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Disorder free many-body localization (MBL) can occur in interacting systems that can dynamically generate their own disorder. We address the thermal-MBL phase transition of two isotropic Heisenberg spin chains that are quasi-periodically coupled to each other. The spin chains are incommensurate and are coupled through a short range exchange interaction of the $XXZ$ type that decays exponentially with the distance. Using exact diagonalization, matrix product states and density matrix renormalization group, we calculate the time evolution of the entanglement entropy at long times and extract the inverse participation ratio in the thermodynamic limit. We show that this system has a robust MBL phase. We establish the phase diagram with the onset of MBL as a function of the interchain exchange coupling and of the incommensuration between the spin chains. The Ising limit of the interchain interaction optimizes the stability of the MBL phase over a broad range of incommensurations above a given critical exchange coupling. Incorporation of interchain spin flips significantly enhances entanglement between the spin chains and produces delocalization, favoring a pre-thermal phase whose entanglement entropy grows logarithmically with time., Comment: 10 pages, 9 figures

Carbon nanotubes (CNTs) are promising candidates to improve the thermal conductivity of nano-composites. The main obstacle to these applications is the extremely high thermal boundary (Kapitza) resistance between the CNTs and their matrix. In this theoretical work our goal is to maximize the heat flux through the CNT by functionalizing the CNT ends. We use a Landauer approach to calculate and optimize the energy flux from a soft to a hard material in one dimension through a connecting continuous medium of varying elasticity and density. The transmission probability of phonons through the system is calculated both numerically and analytically. We find that over 90% of the maximum heat flux into CNT is possible for 1nm length of the intermediate material at room temperature (300K)., Comment: 11 pages, 5 figures, conference proceedings

We describe the conductance of a normal-superconducting junction in systems with Landau levels that preserve time reversal symmetry. Those Landau levels have been observed in strained honeycomb lattices. The current is carried along the edges in both the normal and superconducting regions. When the Landau levels in the normal region are half-filled, Andreev reflection is maximal and the conductance plateaus have a peak as a function of filling factor. The height of those peaks is quantized at $4e^{2}/h$. The interface of the junction has Andreev edge states, which form a coherent superposition of electrons and holes that can carry a net valley current. We identify unique experimental signatures for superconductivity in time reversal invariant Landau levels., Comment: 4+epsilon pages, 5 figures. Fig. 3 corrected. Typos fixed

We have adapted R-matrix theory to calculate phonon scattering across systems of molecular to mesoscopic scale. The key novelty of this work is that the only required information about the scattering region are its normal modes, which are evaluated only once for a system. Thus, R-matrix theory is a computationally efficient and simple approach to calculate phonon scattering in larger systems. To validate and to demonstrate the applicability of the theory, we apply it to two systems: a one dimensional chain of atoms and a graphene nanoribbon. In both cases, we discuss the effect of mass impurities on thermal transport.

Using molecular dynamics(MD) simulations, we study thermal transport in graphene nanoribbons (GNR) subjected to uniform uniaxial and nonuniform strain fields. We predict significant thermal rectification (over 70%) in a rectangular armchair GNR by applying a transverse force asymmetrically. The heat flux is larger from the less stressed region to the more stressed region. Furthermore, we develop a theoretical framework based on the non-equilibrium thermodynamics to discuss when thermal rectification under a stress gradient can occur. We conclude with a discussion of details relevant to experiment.

In dealing with thermal transport in composite systems, high contrast materials pose a special problem for numerical simulation: the time scale or step size in the high conductivity material must be much smaller than in the low conductivity material. In the limit that the higher conductivity inclusion can be treated as having an infinite conductivity, we show how a standard random walk algorithm can be alterred to improve speed while still preserving the second law of thermodynamics. We demonstrate the principle in a 1D system, and then apply it to 3D composites with spherical inclusions., Comment: 16 pages, 7 figures