Analytical approximation of the second-harmonic conversion efficiency.

The second-harmonic generation process of a focused laser beam inside a nonlinear crystal is described by the Boyd-Kleinman theory. Calculating the actual conversion efficiency and upconverted power requires the solution to a double integral that is analytically intractable. We provide an expression that predicts the exact gain coefficient within an error margin of less than 2% over several orders of magnitude of the confocal parameter and as a function of the walk-off parameter. Our result allows for readily tuning the beam parameters to optimize the performance of the upconversion process and improve optical system designs.

Bond order solid of two-dimensional dipolar fermions.

The recent experimental realization of dipolar Fermi gases near or below quantum degeneracy provides an opportunity to engineer Hubbard-like models with long-range interactions. Motivated by these experiments, we chart out the theoretical phase diagram of interacting dipolar fermions on the square lattice at zero temperature and half filling. We show that, in addition to p-wave superfluid and charge density wave order, two new and exotic types of bond order emerge generically in dipolar fermion systems. These phases feature homogeneous density but periodic modulations of the kinetic hopping energy between nearest or next-nearest neighbors. Similar, but manifestly different, phases of two-dimensional correlated electrons have previously only been hypothesized and termed "density waves of nonzero angular momentum." Our results suggest that these phases can be constructed flexibly with dipolar fermions, using currently available experimental techniques.

Functional renormalization group analysis of the half-filled one-dimensional extended Hubbard model.

We study the phase diagram of the half-filled one-dimensional extended Hubbard model at weak coupling using a novel functional renormalization group (FRG) approach. The FRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi points. Our results confirm the existence of a finite region of bond charge density wave, also known as a "bond order wave" near U=2V and clarify why earlier g-ology calculations have not found this phase. We argue that this is an example in which formally irrelevant corrections change the topology of the phase diagram. Whenever marginal terms lead to an accidental symmetry, this generalized FRG method may be crucial to characterize the phase diagram accurately.

Metal-insulator-like behavior in semimetallic bismuth and graphite.

When high quality bismuth or graphite crystals are placed in a magnetic field directed along the c axis (trigonal axis for bismuth) and the temperature is lowered, the resistance increases as it does in an insulator but then saturates. We show that the combination of unusual features specific to semimetals, i.e., low carrier density, small effective mass, high purity, and an equal number of electrons and holes (compensation), gives rise to a unique ordering and spacing of three characteristic energy scales, which not only is specific to semimetals but which concomitantly provides a wide window for the observation of apparent field-induced metal-insulator behavior. Using magnetotransport and Hall measurements, the details of this unusual behavior are captured with a conventional multiband model, thus confirming the occupation by semimetals of a unique niche between conventional metals and semiconductors.

Singular current response from isolated impurities in d-wave superconductors.

The current response of a d-wave superconductor containing a single impurity is calculated and shown to be singular in the low-temperature limit, leading in the case of strong scattering to a 1/T term in the penetration depth lambda(T) similar to that induced by Andreev surface bound states. For a small number of such impurities, we argue this low-T upturn could be observable in cuprate superconductors.