Qijin Chen

BCS–BEC crossover: From high temperature superconductors to ultracold superfluids

Abstract We review the BCS to Bose–Einstein condensation (BEC) crossover scenario which is based on the well known crossover generalization of the BCS ground state wavefunction Ψ 0 . While this ground state has been summarized extensively in the literature, this Review is devoted to less widely discussed issues: understanding the effects of finite temperature, primarily below T c , in a manner consistent with Ψ 0 . Our emphasis is on the intersection of two important problems: high T c superconductivity and superfluidity in ultracold fermionic atomic gases. We address the “pseudogap state” in the copper oxide superconductors from the vantage point of a BCS–BEC crossover scenario, although there is no consensus on the applicability of this scheme to high T c . We argue that it also provides a useful basis for studying atomic gases near the unitary scattering regime; they are most likely in the counterpart pseudogap phase. That is, superconductivity takes place out of a non-Fermi liquid state where preformed, metastable fermion pairs are present at the onset of their Bose condensation. As a microscopic basis for this work, we summarize a variety of T-matrix approaches, and assess their theoretical consistency. A close connection with conventional superconducting fluctuation theories is emphasized and exploited.

Heat Capacity of a Strongly Interacting Fermi Gas

We have measured the heat capacity of an optically trapped, strongly interacting Fermi gas of atoms. A precise addition of energy to the gas is followed by single-parameter thermometry, which determines the empirical temperature parameter of the gas cloud. Our measurements reveal a clear transition in the heat capacity. The energy and the spatial profile of the gas are computed using a theory of the crossover from Fermi to Bose superfluids at finite temperatures. The theory calibrates the empirical temperature parameter, yields excellent agreement with the data, and predicts the onset of superfluidity at the observed transition point.

Pairing Fluctuation Theory of Superconducting Properties in Underdoped to Overdoped Cuprates

Pseudogap phenomena in the cuprates are of interest not only because of the associated unusual normal-state properties, but more importantly because of the constraints which these phenomena impose on the nature of the superconductivity and its associated high Tc. Moreover, this superconducting state presents an interesting challenge to theory: while the normal state is highly unconventional, the superconducting phase exhibits some features of traditional BCS superconductivity along with others which are strikingly different. Thus far, there is no consensus on a theory of cuprate superconductivity. Scenarios which address the pseudogap state below Tc can be distinguished by the character of the excitations responsible for destroying superconductivity. In the theory of Lee and Wen [1], the destruction of the superconducting phase is associated with the excitation of the low-lying quasiparticles near the d-wave gap nodes. By contrast, Emery and Kivelson [2] argue that the destruction of the superconductivity is associated with low frequency, long wavelength phase fluctuations within a microscopically inhomogeneous model, based on one dimensional “stripes.” In the present paper, we present an alternative scenario in which, along with the quasiparticles of the usual BCS theory, there are additionally incoherent (but not preformed) pair excitations of finite momentum q, which assist in the destruction of superconductivity. This approach is based on a self-consistent treatment of the coupling of single particle and pair states. It represents a natural extension of BCS theory to the short coherence length (j) regime and provides a quantitative framework for addressing cuprate superconductivity. Here, we find a pronounced departure from BCS behavior in the underdoped limit which is continuously reduced with increasing hole concentration x. We derive a phase diagram for Tc and the zero temperature gap, Ds0d, as a function of x, which is in semiquantitative agreement with (the anomalous) behavior observed in cuprate experiments, and we compute properties of the associated superconducting state such as the superfluid density rs and Josephson critical current Ic. When these are plotted as rssT dyrss0d and IcsT dyIcs0d ,a s a function of T yTc, we deduce a quite remarkable, nearly

Synthesis of oriented textured diamond films on silicon via hot filament chemical vapor deposition

Oriented diamond films were achieved on Si(001) and Si(111) substrates via hot filament chemical vapor deposition (HFCVD) with the orientation relationship of dia〈110〉//Si〈110〉 and dia(001)//Si(001) for Si(001), and of dia〈110〉//Si〈110〉 and dia(111)//Si(111) for Si(111). The substrates were negatively biased relative to the filament during the nucleation stage. The as‐grown films were characterized by scanning electron microscopy (SEM) and Raman spectroscopy. The role of negative bias is discussed in light of the differences between HFCVD and microwave plasma CVD. In conclusion, the importance of the electron emission from the diamond coating on the substrate holder is highlighted, while the ion bombardment is eliminated as a main factor based on our experiments.

Electron‐emission‐enhanced diamond nucleation on Si by hot filament chemical vapor deposition

Diamond nucleation on mirror‐polished Si was enhanced by electron emission using hot filament chemical vapor deposition. The nucleation density was 108 cm−2. The mechanism of diamond nucleation is carefully discussed. It is surmised that it is electron emission that is responsible for the enhancement of the diamond nucleation in our experiments.

Epitaxially oriented growth of diamond on silicon by hot filament chemical vapor deposition

Expitaxially oriented growth of diamond film on Si(001) was achieved using hot filament chemical vapor deposition. The epitaxial relationship between the film and the substrate was confirmed by the observation through scanning electron microscopy and high‐resolution transmission electron microscopy (HRTEM) as follows: Dia(001)//Si(001) and Dia〈110〉//Si〈110〉 with a misorientation angle of 9° between Dia(001) and Si(001). This reports the HRTEM observation of the largest area of the diamond/Si interface (larger than 880 A). It demonstrates that the intermediate β‐SiC layer is unnecessary for achieving diamond epitaxy on Si. Discussion reveals that the value of the misorientation angle between Dia(001) and Si(001) is not unique and should be controlled to deposit single‐crystal diamond films on Si.

Superconducting transitions from the pseudogap state: d -wave symmetry, lattice, and low-dimensional effects

We investigate the behavior of the superconducting transition temperature within a previously developed BCS-Bose Einstein crossover picture. This picture, based on a decoupling scheme of Kadanoff and Martin, further extended by Patton, can be used to derive a simple form for the superconducting transition temperature in the presence of a pseudogap. We extend previous work which addressed the case of s-wave pairing in jellium, to explore the solutions for T_c as a function of variable coupling in more physically relevant situations. We thereby ascertain the effects of reduced dimensionality, periodic lattices and a d-wave pairing interaction. Implications for the cuprate superconductors are discussed.

Thermodynamics of interacting fermions in atomic traps

We calculate the entropy in a trapped, resonantly interacting Fermi gas as a function of temperature for a wide range of magnetic fields between the BCS and Bose-Einstein condensation end points. This provides a basis for the important technique of adiabatic sweep thermometry and serves to characterize quantitatively the evolution and nature of the excitations of the gas. The results are then used to calibrate the temperature in several ground breaking experiments on (6)Li and (40)K.

Momentum resolved radio frequency spectroscopy in trapped fermi gases.

We address recent momentum-resolved radio frequency (rf) spectroscopy experiments, showing how they yield more stringent tests than other comparisons with theory, associated with the ultracold Fermi gases. We demonstrate that, by providing a clear dispersion signature of pairing, they remove the ambiguity plaguing the interpretation of previous rf experiments. Our calculated spectral intensities are in semiquantitative agreement with the data. Even in the presence of a trap, the spectra are predicted to exhibit two BCS-like branches.

Nature of superfluidity in ultracold Fermi gases near Feshbach resonances

We study the superfluid state of atomic Fermi gases using a BCS-Bose-Einstein-condensation crossover theory. Our approach emphasizes noncondensed fermion pairs which strongly hybridize with their (Feshbach-induced) molecular boson counterparts. These pairs lead to pseudogap effects above