[CCoE Notice] Dissertation Defense: The Coupling Between Quantum Mechanics and Elasticity

[Grayson, Audrey A]

The Coupling Between Quantum Mechanics and Elasticity

Dissertation Defense by Xiaobao Li

Defense Time: 2pm, Friday, Dec. 4th, 2015
Location: N137 Engineering Building 1
Advisor: Dr. Pradeep Sharma
Committee Members:
Dr. Gemunu Gunaratne,
Dr. Yi-chao Chen,
Dr. Yashashree Kulkarni, Dr. Ashutosh Agrawal


Abstract:

    In this dissertation we explore the junction of quantum mechanics and elasticity. Specifically, we attempt to elucidate, in several physical contexts, how mechanical deformation alters the quantum mechanical behavior of nano structures or those of macroscopic materials with nanoscale features.
    The first topic to be addressed in this dissertation is the introduction of a new type of Maxwell stress in soft materials. All dielectrics deform when subjected to an electric field. This behavior is attributed to the so-called (electrical) Maxwell stress and the origins of this phenomenon can be traced to geometric deformation nonlinearities. In particular, the deformation is large when the dielectric is elastically soft (e.g. elastomer) and negligible for most hard materials. In this work, we develop a theoretical framework which shows that a striking analog of the electrostatic Maxwell stress also exists in the context of quantum mechanical-elasticity coupling. The newly derived quantum-elastic Maxwell stress is found to be significant for soft nanoscale structures (such as the DNA) and underscores a fresh perspective on the mechanics and physics of quasi-particles called polarons. We discuss potential applications of the concept for soft nano-actuators and sensors and the relevance for the interpretation of opto-electronic properties.
    Mechanical strain can alter the electronic structure of both bulk semiconductors as well as nano structures such as quantum dots. This fact has been extensively researched and exploited for tailoring electronic properties. The strain mediated interaction between the charge carriers and the lattice is interpreted through the so-called deformation potential. In the case of soft materials or nano structures, such as the DNA, the deformation potential leads to formation of polarons which largely determine the electronic characteristics of the DNA and similar polymer entities. In addition, polarons are also speculated to be responsible for the mechanism of quantum actuation in carbon nanotubes. The deformation potential is usually taken to be a linear function of the lattice deformation ([cid:F9D0F194-8A98-4D5E-A615-6236606AC034]) where [cid:404C8A70-FD06-4C98-A850-89911D281E00]  is the deformation potential ``constant'' that determines the coupling strength and  is the mechanical strain. We find that, carefully accounting for nonlinear geometric deformation (and the introduced quantum Maxwell stress) that has been hitherto ignored so far in this context, we show that the deformation potential constant is renormalized in a  nontrivial manner and is hardly a constant. It varies spatially within the material and with the size of the material. This effect, while negligible for hard materials, emerges to be important for soft materials and critically impacts the interpretation of quantities such as polaron size, binding energy, and accordingly, electronic behavior.
    A rather interesting ramification of quantum mechanics-elasticity coupling transpires in the context of the so-called "quantum capacitance". This is a fundamental quantity that can directly reveal many-body interactions among electrons and is expected to play a critical role in nanoelectronics. One of the many tantalizing recent physical revelations about quantum capacitance is that it can possess a negative value, hence allowing for the possibility of enhancing the overall capacitance in some particular material systems beyond the scaling predicted by classical electrostatics. Using detailed quantum mechanical simulations, we find an intriguing result that mechanical strains can tune both signs and values of quantum capacitance. We used a small coaxially gated carbon nanotube as a paradigmatical capacitor system and showed that, for the range of mechanical strain considered, quantum capacitance can be adjusted from very large positive to very large negative values (in the order of plus/minus hundreds of attofarads), compared to the corresponding classical geometric value (0.31035 aF). This finding opens novel avenues in designing quantum capacitance for applications in nanosensors, energy storage, and nanoelectronics.
    Finally, in the context of DNA like slender structures, we explore how quantum mechanical-elasticity coupling may impact the stability of such soft nano structures.
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