Mesoscopic Systems Research Articles

Hyperaccurate bounds in discrete-state Markovian systems

Generalized empirical currents represent a vast class of thermodynamic observables of mesoscopic systems. Their fluctuations satisfy the thermodynamic uncertainty relations (TURs), as they can be bounded by the average entropy production. Here, we derive a general closed expression for the hyperaccurate current in discrete-state Markovian systems, i.e. the one with the least fluctuations, for both discrete- and continuous-time evolution. We show that its associated hyperaccurate bound is generally much tighter than the one given by the TURs, and might be crucial to providing a reliable estimation of the average entropy production. We also show that one-loop systems (rings) exhibit a hyperaccurate current only for finite times, highlighting the importance of short-time observations. Additionally, we derive two novel bounds for the efficiency of work-to-work converters, solely as a function of either the input or the output power. Finally, our theoretical results are employed to analyze a six-state model network for kinesin, and a chemical system in a thermal gradient exhibiting a dissipation-driven selection of states.

Electronic measurements of entropy in meso- and nanoscale systems

Entropy is one of the most fundamental quantities in physics. For systems with few degrees of freedom, the value of entropy provides a powerful insight into its microscopic dynamics, such as the number, degeneracy, and relative energies of electronic states, the value of spin, degree of localization and entanglement, and the emergence of exotic states such as non-Abelian anyons. As the size of a system decreases, the conventional methods for measuring entropy, based on heat capacity, quickly become infeasible due to the requirement of increasingly accurate measurements of heat. Several methods to directly measure entropy of mesoscopic quantum systems have recently been developed. These methods use electronic measurements of charge, conductance and thermocurrent, rather than heat, and have been successfully applied to a wide range of systems, from quantum dots and molecules, to quantum Hall states and twisted bilayer graphene. In this Review, we provide an overview of electronic direct entropy measurement methods, discuss their theoretical background, compare their ranges of applicability and look into the directions of their future extensions and applications.

Comparative study for two-terminal transport through a lossy one-dimensional quantum wire

Motivated by realization of the dissipative quantum point contact in ultracold atomic gases, we investigate a two-terminal mesoscopic transport system in which a single-particle loss is locally present in a one-dimensional chain. By means of the Dyson equation approach in the Keldysh formalism that can incorporate dissipative effects, we reveal analytic structures of the particle and energy currents whose formal expressions correspond to ones in certain three-terminal systems where the particle loss is absent. The obtained formulas are also consistent with non-hermitian and three-terminal Landauer-B\"{u}ttiiker analyses. The universality on the current expressions holds regardless of quantum statistics and may be useful for understanding lossy two-terminal transport in terms of three-terminal transport and vice versa.

A hybrid Monte Carlo-discrete ordinates method for phonon transport in micro/nanosystems with rough interfaces

In recent years, the rapid development of micro/nanosystems raises the demand of thermal optimization of the new designs, and thus the accurate and efficient prediction of phonon transport in mesoscopic systems with complex interfaces is required. This work proposes a hybrid Monte Carlo-discrete ordinates method (MC-DOM) for steady-state phonon transport in such systems by developing an algorithm to exchange information between MC and DOM subdomains. Based on the phonon Boltzmann transport equation which is physically compatible with the system scale, our formulation exploits the computational efficiency of DOM in the bulk region with flexibility of MC near complex interfaces. The cross-plane phonon transport through the thin films is considered first as the benchmark for method verification, whose results agree well with those calculated by numerical and analytical solutions. It is noteworthy that compared to MC as a pure particle method, the hybrid method runs faster over a hundred of times for the temperature calculation when high-precision results are needed. The hybrid method is then applied to simulate the in-plane phonon transport through the double-layer thin films with rough interfaces. It is found that for rectangular interfaces with different roughness, the interfaces perpendicular to the heat flux will cause a larger thermal resistance than the parallel ones. Our hybrid method enriches numerical tools for mesoscopic phonon transport simulation, and is helpful to reveal the mechanisms behind and optimize the heat transport in micro/nanosystems with complex geometries.

Cavity-induced chiral edge currents and spontaneous magnetization in two-dimensional electron systems

We consider a laterally confined two-dimensional electron gas (2DEG), placed inside a gyrotropic cavity. Splitting of the circularly polarized electromagnetic modes leads to the emergence of the ground state spontaneous magnetization, anomalous Hall effect and chiral edge currents in 2DEG. We examine the dependence of the magnetization and edge current density on the system size for two particular cases of the confining potential: infinite wall and parabolic potentials. We show that paramagnetic and diamagnetic contributions to the edge currents have qualitatively different dependence on the system size. These findings pave the route to the design quantum electrodynamic engineering of the material properties of the mesoscopic electron systems.

