost when TAnn surpasses 250 °C. Consequently, there is a detriment of the magnetic response that reaches its lower value for TAnn around 370 °C, being the latter coincident with a negligible non-equilibrium occupancy. Above TAnñ 450 °C the ferrite progressively enhances its magnetic response. In such case, even though Zn and Fe occupy non-equilibrium sites at surface regions, the deficiency of oxygen predominates over inversion and the former triggers an increment of the magnetic coupling between Fe3+ at octahedral spinel sites. We discuss the magnetic results that account for spin-glass and/or cluster-glass behavior of this geometrically frustrated compound as due to the randomness and frustration introduced by local defects.

Phenomenology of light- and strange-quark simultaneous production at high energies

This letter presents an extension of EPL116(2017)62001 to light- and strange-quark nonequilibrium chemical phase-space occupancy factors ($\gamma_{q,s}$). The resulting damped trigonometric functionalities relating $\gamma_{q,s}$ to the nucleon-nucleon center-of-mass energies $(\sqrt{s_{NN}})$ looks very similar except different coefficients. The phenomenology of the resulting $\gamma_{q,s}(\sqrt{s_{NN}})$ describes a rapid decrease at $\sqrt{s_{NN}}\lesssim7~$GeV followed by a faster increase up to $\sim20~$GeV. Then, both $\gamma_{q,s}$ become nonsensitive to $\sqrt{s_{NN}}$. Although these differ from $\gamma_{s}(\sqrt{s_{NN}})$ obtained at $\gamma_q(\sqrt{s_{NN}})=1$, various particle ratios including $\mathrm{K}^+/\pi^+$, $\mathrm{K}^-/\pi^-$, $\mathrm{\Lambda}/\pi^-$, $\bar{\mathrm{\Lambda}}/\pi^-$, $\mathrm{\Xi}^+/\pi^+$, and $\mathrm{\Omega}/\pi^-$, can well be reproduced, as well. We conclude that $\gamma_{q,s}(\sqrt{s_{NN}})$ should be instead determined from fits of various particle yields and ratios but not merely from fits to the particle ratio $\mathrm{K}^+/\pi^+$.

Nonequilibrium Andreev bound states population in short superconducting junctions coupled to a resonator

Inspired by recent experiments, we study a short superconducting junction of length $L\ll \xi$ (coherence length) inserted in a dc-SQUID containing an ancillary Josephson tunnel junction. We evaluate the nonequilibrium occupation of the Andreev bound states (ABS) for the case of a conventional junction and a topological junction, with the latter case of ABS corresponding to a Majorana mode. We take into account small phase fluctuations of the Josephson tunnel junction, acting as a damped LC resonator, and analyze the role of the distribution of the quasiparticles of the continuum assuming that these quasiparticles are in thermal distribution with an effective temperature different from the environmental temperature. We also discuss the effect of strong photon irradiation in the junction leading to a nonequilibrium occupation of the ABS. We systematically compare the occupations of the bound states and the supercurrents carried by these states for conventional and topological junctions.

