Showing papers in "Journal of the Physical Society of Japan in 2011"

Metal–Insulator Transitions in Pyrochlore Oxides Ln2Ir2O7

Abstract: We report the physical properties of Ln 2 Ir 2 O 7 ( Ln = Nd, Sm, Eu, Gd, Tb, Dy, and Ho), which exhibit metal–insulator transitions (MITs) at different temperatures. The transition temperature T MI increases with a reduction in the ionic radius of Ln . The ionic radius boundary for MITs in Ln 2 Ir 2 O 7 lies between Ln = Pr and Nd. MITs in Ln 2 Ir 2 O 7 have some common features. They are second-order transitions. Under the field cool condition, a weak ferromagnetic component (∼10 -3 µ B /f.u.) caused by Ir 5 d electrons is observed below T MI . The entropy associated with MITs for Ln = Nd, Sm, and Eu is estimated to be 0.47, 2.0, and 1.4 J/(K·mole), respectively. The change in entropy is much smaller than 2 R ln 2 [11.5 J/(K·mole)] expected in a magnetic transition due to localized moments of S = 1/2. The feature of continuous MITs in Ln 2 Ir 2 O 7 is discussed.

SmB6: A Promising Candidate for a Topological Insulator

Abstract: Three-dimensional topological insulators represent a new quantum state. They were originally proposed by a theoretical approach, but subsequently observed experimentally, e.g., in Bi 1- x Sb x and ...

Kondo Effects and Multipolar Order in the Cubic PrTr2Al20 (Tr=Ti, V)

Abstract: Our single crystal study reveals that Pr Tr 2 Al 20 ( Tr = Ti and V) provides the first examples of a cubic Γ 3 nonmagnetic ground doublet system that shows the Kondo effect including a -ln T dependent resistivity. The Γ 3 quadrupolar moments in PrV 2 Al 20 induce anomalous metallic behavior through hybridization with conduction electrons such as T 1/2 dependent resistivity and susceptibility below ∼20 K down to its ordering temperature T O = 0.6 K. In PrTi 2 Al 20 , however, quadrupoles are well-localized and exhibit an order at T O = 2.0 K. Stronger Kondo coupling in PrV 2 Al 20 than in PrTi 2 Al 20 suppresses quadrupolar ordering, and instead promotes hybridization between the Γ 3 doublet and conduction electrons, leading to most likely the quadrupolar Kondo effect.

AMATERAS: A Cold-Neutron Disk Chopper Spectrometer

Abstract: AMATERAS is a new disk-chopper-type spectrometer installed at Materials and Life Science Experimental Facility (MLF) of J-PARC. AMATERAS is equipped with an extra chopper for pulse shaping at the upstream position, in addition to a monochromating chopper, which conventional chopper spectrometers at pulsed source have. Owing to the use of these choppers and the high peak intensity from a coupled moderator source at MLF, the AMATERAS design realizes high-intensity and high-energy-resolution measurements in quasielastic and inelastic neutron scattering experiments. The spectrometer had the first neutron beam in May 2009. During the course of commissioning, the performance of the spectrometer was confirmed by conducting test experiments. AMATERAS is now open to users and is producing scientific outputs.

The Fermi Chopper Spectrometer 4SEASONS at J-PARC

Abstract: 4SEASONS is a Fermi chopper spectrometer in operation at the Materials and Life Science Experimental Facility (MLF) in the Japan Proton Accelerator Research Complex (J-PARC). 4SEASONS is expected to facilitate high-efficiency measurements of weak inelastic signals on novel spin and lattice dynamics using thermal neutrons. The spectrometer is equipped with a coupled moderator and sophisticated components such as an elliptical converging neutron guide with high-critical-angle supermirrors, long (2.5 m) position-sensitive detectors, and a Fermi chopper appropriate for multiple-incident-energy (multi- E i ) measurements by the repetition-rate multiplication technique. Herein, we discuss in detail the design and performance of the spectrometer, and present some examples of the measurements obtained using this spectrometer.

