Books by Mykhailo Moskalets
Mesoscopic physics is one of those branches of modern condensed matter physics that are developin... more Mesoscopic physics is one of those branches of modern condensed matter physics that are developing rapidly. The progress achieved in the last few decades in the manufacture of micron and sub-micron-sized samples has made it possible to discover a whole range of new physical effects that are absent
in macroscopic samples and has made it possible to create solid-state devices whose operating principle is based on quantum laws.
These lecture notes contain the basics of the theory of mesoscopic systems. The presented theory allows us to describe the physics of the main phenomena and the conditions for their observation in such systems. A characteristic feature of a mesoscopic system is that its properties are determined by the behaviour of a single quantum particle. Therefore, preserving the phase coher-
ence, spectrum quantization, and charge quantization are the components that determine the occurrence of mesoscopic effects.
The lecture notes are intended for students and postgraduates who are specializing in condensed matter physics, microelectronics, and nano physics.
Full, but draft version of the book with the same title
Русскоязычный препринт книги "Scattering matrix approach to non-stationary quantum transport". Сп... more Русскоязычный препринт книги "Scattering matrix approach to non-stationary quantum transport". Список литературы не полный. Возможны опечатки в тексте.
The aim of this book is to introduce the basic elements of the scattering matrix approach to tran... more The aim of this book is to introduce the basic elements of the scattering matrix approach to transport phenomena in dynamical quantum systems of non-interacting electrons. This approach admits a physically clear and transparent description of transport processes in dynamical mesoscopic systems promising basic elements of solid-state devices for quantum information processing. One of the key effects, the quantum pump effect, is considered in detail. In addition, the theory for a recently implemented new dynamical source — injecting electrons with time delay much larger than the electron coherence time — is offered. This theory provides a simple description of quantum circuits with such a single-particle source and shows in an unambiguous way that the tunability inherent to the dynamical systems leads to a number of unexpected but fundamental effects.
Heated quantum by Mykhailo Moskalets
We analyze a coherent injection of single electrons on top of the Fermi sea in two situations, at... more We analyze a coherent injection of single electrons on top of the Fermi sea in two situations, at finite-temperature and in presence of pure dephasing. Both finite-temperature and pure dephasing change the property of the injected quantum states from pure to mixed. However, we show that the temperature-induced mixedness does not alter the coherence properties of these single-electronic states. In particular two such mixed states exhibit perfect antibunching while colliding at an electronic wave splitter. This is in striking difference with the dephasing-induced mixedness which suppresses antibunching. On the contrary, a single-particle shot noise is suppressed at finite temperatures but is not affected by pure dephasing. This work therefore extends the investigation of the coherence properties of single-electronic states to the case of mixed states and clarifies the difference between different types of mixedness.
The state of a single particle injected onto the surface of the Fermi sea is a pure state if the ... more The state of a single particle injected onto the surface of the Fermi sea is a pure state if the temperature is zero and is a mixed state if the temperature is finite. Moreover, the state of an injected particle is orthogonal to the state of the Fermi sea at zero temperature, while it is not orthogonal at non-zero temperature. These changes in the quantum state of the injected particles can be detected using the temperature dependence of the shot noise that is generated when the particles one by one pass through a semitransparent quantum point contact. Namely, the shot noise produced by the mixed state is suppressed in comparison with the noise of the pure state. In addition, the correlations between the injected particles and the underlying Fermi sea, present at non-zero temperature, do enhance the shot noise. Furthermore, antibunching of injected particles with possible thermal excitations coming from another input channel of a quantum point contact does suppress shot noise. Here I analyze in detail these three effects, which are responsible for the temperature dependence of the shot noise, and discuss how to distinguish them experimentally.
The state of particles injected onto the surface of the Fermi sea depends essentially on the temp... more The state of particles injected onto the surface of the Fermi sea depends essentially on the temperature. The pure state injected at zero temperature becomes a mixed state if injected at finite temperature. Moreover the electron source injecting a single-particle state at zero temperature may excite a multi-particle state if the Fermi sea is at finite temperature. Here I unveil a symmetry of the scattering amplitude of a source, which is sufficient to preserve a single-particle emission regime at finite temperatures if such a regime is achieved at zero temperature. I give an example and analyze the effect of temperature on time-dependent electrical and heat currents carried by a single-particle excitation.
