Effective action for strongly correlated fermions from functional integrals

Magnetotransport and Fermi surface segmentation in Pauli limited superconductors

We report the first theoretical investigation of the spectroscopic, electrical and optical transport signatures ofd-wave Pauli limited superconductors, based on a non perturbative numerical approach. We demonstrate that the high magnetic field low temperature regime of these materials host a finite momentum paired superconducting phase. Multi-branched dispersion spectra with finite energy superconducting gaps, anisotropic segmentation of the Fermi surface and spatial modulations of the superconducting order characterizes this finite momentum paired phase and should be readily accessible through angle resolved photo emission spectroscopy, quasiparticle interference and differential conductance measurements. Based on the electrical and optical transport properties we capture the non Fermi liquid behavior of these systems at high temperatures, dominated by local superconducting correlations and characterized by resilient quasiparticles which survive the breakdown of the Fermi liquid description. We map out the generic thermal phase diagram of thed-wave Pauli limited superconductors and provide for the first time the accurate estimates of the thermal scales corresponding to the: (a) loss of (quasi) long range superconducting phase coherence (Tc), (b) loss of local pair correlations (Tpg), (c) breakdown of the Fermi liquid theory (Tmax) and cross-over from the non Fermi liquid to the bad metallic phase (TBR). Our thermal phase diagram mapped out on the basis of the spectroscopic and transport properties are found to be in qualitative agreement with the experimental observations on CeCoIn5andκ-BEDT, in terms of the thermodynamic phases and the phase transitions. The results presented in this paper are expected to initiate important transport and spectroscopic experiments on the Pauli limitedd-wave superconductors, providing sharp signatures of the finite momentum Cooper paired state in these materials.

Collective Excitations in Chiral Stoner Magnets

We argue that spin- and valley-polarized metallic phases recently observed in graphene bilayers and trilayers support chiral edge modes that allow spin waves to propagate ballistically along system boundaries without backscattering. The chiral edge behavior originates from the interplay between the momentum-space Berry curvature in Dirac bands and the geometric phase of a spin texture in position space. The edge modes are weakly confined to the edge, featuring dispersion that is robust and insensitive to the detailed profile of magnetization at the edge. This unique character of edge modes reduces their overlap with edge disorder and enhances the mode lifetime. The mode propagation direction reverses upon reversing valley polarization, an effect that provides a clear testable signature of geometric interactions in isospin-polarized Dirac bands.

Euclidean Q-Balls of Fluctuating SDW/CDW in the ‘Nested’ Hubbard Model of High-Tc Superconductors as the Origin of Pseudogap and Superconducting Behaviors

The origin of the pseudogap and superconducting behaviors in high-Tc superconductors is proposed, based on the picture of Euclidean Q-balls formation that carry Cooper/local-pair condensates inside their volumes. Euclidean Q-balls that describe bubbles of collective spin-/charge density fluctuations (SDW/CDW) oscillating in Matsubara time are found as a new self-consistent solution of the Eliashberg equations in the ‘nested’ repulsive Hubbard model of high-Tc superconductors. The Q-balls arise due to global invariance of the effective theory under the phase rotation of the Fourier amplitudes of SDW/CDW fluctuations, leading to conservation of the ‘Noether charge’ Q in Matsubara time. Due to self-consistently arising local minimum of their potential energy at finite amplitude of the density fluctuations, the Q-balls provide greater binding energy of fermions into local/Cooper pairs relative to the usual Frohlich mechanism of exchange with infinitesimal lattice/charge/spin quasiparticles. We show that around some temperature T* the Q-balls arise with a finite density of superconducting condensate inside them. The Q-balls expand their sizes to infinity at superconducting transition temperature Tc. The fermionic spectral gap inside the Q-balls arises in the vicinity of the ‘nested’ regions of the bare Fermi surface. Solutions are found analytically from the Eliashberg equations with the ‘nesting’ wave vectors connecting ‘hot spots’ in the Brillouin zone. The experimental ‘Uemura plot’ of the linear dependence of Tc on superconducting density ns in high-Tc superconducting compounds follows naturally from the proposed theory.

Pauli limited d-wave superconductors: quantum breached pair phase and thermal transitions

We report a quantum phase transition in Pauli limited d-wave superconductors and give the mean field estimates of the associated quantum critical point. For a population imbalanced d-wave superconductor a stable ground state phase viz quantum breached pair phase has been identified which comprises of spatial coexistence of gapless superconductivity and nonzero magnetization. Based on the thermodynamic and quasiparticle indicators we for the first time analyze this phase, discuss the thermal behavior of Pauli limited d-wave superconductor, give accurate estimates of the thermal scales associated with such systems and map out the pseudogap regime. Our work shows that while the Pauli limited superconductors are known to exhibit exotic modulated superconducting phase at large imbalance of fermion populations; in the regime of weak imbalance an intriguing phase of competing orders is realized. We have established that rather than the superconducting pairing field, it is the average magnetization of the system that quantifies this quantum phase transition. Given that the existing Pauli limited superconductors possess unconventional pairing state symmetry of the superconducting order, our work promises to open up new avenues in the experimental research of these materials. We have also demonstrated an alternate scenario wherein the quantum breached pair phase is a natural outcome for a d-wave superconductor with unequal effective masses of the fermion species.

