I. Paul

Centre National de la Recherche Scientifique

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Y. Gallais

Commissariat à l'Énergie Atomique et aux Énergies Alternatives

A. Sacuto

Laboratoire Matériaux et Phénomènes Quantiques

M. Cazayous

Laboratoire Matériaux et Phénomènes Quantiques

Marcello Civelli

Laboratoire de physique des Solides

A. Forget

Service de Physique de l'État Condensé

S. Benhabib

Université Paris-Saclay

D. Colson

CEA Paris-Saclay

M. R. Norman

Argonne National Laboratory

C. Pépin

Commissariat à l'Énergie Atomique et aux Énergies Alternatives

Bastien Loret

Laboratoire Matériaux et Phénomènes Quantiques

Cooperative Institutions

Centre National de la Recherche Scientifique

Laboratoire Matériaux et Phénomènes Quantiques

Université Grenoble Alpes

Université Paris Cité

Université Paris-Saclay

Rutgers, The State University of New Jersey

Laboratoire National des Champs Magnétiques Intenses

Université de Sherbrooke

Karlsruhe Institute of Technology

Laboratoire de physique des Solides

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Sum rules and Ward identities in the Kondo lattice

Physical Review B (2005)

Piers Coleman I. Paul Jérôme Rech

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.

Fermi energy

Pseudogap

10.1103/physrevb.72.094430

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Citations (54)

Aharonov-Bohm oscillations in the local density of states

Physical Review B (2009)

A. Cano I. Paul

The scattering of electrons with inhomogeneities produces modulations in the local density of states of a metal. We show that electron interference contributions to these modulations are affected by the magnetic field via the Aharonov-Bohm effect. This can be exploited in a simple scanning-tunneling-microscopy setup that serves as an Aharonov-Bohm interferometer at the nanometer scale.

Aharonov–Bohm effect

Density of states

10.1103/physrevb.80.153401

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Citations (14)

Theory of disorder-limited transport anisotropy in Fe-based superconductors

Bulletin of the American Physical Society (2014)

P. J. Hirschfeld Yan Wang I. Paul

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Exceptional van Hove Singularities in Pseudogapped Metals

arXiv (Cornell University) (2022)

I. Paul Marcello Civelli

Motivated by the pseudogap state of the cuprates, we introduce the concept of an "exceptional" van Hove singularity that appears when strong electron-electron interaction splits an otherwise simply connected Fermi surface into multiply connected pieces. The singularity describes the touching of two pieces of the split Fermi surface. We show that this singularity is proximate to a second order van Hove singularity, which can be accessed by tuning a dispersion parameter. We argue that, in a wide class of cuprates, the end-point of the pseudogap is accessed only by triggering the exceptional van Hove singularity. The resulting Lifshitz transition is characterized by enhanced specific heat and nematic susceptibility, as seen in experiments.

Van Hove singularity

Pseudogap

10.48550/arxiv.2210.01830

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Manifestation of nematic degrees of freedom in the Raman response function of iron pnictides

Physical Review B (2015)

Una Karahasanovic Florian Kretzschmar Thomas Böhm R. Hackl I. Paul

We establish a relation between the Raman response function in the $B_{1g}$ channel and the electronic contribution to the nematic susceptibility within the spin-driven approach to electron nematicity of the iron based superconductors. The spin-driven nematic phase, characterized by the broken $C_4$ symmetry, but unbroken $O(3$) spin-rotational symmetry, is generated by the presence of magnetic fluctuations associated with the striped phase. It occurs as a separate phase between $T_N$ and $T_s$ in systems where the structural and magnetic phase transitions are separated. Detecting the presence of nematic degrees of freedom in iron-based superconductors is a difficult task, since it involves measuring higher order spin correlation functions. We show that the nematic degrees of freedom manifest themselves in the experimentally measurable Raman response function. We calculate the Raman response function in tetragonal phase in the large $N$ limit by considering Aslamazov-Larkin type of diagrams that contain a series of inserted fermionic boxes that resemble the nematic coupling constant of the theory. These diagrams effectively account for collisions between spin fluctuations. By summing an infinite number of such higher order diagrams, we demonstrate that the electronic Raman response function shows a clear maximum at the structural phase transition in the $B_{1g}$ channel. Hence, the Raman response function can be used to probe nematic degrees of freedom.

