# Lecture Videos

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.

Randy Feenstra (CMU) discusses the use of both first-principles computational methods and low-energy electron microscopy in the investigation of two-dimensional transition-metal dichalcogenide materials as potential candidates for interlayer tunneling devices.

He uses the former to realistically estimate the values of tunneling currents and the latter to characterize the layers. He discusses as well the progress towards fabricating a full interlayer tunneling device.

Ken Jordan (Pitt) shows how electronic correlation in a system can be taken into account via a Drude oscillator.

First he demonstrates Feyman's "conjecture", which states that two atoms at long distance acquire permanent dipoles due to dispersion interactions. The dipole and atomic force both vary as R-7.

He shows that the permanent dipole on an atom is induced by the coupling of the instantaneous dipole on the other atom and its hyperpolarizability, and that, as predicted by Feynman, the two negative ends of the dipoles point toward each other.

David Pekker's (Pitt) talk is about emergent conserved quantities in strongly disordered matter.

He explains how the conventional wisdom that states that interacting systems are their own heat baths breaks down via the spontaneous appearance of local quantum numbers and describes the renormalization method he used to find them. This approach, called a Wegner flow, could be a foundation for the analytical theory of many-body localization transitions.

Vincent Sokalksi (CMU) presents his new study on the energetic molding of fermion-like magnetic bubbles.

He first introduces the Dzyaloshinskii-Moriya interaction (DMI), which is the origin of skyrmions and magnetism, and then proceeds to describe how to measure this interaction.

He shows, using a Wolff construction, how DMI impacts the growth behavior of magnetic bubbles.