Temperature and voltage measurement in quantum systems far from equilibrium

Shastry, Abhay; Stafford, Charles

doi:10.1103/physrevb.94.155433

Cited by 28 publications

(50 citation statements)

References 79 publications

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“…Other numerical calculations have predicted the emergence of quantum oscillations of local temperature in various nanostructures [243,334,412,425]. However, the ranges of these temperature oscillations in nanosystems are usually less than 1 nm, which is beyond the spatial resolution of the present thermometry [404].…”

Section: Practical Applications 421 Quantum Oscillations Of Local mentioning

confidence: 83%

“…If T p is hotter than T eq , such as the point Q in Figure 32(a), the heat current will flow from the probe into the system, namely J p < 0, and vice versa. Analogously, when a voltage probe is weakly coupled to the two-level system [243], the local electrochemical potential of the system is obtained as µ * = µ p in the case of I p (µ p , T p ) = 0. Figure 32(b) shows the dependence of the probe electrochemical potential µ p on the probe temperature T p .…”

Section: Implications and Applications Of Non-equilibrium Local Tempementioning

confidence: 99%

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Local temperatures out of equilibrium

2019

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The temperature of a physical system is operationally defined in physics as "that quantity which is measured by a thermometer" weakly coupled to, and at equilibrium with the system. This definition is unique only at global equilibrium in view of the zeroth law of thermodynamics: when the system and the thermometer have reached equilibrium, the "thermometer degrees of freedom" can be traced out and the temperature read by the thermometer can be uniquely assigned to the system. Unfortunately, such a procedure cannot be straightforwardly extended to a system out of equilibrium, where local excitations may be spatially inhomogeneous and the zeroth law of thermodynamics does not hold. With the advent of several experimental techniques that attempt to extract a single parameter characterizing the degree of local excitations of a (mesoscopic or nanoscale) system out of equilibrium, this issue is making a strong comeback to the forefront of research. In this paper, we will review the difficulties to define a unique temperature out of equilibrium, the majority of definitions that have been proposed so far, and discuss both their advantages and limitations. We will then examine a variety of experimental techniques developed for measuring the non-equilibrium local temperatures under various conditions. Finally we will discuss the physical implications of the notion of local temperature, and present the practical applications of such a concept in a variety of nanosystems out of equilibrium. Figure 4: (a) The product of the density of states η(E) times the global distribution function ϕ|ρ|ϕ forms a strongly pronounced peak at the expectation value of the global system energyĒ. (b) The logarithm of the local distribution function a|ρ|a (solid line) and the logarithm of a canonical distribution (dashed line) with the same local temperature for a harmonic chain. (a) and (b) are reprinted with permission from [74].

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Section: Practical Applications 421 Quantum Oscillations Of Local mentioning

confidence: 83%

Section: Implications and Applications Of Non-equilibrium Local Tempementioning

confidence: 99%

Local temperatures out of equilibrium

2019

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“…In the same spirit a number of authors have considered a temperature probe [210][211][212][213][214] intended to model a device that measures the temperature at a given point in a nano-structure. An ideal such probe is a large but finite sized reservoir coupled to the system, as sketched in Fig.…”

Section: Inelastic Scattering and Probe Reservoirsmentioning

confidence: 99%

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

et al. 2017

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In recent years, the study of heat to work conversion has been re-invigorated by nanotechnology. Steady-state devices do this conversion without any macroscopic moving parts, through steady-state flows of microscopic particles such as electrons, photons, phonons, etc. This review aims to introduce some of the theories used to describe these steady-state flows in a variety of mesoscopic or nanoscale systems. These theories are introduced in the context of idealized machines which convert heat into electrical power (heat-engines) or convert electrical power into a heat flow (refrigerators). In this sense, the machines could be categorized as thermoelectrics, although this should be understood to include photovoltaics when the heat source is the sun. As quantum mechanics is important for most such machines, they fall into the field of quantum thermodynamics. In many cases, the machines we consider have few degrees of freedom, however the reservoirs of heat and work that they interact with are assumed to be macroscopic. This review discusses different theories which can take into account different aspects of mesoscopic and nanoscale physics, such as coherent quantum transport, magnetic-field induced effects (including topological ones such as the quantum Hall effect), and single electron charging effects. It discusses the efficiency of thermoelectric conversion, and the thermoelectric figure of merit. More specifically, the theories presented are (i) linear response theory with or without magnetic fields, (ii) Landauer scattering theory in the linear response regime and far from equilibrium, (iii) Green-Kubo formula for strongly interacting systems within the linear response regime, (iv) rate equation analysis for small quantum machines with or without interaction effects, (v) stochastic thermodynamic for fluctuating small systems. In all cases, we place particular emphasis on the fundamental questions about the bounds on ideal machines. Can magnetic-fields change the bounds on power or efficiency? What is the relationship between quantum theories of transport and the laws of thermodynamics? Does quantum mechanics place fundamental bounds on heat to work conversion which are absent in the thermodynamics of classical systems?

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“…These errors [32] can be quite large for systems with large thermoelectric responses. A temperature probe therefore has to remain in thermal and electrical equilibrium with the nonequilibrium sample [18,19,26,27,32,33], thereby ensuring true thermodynamic equilibrium of the measurement apparatus.…”

Section: Temperature Measurementmentioning

confidence: 99%

Scanning Tunneling Thermometry

2020

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Temperature imaging of nanoscale systems is a fundamental problem which has myriad potential technological applications. For example, nanoscopic cold spots can be used for spot cooling electronic components while hot spots could be used for precise activation of chemical or biological reactions. More fundamentally, imaging the temperature fields in quantum coherent conductors can provide a wealth of information on heat flow and dissipation at the smallest scales. However, despite significant technological advances, the spatial resolution of temperature imaging remains in the few nanometers range. Here we propose a method to map electronic temperature variations in operating nanoscale conductors by relying solely upon electrical tunneling current measurements. The scanning tunneling thermometer, owing to its operation in the tunneling regime, would be capable of mapping subangstrom temperature variations, thereby enhancing the resolution of scanning thermometry by some two orders of magnitude.Thermal imaging of nanoscale systems is of crucial importance not only due to its potential to enable

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Temperature and voltage measurement in quantum systems far from equilibrium

Cited by 28 publications

References 79 publications

Local temperatures out of equilibrium

Local temperatures out of equilibrium

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

Scanning Tunneling Thermometry

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