Tetragonal crystal system

10.1103/physrevb.92.075134

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Citations (31)

Designing heterostructures with higher-temperature superconductivity

Physical Review B (2011)

Karyn Le Hur Chung‐Hou Chung I. Paul

We propose to increase the superconducting transition temperature Tc of strongly correlated materials by designing heterostructures which exhibit a high pairing energy as a result of magnetic fluctuations. More precisely, applying an effective theory of the doped Mott insulator, we envisage a bilayer Hubbard system where both layers exhibit prominent intralayer (intraband) d-wave superconducting correlations. Introducing a finite asymmetry between the hole densities of the two layers such that one layer becomes slightly more underdoped and the other more overdoped, we evidence a visible enhancement of Tc compared to the optimally doped isolated layer. Using the bonding and antibonding band basis, we show that the mechanism behind this enhancement of Tc is the interband pairing correlation mediated by the hole asymmetry which strives to decrease the paramagnetic nodal contribution to the superfluid stiffness. For two identical layers, Tc remains comparable to that of the isolated layer until moderate values of the interlayer single-particle tunneling term. These heterostructures shed new light on fundamental questions related to superconductivity.

Mott insulator

10.1103/physrevb.84.024526

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Citations (5)

Nesting-induced large magnetoelasticity in the iron-arsenide systems

Physical Review B (2014)

I. Paul

A novel feature of the iron arsenides is the magnetoelastic coupling between the long-wavelength in-plane strains of the lattice and the collective spin fluctuations of the electrons near the magnetic ordering wave vectors. Here, we study its microscopic origin from an electronic model with nested Fermi pockets and a nominal interaction. We find that the couplings diverge with a power law as the system is tuned to perfect nesting. Furthermore, the theory reveals how nematicity is boosted by nesting. These results are relevant for other systems with nesting-driven density wave transitions.

Nesting (process)

Lattice (music)

10.1103/physrevb.90.115102

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Citations (11)

Nematic Resonance in the Raman Response of Iron-Based Superconductors

Physical Review Letters (2016)

Y. Gallais I. Paul L. Chauvière Jörg Schmalian

In a fully-gapped superconductor the electronic Raman response has a pair-breaking peak at twice the superconducting gap $\Delta$, if the Bogoliubov excitations are uncorrelated. Motivated by the iron based superconductors, we study how this peak is modified if the superconducting phase hosts a nematic-structural quantum critical point. We show that, upon approaching this point by tuning, e.g., doping, the growth of nematic correlations between the quasiparticles transforms the pair-breaking peak into a nematic resonance. The mode energy is below 2$\Delta$, and stays finite at the quantum critical point, where its spectral weight is sharply enhanced. The latter is consistent with recent experiments on electron-doped iron based superconductors and provides direct evidence of nematic correlations in their superconducting phases.

Iron-based superconductor

Critical point (mathematics)

10.1103/physrevlett.116.017001

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Citations (40)

Signature of Kondo breakdown quantum criticality in optical conductivity

Physical Review B (2010)

I. Paul Marcello Civelli

We show that the behavior of the finite-frequency interband transition peak in the optical conductivity of the heavy fermions can provide definitive experimental proof of the Kondo breakdown phenomenon in which the lattice Kondo temperature vanishes at a quantum critical point. Approaching such a phase transition from the heavy Fermi-liquid side, we find a new crossover regime where the peak position is related to, but is not directly proportional to the lattice Kondo scale. The peak position moves to lower energies but remains finite, while the peak value changes nonmonotonically and it eventually disappears at the quantum critical point. These are unique signatures which distinguish a Kondo breakdown transition from a spin-density wave driven transition.

Optical conductivity

Kondo insulator

10.1103/physrevb.81.161102

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Citations (5)

Variation of shear moduli across superconducting phase transitions

Physical review. B./Physical review. B (2020)

Dimitri Labat Panagiotis Kotetes Brian M. Andersen I. Paul

We study how shear moduli of a correlated metal change across superconducting phase transitions. Using a microscopic theory we explain why for most classes of superconductors this change is small. The Fe-based and the A15 systems are notable exceptions where the change is boosted by five orders of magnitude. We show that this boost is a consequence of enhanced nematic correlation. The theory explains the unusual temperature dependence of the orthorhombic shear and the back-bending of the nematic transition line in the superconducting phase of the Fe-based systems.

Orthorhombic crystal system

Shear modulus

10.1103/physrevb.101.144502

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Citations (2)