In recent years there have been fascinating discoveries of several types of quantum condensed forms of matter exhibiting novel phenomena arising from interactions among the constituents, such as, electrons in solids, or atoms & molecules in ultracold matter. Common to all of these is the emergence of spectacular phases with novel macroscopic behavior in the vicinity of quantum instabilities. Phenomena such as these give glimpses into the nature of the rich underlying quantum world, and provide motivation for theoretical study of correlated Fermi systems.
Specific Research Efforts:
- Study, in general terms, of quantum fluctuations, excitations, transport and superconducting properties of strongly correlated 3D electron systems in sectors delineated by Pomeranchuk instabilities (related to quantum critical points): paramagnetic (PM), ferromagnetic (FM), density/charge instability or phase separation (PS), mixed FM and PS sectors. For this, a reformulation of TCSE method for the non-PM sectors is being carried out. Specific system under study are ferromagnetic superconductors and systems exhibiting exotic magnetism and unconventional superconductivity. Study of excitations, thermodynamic, transport and superconducting properties involve use of TCSE method, concepts of local Fermi liquid theory, ferromagnetic Fermi liquid theory and quasi-classical kinetic theory. Exploration of physics around the Pomeranchuk instabilities connected with spin and charge instabilities is expected to shed perspective on behavior around the associated QCP.
- Development of TSCE formalism for correlated 2D systems, enabling applications to specific systems, such as, graphene, thin films, and anisotropic layered materials.The method is also being extended beyond spherically symmetric systems to for example 2D square lattices. Part of this work is being done in collaboration with K. Bedell’s group at Boston College.
- Linking of TCSE method with dynamical mean-field theory (DMFT) to complement the respective methods, thus properly treating dynamics and momentum dependence of interactions and self energies. This is at an initial phase and may involve collaboration with G. Kotliar at Rutgers University.
- Electronic Structure, vibrational modes and novel phases in iron pnictide materials. Currently studying the 122 pnictides in collaboration with M. Widom at CMU. There have been some promising results, a paper published, and another paper on Lifshitz transition submitted.
- The scope of recent and ongoing work on cold atomic fermions is being expanded. Recent/ongoing research explores quantum instabilities and novel phases in population imbalanced 2D and 3D Fermi systems subject to repulsive, as well as attractive, interactions of arbitrary strength; this is relevant for cold fermion systems. Study includes consideration of different order parameter symmetry (e.g. s-, s*-, d-, p-wave), possibility of breached pair states (interior gap superfluidity), atoms trapped in optical lattices, and topological nature of superfluid ground states. Current work relates to instabilities in Fermi systems subject to dipolar interactions, which are long-range in nature. Calculation of many-body t-matrix will serve as input into calculations in random phase approximation and TCSE. This will be directly relevant to cold fermion systems
- "Lifshitz and other transitions in alkaline-earth 122 pnictides under pressure," Khandker Quader and Michael Widom, Phys. Rev. B 90, 144512 (2014)
- "Approaching Pomeranchuk Instabilities from Ordered Phase: A Crossing-symmetric Equation Method," Kelly Reidy, Khandker Quader, Kevin Bedell, Nuclear Physics A 928, 168 (2014)
- "p-wave pairing in a two-component Fermi system with unequal population: Weak-coupling BCS to strong-coupling BEC regimes," Renyuan Liao, Florentin Popescu, and Khandker Quader, Phys. Rev. B 88, 134507 (2013)