The state of electrons injected onto the surface of the Fermi sea depends on temperature. The sta... more The state of electrons injected onto the surface of the Fermi sea depends on temperature. The state is pure at zero temperature and is mixed at finite temperature. In the case of a single-electron injection, such a transformation can be detected as a decrease in shot noise with increasing temperature. In the case of a multi-electron injection, the situation is more subtle. The mixedness helps the development of quantum-mechanical exchange correlations between injected electrons, even if such correlations are absent at zero temperature. These correlations enhance the shot noise, what in part counteracts the reduction of noise with temperature. Moreover, at sufficiently high temperatures, the correlation contribution to noise predominates over the contribution of individual particles. As a result, in the system of N electrons, the apparent charge (which is revealed via the shot noise) is changed from e at zero temperature to N e at high temperatures. It looks like the exchange correlations glue up electrons into one particle of total charge and energy. This point of view is supported by both charge noise and heat noise. Interestingly, in the macroscopic limit, N → ∞, the correlation contribution completely suppresses the effect of temperature on noise.
The single-particle state is not expected to demonstrate second-order coherence. This proposition... more The single-particle state is not expected to demonstrate second-order coherence. This proposition, correct in the case of a pure quantum state, is not verified in the case of a mixed state. Here I analyze the consequences of this fact for the second-order correlation function, G (2) , of electrons injected on top of the Fermi sea with nonzero temperature. At zero temperature, the function G (2) unambigu-ously demonstrates whether the injected state is a single-or a multi-particle state: G (2) vanishes in the former case, while it does not vanish in the latter case. However, at nonzero temperatures, when the quantum state of injected electrons is a mixed state, the purely single-particle contribution makes the function G (2) to be non vanishing even in the case of a single-electron injection. The single-particle contribution puts the lower limit to the second-order correlation function of electrons injected into conductors at nonzero temperatures. The existence of a single-particle contribution to G (2) can be verified experimentally by measuring the cross-correlation electrical noise.
Coherent heatronics by Mykhailo Moskalets
Physical Review X, 2021
We establish a family of new thermodynamic constraints on heat and particle transport in coherent... more We establish a family of new thermodynamic constraints on heat and particle transport in coherent multi-terminal conductors subject to slowly oscillating driving fields as well as moderate electrical and thermal biases. These bounds depend only on the number of terminals of the conductor and the base temperature of the system. Going beyond the second law of thermodynamics, they imply that every local current puts a lower limit on the mean dissipation caused by the overall transport process. As a key application of this result, we derive two novel trade-off relations restricting the performance of adiabatic quantum pumps and isothermal engines. On the technical level, our work combines Floquet scattering and linear-adiabatic-response theory with recent techniques from small-scale thermodynamics. Using this framework, we illustrate our general findings by working out two specific models describing either a quantum pump or an isothermal engine. These case studies show that our bounds are tight and provide valuable benchmarks for realistic devices.
Physical Review B, Jan 1, 2009
We analyze the frequency-dependent noise and the heat production rate for a dynamical quantum cap... more We analyze the frequency-dependent noise and the heat production rate for a dynamical quantum capacitor in the regime in which it emits single particles, electrons and holes. At low temperature and slow driving the relaxation resistance quantum, R_{q} = h/(2e^2), defines the heat production rate in both the linear and non-linear response regimes. If a double-cavity capacitor emits particles in pairs, the noise is enhanced. In contrast the energy dissipated is suppressed or enhanced depending on whether an electron-hole pair or an electron-electron (a hole-hole) pair is emitted.
Optimal single electron sources emit regular streams of particles, displaying no low-frequency ch... more Optimal single electron sources emit regular streams of particles, displaying no low-frequency charge current noise. Because of the wave packet nature of the emitted particles, the energy is, however, fluctuating, giving rise to heat current noise. We investigate theoretically this quantum source of heat noise for an emitter coupled to an electronic probe in the hot-electron regime. The distribution of temperature and potential fluctuations induced in the probe is shown to provide direct information on the single-particle wave function properties and display strong nonclassical features.
In the framework of the Floquet scattering-matrix theory we discuss how electrical and heat curre... more In the framework of the Floquet scattering-matrix theory we discuss how electrical and heat currents accessible in mesoscopics are related to the state of excita-tions injected by a single-electron source into an electron waveguide. We put forward an interpretation of a single-particle heat current, which differs essentially from that of an electrical current. We show that the knowledge of both a time-dependent electrical current and a time-dependent heat current allows the full reconstruction of a single-electron wave function. In addition we compare electrical and heat shot noise caused by splitting of a regular stream of single-electron excitations. If only one stream impinges on a wave split-ter, the heat shot noise is proportional to the well-know expression of the charge shot noise, reflecting the partitioning of the incoming single particles. The situation differs when two electronic streams collide at the wave splitter. The shot noise suppression, due to the Pauli exclusion principle, is governed by different overlap inte-grals in the case of charge and of heat.