Experimental verification of arcsine laws in mesoscopic nonequilibrium systems.

A large number of processes in the mesoscopic world occur out of equilibrium, where the time evolution of a system becomes immensely important since it is driven principally by dissipative effects. Nonequilibrium steady states (NESS) represent a crucial category in such systems, where relaxation timescales are comparable to the operational timescales. In this study, we employ a model NESS stochastic system, which is comprised of a colloidal microparticle optically trapped in a viscous fluid, externally driven by a temporally correlated noise, and show that time-integrated observables such as the entropic current, the work done on the system or the work dissipated by it, follow the three Lévy arcsine laws [A.C. Barato et al., Phys. Rev. Lett. 121, 090601 (2018)0031-900710.1103/PhysRevLett.121.090601], in the large time limit. We discover that cumulative distributions converge faster to arcsine distributions when it is near equilibrium and the rate of entropy production is small, because in that case the entropic current has weaker temporal autocorrelation. We study this phenomenon by changing the strength of the added noise as well as by perturbing our system with a flow field produced by a microbubble at close proximity to the trapped particle. We confirm our experimental findings with theoretical simulations of the systems. Our work provides an interesting insight into the NESS statistics of the meso-regime, where stochastic fluctuations play a pivotal role.

Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials

The Landauer formula provides a general scattering formulation of electrical conduction. Despite its utility, it has been mainly applied to the linear-response regime, and a scattering theory of nonlinear response has yet to be fully developed. Here, we extend the Landauer formula to the nonlinear-response regime. We show that while the linear conductance is directly related to the transmission probability, the nonlinear conductance is given by its derivatives with respect to energy. This sensitivity to the energy derivatives is shown to produce unique nonlinear transport phenomena of mesoscopic systems including disordered and topological materials. By way of illustration, we investigate nonlinear conductance of disordered chains and identify their universal behavior according to symmetry. In particular, we find large singular nonlinear conductance for zero modes, including Majorana zero modes in topological superconductors. We also show the critical behavior of nonlinear response around the mobility edges due to the Anderson transitions. Moreover, we study nonlinear response of graphene as a prime example of topological materials featuring quantum anomaly. Furthermore, considering the geometry of electronic wave functions, we develop a scattering theory of the nonlinear Hall effect. We establish a new connection between the nonlinear Hall response and the nonequilibrium quantum fluctuations. We also discuss the influence of disorder and Anderson localization on the nonlinear Hall effect. Our work opens a new avenue in quantum physics beyond the linear-response regime.

Multifractal Conductance Fluctuations in High-Mobility Graphene in the Integer Quantum Hall Regime.

We present the first experimental evidence for the multifractality of a transport property at a topological phase transition. In particular, we show that conductance fluctuations display multifractality at the integer quantum Hall plateau-to-plateau transitions in high-mobility mesoscopic graphene devices. The multifractality gets rapidly suppressed as the chemical potential moves away from these critical points. Our combination of experimental study and multifractal analysis provides a novel method for probing the criticality of wave functions at phase transitions in mesoscopic systems, and quantum criticality in several condensed-matter systems.

A divide-and-conquer method to improve performance in quantum transport calculations: conductance in rotated graphene nanoribbons side-contact junctions

We propose a divide-and-conquer algorithm to find recursively the scattering matrix of general tight-binding structures. The scattering matrix allows a direct calculation of transport properties in mesoscopic systems by using the Landauer formula. The method is exact, and by analyzing the performance of the algorithm in square, triangular and honeycomb lattices, we show a significant improvement in comparison to other state-of-the-art recursive and non-recursive methods. We utilize this algorithm to compute the conductance of a rotated graphene nanoribbon side-contact junction, revealing that for electrons with energies smaller than −2.7 eV the transmission function depends negligibly on the angle of the junction, whereas for electrons with energies greater than −2.7 eV, there exists a set of angles for the system that increase its conductance independently of the energy of the particles.

Homeostatic and adaptive energetics: Nonequilibrium fluctuations beyond detailed balance in voltage-gated ion channels.