Spin-Driven Ferroelectricity and Magneto-Electric Effects in Frustrated Magnetic Systems

Abstract: The interplay between magnetism and electricity in matter has become a central issue of condensed-matter physics. This review focuses on the ferroelectricity induced by magnetic order mostly in frustrated magnets, which is nowadays referred to as magneto-electric (ME) multiferroic, or often only as multiferroic. Some distinct types of microscopic origins relevant to the spin-driven ferroelectricity are discussed in detail. Then one sees that the frustration-based spin-driven ferroelectrics can exhibit nonlinear and giant ME responses of phase-transition type and of domain-control type, in contrast to the conventional magnetoelectrics hosting linear ME effects.

Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet

Abstract: We study the system size dependence of the singlet–triplet excitation gap in the S =1/2 kagome-lattice Heisenberg antiferromagnet by numerical diagonalization. We successfully obtain a new result of a cluster of 42 sites. The two sequences of gaps of systems with even-number sites and that with odd-number sites are separately analyzed. Careful examination clarifies that there is no contradiction when we consider the system to be gapless.

Superconductivity at 38 K in Iron-Based Compound with Platinum–Arsenide Layers Ca10(Pt4As8)(Fe2-xPtxAs2)5

Abstract: We report superconductivity in novel iron-based compounds Ca 10 (Pt n As 8 )(Fe 2- x Pt x As 2 ) 5 with n = 3 and 4. Both compounds crystallize in triclinic structures (space group P \bar1), in which Fe 2 As 2 layers alternate with Pt n As 8 spacer layers. Superconductivity with a transition temperature of 38 K is observed in the n = 4 compound with a Pt content of x ≃0.36 in the Fe 2 As 2 layers. The compound with n = 3 exhibits superconductivity at 13 K.

Three-Dimensional Dirac Electrons at the Fermi Energy in Cubic Inverse Perovskites: Ca3PbO and Its Family

Abstract: The band structure of cubic inverse perovskites, Ca 3 PbO and its family, are investigated with the first-principles method. A close observation of the band structure reveals that six equivalent Dirac electrons with a very small mass exist on the line connecting the Γ- and X-points, and at the symmetrically equivalent points in the Brillouin zone. The discovered Dirac electrons are three-dimensional and remarkably located exactly at the Fermi energy. A tight-binding model describing the low-energy band structure is also constructed and used to discuss the origin of the Dirac electrons in this material. Materials related to Ca 3 PbO are also studied, and some design principles for the Dirac electrons in this series of materials are proposed.

Superconductivity in the Honeycomb-Lattice Pnictide SrPtAs

Abstract: Pnictides without iron also exhibit superconductivity, though Tc is markedly lower than that of the iron-based superconductors. For example, Tc 1⁄4 3 and 0.7K in BaNi2P2 and BaNi2As2 5) with a ThCr2Si2-type structure, respectively. Tc 1⁄4 5:2K in SrPt2As2 with a CaBe2Ge2-type structure. These superconducting pnictides share a common crystal structure with a square lattice of transition-metal elements. A honeycomb lattice is also an attractive playground for superconductivity. MgB2 (Tc 1⁄4 39K) with an AlB2type structure, CaAlSi (Tc 1⁄4 5:68{7:7K) with an AlB2 derivative structure, and CaC6 (Tc 1⁄4 11:5K) with an intercalated-graphite structure exhibit superconductivity with a relatively high Tc owing to a strong electron–phonon coupling, soft phonons, multibands/multigaps, and interlayer bands. In this paper, we report superconductivity in SrPtAs with Tc 1⁄4 2:4K. To our knowledge, this is the first superconducting pnictide with a honeycomb lattice structure. SrPtAs crystallizes in a hexagonal KZnAs-type structure with the space group P63=mmc (#194). 18) This structure is derived from the binary AlB2-type structure with the space group P6=mmm (#191). The schematic views of AlB2 and SrPtAs are shown in Fig. 1. In AlB2, boron atoms form honeycomb layers and aluminum atoms are intercalated between them. In SrPtAs, the aluminum sites are occupied by strontium atoms and the boron sites are occupied by either platinum or arsenic atoms so that they alternate in the honeycomb layer as well as in the c-axis. Thus, the structure can be viewed as an ordered variant of the AlB2-type structure. Polycrystalline samples of SrPtAs were synthesized by a solid-state reaction. The PtAs2 precursor was first synthesized by heating Pt powder and As grains at 700 C in an evacuated quartz tube. Then, Sr, Pt, and PtAs2 powders of stoichiometric amounts were mixed and ground. The resulting powder was placed in an alumina crucible and sealed in an evacuated quartz tube. The ampule was heated at 700 C for 3 h and then at 1000 C for 24 h. After furnace cooling, the sample was ground, pelletized, wrapped with Ta foil, and heated at 950 C for 2 h in an evacuated quartz tube. The products were confirmed to be a single phase of SrPtAs by powder X-ray diffraction. Lattice parameters were estimated to be a 1⁄4 4:244 A and c 1⁄4 8:989 A, consistent with the previous report. The magnetization M was measured from 1.7 to 5K under a magnetic field of 30Oe with the Magnetic Property Measurement System (Quantum Design). The electrical resistivity was measured by the standard DC four-terminal method in the temperature range between 1.8 and 300K under magnetic fields up to 1000Oe using the physical property measurement system (Quantum Design). Figure 2 shows the temperature dependence of magnetization divided by the applied field, M=H , of SrPtAs at 30Oe under zero-field-cooling and field-cooling conditions. M exhibited a diamagnetic behavior below about 2.4K, indicating the occurrence of superconductivity at Tc 1⁄4 2:4K. The shielding and flux exclusion signals at 1.7K correspond to 45 and 23% of perfect diamagnetism, respectively. The data support the appearance of bulk superconductivity at Tc 1⁄4 2:4K in SrPtAs. Fig. 1. (Color online) Crystal structures of (a) AlB2 (space group P6=mmm) and (b) SrPtAs (space group P63=mmc).