The tunneling Hamiltonian describes a particle transfer from one region to the other. While there... more The tunneling Hamiltonian describes a particle transfer from one region to the other. While there is no particle storage in the tunneling region itself, it has associated certain amount of energy. We name the corresponding flux energy reactance since, like an electrical reactance, it manifests itself in time-dependent transport only. Noticeably, this quantity is crucial to reproduce the universal charge relaxation resistance for a single-channel quantum capacitor at low temperatures. We show that a conceptually simple experiment is capable of demonstrating the existence of the energy reactance.
We analyze the time-resolved energy transport and the entropy production in ac-driven quantum coh... more We analyze the time-resolved energy transport and the entropy production in ac-driven quantum coherent electron systems coupled to multiple reservoirs at finite temperature. At slow driving we formulate the first and second laws of thermodynamics valid at each instant of time. We identify heat fluxes flowing though the different pieces of the device and emphasize the importance of the energy stored in the contact and central regions for the second law of thermodynamics to be instantaneously satisfied. In addition, we discuss conservative and dissipative contributions to the heat flux and to the entropy production as a function of time. We illustrate these ideas with a simple model corresponding to a driven level coupled to two reservoirs with different chemical potentials.
The prospect of time controlled information processing with individual electrons in nanoscale sys... more The prospect of time controlled information processing with individual electrons in nanoscale systems provides strong motivation for investigations of coupled charge and energy transport properties of single electron sources. Building on our recent work [F. Battista et al., Phys. Rev. Lett. 110, 126602 (2013)] we investigate theoretically the statistical properties of temperature and potential fluctuations in an electronic probe coupled to a generic single electron source. A detailed derivation of the cumulant generating function of the joint probability distribution is presented. Moreover, the probability distribution in stationary phase approximation is analysed.
We analyze the time-dependent energy and heat flows in a resonant level coupled to a fermionic co... more We analyze the time-dependent energy and heat flows in a resonant level coupled to a fermionic continuum. The level is periodically forced with an external power source that supplies energy into the system. Based on the tunneling Hamiltonian approach and scattering theory, we discuss the different contributions to the total energy flux. We then derive the appropriate expression for the dynamical dissipation, in accordance with the fundamental principles of thermodynamics. Remarkably, we find that the dissipated heat can be expressed as a Joule law with a universal resistance that is constant at all times.
I present the Floquet scattering matrix theory of low-frequency heat fluctuations in driven quant... more I present the Floquet scattering matrix theory of low-frequency heat fluctuations in driven quantum-coherent conductors in the linear response regime and beyond. The Floquet theory elucidates the use of the Callen-Welton fluctuation-dissipation theorem for description of heat fluctuations in a multi-terminal case. The intrinsic fluctuations of energy of dynamically excited electrons are identified as the fundamental source of a heat noise not revealed by the electrical noise. The role of backscattering in the increase of a heat noise above the level defined by the Callen-Welton theorem, is highlighted. PACS numbers: 73.23.-b, 73.50.Td, 72.70.+m
In this paper we investigate the thermoelectric performance of a double-dot device driven by time... more In this paper we investigate the thermoelectric performance of a double-dot device driven by timedependently modulated gate voltages. We show that if the modulation frequency Ω is sufficiently small, not only quantized charge pumping can be realized, but also the heat current flowing in the leads is quantized and exhibits plateaux in units of Ω 2π kBT ln 2. The factor ln2 stems from the degeneracy of the double-dot states involved into transport. This opens the possibility of using the pumping cycle to transfer heat against a temperature gradient or to extract work from a hot reservoir with Carnot efficiency. However, the performance of a realistic device is limited by dissipative effects due to leakage currents and finite-frequency operation, which we take into account rigorously by means of a real-time diagrammatic approach in the regime where the double dot is weakly coupled to the leads. We show that despite these effects, the efficiency of a double-dot charge pump performing work against a dc-source can reach of up to 70% of the ideal value.
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Books by Mykhailo Moskalets
in macroscopic samples and has made it possible to create solid-state devices whose operating principle is based on quantum laws.
These lecture notes contain the basics of the theory of mesoscopic systems. The presented theory allows us to describe the physics of the main phenomena and the conditions for their observation in such systems. A characteristic feature of a mesoscopic system is that its properties are determined by the behaviour of a single quantum particle. Therefore, preserving the phase coher-
ence, spectrum quantization, and charge quantization are the components that determine the occurrence of mesoscopic effects.
The lecture notes are intended for students and postgraduates who are specializing in condensed matter physics, microelectronics, and nano physics.
Heated quantum by Mykhailo Moskalets
Coherent heatronics by Mykhailo Moskalets