Topological insulators (TIs) are newly discovered states of matter with robust metallic surface states protected by the topological properties of the bulk wavefunctions [1][2][3][4][5][6]. A quantum phase transition (QPT) from a TI to a conventional insulator and a change in topological class can only occur when the bulk band gap closes [3]. In this work, we have utilized time-domain terahertz spectroscopy (TDTS) to investigate the low frequency conductance in (Bi 1−x In x ) 2 Se 3 as we tune through this transition by indium substitution. Above certain substitution levels we observe a collapse in the transport lifetime that indicates the destruction of the topological phase. We associate this effect with the threshold where states from opposite surfaces hybridize. The substitution level of the threshold is thickness dependent and only asymptotically approaches the bulk limit x ≈ 0.06 where a maximum in the midinfrared absorption is exhibited. This absorption can be identified with the bulk band gap closing and a change in topological class. The correlation length associated with the QPT appears as the evanescent length of the surface states. The observation of the thickness-dependent collapse of the transport lifetime shows the unusual role that finite size effects play in this topological QPT.The topological character of TIs is determined by the nature of their valence-band wave functions, which can be quantified by 4 Z 2 invariants. Fu and Kane have shown that for inversion symmetric crystals it is possible to evaluate these invariants directly with knowledge of the parity of Bloch wave functions for the occupied electronic states at high symmetry points in the Brillouin zone [10]. Although their argument is formulated for inversion symmetric systems, a material's topological classification does not require inversion or translation symmetry. Therefore the expectation is that the alloying of known TIs with lighter elements by reducing spin-orbit coupling or the tuning of lattice constant can cause the bulk band gap ∆ to close and invert at a quantum critical point where the topological class changes (See cartoon * Electronic address: npa@pha.jhu.edu Fig. 1a). This has been investigated in the thalliumbased ternary chalcogenide alloy TlBi(S 1−x Se x ) 2 [7-9], but thus far only with photoemission (Supplementary Information (SI) section B). Although signatures of topological surface state (TSS) conduction have been found in Bi 2 Se 3 [11-14], a demonstration that the surface transport changes dramatically when the band gap closes and the bulk changes topological class [15] would be strong evidence for the topological nature of these materials and is still lacking. In this regard, it was pointed out recently that indium (In) substitutes for bismuth to form a solid solution in Bi 2 Se 3 and that the non-topological end member In 2 Se 3 of the (Bi 1−x In x ) 2 Se 3 series shares the common rhombohedral D 5 3d structure with Bi 2 Se 3 [6]. In Ref.[6] a topological to trivial transition was observed in a range x ∼ 0.0...
We measured the electronic-structure of FeSexTe1−x above and below Tc. In the normal state we find multiple bands with remarkably small values for the Fermi energy εF . Yet,below Tc we find a superconducting gap ∆ that is comparable in size to εF , leading to a ratio ∆/εF ≈ 0.5 that is much larger than found in any previously studied superconductor. We also observe an anomalous dispersion of the coherence peak which is very similar to the dispersion found in cold Fermi-gas experiments and which is consistent with the predictions of the BCS-BEC crossover theory.PACS numbers:
The presence of optical polarization anisotropies, such as Faraday/Kerr effects, linear birefringence, and magnetoelectric birefringence are evidence for broken symmetry states of matter. The recent discovery of a Kerr effect using near-IR light in the pseudogap phase of the cuprates can be regarded as a strong evidence for a spontaneous symmetry breaking and the existence of an anomalous long-range ordered state. In this work we present a high precision study of the polarimetry properties of the cuprates in the THz regime. While no Faraday effect was found in this frequency range to the limits of our experimental uncertainty (1.3 milli-radian or 0.07• ), a small but significant polarization rotation was detected that derives from an anomalous linear dichroism. In YBa2Cu3Oy the effect has a temperature onset that mirrors the pseudogap temperature T * and is enhanced in magnitude in underdoped samples. In x = 1/8 La2−xBaxCuO4, the effect onsets above room temperature, but shows a dramatic enhancement near a temperature scale known to be associated with spin and charge ordered states. These features are consistent with a loss of both C4 rotation and mirror symmetry in the electronic structure of the CuO2 planes in the pseudogap state.PACS numbers: 74.25. Gz, 74.72.Kf, An extensive research effort has been carried out over the last two decades on defining the role and origin of the pseudogap phase in the cuprates. The pseudogap, a regime of the phase diagram generally located at higher temperatures than the superconducting state, is characterized by an energy gap in the density of states at the Fermi level as well as various transport and magnetic anomalies. Whether this gap is related to superconductivity or competes with it, and whether it realizes an additional long-range ordered state is controversial [1,2]. Characterization of a stable static order with true broken symmetry in the pseudogap regime could solve the mystery surrounding its origin.Optical polarization anisotropies, such as Faraday/Kerr effects, gyrotropic rotation, linear birefringence, and magneto-electric birefringence can be sensitive tools for the detection of broken symmetry states of matter. For instance, materials with anti-symmetric off-diagonal components in the dielectric tensor can rotate the plane of polarization of linearly polarized light. Such tensor elements are only allowed in a material that breaks either time-reversal or inversion and mirror symmetries. Such effects are referred to as circular, since the eigenmodes of their transmission or reflection matrices are left and right circular polarizations. The most common such "circular" effects are magneto-optical ones arising from time-reversal symmetry breaking from magnetic moments aligned either by applying external magnetic field or spontaneous magnetization. Another circular effect arises in so-called gyrotropic ordered materials that breaks all mirror symmetries. Spiral structures and cholesteric textures have such optical activity and can rotate polarization in the absence o...
