Fermion pairing in mixed-dimensional atomic mixtures

We investigate the quantum phases of mixed-dimensional cold atom mixtures. In particular, we consider a mixture of a Fermi gas in a two-dimensional lattice, interacting with a bulk Fermi gas or a Bose-Einstein condensate in a three-dimensional lattice. The effective interaction of the two-dimensional system mediated by the bulk system is determined. We perform a functional renormalization group analysis, and demonstrate that by tuning the properties of the bulk system, a subtle competition of several superconducting orders can be controlled among $s$-wave, $p$-wave, $d_{x^2-y^2}$-wave, and $g_{xy(x^2-y^2)}$-wave pairing symmetries. Other instabilities such as a charge-density wave order are also demonstrated to occur. In particular, we find that the critical temperature of the $d$-wave pairing induced by the next-nearest-neighbor interactions can be an order of magnitude larger than that of the same pairing induced by doping in the simple Hubbard model. We expect that by combining the nearest-neighbor interaction with the next-nearest-neighbor hopping (known to enhance $d$-wave pairing), an even higher critical temperature may be achieved.Comment: 10 pages, 10 figure

Theoretical study of charge density waves in transition metal materials

In this thesis we theoretically study new aspects of charge density waves in transition metal materials recently revealed by scanning tunneling microscopy measurements. The two important problems that we have investigated are the effects of orbital degeneracy on the formation of the charge-density waves in cobalt nanowires, and the effects of dilute but strongly pinning impurities on the charge-density wave in niobium diselenide. We first present an overview on charge-density waves, and then introduce a general theoretical model describing charge-density waves. We also explain several known results about disorder effects on charge-density waves. We briefly touch on the principle of scanning tunneling microscopy and its advantages compared to other experimental tools. Second, we discuss the physics of one-dimensional cobalt nanowires along with experimental results. We propose a theoretical model that is relevant to cobalt nanowires, and then analyze the model by two theoretical tools: mean-field theory and bosonization. Our results show that the multi-orbitals allow a spin-triplet interaction among electrons leading to different phase diagrams from the ones considered previously for similar models. Numerical results obtained by first-principles calculations are also briefly explained. Third, we consider the effects of dilute strong impurities on the charge-density wave in niobium diselenide, a transition metal dichalcogenide. We first explain the material and properties of its charge-density wave phase. Then, detailed analysis of a scanning tunneling microscopy measurement is presented. Next, we analytically and numerically study a phenomenological model relevant to the experiment. We show that the dilute strong impurities have little effects at large length scales compared to the average inter-impurity distance, leading to a topologically ordered phase with a (quasi-)long-range autocorrelation; this result is quite different from conventional pictures predicting short-range order with the proliferation of topological defects

Interaction-driven dynamical quantum phase transitions in a strongly correlated bosonic system

We study dynamical quantum phase transitions (DQPTs) in the extended Bose-Hubbard model after a sudden quench of the nearest-neighbor interaction strength. Using the time-dependent density matrix renormalization group, we demonstrate that interaction-driven DQPTs can appear after quenches between two topologically trivial insulating phases -- a phenomenon that has so far only been studied between gapped and gapless phases. These DQPTs occur when the interaction strength crosses a certain threshold value that does not coincide with the equilibrium phase boundaries, which is in contrast to quenches that involve a change of topology. In order to elucidate the nonequilibrium excitations during the time evolution, we define a new set of string and parity order parameters. We find a close connection between DQPTs and these newly defined order parameters for both types of quenches. In the interaction-driven case, the order parameter exhibits a singularity at the time of the DQPT only when the quench parameter is close to the threshold value. Finally, the timescales of DQPTs are scrutinized and different kinds of power laws are revealed for the topological and interaction-driven cases.Comment: 6 pages, 4 figures, and supplemental materia

Full-Hiding (Unbounded) Multi-Input Inner Product Functional Encryption from the kk-Linear Assumption

This paper presents two non-generic and practically efficient private key multi-input functional encryption (MIFE) schemes for the multi-input version of the inner product functionality that are the first to achieve simultaneous message and function privacy, namely, the full-hiding security for a non-trivial multi-input functionality under well-studied cryptographic assumptions. Our MIFE schemes are built in bilinear groups of prime order, and their security is based on the standard $k$-Linear ($k$-LIN) assumption (along with the existence of semantically secure symmetric key encryption and pseudorandom functions). Our constructions support polynomial number of encryption slots (inputs) without incurring any super-polynomial loss in the security reduction. While the number of encryption slots in our first scheme is apriori bounded, our second scheme can withstand an arbitrary number of encryption slots. Prior to our work, there was no known MIFE scheme for a non-trivial functionality, even without function privacy, that can support an unbounded number of encryption slots without relying on any heavy-duty building block or little-understood cryptographic assumption