We study the deconfined quantum critical point of the Kondo-Heisenberg lattice in three dimensions using a fermionic representation for the localized spins. The mean-field phase diagram exhibits a zero temperature quantum critical point separating a spin liquid phase where the hybridization vanishes and a Kondo phase where it does not. Two solutions can be stabilized in the Kondo phase: namely, a uniform hybridization when the band masses of the conduction electrons and the spinons have the same sign, and a modulated one when they have opposite sign. For the uniform case, we show that above a very small temperature scale, the critical fluctuations associated with the vanishing hybridization have dynamical exponent z=3, giving rise to a resistivity that has a TlogT behavior. We also find that the specific heat coefficient diverges logarithmically in temperature, as observed in a number of heavy fermion metals.

We review the recent developments in electronic Raman scattering measurements of charge nematic fluctuations in iron-based superconductors. A simple theoretical framework of a d-wave Pomeranchuk transition is proposed in order to capture the salient features of the spectra. We discuss the available Raman data in the normal state of 122 iron-based systems, particularly Co doped BaFe2As2, and we show that the low energy quasi-elastic peak, the extracted nematic susceptibility and the scattering rates are consistent with an electronic driven structural phase transition. In the superconducting state with a full gap the quasi-elastic peak transforms into a finite frequency nematic resonance, evidences for which are particularly strong in the electron doped systems. A crucial feature of the analysis is the fact that the electronic Raman signal is unaffected by the acoustic phonons. This makes Raman spectroscopy a unique probe of electronic nematicity.

Using electronic Raman spectroscopy, we report direct measurements of charge nematic fluctuations in the tetragonal phase of strain-free Ba(Fe1−xCox)2As2 single crystals. The strong enhancement of the Raman response at low temperatures unveils an underlying charge nematic state that extends to superconducting compositions and which has hitherto remained unnoticed. Comparison between the extracted charge nematic susceptibility and the elastic modulus allows us to disentangle the charge contribution to the nematic instability, and to show that charge nematic fluctuations are weakly coupled to the lattice.

The interplay between the structural and magnetic phase transitions occurring in the Fe-based pnictide superconductors is studied within a Ginzburg-Landau approach. We show that the magnetoelastic coupling between the corresponding order parameters is behind the salient features observed in the phase diagram of these systems. This naturally explains the coincidence of transition temperatures observed in some cases as well as the character (first or second-order) of the transitions. We also show that magnetoelastic coupling is the key ingredient determining the collinearity of the magnetic ordering, and we propose an experimental criterion to distinguish between a pure elastic from a spin-nematic-driven structural transition.PACS numbers: 74.70. Xa, 74.90.+n, 75.80.+q Introduction.-The discovery of an unconventional high-temperature superconductivity in the F-doped arsenic-oxide LaFeAsO 1 has given rise to a great interest on iron pnictide compounds. To date several families of Fe-based superconductors have been discovered, and the superconducting transition temperature has been raised to above 50 K.2 All of these systems display an intriguing competition between structural, magnetic and superconducting transitions.2,3 The parent compounds of the so-called 1111 and 111 families undergo a structural transition (ST) followed by a magnetic transition (MT) at a lower temperature, 4 whereas in the 122 and 11 cases these two transitions take place simultaneously. [5][6][7] In any case these orderings are quickly suppressed by doping or by applying pressure, which eventually gives rise to superconductivity. The role, if any, of magnetic and elastic degrees of freedom in inducing this superconductivity is currently an open question. There is already a growing body of theoretical works advocating for spin fluctuation mediated superconductivity, 8 but the isotope effect observed in both magnetism and superconductivity suggests that the elastic medium also plays a role.9 It is therefore compelling to understand the connection between the ST and the MT in these systems.

Theoretically, it is commonly held that in metals near a nematic quantum critical point the electronic excitations become incoherent on the entire "hot" Fermi surface, triggering non-Fermi-liquid behavior. However, such conclusions are based on electron-only theories, ignoring a symmetry-allowed coupling between the electronic nematic variable and a suitable crystalline lattice strain. Here, we show that including this coupling leads to entirely different conclusions because the critical fluctuations are mostly cut off by the noncritical lattice shear modes. At sufficiently low temperatures the thermodynamics remain Fermi-liquid type, while, depending on the Fermi surface geometry, either the entire Fermi surface stays cold, or at most there are hot spots. In particular, our predictions are relevant for the iron-based superconductors.

The spontaneous appearance of nematicity, a state of matter that breaks rotation but not translation symmetry, is one of the most intriguing properties of the iron-based superconductors (Fe SC), and has relevance for the cuprates as well. Establishing the critical electronic modes behind nematicity remains a challenge, however, because their associated susceptibilities are not easily accessible by conventional probes. Here, using FeSe as a model system, and symmetry-resolved electronic Raman scattering as a probe, we unravel the presence of critical charge nematic fluctuations near the structural/nematic transition temperature, T S ∼ 90 K. The diverging behavior of the associated nematic susceptibility foretells the presence of a Pomeranchuk instability of the Fermi surface with d-wave symmetry. The excellent scaling between the observed nematic susceptibility and elastic modulus data demonstrates that the structural distortion is driven by this d-wave Pomeranchuk transition. Our results make a strong case for chargeinduced nematicity in FeSe.nematicity | superconductivity | Raman scattering

We derive a generalized Luttinger-Ward expression for the Free energy of a many body system involving a constrained Hilbert space. In the large N limit, we are able to explicitly write the entropy as a functional of the Green's functions. Using this method we obtain a Luttinger sum rule for the Kondo lattice. One of the fascinating aspects of the sum rule, is that it contains two components, one describing the heavy electron Fermi surface, the other, a sea of oppositely charged, spinless fermions. In the heavy electron state, this sea of spinless fermions is completely filled and the electron Fermi surface expands by one electron per unit cell to compensate the positively charged background, forming a "large" Fermi surface. Arbitrarily weak magnetism causes the spinless Fermi sea to annihilate with part of the Fermi sea of the conduction electrons, leading to a small Fermi surface. Our results thus enable us to show that the Fermi surface volume contracts from a large, to a small volume at a quantum critical point. However, the sum rules also permit the possible formation of a new phase, sandwiched between the antiferromagnet and the heavy electron phase, where the charged spinless fermions develop a true Fermi surface.

We report a fine tuned doping study of strongly overdoped Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} single crystals using electronic Raman scattering. Combined with theoretical calculations, we show that the doping, at which the normal-state pseudogap closes, coincides with a Lifshitz quantum phase transition where the active holelike Fermi surface becomes electronlike. This conclusion suggests that the microscopic cause of the pseudogap is sensitive to the Fermi surface topology. Furthermore, we find that the superconducting transition temperature is unaffected by this transition, demonstrating that their origins are different on the overdoped side.