Ferromagnetic quantum critical endpoint in UCoAl

Abstract: Resistivity and magnetostriction measurements were performed at high magnetic fields and under pressure on UCoAl. At ambient pressure, the 1st order metamagnetic transition at H m ∼0.7 T from the paramagnetic ground state to the field-induced ferromagnetic state changes to a crossover at finite temperature T 0 ∼11 K. With increasing pressure, H m linearly increases, while T 0 decreases and is suppressed at the quantum critical endpoint (QCEP, P QCEP ∼1.5 GPa, H m ∼7 T). At higher pressure, the value of H m identified as a crossover continuously increases, while a new anomaly appears above P QCEP at higher field H * in resistivity measurements. The field dependence of the effective mass ( m * ) obtained by resistivity and specific heat measurements exhibits a step-like drop at H m at ambient pressure. With increasing pressure, it gradually changes into a peak structure and a sharp enhancement of m * is observed near the QCEP. Above P QCEP , the enhancement of m * is reduced, and a broad plateau is found be...

Possible three-dimensional nodes in the s± superconducting gap of BaFe 2 (As 1-x P x ) 2

Abstract: We theoretically examine the superconducting state of BaFe 2 (As 1- x P x ) 2 , an isovalent doping 122-iron-pnictide superconductor. We construct a three-dimensional 10-orbital model by first-principles band calculation, and investigate the superconducting gap within the spin-fluctuation-mediated pairing mechanism. The gap is basically s ±, where the gap changes its sign between electron and hole Fermi surfaces, but three-dimensional nodal structures appear in the largely warped hole Fermi surface having a strong Z 2 / XZ / YZ orbital character. The present result, together with our previous study of the 1111 systems, explains the strong material dependence of the superconducting gap in iron pnictides.

IN5 Cold Neutron Time-of-Flight Spectrometer, Prepared to Tackle Single Crystal Spectroscopy

Abstract: The fully overhauled IN5 was the first cold neutron time-of-flight spectrometer equipped with position sensitive detectors. It has been in scheduled operation since end of 2008. The experience of use has confirmed the expectations in terms of both a qualitative and quantitative efficiency increase, allowing to open new opportunities for time-of-flight spectroscopy. Using the full potential of the position sensitive detectors has brought up an increasing demand for single crystal spectroscopy while the enhanced count-rate and better signal-to-noise allow studying smaller samples or weaker scatterers in the more conventional field of quasi-elastic scattering. Additional effort with sample environment – dedicated magnet and polarization analysis option – are expected to improve further the potential for study of strongly correlated electron systems.

