Origin of the quantum shape effect.

The quantum size and shape effects are often considered difficult to distinguish from each other because of their coexistence. Essentially, it is possible to separate them and focus solely on the shape effect by considering a size-invariant shape transformation, which changes the discrete energy spectra of strongly confined systems and causes the quantum shape effects. The size-invariant shape transformation is a geometric technique of transforming shapes by preserving the boundary curvature, topology, and the Lebesgue measure of a bounded domain. The quantum shape effect is a quite different phenomenon from quantum size effects, as it can have the opposite influence on the physical properties of nanoscale systems. While quantum size effects can usually be obtained via bounded continuum approximation, the quantum shape effect is a direct consequence of the energy quantization in specifically designed confined geometries. Here, we explore the origin of the quantum shape effect by theoretically investigating the simplest system that can produce the same physics: quantum particles in a one-dimensional box separated by a moving partition. The partition moves quasistatically from one end of the box to the other, allowing the system to remain in equilibrium with a reservoir throughout the process. The partition and the boundaries are impenetrable by particles, forming two effectively interconnected regions. The position of the partition becomes the shape variable. We investigate the quantum shape effect on the thermodynamic properties of confined particles considering their discrete spectrum. In addition, we applied an analytical model based on dimensional transitions to predict thermodynamic properties under the quantum shape effect accurately. A fundamental understanding of quantum shape effects could pave the way for employing them to engineer physical properties and design better materials at the nanoscale.

Thermodefect voltage in graphene nanoribbon junctions.

Thermoelectric junctions are often made of components of different materials characterized by distinct transport properties. Single material junctions, with the same type of charge carriers, have also been considered to investigate various classical and quantum effects on the thermoelectric properties of nanostructured materials. We here introduce the concept of defect-induced thermoelectric voltage, namely,thermodefect voltage, in graphene nanoribbon (GNR) junctions under a temperature gradient. Our thermodefect junction is formed by two GNRs with identical properties except the existence of defects in one of the nanoribbons. At room temperature the thermodefect voltage is highly sensitive to the types of defects, their locations, as well as the width and edge configurations of the GNRs. We computationally demonstrate that the thermodefect voltage can be as high as 1.7 mV K-1for 555-777 defects in semiconducting armchair GNRs. We further investigate the Seebeck coefficient, electrical conductance, and electronic thermal conductance, and also the power factor of the individual junction components to explain the thermodefect effect. Taken together, our study presents a new pathway to enhance the thermoelectric properties of nanomaterials.

Fractional integral representation in statistical thermodynamics of confined systems.

Confined systems are usually treated as integer dimensional systems, like two dimensional (2D), 1D, and 0D, by considering extreme confinement conditions in one or more directions. This approach costs piecewise representations, some limitations in confinement interval, and the deviations from the true behaviors, especially when the confinement is neither strong nor weak. In this study, fractional integral representation (FIR) is proposed as a methodology to calculate the infinite summations in statistical thermodynamics for any dimension and confinement values. FIR directly incorporates the dimension as a control variable into calculation procedures and allows us to get solutions valid for the whole confinement and dimension scales, including the fractional ones. We define the dimension of a summation and used it in the proposed FIR to calculate the partition function. The first and the higher-order FIR are introduced and high accuracy results are achieved. FIR is then extended for a generalized function to calculate thermodynamic properties directly from their fundamental expressions based on infinite sums. By using the proposed FIR approach, the thermodynamic properties of a noninteracting Maxwell-Boltzmann gas confined in an elongated rectangular domain are determined. The excess quantities induced by confinement are examined for different confinement scenarios. FIR successfully predicts the true behavior of thermodynamic properties for the whole range of confinement and dimension scales. Defining and controlling the dimension allows designing new types of thermodynamic cycles. Besides the infinite-well potential for the confinement of particles with quadratic and linear dispersion relations, quadratic and quartic confining potentials are also considered to show the success of FIR. The proposed method not only incorporates the dimension into the calculation procedures but also constitutes an application of fractional calculus in statistical thermodynamics. FIR has many potential applications especially for Bose-Einstein condensation phenomenon which inherently contains dimensional transitions.

Quantum shape oscillations in the thermodynamic properties of confined electrons in core-shell nanostructures.

Quantum shape effect appears under the size-invariant shape transformations of strongly confined structures. Such a transformation distinctively influences the thermodynamic properties of confined particles. Due to their characteristic geometry, core-shell nanostructures are good candidates for quantum shape effects to be observed. Here we investigate the thermodynamic properties of non-interacting degenerate electrons confined in core-shell nanowires consisting of an insulating core and a GaAs semiconducting shell. We derive the expressions of shape-dependent thermodynamic quantities and show the existence of a new type of quantum oscillations due to shape dependence, in chemical potential, internal energy, entropy and specific heat of confined electrons. We provide physical understanding of our results by invoking the quantum boundary layer concept and evaluating the distributions of quantized energy levels on Fermi function and in state space. Besides the density, temperature and size, the shape per se also becomes a control parameter on the Fermi energy of confined electrons, which provides a new mechanism for fine tuning the Fermi level and changing the polarity of semiconductors.

Landauer's Principle in a Quantum Szilard Engine without Maxwell's Demon.

Quantum Szilard engine constitutes an adequate interplay of thermodynamics, information theory and quantum mechanics. Szilard engines are in general operated by a Maxwell's Demon where Landauer's principle resolves the apparent paradoxes. Here we propose a Szilard engine setup without featuring an explicit Maxwell's demon. In a demonless Szilard engine, the acquisition of which-side information is not required, but the erasure and related heat dissipation still take place implicitly. We explore a quantum Szilard engine considering quantum size effects. We see that insertion of the partition does not localize the particle to one side, instead creating a superposition state of the particle being in both sides. To be able to extract work from the system, particle has to be localized at one side. The localization occurs as a result of quantum measurement on the particle, which shows the importance of the measurement process regardless of whether one uses the acquired information or not. In accordance with Landauer's principle, localization by quantum measurement corresponds to a logically irreversible operation and for this reason it must be accompanied by the corresponding heat dissipation. This shows the validity of Landauer's principle even in quantum Szilard engines without Maxwell's demon.