Quantum Matter

A fundamental open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. In this talk I describe recent work showing that there are 6 new electronic topological insulators that have no non-interacting counterpart. Combined with the previously known band-insulators, these produce a total of 8 topologically distinct phases. Two of the new topological insulators have a simple physical description as Mott insulators in which the electron spins form spin analogs of the familiar topological band-insulator. The remaining are obtained as combinations of these two `topological paramagnets' and the topological band insulator. These 8 phases form a complete list of all possible interacting topological insulators, and are classified by a $\mathbb{Z}_2^3$ group-structure. As a necessary part of the talk I will also review progress in the theory of bosonic Symmetry Protected Topological phases in 3d.

We present a set of models which realize interacting topological phases. The models are constructed in 2 dimensions for a system with U(1)xU(1) symmetry. We demonstrate that the models are topological by measuring their Hall conductivity, and demonstrating that they have gapless edge modes. We have also studied the models numerically.

In this talk, I will present recent work aimed at tackling two cornerstone problems in the field of strongly correlated electrons---(1) conducting non-Fermi liquid electronic fluids and (2) the continuous Mott metal-insulator transition---via controlled numerical and analytical studies of concrete electronic models in quasi-one-dimension.  The former is motivated strongly by the enigmatic "strange metal" central to the cuprates, while the latter is pertinent to, e.g., the spin-liquid candidate 2D triangular
lattice organic materials \kappa-(BEDT-TTF)_{2}Cu_{2}(CN)_{3} and EtMe_{3}Sb[Pd(dmit)_{2}]_{2}.  In the first part of the talk, I will focus on point (1) and discuss our realization on the two-leg ladder of a novel non-Fermi liquid quantum phase---the "d-wave metal"---which we construct by placing the charge sector of the electronic system into a "Bose metal" with strong d-wave correlations.  Importantly, this phase is non-perturbative in that it cannot be accessed starting from free electrons and slowly turning on interactions.  Remarkably, we are able to realize this strange metal as the ground state of reasonable microscopic Hamiltonian by augmenting the t-J model with a simple, local four-site ring-exchange interaction.  In the second half of the talk, I will discuss recent work on various half-filled electronic models on the two-leg triangular strip in which we have identified a continuous Mott transition between a metal and "spin Bose metal", where the latter is a novel
Mott-insulating spin-liquid phase obtained from the former by gapping out only the overall charge mode at strong coupling. Our Mott transition is shown to be in the XY universality class and thus
constitutes a clear and direct quasi-1D analog of the elegant higher-dimensional scenario recently proposed by Senthil [1].  Finally, I will touch on the potential relevance of these studies to the actual 2D materials which inspired them:  the cuprates and the organics.

[1]  T. Senthil, PRB 78, 045109 (2008).

The decomposition of the magnetic moments in spin ice into freely moving magnetic monopoles has added a new dimension to the concept of fractionalization, showing that geometrical frustration, even in the absence of quantum fluctuations, can lead to the apparent reduction of fundamental objects into quasi particles of reduced dimension [1]. The resulting quasi-particles map onto a Coulomb gas in the grand canonical ensemble [2]. By varying the chemical potential one can drive the ground state from a vacuum to a monopole crystal with the Zinc blend structure [3].

The condensation of monopoles into the crystallized state leads to a new level of fractionalization:
the magnetic moments appear to collectively break into two distinct parts; the crystal of magnetic charge and a magnetic fluid showing correlations characteristic of an emergent Coulomb phase [4].

The ordered magnetic charge is synonymous with magnetic order, while the Coulomb phase space is equivalent to that of hard core dimers close packed onto a diamond lattice [5]. The relevance of these results to experimental systems will be discussed.

[1] C. Castelnovo, R. Moessner, and S. L. Sondhi, Nature 451, 42 (2008).
[2] L. D. C. Jaubert and P. C. W. Holdsworth, Nature Physics 5, 258 (2009).
[3] M. Brooks-Bartlett, A. Harman-Clarke, S. Banks, L. D. C. Jaubert and P. C. W. Holdsworth, In Preparation, (2013).
[4] C. L. Henley, Annual Review of Condensed Matter Physics 1, 179 (2010).
[5] D. A. Huse, W. Krauth, R. Moessner, and S. L. Sondhi, Phys. Rev. Lett. 91, 167004 (2003).

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}.