Quadrupole Effects of Layered Iron Pnictide Superconductor Ba(Fe0.9Co0.1)2As2

Abstract: Elastic constant measurements on iron pnictide Ba(Fe 0.9 Co 0.1 ) 2 As 2 with an optimal superconducting transition temperature of T SC = 23 K have been performed by the ultrasonic pulse echo method. The shear elastic constant of C 66 associated with elastic strain e x y reveals considerable softening of 21% below 300 K down to T SC and becomes increasing in the superconducting phase below T SC , while other shear elastic constants of ( C 11 - C 12 )/2 and C 44 show no sign of softening below 80 K down to 4.2 K. The electric quadrupole O v ' existing in the degenerate d y ' z and d z x ' bands participates in the superconductivity of the present iron pnictide system.

Spin Dynamics at Very Low Temperature in Spin Ice Dy2Ti2O7

Abstract: We have performed AC susceptibility and DC magnetic relaxation measurements on the spin ice system Dy 2 Ti 2 O 7 down to 0.08 K. The relaxation time of the magnetization has been estimated below 2 K down to 0.08 K. The spin dynamics of Dy 2 Ti 2 O 7 is well described by using two relaxation times [τ S (short time) and τ L (long time)]. Both τ S and τ L increase on cooling. Assuming the Arrhenius law in the temperature range 0.5–1 K, we obtained an energy barrier of 9 K. Below 0.5 K, both τ S and τ L show a clear deviation from the thermal activated dynamics toward temperature independent relaxation, suggesting a quantum dynamics.

On the Puzzle of Odd-Frequency Superconductivity

Abstract: Since the first theoretical proposal by Berezinskii, an odd-frequency superconductivity has encountered the fundamental problems on its thermodynamic stability and rigidity of a homogenous state accompanied by unphysical Meissner effect. Recently, Solenov et al. [Phys. Rev. B 79 (2009) 132502] have asserted that the path-integral formulation gets rid of the difficulties leading to a stable homogenous phase with an ordinary Meissner effect. Here, we show that it is crucial to choose the appropriate saddle-point solution that minimizes the effective free energy, which was assumed implicitly in the work by Solenov and co-workers. We exhibit the path-integral framework for the odd-frequency superconductivity with general type of pairings, including an argument on the retarded functions via the analytic continuation to the real axis.

Antiferro-Quadrupolar Ordering at the Lowest Temperature and Anisotropic Magnetic Field–Temperature Phase Diagram in the Cage Compound PrIr2Zn20

Abstract: The cage compound PrIr 2 Zn 20 with the non-Kramers doublet ground state shows a phase transition at T Q ∼0.11 K. To investigate the origin of the phase transition, we have carried out ultrasonic measurements on single-crystalline samples. From the disappearance of electric quadrupole degrees of freedom at T Q and the negative sign of a quadrupole–quadrupole coupling constant, we clarified that the phase transition is antiferro-quadrupolar ordering at the lowest temperature ever measured. We also found anisotropic magnetic field H dependence and the re-entrant behavior of T Q ( H ) from the measurements in H parallel to the [100], [110], and [111] axes. The quadrupole Kondo effect interrupts the long-range quadrupole interaction at very low temperatures and thus lowers T Q . We first reported the rattling motion of Zn atoms at the 16 c site in the R T 2 Zn 20 system.

On the Hidden Order in URu2Si2 – Antiferro Hexadecapole Order and Its Consequences

Abstract: An antiferro ordering of an electric hexadecapole moment is discussed as a promising candidate for the long standing mystery of the hidden order phase in URu 2 Si 2 . Based on localized f -electron picture, we discuss the rationale of the selected multipole and the consequences of the antiferro hexadecapole order of x y ( x 2 - y 2 ) symmetry. The mean-field solutions and the collective excitations from them explain reasonably significant experimental observations: the strong anisotropy in the magnetic susceptibility, characteristic behavior of pressure versus magnetic field or temperature phase diagrams, disappearance of inelastic neutron-scattering intensity out of the hidden order phase, and insensitiveness of the NQR frequency at Ru-sites upon ordering. A consistency with the strong anisotropy in the magnetic responses excludes all the multipoles in two-dimensional representations, such as ( O y z , O z x ). The expected azimuthal angle dependences of the resonant X-ray scattering amplitude are given....

