We investigate strong-coupling effects on normal state properties of an ultracold Fermi gas.Within the framework of T -matrix approximation in terms of pairing fluctuations, we calculate the single-particle density of states (DOS), as well as the spectral weight, over the entire BCS-BEC crossover region above the superfluid phase transition temperature T c . Starting from the weakcoupling BCS regime, we show that the so-called pseudogap develops in DOS above T c , which becomes remarkable in the crossover region. The pseudogap structure continuously changes into a fully gapped one in the strong-coupling BEC regime, where the gap energy is directly related to the binding energy of tightly bound molecules. We determine the pseudogap temperature T * where the dip structure in DOS vanishes. The value of T * is shown to be very different from another characteristic temperature T * * where a BCS-type double peak structure disappears in the spectral weight. While one finds T * > T * * in the BCS regime, T * * becomes higher than T * in the crossover region and BEC regime. Including this, we determine the pseudogap region in the phase diagram of ultracold Fermi gases. Our results would be useful in the search for the pseudogap region in ultracold 6 Li and 40 K Fermi gases.

In our paper, the effects of the superfluid order parameter were underestimated in the crossover region due to a computational mistake in the treatment of the off-diagonal self-energy. The corrected calculation gives a larger superfluid gap E SF , so that Fig. 4(a) should be replaced by the corrected one shown below.In the weak-coupling BCS regime and the strong-coupling BEC regime, the density of states ρ(ω), as well as the spectral weight A p (ω), are almost unaltered by this correction, because pairing fluctuations are less important there. On the other hand, Fig. 6, which shows the detailed competition between the pseudogap and superfluid gap in the unitarity regime, should be replaced by the corrected one presented here. In our paper, we reported that the superfluid gap started to open below 0.9T c , after the pseudogap almost disappears. In the correct result, however, since effects of the superfluid order are more remarkable, the superfluid gap starts to develop below T c , before the pseudogap disappears completely, as shown in the corrected Fig. 6. As expected, far below T c , the ordinary BCS-type superfluid density of states is obtained, as shown in the corrected Fig. 6(a4). FIG. 4. (Color online) (a) Comparison of the pseudogap size E PG at T c and superfluid gap size E SF at T = 0 evaluated from ρ(ω). For comparison, we also show the energy gap E G in the BCS-Leggett crossover theory [1] (which equals when μ > 0, and equals μ 2 + 2 when μ < 0). * rwatanab@rk.phys.keio.ac.jp FIG. 6. (Color online) Temperature dependence of DOS ρ(ω) and intensity of spectral weight A( p,ω) in the crossover regime [(k F a s ) −1 = 0 (unitarity limit)].In our paper, we have introduced the pseudogap temperature T * at which the superfluid gap structure starts to appear in ρ(ω). However, since the corrected Fig. 6 indicates that the superfluid gap starts to develop without the disappearance of the pseudogap, the previous simple definition for T * is insufficient to discuss effects of pairing fluctuations below T c . Thus, to definitely determine T * , in this erratum we redefine this pseudogap temperature as the temperature at which the superfluid density of states at ω = 0 [ρ(ω = 0)] decreases by 50% compared with the value at T c [ρ c0 ≡ ρ(ω = 0,T = T c )]. Below this temperature, the superfluid density of states ρ(ω) around ω = 0 is remarkably suppressed, which means the suppression of pairing fluctuations due to the development of superfluid order. The resulting pseudogap regime in Fig. 8(b) is almost unaltered (although the definition of T * is different). We briefly note that T * is a crossover temperature without being accompanied by any phase transition, so that it depends on the choice of the value of R ≡ ρ(ω = 0)/ρ c0 . For the readers' convenience, we show T * for various values of R in Fig. 8(c) as supplementary information. 039908-1 1050-2947/2012/85(3)/039908 (2)

We investigate magnetic properties and effects of pairing fluctuations in the BCS (BardeenCooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas.Recently, Liu and Hu, and Parish, pointed out that the strong-coupling theory developed by Nozières and Schmitt-Rink (NSR), which has been extensively used to successfully clarify various physical properties of cold Fermi gases, unphysically gives negative spin susceptibility in the BCS-BEC crossover region. The same problem is found to also exist in the ordinary non-self-consistent T -matrix approximation. In this paper, we clarify that this serious problem comes from incomplete treatment in term of pseudogap phenomena originating from strong pairing fluctuations, as well as effects of spin fluctuations on the spin susceptibility. Including these two key issues, we construct an extended T -matrix theory which can overcome this problem. The resulting positive spin susceptibility agrees well with the recent experiment on a 6 Li Fermi gas done by Sanner and co-workers. We also apply our theory to a polarized Fermi gas to examine the superfluid phase transition temperature T c , as a function of the polarization rate. Since the spin susceptibility is an important physical quantity, especially in singlet Fermi superfluids, our results would be useful in considering how singlet pairs appear above and below T c in the BCS-BEC crossover regime of cold Fermi gases.

The quantum anomalous Hall effect (QAHE) is an exotic quantum phenomenon originating from dissipation-less chiral channels at the sample edge. While the QAHE has been observed in magnetically doped topological insulators (TIs), exploiting magnetic proximity effect on the TI surface from adjacent ferromagnet layers may provide an alternative approach to the QAHE by opening an exchange gap with less disorder than that in the doped system. Nevertheless, the engineering of a favorable heterointerface that realizes the QAHE based on the magnetic proximity effect remains to be achieved. Here, we report on the observation of the QAHE in a proximity coupled system of nonmagnetic TI and ferromagnetic insulator (FMI). We have designed sandwich heterostructures of (Zn,Cr)Te/(Bi,Sb)2Te3/(Zn,Cr)Te that fulfills two prerequisites for the emergence of the QAHE; the formation of a sizable exchange gap at the TI surface state and the tuning of the Fermi energy into the exchange gap. The efficient proximity coupling in the all-telluride based heterostructure as demonstrated here will enable a realistic design of versatile tailor-made topological materials coupled with ferromagnetism, ferroelectricity, superconductivity, and so on.

We theoretically investigate excitation properties in the pseudogap regime of a trapped Fermi gas. Using a combined T -matrix theory with the local density approximation, we calculate strongcoupling corrections to single-particle local density of states (LDOS), as well as the single-particle local spectral weight (LSW). Starting from the superfluid phase transition temperature T c , we clarify how the pseudogap structures in these quantities disappear with increasing the temperature.As in the case of a uniform Fermi gas, LDOS and LSW give different pseudogap temperatures T * and T * * at which the pseudogap structures in these quantities completely disappear. Determining T * and T * * over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensate) crossover region, we identify the pseudogap regime in the phase diagram with respect to the temperature and the interaction strength. We also show that the so-called back-bending peak recently observed in the photoemission spectra by JILA group may be explained as an effect of pseudogap phenomenon in the trap center. Since strong pairing fluctuations, spatial inhomogeneity, and finite temperatures, are important keys in considering real cold Fermi gases, our results would be useful for clarifying normal state properties of this strongly interacting Fermi system.