Stochastic thermodynamics has largely succeeded in characterizing both equilibrium and far-from-equilibrium phenomena. Yet many opportunities remain for application to mesoscopic complex systems-especially biological ones-whose effective dynamics often violate detailed balance and whose microscopic degrees of freedom are often unknown or intractable. After reviewing excess and housekeeping energetics-the adaptive and homeostatic components of a system's dissipation-we extend stochastic thermodynamics with a trajectory class fluctuation theorem for nonequilibrium steady-state, nondetailed-balanced complex systems. We then take up the neurobiological examples of voltage-gated sodium and potassium ion channels to apply and illustrate the theory, elucidating their nonequilibrium behavior under a biophysically plausible action potential drive. These results uncover challenges for future experiments and highlight the progress possible understanding the thermodynamics of complex systems-without exhaustive knowledge of every underlying degree of freedom.

First-order coherence of light emission from inhomogeneously broadened mesoscopic ensembles

Inhomogeneous broadening is well known to hinder individual characteristics of emitters, supplanting the single-particle properties by their broader probability distribution. Here, we present an analysis of the emission spectra of mesoscopic ensembles of inhomogeneously distributed emitters below the thermodynamic limit (10 - 10^4 emitters). Based on a simple analytical model and an extensive numerical analysis, we show that the number and individual linewidths of the emitters can be directly estimated from the ensemble autocorrelation function in spite of an inhomogeneously broadened emission. As an application, we analyze the photoluminescence of colloidal nanocrystal aggregates embedded in a gold shell. Our general method can be applied to a wide range of mesoscopic many-body systems and could provide new insights into their first-order coherence properties.

Electronic transport in three-terminal chaotic systems with a tunnel barrier

We consider the problem of electronic quantum transport through ballistic mesoscopic systems with chaotic dynamics, connected to a three-terminal architecture in which one of the terminals has a tunnel barrier. Using a semiclassical approximation based on matrix integrals, we calculate several transport statistics, such as average and variance of conductance, average shot-noise power, among others, that give access to the extreme quantum regime (small channel numbers in the terminal) for broken and intact time-reversal symmetry, which the traditional random matrix approach does not access. As an application, we treat the dephasing regime.

Non-Hermitian dynamics andPT-symmetry breaking in interacting mesoscopic Rydberg platforms

We simulate the dissipative dynamics of a mesoscopic system of long-range interacting particles which can be mapped into non-Hermitian spin models with a $\mathcal{PT}$ symmetry. We find rich $\mathcal{PT}$-phase diagrams with $\mathcal{PT}$-symmetric and $\mathcal{PT}$-broken phases. The dynamical regimes can be further enriched by modulating tunable parameters of the system. We outline how the $\mathcal{PT}$ symmetries of such systems may be probed by studying their dynamics. We note that systems of Rydberg atoms and systems of Rydberg ions with strong dipolar interactions are particularly well suited for such studies. We show that for realistic parameters, long-range interactions allow the emergence of new $\mathcal{PT}$-symmetric regions, generating new $\mathcal{PT}$-phase transitions. In addition, such $\mathcal{PT}$-symmetry phase transitions are found by changing the Rydberg atoms configurations. We monitor the transitions by accessing the populations of the Rydberg states. Their dynamics display oscillatory or exponential dependence in each phase.

Manganese phosphide nano-clusters embedded in a polystyrene matrix

A procedure is reported to obtain MnP nanoparticles in powder form or embedded within a polymer (polystyrene) matrix, referred to as Ps:MnP. Ps:MnP nanoaggregates are obtained starting from bulk crystalline MnP or from polycrystalline films grown from the vapor phase on glass substrates. Laser ablation (100 to 200 mW power) is used to produce the nanoparticles within a solvent. This method to produce nanoparticles shows a large dispersion of particle size near the 30 nm range. Ablated nanoparticles are distributed into the polymeric solution and solidified. A study of the nanoparticles structure and magnetic properties of the Ps:MnP nanoaggregates were carried out. The magnetization near room temperature characterizes the ferro- to para-magnetic transition. A critical region extending for more than 4 K, rather than a critical point, has been determined with an apparent or average TC≈284.6±0.5K for the Ps:MnP. A spontaneous magnetization is observed above 300 K, showing that there are nanoaggregates which exhibit ferromagnetism beyond the Curie temperature (∼291 K) of bulk MnP. It is suggested that finite size effects, as well as a wide distribution of sizes, determine the critical behavior in the Ps:MnP magnetically inhomogeneous mesoscopic system.