Evolution toward Quantum Critical End Point in UGe2

Abstract: We report on Hall resistivity and electrical resistivity measurements under pressure and magnetic field in UGe 2 with ferromagnetic (FM) tricriticality. The Hall resistivity sensitively detects the first order metamagnetic transition from a paramagnetic (PM) phase to a FM phase in a large pressure range almost up to the quantum critical end point (QCEP). The drastic change in the Fermi surface at the PM–FM transition is detected up to the vicinity of the QCEP, while a strong modification in the field variation of the inelastic scattering between electrons is observed toward the QCEP. The comparison with the theoretical predictions is made.

Surface Majorana Cone of the Superfluid 3He B Phase

Abstract: The superfluid 3 He B phase, one of the oldest unconventional fermionic condensates experimentally realized, is recently predicted to support Majorana fermion surface states. Majorana fermion, which is characterized by the equivalence of particle and antiparticle, has a linear dispersion relation referred to as the Majorana cone. We measured the transverse acoustic impedance Z of the superfluid 3 He B phase changing its boundary condition and found a growth of peak in Z on a higher specularity wall. Our theoretical analysis indicates that the variation of Z is induced by the formation of the cone-like dispersion relation and thus confirms the important feature of the Majorana fermion in the specular limit.

Unusual Field-Insensitive Phase Transition and Kondo Behavior in SmTi2Al20

Abstract: Magnetization, electrical resistivity and specific heat measurements were performed on high-quality single crystalline SmTi 2 Al 20 (residual resistivity ratio ∼40) grown by Al self-flux method. A Kondo-like log T dependence in the resistivity is observed below 50 K. We discovered a field-insensitive phase transition at T x = 6.5 K and a field-insensitive heavy fermion behavior with the electronic specific heat coefficient γ= 150 mJ/(K 2 mol). Specific heat analysis reveals that the ground state is a Γ 8 quartet state and the Sm magnetic dipole moment m Sm (∼0.5µ B at T ≃0) orders below T x in spite of the field-insensitive behavior. Possible reasons for the field insensitiveness will be discussed.

Electronic structure of graphene with a topological line defect

Abstract: Using the first-principle total-energy procedure within the framework of density functional theory, we study the electronic structure of graphene with a topological line defect that is comprised of a pair of fused pentagons and an octagon. We find that introduction of the topological line defect effectively terminates the sp 2 network of graphene leading the flat dispersion band around the Γ point. A detailed investigation of the wave function of this flat-band state reveals its edge-state nature, which is particular to graphene nanoribbons with zigzag edges. Our tight-binding molecular dynamics simulation also reveals that the topological line defect is spontaneously formed from defects in the graphene sheet when held at a temperature of 1000 K.

Super high resolution powder diffractometer at J-PARC

Abstract: Super High Resolution Powder Diffractometer, SuperHRPD, is located at about 100 m from a thin side of a decoupled poisoned moderator at the Materials and Life Science Experimental Facility in the Japan Proton Accelerator Research Complex. The first neutron was produced successfully from a spallation neutron source in J-PARC in the end of May of 2008, and SuperHRPD has achieved the world best resolution Δ d / d = 0.035% in June using the existing Sirius 1) chamber. In the summer of 2009, a new SuperHRPD chamber was installed aiming at increasing the detector solid angle and expanding d -range / Q -range, with at most 1500 one-dimensional 3 He position-sensitive detectors of 1/2 inch in diameter. The on-beam commissioning of the new SuperHRPD was started in the autumn of 2009.

Magnetic Structure Determination of CeT2Al10 (T = Ru and Os): Single Crystal Neutron Diffraction Studies

Abstract: Neutron diffraction studies of Ce T 2 Al 10 ( T = Ru and Os), which shows an anomalous transition at T 0 = 27 K for CeRu 2 Al 10 and at 29 K for CeOs 2 Al 10 , have been carried out using single crystal samples of the compounds. In the ordered state below T 0 , obvious superlattice reflections have been found, indicating the appearance of ordered magnetic moments. The magnetic structures of both compounds could be commonly explained with a propagation vector q = (0, 1, 0), where collinear antiferromagnetic moments with magnitudes of 0.42(1) µ B for CeRu 2 Al 10 and of 0.29(1) µ B for CeOs 2 Al 10 are aligned along the c -axis.