The phase diagram of the superconducting high-T(c) cuprates is governed by two energy scales: T*, the temperature below which a gap is opened in the excitation spectrum, and T(c), the superconducting transition temperature. The way these two energy scales are reflected in the low-temperature energy gap is being intensively debated. Using Zn substitution and carefully controlled annealing we prepared a set of samples having the same T* but different T(c)'s, and measured their gap using angle-resolved photoemission spectroscopy (ARPES). We show that T(c) is not related to the gap shape or size, but it controls the size of the coherence peak at the gap edge.
We investigate the cross-over temperature T * as a function of doping in (CaxLa1−x)(Ba1.75−xLa0.25+x)Cu3Oy, where the maximum Tc (T max c ) varies continuously by 30% between families (x) with minimal structural changes. T * is determined by DC-susceptibility measurements. We find that T * scales with the maximum Néel temperature T max N of each family. This result strongly supports a magnetic origin of T * , and indicates that three dimensional interactions play a role in its magnitude.PACS numbers: 74.25. Dw,74.25.Ha, Free electrons do not have high temperature crossovers such as a pseudogap (PG), spin gap (SG), or development of antiferromagnetic (AFM) correlations. In the cuprates all of these exist, yet the interactions that lead to them are not completely clear. Nevertheless, the crossovers occur at a temperature T * which is much higher than T c , and closer to the three dimensional (3D) ordering temperature of the parent compound in the AFM state. Therefore, it is speculated that T * emerges from AFM fluctuations, and that the cross-overs are intimately linked, namely, the interaction responsible for one might be responsible for all [1,2,3]. Therefore, it is crucial to test the possibility of correlations between T ⋆ of a particular system and its magnetic properties, such as the Néel temperature T N of the parent compound, or its constituents, the in-and out-of-plane Heisenberg coupling constant J and J ⊥ , respectively. This is the motivation of the work presented here. We provide experimental evidence that strongly supports a magnetic origin for T * . Moreover, we show that T * stems from 3D interactions, similar to the Néel order, involving both J and J ⊥ .We investigate the origin of the T ⋆ by studying its variations as a function of the compound's magnetic properties, where small chemical changes are an implicit parameter. The variations in the magnetic properties are achieved by using four different families of the (Ca x La 1−x )(Ba 1.75−x La 0.25+x )Cu 3 O y (CLBLCO) system, having the YBa 2 Cu 3 O y (YBCO) structure, with x = 0.1 . . . 0.4. The phase diagram of the CLBLCO families is shown in Fig. 1(a). T c was measured by resistivity [4], and the spin glass temperature T g [5] and T N [6] by muon spin relaxation. Despite the rich phase diagram, the different CLBLCO families have negligible structural differences. All compounds are tetragonal, and there is no oxygen chain ordering as in YBCO [4]. The hole concentration in the CuO 2 planes does not depend on x [7,8]. The difference in the unit cell parameters a and c/3 between the two extreme families (x = 0.1 and 0.4) is 1% [4]. Thus, variations in T max c due to variations in ionic radii are not relevant [9]. The level of disorder, as detected by Cu and Ca nuclear magnetic resonance, is also identical for the different families [8,10]. In fact, the only strong variation between families noticed at present is the in-plane oxygen buckling angle [11]. This property can modify the intraplane near-and next-nearneighbors hopping, or interplane hoppi...
In semiconductor chip manufacturing, dedicated metrology targets are used for measuring overlay (OVL) between layers after the lithographic process step. Until recently, overlay targets have had typical dimensions of 20x20 microns, but have been reduced in size to allow for more critical product real estate. Reducing metrology target size, however, increases optical crosstalk and diffractions from the target’s edges which can introduce significant errors in the reported OVL values. In this work, we will evaluate the following parameters: 1. The beam spot shape on the metrology target 2. The best target design under size/wavelength constraints 3. Improved OVL extraction algorithm We will present the hardware and software optimizations for experimental measurements taken over a cascade of targets. While decreasing the target’s size, we quantified the OVL measurement performance via dynamic precision, tool-induced shift (TIS), and results through focus (Z position). We will demonstrate how these optimizations enable the measurement of targets as small as 6x6 microns without compromising throughput or measurement quality.
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