Vladimir M. Stojanović, Dr.

We study graphene antidot lattices -- superlattices of perforations (antidots) in a graphene sheet -- using a model that accounts for the phonon-modulation of the π-electron hopping integrals. We calculate the phonon spectra of selected antidot lattices using two different semi-empirical interatomic potentials. Based on the adopted model and the obtained phonon modes, we quantify the nature of charge-carriers in the system by computing the quasiparticle spectral weight due to the electron-phonon interaction for an excess electron in the conduction band. We show that the phonon-induced renormalization is much stronger than in graphene, with the effective electron masses exhibiting an interesting nonmonotonic dependence on the superlattice period for a given antidot diameter. Our study provides an indication of polaronic behavior and points to the necessity of taking into account the inelastic degrees of freedom in future studies of electronic transport in graphene antidot lattices.

Graphene antidot lattices have recently been proposed as a new breed of graphene-based superlattice structures. We study electronic properties of triangular antidot lattices, with emphasis on the occurrence of dispersionless (flat) bands and the ensuing electron localization. Apart from strictly flat bands at zero energy (Fermi level), whose existence is closely related to the bipartite lattice structure, we also find quasiflat bands at low energies. We predict the real-space electron density profiles due to these localized states for a number of representative antidot lattices. We point out that the studied low-energy localized states compete with states induced by the superlattice-scale defects in this system, which have been proposed as hosts for electron-spin qubits. Furthermore, we suggest that local moments formed in these midgap zero-energy states may be at the origin of a surprising saturation of the electron dephasing length observed in recent weak localization measurements in graphene antidot lattices.

We describe quantum entanglement inherent to the polaron ground states of coupled electron-phonon (or, more generally, particle-phonon) systems based on a model comprising both local (Holstein-type) and nonlocal (Peierls-type) couplings. We study this model using a variational method supplemented by the exact numerical diagonalization on a system of finite size. By way of subsequent numerical diagonalization of the reduced density matrix, we determine the particle-phonon entanglement as given by the von Neumann and linear entropies. Our results are strongly indicative of the intimate relationship between the particle localization/delocalization and the particle-phonon entanglement. In particular, we find a compelling evidence for the existence of a nonanalyticity in the entanglement entropies with respect to the Peierls-coupling strength. The occurrence of such nonanalyticity - not accompanied by an actual quantum phase transition - reinforces analogous conclusion drawn in several recent studies of entanglement in the realm of quantum-dissipative systems. In addition, we demonstrate that the entanglement entropies saturate inside the self-trapped region where the small-polaron states are nearly maximally mixed.

We study bosons in the first excited Bloch band of a double-well optical lattice, recently realized at NIST. By calculating the relevant parameters from a realistic nonseparable lattice potential, we find that in the most favorable cases, the boson lifetime in the first excited band can be several orders of magnitude longer than the typical nearest-neighbor tunneling time scales, in contrast with that of a simple single-well lattice. In addition, for sufficiently small lattice depths, the excited band has minima at nonzero momenta incommensurate with the lattice period, which opens a possibility to realize an exotic superfluid state that spontaneously breaks the time-reversal, rotational, and translational symmetries. We discuss possible experimental signatures of this novel state.

Recently, a homogeneous superfluid state with a single gapless Fermi surface was predicted to be the ground state of an ultracold Fermi gas with spin population imbalance in the regime of molecular Bose-Einstein condensation. We study vortices in this novel state using a symmetry-based effective field theory, which captures the low-energy physics of gapless fermions and superfluid phase fluctuations. This theory is applicable to all spin-imbalanced ultracold Fermi gases in the superfluid regime, regardless of whether the original fermion-pairing interaction is weak or strong. We find a remarkable, unconventional form of the interaction between vortices. The presence of gapless fermions gives rise to a spatially oscillating potential, akin to the RKKY indirect-exchange interaction in non-magnetic metals. We compare the parameters of the effective theory to the experimentally measurable quantities and further discuss the conditions for the verification of the predicted new feature. Our study opens up an interesting question as to the nature of the vortex lattice resulting from the competition between the usual repulsive logarithmic (2D Coulomb) and predominantly attractive fermion-induced interactions.

We develop a variational approach to an extended Holstein model, comprising both local and nonlocal electron-phonon coupling. The approach is based on the minimization of a Bogoliubov bound to the Helmholtz free energy. The ambivalent character of nonlocal coupling, which both promotes and hinders transport, is clearly observed. Furthermore, a salient feature of our results is that the local and nonlocal couplings can compensate each other, leading to a reduction of polaronic effects and a quasi-free character of the excitation. Our findings have implications for organic crystals of π-conjugated molecules, where this electron-phonon coupling mechanism plays an important role.

We present a theoretical description of polaron bandwidth narrowing in organic molecular crystals. Based on a solution of a Holstein-Peierls model for tightly bound electrons interacting with phonons, an explicit expression for the temperature dependence of the electronic bandwidths is found. This formula generalizes the result of Holstein polaron theory by treating local and nonlocal electron-phonon coupling on equal footing. The usefulness of the method is demonstrated by model studies for oligo-acene crystals from which microscopic insight into the relevance of the different coupling mechanisms is obtained.

We present a theoretical description of polaron band narrowing in oligo-acene crystals due to electron-lattice interaction. The analysis is based on a model which takes both local and nonlocal contributions to the electron-phonon coupling into account. Different approximation schemes are discussed and compared. The theory is supplemented by quantitative ab-initio calculations of the temperature dependence of polaron bandwidths in oligo-acene crystals which show the important role of in-plane nonlocal electron-phonon coupling.