Fractional topological insulators of Cooper pairs induced by the proximity effect.

Certain insulating materials with strong spin-orbit interaction can conduct currents along their edges or surfaces owing to the nontrivial topological properties of their electronic band structure. This phenomenon is somewhat similar to the integer quantum Hall effect of electrons in strong magnetic fields. Topological insulators analogous to the fractional quantum Hall effect are also possible, but have not yet been observed in any material. Here we show that a quantum well made from a topological band insulator such as Bi2Se3 or Bi2Te3, placed in contact with a superconductor, can be used to realize a two-dimensional topological state with macroscopic many-body quantum entanglement whose excitations carry fractional amounts of an electron's charge and spin. This fractional topological insulator is a "pseudogap" state of induced spinful p-wave Cooper pairs, a new strongly correlated quantum phase with possible applications to spintronic devices and quantum computing.

Large D-2 theory of superconducting fluctuations in a magnetic field and its application to iron pnictides.

A Ginzburg-Landau approach to fluctuations of a layered superconductor in a magnetic field is used to show that the interlayer coupling can be incorporated within an interacting self-consistent theory of a single layer, in the limit of a large number of neighboring layers. The theory exhibits two phase transitions-a vortex liquid-to-solid transition is followed by a Bose-Einstein condensation into the Abrikosov lattice-illustrating the essential role of interlayer coupling. By using this theory, explicit expressions for magnetization, specific heat, and fluctuation conductivity are derived. We compare our results with recent experimental data on the iron-pnictide superconductors.

Restoration of the magnetic hc/e-periodicity in unconventional superconductors.

We consider the energy of the filled quasiparticle's Fermi sea of a macroscopic superconducting ring threaded by an hc/2e vortex, when the material of the ring is of an unconventional pairing symmetry. The energy relative to the one for the hc/e vortex configuration is finite, positive, and inversely proportional to the ring's inner radius. We argue that the existence of this energy in unconventional superconductors removes the commonly assumed degeneracy between the odd and the even vortices, with the loss of the concomitant hc/2e-periodicity in an external magnetic field as a consequence. This macroscopic quantum effect should be observable in nanosized unconventional superconductors with a small phase stiffness, such as deeply underdoped YBCO with Tc<5 K.

Charge modulation, spin response, and dual Hofstadter butterfly in high-Tc cuprates.

The modulated density of states observed in recent STM experiments in underdoped cuprates is argued to be a manifestation of the charge-density wave of Cooper pairs (CPCDW). CPCDW formation is due to superconducting phase fluctuations enhanced by Mott-Hubbard correlations near half-filling. The physics behind the CPCDW is related to a Hofstadter problem in a dual superconductor. It is shown that CPCDW does not impact nodal fermions at the leading order. An experiment is proposed to probe coupling of the CPCDW to the spin carried by nodal quasiparticles.

Quantum criticality of D-wave quasiparticles and superconducting phase fluctuations.

We present finite temperature (T) extension of the (2+1)-dimensional QED (QED3) theory of under-doped cuprates. The theory describes nodal quasiparticles whose interactions with quantum proliferated hc/2e vortex-antivortex pairs are represented by an emergent U(1) gauge field. Finite T introduces a scale beyond which the spatial fluctuations of vorticity are suppressed. As a result, the spin susceptibility of the pseudogap state is bounded by T2 at low T and crosses over to approximately T at higher T, while the low-T specific heat scales as T2, reflecting the thermodynamics of QED3. The Wilson ratio vanishes as T-->0; the pseudogap state is a "thermal (semi)metal" but a "spin-charge dielectric." This non-Fermi liquid behavior originates from two general principles: spin correlations induced by "gauge" interactions of quasiparticles and fluctuating vortices and the "relativistic" scaling of the T=0 fixed point.