Quasi-two dimensional itinerant fermions in the Anti-Ferro-Magnetic (AFM) quantum-critical region of their phase diagram, such as in the Fe-based superconductors or in some of the heavy-fermion compounds, exhibit a resistivity varying linearly with t
emperature and a contribution to specific heat or thermopower proportional to $T ln T$. It is shown here that a generic model of itinerant AFM can be canonically transformed such that its critical fluctuations around the AFM-vector $Q$ can be obtained from the fluctuations in the long wave-length limit of a dissipative quantum XY model. The fluctuations of the dissipative quantum XY model in 2D have been evaluated recently and in a large regime of parameters, they are determined, not by renormalized spin-fluctuations but by topological excitations. In this regime, the fluctuations are separable in their spatial and temporal dependence and have a dynamical critical exponent $z =infty.$ The time dependence gives $omega/T$-scaling at criticality. The observed resistivity and entropy then follow directly. Several predictions to test the theory are also given.
The formation of heavy fermion bands can occur by means of the conversion of a periodic array of local moments into itinerant electrons via the Kondo effect and the huge consequent Fermi-liquid renormalizations. Leggett predicted for liquid $^3$He th
at Fermi-liquid renormalizations change in the superconducting state, leading to a temperature dependence of the London penetration depth~$Lambda$ quite different from that in the BCS theory. Using Leggetts theory, as modified for heavy fermions, it is possible to extract from the measured temperature dependence of $Lambda$ in high quality samples both Landau parameters $F_0^s$ and $F_1^s$; this has never been accomplished before. A modification of the temperature dependence of the specific heat $C_mathrm{el}$, related to that of $Lambda$, is also expected. We have carefully determined the magnitude and temperature dependence of $Lambda$ in CeCoIn$_5$ by muon spin relaxation rate measurements to obtain $F_0^s = 36 pm 1$ and $F_1^s = 1.2 pm 0.3$, and find a consistent change in the temperature dependence of electronic specific heat $C_mathrm{el}$. This, the first determination of $F_1^s$ with a value~$ll F_0^s$ in a heavy fermion compound, tests the basic assumption of the theory of heavy fermions, that the frequency dependence of the self-energy is much more important than its momentum dependence.
The order parameter and its variations in space and time in many different states in condensed matter physics at low temperatures are described by the complex function $Psi({bf r}, t)$. These states include superfluids, superconductors, and a subclas
s of antiferromagnets and charge-density waves. The collective fluctuations in the ordered state may then be categorized as oscillations of phase and amplitude of $Psi({bf r}, t)$. The phase oscillations are the {it Goldstone} modes of the broken continuous symmetry. The amplitude modes, even at long wavelengths, are well defined and decoupled from the phase oscillations only near particle-hole symmetry, where the equations of motion have an effective Lorentz symmetry as in particle physics, and if there are no significant avenues for decay into other excitations. They bear close correspondence with the so-called {it Higgs} modes in particle physics, whose prediction and discovery is very important for the standard model of particle physics. In this review, we discuss the theory and the possible observation of the amplitude or Higgs modes in condensed matter physics -- in superconductors, cold-atoms in periodic lattices, and in uniaxial antiferromagnets. We discuss the necessity for at least approximate particle-hole symmetry as well as the special conditions required to couple to such modes because, being scalars, they do not couple linearly to the usual condensed matter probes.
The optical effects due to the loop-current order parameter in under-doped cuprates are studied in order to understand the recent observation of unusual birefringence in electromagnetic propagation in under-doped cuprates. It is shown why birefringen
ce occurs even in multiple domains of order with size of domains much smaller than the wave-length and in twinned samples. Not only is there a rotation of polarization of incident light but also a rotation of the principal optical axis from the crystalline axes. Both are calculated in relative agreement with experiments in terms of the same parameters. The magnitude of the effect is orders of magnitude larger than the unusual Kerr effect observed in under-doped cuprates earlier. The new observations, including their comparison with the Kerr effect, test the symmetry of the proposed order decisively and confirm the conclusions from polarized neutron scattering.
We study the free energy landscape of a minimal model for relaxor ferroelectrics. Using a variational method which includes leading correlations beyond the mean-field approximation as well as disorder averaging at the level of a simple replica theory
, we find metastable paraelectric states with a stability region that extends to zero temperature. The free energy of such states exhibits an essential singularity for weak compositional disorder pointing to their necessary occurrence. Ferroelectric states appear as local minima in the free energy at high temperatures and become stable below a coexistence temperature $T_c$. We calculate the phase diagram in the electric field-temperature plane and find a coexistence line of the polar and non-polar phases which ends at a critical point. First-order phase transitions are induced for fields sufficiently large to cross the region of stability of the metastable paraelectric phase. These polar and non-polar states have distinct structure factors from those of conventional ferroelectrics. We use this theoretical framework to compare and to gain physical understanding of various experimental results in typical relaxors.
We show that a finite Hall effect in zero applied magnetic field occurs for partially filled bands in certain time-reversal violating states with zero net flux per unit-cell. These states are the Magneto-chiral states with parameters in the effective
one-particle Hamiltonian such that they do not satisfy the Haldane-type constraints for topological electronic states. The results extend an earlier discussion of the Kerr effect observed in the cuprates but may be applicable to other experimental situations.
We study a minimal model for a relaxor ferroelectric including dipolar interactions, and short-range harmonic and anharmonic forces for the critical modes as in the theory of pure ferroelectrics together with quenched disorder coupled linearly to the
critical modes. We present the simplest approximate solution of the model necessary to obtain the principal features of the correlation functions. Specifically, we calculate and compare the structure factor measured by neutron scattering in different characteristic regimes of temperature in the relaxor PbMg$_{1/3}$Nb$_{2/3}$O$_3$.
A brief summary of collective mode excitations that can exist in singlet superconductors with irreducible representation $L$ is given. Such excitations may be classified as the coupled excitations of the charge density $rho$ and the phase $phi $ of t
he order parameter, or of the amplitude $Delta$ of order parameter. Each of these classes may be further characterized in the long wavelength limit by the irreducible representation $ell$ of the excitation, which may or may not be the same as the ground state $L$.
A d-wave superconducting phase with coexisting intra-unit-cell orbital current order has the remarkable property that it supports finite size Fermi pockets of Bougoliubov quasiparticles. Experimentally detectable consequences of this include a residu
al $T$-linear term in the specific heat in the absence of disorder and residual features in the thermal and microwave conductivity in the low disorder limit.
The concept of broken symmetry, that the symmetry of the vacuum may be lower than the Hamiltonian of a quantum theory, plays an important role in modern physics. A manifestation of this phenomena is the Higgs boson in particle physics whose long awai
ted discovery is imminent. An equivalent mode in superconductors is implicit in the early theories of their collective fluctuations. Spurred by some mysterious experimental results, the theory of the oscillation of the amplitude of superconductivity order parameter, which is the equivalent to the Higgs modes in s-wave superconductors and its identification in the experiments, was explicitly provided. It was also shown that a necessary condition for this to occur is the emergent Lorentz invariance in the superconducting state while the metallic state and the region just below $T_c$ is manifestly non-Lorentz invariant. Here we show that d-wave superconductors, such as the high temperature Cuprate superconductors, should have a rich assortment of Higgs bosons, each in a different irreducible representation of the point-group symmetries of the lattice. We also show that these modes have a characteristic singular spectral structure which can be discovered in Raman scattering experiments.