Something Can Come of Nothing: Surface Approaches to Quantum Fluctuations and the Casimir Force

The Casimir force provides a striking example of the effects of quantum fluctuations in a mesoscopic system. Because it arises from the objects’ electromagnetic response, the necessary calculations in quantum field theory are most naturally expressed in terms of electromagnetic scattering from each object. In this review, we illustrate a variety of such techniques, with a focus on those that can be expressed in terms of surface effects, including both idealized boundary conditions and their physical realization in terms of material properties.

Signatures of quantum chaos in low-energy mixtures of few fermions

The low energy dynamics of mesoscopic systems strongly depends on the presence of internal equilibration. For this reason, a better interpretation of ultracold atom experiments requires a more accurate understanding of how quantum chaos manifests itself in these systems. In this paper, we consider a simple but experimentally relevant one-dimensional system of a few ultracold fermions moving in a double-well potential. We analyze its many-body spectral properties, which are commonly used to trace quantum chaos. We observe some signatures of quantum chaos already in the system with three particles. Generally, these signatures become more pronounced when fermions are evenly added to both components. On the contrary, they become suppressed when the particle imbalance is increased.

A Mechanism to Attract Electrons

In a startling discovery it has been recently found that certain density of states (DOS) can become negative in mesoscopic systems wherein electrons can travel back in time and that affects certain thermodynamic properties as well. The objective of this work is to specify some related robust phenomenon that can be experimentally observed with present day technologies. Such observations will provide indirect evidence of time travel and also demonstrate some counter intuitive quantum effects. Essentially certain members of the hierarchy of DOS become negative in these regimes and that can attract other electrons and may even lead to electron-electron attraction.

Scanning near-field optical spectroscopy and carrier transport based analysis in mesoscopic regions for two-dimensional semiconductors

The measurements of photoexcited transport in mesoscopic regimes reveal the states and properties of mesoscopic systems. In this study, we focused on direct measurements of electromagnetic energy transports in the mesoscopic regions and constructed a scanning tunnelling microscope-assisted multi-probe scanning near-field optical microscope spectroscopy system. After producing an emission energy map through a single-probe measurement, two-probe measurement enables us to observe and analyse carrier transport characteristics. It suggests that exciton generation and transport in the mesoscopic region of semiconductors with quantum structure changes, such as the bias of dopant, affect the excited carrier emission recombination process. The measured probability density of the carrier transported with quantum effects can be used for applications in natural intelligence research by combining it with the analysis using tournament structures. Our developed measurement and analysis methods are expected to clarify the details of carrier's behaviour in the mesoscopic region in various materials and lead to applications for novel optoelectronic devices.

Observation of Cooper pairs in a mesoscopic two-dimensional Fermi gas.

The formation of strongly correlated fermion pairs is fundamental for the emergence of fermionic superfluidity and superconductivity1. For instance, Cooper pairs made of two electrons of opposite spin and momentum at the Fermi surface of the system are a key ingredient of Bardeen-Cooper-Schrieffer (BCS) theory-the microscopic explanation of the emergence of conventional superconductivity2. Understanding the mechanism behind pair formation is an ongoing challenge in the study of many strongly correlated fermionic systems3. Controllable many-body systems that host Cooper pairs would thus be desirable. Here we directly observe Cooper pairs in a mesoscopic two-dimensional Fermi gas. We apply an imaging scheme that enables us to extract the full in situ momentum distribution of a strongly interacting Fermi gas with single-particle and spin resolution4. Our ultracold gas enables us to freely tune between a completely non-interacting, unpaired system and weak attractions, where we find Cooper pair correlations at the Fermi surface. When increasing the attractive interactions even further, the pairs gradually turn into deeply bound molecules that break up the Fermi surface. Our mesoscopic system is closely related to the physics of nuclei, superconducting grains or quantum dots5-7. With the precise control over the interactions, particle number and potential landscape in our experiment, the observables we establish in this work provide an approach for answering longstanding questions concerning not only such mesoscopic systems but also their connection to the macroscopic world.

Density Matrix Renormalization Group for Continuous Quantum Systems.

We introduce a versatile and practical framework for applying matrix product state techniques to continuous quantum systems. We divide space into multiple segments and generate continuous basis functions for the many-body state in each segment. By combining this mapping with existing numerical density matrix renormalization group routines, we show how one can accurately obtain the ground-state wave function, spatial correlations, and spatial entanglement entropy directly in the continuum. For a prototypical mesoscopic system of strongly interacting bosons we demonstrate faster convergence than standard grid-based discretization. We illustrate the power of our approach by studying a superfluid-insulator transition in an external potential. We outline how one can directly apply or generalize this technique to a wide variety of experimentally relevant problems across condensed matter physics and quantum field theory.