Quantum Matter

Many of the topological insulators, in their naturally
available form are not insulating in the bulk. It has been  shown that some of these metallic compounds,
become superconductor at low enough temperature and the nature of their
superconducting phase is still widely debated. In this talk I show that even
the s-wave superconducting phase of doped topological insulators, at low
doping, is different from ordinary s-wave superconductors and goes through a
topological phase transition to an ordinary s-wave state by increasing the
doping. I show that the critical doping is determined using the
SU(2) Berry phase on the fermi surface of doped
topological insulator and can be modified by different tunable features of the
material. At the end I present the results of a recent experiment on the
Josephson junctions made of thin films of Bismuth selenide , which can be
explained using our theory of doping induced phase transition in topological
insulators.

The existence of three generations of neutrinos and their mass mixing is a deep mystery of our universe. Majorana's elegant work on the real solution of Dirac equation predicted the existence of Majorana particles in our nature, unfortunately, these Majorana particles have never been observed. In this talk, I will begin with a simple 1D condensed matter model which realizes a T^2=-1time reversal symmetry protected superconductors and then discuss the physical property of its boundary Majorana zero modes. It is shown that these Majorana zero modes realize a T^4=-1 time reversal doubelets and carry 1/4 spin. Such a simple observation motivates us to revisit the CPT symmetry of those ghost particles--neutrinos by assuming that they are topological Majorana particles made by four
Majorana zero modes. Interestingly, we find that Majorana zero modes will realize a P^4=-1 parity symmetry as well. It can even realize a nontrivial C^4=-1 charge conjugation symmetry, which is a big surprise from a usual perspective that the charge conjugation symmetry for a Majorana particle is trivial. Indeed, such a C^4=-1 charge conjugation symmetry can be promoted to a Z_2 gauge symmetry and its spontaneously breaking leads to the origin of neutrino mass. We further attribute
the origin of three generations of neutrinos to three distinguishable ways of defining two complex fermions from four Majorana zero modes.
The above assumptions lead to a D2 symmetry in the generation space and uniquely determine the mass mixing matrix with no adjustable parameters! In the absence of CP violation, we derive
\theta_12=32degree, \theta_23=45degree and \theta_13=0degree, which is intrinsically closed to
the current experimental results. We further predict an exact mass ratio of the three mass eigenstate with m_1/m_3=m_2/m_3=3/\sqrt{5}.