Charge-vibration interaction effects in normal-superconductor quantum dots

We study the quantum transport and the nonequilibrium vibrational states of a quantum dot embedded between a normal and a superconducting lead with the charge on the quantum dot linearly coupled to a harmonic oscillator of frequency $\omega$. To the leading order in the charge-vibration interaction, we calculate the current and the nonequilibrium phonon occupation by the Keldsyh Green's function technique. We analyze the inelastic, vibration-assisted tunneling processes in the regime $\omega <\Delta$, with the superconducting energy gap $\Delta$, and for sharp resonant transmission through the dot. When the energy $\varepsilon_0$ of the dot's level is close to the Fermi energy $\mu$, i.e. $|\varepsilon_0-\mu|\ll \Delta$, inelastic Andreev reflections dominate up to voltage $eV\gtrsim\Delta$. The inelastic quasiparticle tunneling becomes the leading process when the dot's level is close to the gap $|\varepsilon_0-\mu|\sim \Delta \pm \omega$. In both cases, the inelastic tunneling processes appear as sharp and prominent peaks - not broadened by temperature - in the $I$-$V$ characteristic and pave the way for inelastic spectroscopy of vibrational modes even at temperatures $T \gg \omega$. We also found that inelastic Andreev reflections as well as quasiparticle tunneling induce a strong nonequilibrium state of the oscillator. In different ranges on the dot's level, we found that the current produces: (i) ground-state cooling of the oscillator with phonon occupation $n\ll 1$, (ii) accumulation of energy in the oscillator with $n\gg 1$ and (iii) a mechanical instability which is a precursor of self-sustained oscillations. We show that ground-state cooling is achieved simultaneously for several modes of different frequencies. Finally, we discuss how the nonequilibrium vibrational state can be detected by the asymmetric behavior of the inelastic current peaks respect to the gate voltage.

Microwave-Induced Oscillations in Magnetocapacitance: Direct Evidence for Nonequilibrium Occupation of Electronic States.

In a two-dimensional electron system, microwave radiation may induce giant resistance oscillations. Their origin has been debated controversially and numerous mechanisms based on very different physical phenomena have been invoked. However, none of them have been unambiguously experimentally identified, since they produce similar effects in transport studies. The capacitance of a two-subband system is sensitive to a redistribution of electrons over energy states, since it entails a shift of the electron charge perpendicular to the plane. In such a system, microwave-induced magnetocapacitance oscillations have been observed. They can only be accounted for by an electron distribution function oscillating with energy due to Landau quantization, one of the quantum mechanisms proposed for the resistance oscillations.

Synchrotron X-ray absorption spectroscopy study of disordered cation distribution of nanosized zinc ferrite powders

The zinc ferrite (ZnFe2O4) powders of various nanoparticle sizes were synthesised at different milling times (0 to 24 h) of the as-combusted powders. The non-equilibrium site occupancy of zinc (Zn2+) and ferric (Fe3+) ions was investigated through Zn and Fe K-edge X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) spectra. The XRD and SEM strongly confirm the particle size of these ferrites decreasing with the increasing milling time. Compared with the bulk specimen of zinc ferrite, both XANES and EXAFS spectra of zinc ferrite powders clearly exhibit the large translocation of Zn2+ ions from the tetrahedral (A) sites to the octahedral (B) sites and the opposite translocation of some of Fe3+ ions without affecting the long-range structural order. Moreover, the curve-fitting analysis of Zn and Fe K-edge EXAFS spectra indicates that the degree of inversion increases as the particle size decreases resulting in significant differences in the magnetic behaviours.

Superlinear composition-dependent photocurrent in CVD-grown monolayer MoS2(1-x)Se2x alloy devices.

Transition metal dichalcogenides (TMDs) have emerged as a new class of two-dimensional materials that are promising for electronics and photonics. To date, optoelectronic measurements in these materials have shown the conventional behavior expected from photoconductors such as a linear or sublinear dependence of the photocurrent on light intensity. Here, we report the observation of a new regime of operation where the photocurrent depends superlinearly on light intensity. We use spatially resolved photocurrent measurements on devices consisting of CVD-grown monolayers of TMD alloys spanning MoS2 to MoSe2 to show the photoconductive nature of the photoresponse, with the photocurrent dominated by recombination and field-induced carrier separation in the channel. Time-dependent photoconductivity measurements show the presence of persistent photoconductivity for the S-rich alloys, while photocurrent measurements at fixed wavelength for devices of different alloy compositions show a systematic decrease of the responsivity with increasing Se content associated with increased linearity of the current-voltage characteristics. A model based on the presence of different types of recombination centers is presented to explain the origin of the superlinear dependence on light intensity, which emerges when the nonequilibrium occupancy of initially empty fast recombination centers becomes comparable to that of slow recombination centers.