Building upon an analytical technique introduced by Chung and Peschel ͓Phys. Rev. B 64, 064412 ͑2001͔͒, we calculated the many-body density matrix B of a finite block of B sites within an infinite system of free spinless fermions in arbitrary dimensions. In terms of the block Green function matrix G ͑whose elements are G i ¯jϭ ͗c i † c j ͘, where c i † and c j are fermion creation and annihilation operators acting on sites i and j within the block, respectively͒, the density matrix can be written as B ϭdet(1ϪG)exp"͚ i j ͓ln G(1ϪG) Ϫ1 ͔ i j c i † c j …. Our results suggest that Hilbert space truncation schemes should retain the states created by a subset of the c i † 's ͑in any combination͒, rather than selecting eigenvectors of B independently based on the eigenvalue.

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A systematic study on the magnetic and electrical transport properties of single-phase wurtzite Zn1−xCuxO is performed. Efros variable range hopping dominates the conduction, which is accompanied by a ferromagnetic order up to 700 K for x>1%. Both the first-principles calculations and Cu/Al co-doping experiments suggest that the spontaneous spin polarization originates from the p-d exchange interaction between O 2p and Cu 3d orbitals. Furthermore, our results are consistent with the scenario that the intrinsic ferromagnetism is established through indirect interactions between bound magnetic polarons mediated by magnetic impurities.

Using terahertz time-domain spectroscopy, the real part of optical conductivity [σ1(ω)] of twisted bilayer graphene was obtained at different temperatures (10 -300 K) in the frequency range 0.3 -3 THz. On top of a Drude-like response, we see a strong peak in σ1(ω) at ∼2.7 THz. We analyze the overall Drude-like response using a disorder-dependent (unitary scattering) model, then attribute the peak at 2.7 THz to an enhanced density of states at that energy, that is caused by the presence of a van Hove singularity arising from a commensurate twisting of the two graphene layers.Compared to single-layer graphene (SLG), where there are two non-equivalent lattice sites (A and B), bilayer graphene (BLG) has two SLGs stacked in the third direction. In the most common Bernal (AB) stacking of BLG, adjacent layers are rotated by 60 • , so that the B atoms of layer 2 (B ′ ) sits directly on top of A atoms in layer 1 (A), and B and A ′ atoms are in the center of the hexagons of the opposing layer. Electrons can then hop between these two A sites with a hopping energy t ⊥ . In the undoped case, though both SLG and BLG are gapless semi-metals, carriers in SLG exhibit linear dispersion, while those in BLG show quadratic dispersion. An energy gap in SLG opens up due to finite geometry effects, but its control has proven to be unreliable [1]. On the other hand, the electronic gap in BLG can be reliably opened and controlled by an applied electric field, shown theoretically and demonstrated experimentally [2][3][4][5], and promises interesting applications. Both SLG and BLG however, are sensitive to disorder. Hence, to realize graphene-based optoelectronic devices, an understanding of the temperature and disorder effects in the transport and spectroscopic properties of BLG is needed. Temperature and disorder-dependent conductivity of BLG have been derived theoretically [1,6]. Experimentally, spectroscopies (from terahertz (THz) to visible) and ultrafast dynamics of various flavors of graphene have been reported, such as SLG, few and many-layer graphene, and graphite [7][8][9][10][11]. For example, Fourier-transform infrared spectroscopy (FTIR) on large-area SLG grown by chemical vapor deposition (CVD) revealed a Drude-like frequency dependence of the spectral density from THz to mid-infrared at different carrier concentrations [12]. In addition, graphene plasmons, which lie in the THz range, are strongly coupled to the interband electronic transitions and decay by exciting interband electron-hole pairs [13]. Hence knowledge of graphene's electromagnetic response, as a function of disorder, in the THz frequency range is critical for applications such as graphene-based THz oscillators [14].

Temperature-dependent terahertz conductivity of tin oxide (SnO 2) nanowire films was measured from 10 to 300 K using terahertz time-domain spectroscopy. The optical parameters, including the complex refractive index, optical conductivity and dielectric function, were obtained using a simple effective medium theory. The complex conductivity was fitted with the Drude-Smith model and the plasmon model. The results show that the carrier density (N) and plasmon resonance frequency (ω 0) increase while the scattering time decreases with increasing temperature. The reduced carrier mobility compared with bulk SnO 2 indicates the presence of carrier localization or trapping in these nanowires.

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a b s t r a c tWe calculated the cross correlations between the half-hourly times series of the ten Dow Jones US economic sectors over the period and also over 11 segments within the present financial crisis, to construct minimal spanning trees (MSTs) of the US economy at the sector level. In all MSTs, a core-fringe structure is found, with consumer goods, consumer services, and the industrials consistently making up the core, and basic materials, oil & gas, healthcare, telecommunications, and utilities residing predominantly on the fringe. More importantly, we find that the MSTs can be classified into two distinct, statistically robust, topologies: (i) star-like, with the industrials at the center, associated with low-volatility economic growth; and (ii) chain-like, associated with high-volatility economic crisis. Finally, we present statistical evidence, based on the emergence of a starlike MST in Sep 2009, and the MST staying robustly star-like throughout the Greek Debt Crisis, that the US economy is on track to a recovery.