# Lecture Videos

Learning quantum mechanics is challenging, in part due to the non-intuitive nature of the subject matter. Our research shows that the patterns of reasoning difficulties in learning quantum mechanics are often universal similar to the universal nature of reasoning difficulties found in introductory physics. Our research also shows that students often have difficulty in monitoring their learning while learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) as well as tools for peer-instruction. The goal of QuILTs and peer-instruction tools is to actively engage students in the learning process and to help them build links between the formalism and the conceptual aspects of quantum physics without compromising the technical content. I will discuss the assessment of these learning tools.

Editor's Note: There were some technical difficulties at the beginning of the talk so the video begins a moment or two after the speaker begins. We apologize for this and hope you enjoy the seminar.

Molecular crystals have applications in nonlinear optics, organic electronics, and particularly in pharmaceuticals because most drugs are marketed as crystals of the pharmaceutically active ingredient. Molecular crystals are held together by van der Waals (vdW) interactions (also known as dispersion interactions) between molecules. Unlike chemical bonds, van der Waals interactions do not involve overlap of electron densities. Rather, they arise from quantum fluctuations of the electron density that lead to the formation of dipoles and higher order multipoles. The electrostatic interaction between these generates a weak but long-ranged attractive force. Owing to the weak nature of van der Waals interactions, a given molecule may crystallize in more than one structure. This is known as polymorphism. Polymorphic forms of the same molecule may possess markedly different physical and chemical properties. Crystal structure may profoundly influence the bioavailability, toxicity, manufacturability, and stability of drugs. In the context of technological applications, crystal structure affects the electronic and optical properties. We use computer simulations to perform structure prediction and design of molecular crystals from first principles, based solely on the knowledge of their elemental composition and the laws of quantum mechanics. We develop genetic algorithms, which are guided to the most promising regions of the configuration space by the evolutionary principle of survival of the fittest. Offspring are generated by combining structural “genes” of the fittest structures in the population to propagate desirable features, while random mutations are employed to maintain diversity. We are particularly interested in optimizing crystal packing for high-performance organic electronics and solar cells.

Two-dimensional (2D) materials are molecularly thin, layered materials held together by van der Waals forces. Because charge moves freely in the 2D plane, these materials have potential application in electronics; however, conventional doping strategies have not been developed for 2D materials. An alternative approach is to use electrolyte gating. Under an applied gate voltage, ions in the electrolyte create an electrostatic double layer (EDL) at the interface between the electrolyte and the semiconductor; the EDL can induce sheet carrier densities on the order of 1014 cm-2 for both electrons and holes–more than one order of magnitude larger than conventional gating techniques. I will describe our work using electrolytes to dope transistors and memory devices based on graphene and transition metal dichalcogenides (TMDs). Our group has developed a 2D electrolyte for use in memory devices based on 2D crystals, and the first device characteristics will be presented.

This work was supported in part by the Center for Low Energy Systems Technology (LEAST), one of six SRC STARnet Centers, sponsored by MARCO and DARPA, and NSF grant #ECCSGOALI-1408425.

Ultrafast time-resolved spectroscopy, and in particular its extension to multidimensional techniques, can tell us a lot about solvation dynamics, structural dynamics and energy transfer processes of solution phase molecular systems. I will illustrate applications of these spectroscopies by discussing a couple of quite diverse examples that lie at the interface between Physics, Biology and Chemistry. In different ways, these examples highlight the importance of water as a very special substance. That is, I will start out with the ultrafast structural dynamics of bulk water and concentrated salt solution observed by THz photon echoes (Physics), continue with the catalytic cycle of an artificial photosynthetic system designed for light-driven water splitting (Chemistry), and finally discuss the response of an allosteric protein upon an external perturbation (Biology). Also the latter is in fact dictated by the dynamics of the water solvation layer.

Quantum transport theory yields the celebrated Landauer formula for the conductance of a two-terminal device at zero bias in terms of T(EF,0), the transmission coefficient T(E,V) evaluated at the Fermi energy EF and V=0. For finite biases, one must use the nonequilibrium Green’s function (NEGF) method, which entails substantial difficulties. Instead of NEGF calculations, T(E,0) is often interpreted as representing transport at V=E/e. This practice is seriously flawed. In its stead, we employ quantum transport theory to derive a simple finite-bias analog of the Landauer formula. The new formula expresses the differential conductance dI/dV at a bias V in terms of T(μL,2V)+T(μR,2V) and reduces to the Landauer formula at V=0. This new formula is tested for a benzene molecular junction and a magnetic tunnel junction, and is shown to yield excellent agreement with a full NEGF calculation without the need for a self-consistent calculation of T(E,V).

