Scientific Series

A pedagogic introduction will be given to: i) Emergent Majorana fermions and Majorana zero modes in certain condensed matter models and ii) Kondo insulators. This will be followed by discussion of a remarkable Quantum Oscillation Anomaly seen in recent experiments in SmB6, a Kondo insulator, by the Cambridge group [1], as providing evidence [2] for presence of Majorana fermi sea, in an unexpected place. We show a counter intuitive result that these Majorana fermions though neutral, exhibit Landau diamagnetism.

[1] B.S. Tan et al., Science, vol.349, pp. 287-29 (2015), arXiv:1507.01129 [1] G. Baskaran, arXiv:1507.03477

Current and near-future cosmological surveys can provide powerful tests of gravity on the largest scales. However, in order to extract this information, it is essential to understand the host of parameter degeneracies which may arise. I present two approaches towards this goal, with a focus on the use of weak gravitational lensing measurements in combination with other probes. First, I discuss a novel expression for a weak lensing power spectrum under alternative theories of gravity. Obtained by considering small deviations from GR, this expression separates various physical effects of modifications to GR, thus allowing a quantitative understanding of degeneracies between gravitational parameters. Second, I present an investigation into the theoretical uncertainty inherent to the popular gravity-testing statistic E_G. By improving our understanding of the theoretical value of E_G, we can use it to make more robust statements about the viability of alternative theories of gravity on cosmological scales.

On small scales, our understanding of dark matter in galaxies is incomplete. One example is that high resolution simulations predict a large number of subhalos in dark matter halos, which should be seen in our Milky Way galaxy as a host of satellite galaxies. Many plausible astrophysical mechanisms have been proposed to explain why we don't clearly see large numbers of such satellite galaxies, but this remains a test of the cold dark matter scenario that has yet to be passed. Gravitational lensing provides a direct probe of subhalos in distant galaxies, but requires high sensitivity and angular resolution. I will talk about a search that is now started using strong lensing of the mm and submm-wave emission from dust grains in high-redshift star-forming galaxies. The properties of the dust emission are well-matched to the typical expected scales of the dark matter subhalos, and ALMA (the Atacama Large Millimeter Array) now has the sensitivity and angular resolution to start to see the lensing signature of these subhalos. We haven't found any yet in early data, but we should see some soon if the cold dark matter paradigm is correct.

Eugenio Bianchi and Matteo Smerlak have found a beautiful relationship between the Hawking radiation energy and von Neumann entropy in a conformal field emitted by a semiclassical two-dimensional black hole. Shohreh Abdolrahimi and I compared this relationship with what might be expected for unitary evolution of a quantum black hole in four and higher dimensions. If one neglects the expected increase in the radiation entropy over the decrease in the black hole Bekenstein-Hawking A/4 entropy that arises from the scattering of the radiation by the barrier near the black hole, the relation works very well, except near the peak of the radiation von Neumann entropy and near the final evaporation. These discrepancies are calculated and discussed as tiny differences between a semiclassical treatment and a quantum gravity treatment.

In describing condensed matter, some well established paradigms have allowed much progress to be made in understanding and using materials.  But in the last 15 - 20 years, new materials, such as heavy fermions, high temperature superconductors, and now charge density wave-supporting materials,  have been shown to require new paradigms in describing them.  While much progress has been achieved in that time, we still do not have  a widely accepted theoretical description of the nature of their electronic excitations.

Fractional quantum Hall effect in the sequence of filling factors n/(2np +- 1) is well understood by the integer quantum Hall effect of the composite fermions at the filling factor n. A composite fermion (CF) is a bound state of an electron and 2p number of quantized vortices. However, the experimentally observed states such as 4/11, 5/13, and 3/8 which are between 1/3 and 2/5 cannot be accommodated in the conventional noninteracting theory of composite fermions. The interaction between CFs in partially filled second effective Landau levels of CFs is important for these states. However, conventional fractional quantum Hall effect of these interacting composite fermions do not reproduce these incompressible states. By diagonalizing Coulomb Hamiltonian in a restricted Hilbert space of the CFs, we find that these states are incompressible for flux-particle relationships that are different from the conventional considerations. We interpret that 4/11 and 5/13 states occur due to fractional quamtum Hall effect of the composite fermions for Haldane Pseudopotential V_3 rather than V_1. And the panti-Pfaffian pair correlation between CFs in the half-filled second effective Landau level creates incompressible 3/8 state. The unconventional topologies of these states are reflected in anomalously low magneto-roton energies for these states.