One-sentence summary:We report a sequence of quantized conductance plateaus that follows the third diagonal of Pascal's triangle. Abstract:The ability to create and investigate composite fermionic phases opens new avenues for the investigation of strongly correlated quantum matter. We report the experimental observation of a series of quantized conductance steps within strongly interacting electron waveguides formed at the LaAlO3/SrTiO3 interface. The waveguide conductance follows a characteristic sequence within Pascal's triangle: (1, 3, 6, 10, 15,…) ⋅ 2 /ℎ, where is the electron charge and ℎ is the Planck constant. The robustness of these steps with respect to magnetic field and gate voltage indicate the formation of a new family of degenerate quantum liquids formed from bound states of n = 2, 3, 4, … electrons. These experiments could provide solid-state analogues for a wide range of composite fermionic phases ranging from neutron stars to solid-state materials to quark-gluon plasmas.

Water confined within nanoscale geometries under external field has many interesting properties which is very important for its application in biological processes and engineering. Using molecular dynamics simulations, we investigate the effect of external fields on polarization and structure as well as phase transformations of water confined within carbon nanotubes. We find that dipoles of water molecules tend to align along external field in nanoscale cylindrical confinement. Such alignment directly leads to the longitudinal electrostriction and cross-sectional dilation of water in nanotube. It also influences the stability of ice structures. As the electrostatic field strengthens, the confined water undergoes phase transitions from a prism structure to a helical one to a single chain as the electrostatic field strengthens. These results imply a rich phase diagram of the confined water due to the presence of external electriostatic field, which can be of importance for the industrial applications in nanopores.

We study the formation of bound states in a one-dimensional, single-component Fermi chain with attractive interactions. The phase diagram, computed from DMRG (density matrix renormalization group), shows not only a superfluid of paired fermions (pair phase) and a liquid of fermion triplets (trion phase), but also a phase with two gapless modes. We show that the latter phase is described by a 2-component Tomonaga-Luttinger liquid (TLL) theory, consisting of one charged and one neutral mode. We argue based on our numerical data, that the single, pair, and trion phases are descendants of the 2-component TLL theory. We speculate on the nature of the phase transitions amongst these phases.Tomonaga-Luttinger liquid (TLL) theory captures the physics of many 1-D quantum systems like spin chains, spin ladders, nanotubes [1], nanowires [2] and cold atoms confined to 1-D tubes [3][4][5]. In higher dimensional systems, TLL is a tool that is often used, e.g. in edge theory [6] and coupled-wire constructions [7][8][9].