Magnetic and Transport Properties ofROs2Al10(R=Pr, Nd, Sm, and Gd)

Abstract: We report on the synthesis and measurements of the magnetic susceptibility, electrical resistivity, and specific heat of R Os 2 Al 10 ( R =Pr, Nd, Sm, and Gd). All compounds are isostructural with a Kondo semiconductor CeOs 2 Al 10 showing an unusual phase transition at T 0 =28.6 K. For R =Pr, no magnetic transitions were observed down to 0.4 K, whereas compounds with R =Nd, Sm, and Gd undergo antiferromagnetic transitions at T N = 2.2, 12.5, and 18 K, respectively. Moreover, successive magnetic transitions occur for R =Sm and Gd. The resistivity of the compounds with R =Sm and Gd increases on cooling below T N due to the superzone-gap formation. The fact that T N =18 K for R = Gd is lower than T 0 for R = Ce indicates that the phase transition in CeOs 2 Al 10 is not originated from the RKKY interaction alone but from the anisotropic hybridization of the 4 f state with conduction bands.

Dust Static Spherically Symmetric Solution in f(R) Gravity

Abstract: In this paper, we take dust matter and investigate static spherically symmetric solution of the field equations in metric f ( R ) gravity. The solution is found with constant Ricci scalar curvature and its energy distribution is evaluated by using Landau–Lifshitz energy-momentum complex. We also discuss the stability condition and constant scalar curvature condition for some specific popular choices of f ( R ) models in addition to their energy distribution.

Superconductivity Reinforced by Magnetic Field and the Magnetic Instability in Uranium Ferromagnets

Abstract: We review our recent results on ferromagnetic superconductors, URhGe and UCoGe High quality single crystals of both compounds were successfully grown The specific heat shows a clear jump related to the superconducting transition in UCoGe The finite values of C / T at 0 K are discussed in terms of the self-induced vortex state and the value of the ordered moment With increasing fields for H ∥ b -axis in URhGe, the jump of thermal expansion increases and shifts to lower temperature The re-entrant and S-shaped superconducting phases for URhGe and UCoGe respectively are explained by the unusual field dependence of the effective mass, which is induced by the ferromagnetic instability when the field is applied along the hard magnetization b -axis The magnetic fluctuations are very sensitive to the field orientation This is reflected in the H c2 and the anisotropy of the effective mass

Topological Insulators from Spontaneous Symmetry Breaking Induced by Electron Correlation on Pyrochlore Lattices

Abstract: We study an extended Hubbard model with the nearest-neighbor Coulomb interaction on the pyrochlore lattice at half filling. An interaction-driven insulating phase with nontrivial Z 2 invariants emerges at the Hartree–Fock mean-field level in the phase diagram. This topological insulator phase competes with other ordered states and survives in a parameter region surrounded by a semimetal, antiferromagnetic and charge ordered insulators. The symmetries of these phases are group-theoretically analyzed. We also show that the ferromagnetic interaction enhances the stability of the topological phase.

Charged Perfect Fluid Cylindrical Gravitational Collapse

Abstract: This paper is devoted to study the charged perfect fluid cylindrical gravitational collapse. For this purpose, we find a new analytical solution of the field equations for non-static cylindrically symmetric spacetime. We discuss physical properties of the solution which predict gravitational collapse. It is concluded that in the presence of electromagnetic field the outgoing gravitational waves are absent. Further, it turns out that when longitudinal length reduces to zero due to resultant action of gravity and electromagnetic field, then the end state of the gravitational collapse is a conical singularity. We also explore the smooth matching of the collapsing cylindrical solution to a static cylindrically symmetric solution. In this matching, we take a special choice of constant radius of the boundary surface. We conclude that the gravitational and Coulomb forces of the system balance each other.

Disorder-induced multiple transition involving Z2 topological insulator

Abstract: Effects of disorder on two-dimensional Z 2 topological insulator are studied numerically by the transfer matrix method. Based on the scaling analysis, the phase diagram is derived for a model of HgTe quantum well as a function of disorder strength and magnitude of the energy gap. In the presence of s z non-conserving spin–orbit coupling, a finite metallic region is found that partitions the two topologically distinct insulating phases. As disorder increases, a narrow-gap topologically trivial insulator undergoes a series of transitions; first to metal, second to topological insulator, third to metal, and finally back to trivial insulator. We show that this multiple transition is a consequence of two disorder effects; renormalization of the band gap, and Anderson localization. The metallic region found in the scaling analysis corresponds roughly to the region of finite density of states at the Fermi level evaluated in the self-consistent Born approximation.