Catherine Pépin

What is the fate of the heavy electron at a quantum critical point

A growing body of evidence suggests that the quantum critical behavior at the onset of magnetism in heavy fermion systems cannot be understood in terms of a simple quantum spin density wave. This talk will discuss the consequences of this conclusion, touching on its possible implications in the realm of 2D systems and outlining current theoretical and experimental efforts to characterize the nature of the critical point in heavy fermion materials.

Cascade of phase transitions in the vicinity of a quantum critical point

We study the timely issue of charge order checkerboard patterns observed in a variety of cuprate superconductors. We suggest a minimal model in which strong quantum fluctuations in the vicinity of a single antiferromagnetic quantum critical point generate the complexity seen in the phase diagram of cuprates superconductors and, in particular, the evidenced charge order. The Fermi surface is found to fractionalize into hotspots and antinodal regions, where physically different gaps are formed. In the phase diagram, this is reflected by three transition temperatures for the formation of pseudogap, charge density wave, and superconductivity (or quadrupole density wave if a sufficiently strong magnetic field is applied). The charge density wave is characterized by modulations along the bonds of the CuO lattice with wave vectors connecting points of the Fermi surface in the antinodal regions. These features, previously observed experimentally, are so far unique to the quantum critical point in two spatial dimensions and shed a new light on the interplay between strongly fluctuating critical modes and conduction electrons in high-temperature superconductors.

Pseudogap, charge order, and pairing density wave at the hot spots in cuprate superconductors

We address the timely issue of the presence of charge ordering at the hot-spots in the pseudo-gap phase of cuprate superconductors in the context of an emergent SU(2)-symmetry which relates the charge and pairing sectors. Performing the Hubbard-Stratonovich decoupling such that the free energy stays always real and physically meaningful we exhibit three solutions of the spin-fermion model at the hot spots. A careful examination of their stability and free energy shows that, at low temperature, the system tends towards a co-existence of charge density wave (CDW) and the composite order parameter made of diagonal quadrupolar density wave and pairing fluctuations of Ref. [Nat. Phys.

Fractionalization and Fermi-surface volume in heavy-fermion compounds: the case of YbRh2Si2.

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Modulated spin liquid: a new paradigm for URu2Si2.

, 1745 (2013)].The CDW is sensitive to the shape of the Fermi surface in contrast to the diagonal quadrupolar order, which is immune to it. SU(2) symmetry within the pseudo-gap phase also applies to the CDW state, which therefore admits a pairing density pave counterpart breaking time reversal symmetry.

ORDER FROM DISORDER : NONMAGNETIC IMPURITIES IN THE SPIN-GAP PHASE OF THE CUPRATES

We establish an effective theory for heavy-fermion compounds close to a zero temperature antiferromagnetic (AFM) transition. Coming from the heavy Fermi liquid phase across to the AFM phase, the heavy electron fractionalizes into a light electron, a bosonic spinon, and a new excitation: a spinless fermionic field. Assuming this field acquires dynamics and dispersion when one integrates out the high energy degrees of freedom, we give a scenario for the volume of its Fermi surface through the phase diagram. We apply our theory to the special case of YbRh2(Si1-xGex)2 where we recover, within experimental resolution, several low temperature exponents for transport and thermodynamics.

Effect of magnetic field on the competition between superconductivity and charge order below the pseudogap state

We argue that near a Kondo breakdown critical point, a spin liquid with spatial modulations can form. Unlike its uniform counterpart, we find that this occurs via a second order phase transition. The amount of entropy quenched when ordering is of the same magnitude as for an antiferromagnet. Moreover, the two states are competitive, and at low temperatures are separated by a first order phase transition. The modulated spin liquid we find breaks Z4 symmetry, as recently seen in the hidden order phase of URu2Si2. Based on this, we suggest that the modulated spin liquid is a viable candidate for this unique phase of matter.

Supersymmetric spin operators

We solve the problem of

Density of states of a d -wave superconductor in the presence of strong impurity scatterers: A nonperturbative result

N

Supersymmetric Hubbard operators

non magnetic impurities in the staggered flux phase of the Heisenberg model which we assume to be a good mean-field approximation for the spin-gap phase of the cuprates. The density of states is evaluated exactly in the unitary limit and is porportional to