### Xion-Jun Liu (Peking University): Symmetry-Protected Non-Abelian Braiding of Majorana Kramers' Pairs

Topological superconductors, which host Majorana zero modes, are a most attractive research topic in condensed matter physics. Due to the Kramers theorem, in a time-reversal invariant topological superconductor the Majorana modes come in pairs, called Majorana Kramer pairs (MKPs). The recent study showed that, due to the time-reversal symmetry protection, the MKPs may obey non-Abelian braiding statistics, while it was later suggested that local rotation among a single MKP may cause errors in MKP-based qubits. In the work presented in this talk, I shall show the complete symmetry condition for non-Abelian braiding of MKPs. By introducing an effective Hamiltonian approach to describe the braiding of MKPs, we show that the ideal non Abelian braiding is protected when the effective Hamiltonian exhibits a new time-reversal like anti-unitary symmetry, which is satisfied if the system is free of dynamical noise. On the other hand, the presence of dynamical noise may bring about decoherence only when the correlation function of such noise breaks the time-reversal like symmetry in the time domain. Interestingly, the resulted error is found to be a higher order effect, compared with the decoherence of Majorana qubits without time-reversal symmetry protection, caused by the dynamical perturbations. These results show that the non-Abelian braiding of MKPs is observable and may have versatile applications to future quantum computation technologies.

Computational materials design offers tremendous potential for discovery and innovation. This powerful concept relies on computational exploration of the vast configuration space of materials structure and composition to identify promising candidates with desired properties for target applications. In fact, many applications do not rely on a single material but on the combination of several materials in a functional nano-structure. Examples for functional nano-structures include the dye-oxide interface, at which charge separation is achieved in dye-sensitized solar cells, and nanocatalysts based on clusters dispersed on a large surface area support. Therefore, we would like to design not just a material, but a functional nano-structure. This requires the combination of accurate electronic structure methods with efficient optimization algorithms.

The electronic properties and the resulting functionality of a nano-structure cannot be deduced directly from those of its isolated constituents. Rather, they emerge from a complex interplay of quantum mechanical interactions that depend on the local environment at the nano-scale. Describing these effects requires a fully quantum mechanical first principles approach. In the first part of the talk, many-body perturbation theory within the GW approximation, where G is the one-particle Green’s function and W is the screened Coulomb interaction, is used to elucidate the size effects in the energy level alignment at the interface between dye molecules and TiO2 clusters of increasing size.

In the second part of the talk, a new approach is presented for computational design of clusters using property-based genetic algorithms (GAs). These algorithms perform optimization by simulating an evolutionary process, whereby child structures are created by combining fragments (“mating”) of the fittest parent structures with respect to the target property. Property-based GAs tailored to search for low energy, high vertical electron affinity (VEA), and low vertical ionization potential (VIP) are applied to TiO2 clusters with up to 20 stoichiometric units. Analysis of the resulting structures reveals the structural features associated with a high VEA and a low VIP and explains the absence of the expected size trends.

In his talk, Peng Liu (Pitt), describes the challenges of applying quantum mechanics to organic chemistry in order to explain and predict the underlying mechanisms of organic reactions.

In his studies, he applies theoretical models to investigate the mechanisms and origins of reactivity and selectivity of synthetically useful transition-metal-catalyzed reactions. He also develops new models for the analysis of catalyst-substrate interactions for the generation of quantitative, chemically meaningful, and predictive results that can be translated to the concepts of experimental organic chemistry.

In his talk, Robert Griffiths (CMU) wonders "where was the photon?" in a nested Mach-Zehnder interferometer.

He walks us along the path taken by a wave passing through a beam splitter before reaching a detector with pedagogy and humor!

Liang Fu (MIT) talks about recent developments in the control of Majorana fermions using the charging energy in mesoscopic systems.

In his talk, he addresses the following questions: can one probe the topological properties of Majorana Fermions in the solid state, specifically their non-locality as two Majorana Fermions share a single state. Then, can one use those topological properties in the field of quantum computation.

He then proceeds to demonstrate the latest developments in the entangled ares of theoretical physics, quantum information, and quantum materials.