Orbital Mott transition in two dimensional pyrochlore lattice

We study orbital Mott transition in two dimensional pyrochlore lattice, using a two orbital Hubbard model with only inter-orbital electronic hopping. We use a real space Monte Carlo based approach to study the model at finite temperature, and establish temperature-interaction phase diagram that highlights the Mott transition, orbital ordering, and spectral trends, and possible window of pseudogap. Due to only inter-orbital hopping, the Mott insulator 'generates' ferro exchange resulting in ferro-orbital ordering, with T _corr/t peaked at ≈0.2 around U/t ≈ 6. The optical conductivity shows unusual two peak feature due to two dimensional pyrochlore lattice.

Current-induced effective Dzyaloshinskii-Moriya interaction and its Kondo enhancement in double quantum dot

We studied the nonequilibrium transport of serially coupled double quantum dots connected to ferromagnetic electrodes. We demonstrated that the nonadiabatic part of the spin gauge field resulted in a current-induced Dzyaloshinskii-Moriya (DM) interaction effect in a double quantum dot and numerically confirmed this observation through the hierarchical equations of motion approach. We report that the spin current and the effective DM interaction are enhanced in the Kondo regime. We demonstrate that this enhancement occurs because the Kondo resonance, which is supposed to be suppressed by the local ferromagnetic exchange, is enhanced by the inter-dot coupling. This additional Kondo resonance channel increases the spin current. In addition, the impact of the spin-spin interaction and the Kondo effect on tunnel magnetoresistance is discussed. Our results offer a new approach for controlling the non-collinear spin interaction in double quantum dot devices.

Anomalous magnetoresistance due to longitudinal spin fluctuations in a Jeff = 1/2 Mott semiconductor

As a hallmark of electronic correlation, spin-charge interplay underlies many emergent phenomena in doped Mott insulators, such as high-temperature superconductivity, whereas the half-filled parent state is usually electronically frozen with an antiferromagnetic order that resists external control. We report on the observation of a positive magnetoresistance that probes the staggered susceptibility of a pseudospin-half square-lattice Mott insulator built as an artificial SrIrO₃/SrTiO₃ superlattice. Its size is particularly large in the high-temperature insulating paramagnetic phase near the Néel transition. This magnetoresistance originates from a collective charge response to the large longitudinal spin fluctuations under a linear coupling between the external magnetic field and the staggered magnetization enabled by strong spin-orbit interaction. Our results demonstrate a magnetic control of the binding energy of the fluctuating particle-hole pairs in the Slater-Mott crossover regime analogous to the Bardeen-Cooper-Schrieffer-to-Bose-Einstein condensation crossover of ultracold-superfluids.

Spin-charge interactions are at the core of electronic correlation phenomena in Mott insulators. Here, the authors observe a positive anomalous magnetoresistance in a SrIrO₃/SrTiO₃ superlattice, indicative of strong spin-charge fluctuations in this pseudospin-half square-lattice Mott insulator.

Topological order in the pseudogap metal

We compute the electronic Green's function of the topologically ordered Higgs phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square lattice. The results are compared with cluster extensions of dynamical mean field theory, and quantum Monte Carlo calculations, on the pseudogap phase of the strongly interacting hole-doped Hubbard model. Good agreement is found in the momentum, frequency, hopping, and doping dependencies of the spectral function and electronic self-energy. We show that lines of (approximate) zeros of the zero-frequency electronic Green's function are signs of the underlying topological order of the gauge theory and describe how these lines of zeros appear in our theory of the Hubbard model. We also derive a modified, nonperturbative version of the Luttinger theorem that holds in the Higgs phase.

Magnetic order and Mott transition on the checkerboard lattice

The checkerboard lattice, with alternating 'crossed' plaquettes, serves as the two dimensional analog of the pyrochlore lattice. The corner sharing plaquette structure leads to a hugely degenerate ground state, and no magnetic order, for classical spins with short range antiferromagnetic interaction. For the half-filled Hubbard model on this structure, however, we find that the Mott insulating phase involves virtual electronic processes that generate longer range and multispin couplings. These couplings lift the degeneracy, selecting a 'flux like' state in the Mott insulator. Increasing temperature leads, strangely, to a sharp crossover from this state to a '120 degree' correlated state and then a paramagnet. Decrease in the Hubbard repulsion drives the system towards an insulator-metal transition-the moments reduce, and a spin disordered state wins over the flux state. Near the insulator-metal transition the electron system displays a pseudogap extending over a large temperature window.

The Hubbard dimer: a density functional case study of a many-body problem

This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy-Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the 'failure' of the Kohn-Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree-Fock and Bethe ansatz local density approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2.

Possible anomalous spin dynamics of the Hubbard model on a honeycomb lattice

In this paper, the Hubbard model on a honeycomb lattice is investigated by using an O(3) nonlinear σ model. A possible candidate for a quantum non-magnetic insulator in a narrow parameter region is found near the metal-insulator transition. After studying the magnetic properties of the quantum non-magnetic insulator, anomalous spin dynamics is shown. In addition, we find that this region could be widened by hole doping.

A functional renormalization group approach to the Anderson impurity model

We develop a functional renormalization group approach which describes the low-energy single-particle properties of the Anderson impurity model up to intermediate on-site interactions [Formula: see text], where Δ is the hybridization in the wide-band limit. Our method is based on a generalization of a method proposed by Schütz et al (2005 Phys. Rev. B 72 035107), using two independent Hubbard-Stratonovich fields associated with transverse and longitudinal spin fluctuations. Although we do not reproduce the exponentially small Kondo scale in the limit [Formula: see text], the spin fluctuations included in our approach remove the unphysical Stoner instability predicted by mean field theory for U>πΔ. We discuss different decoupling schemes and show that a decoupling which manifestly respects the spin-rotational invariance of the problem gives rise to the lowest quasiparticle weight. To obtain a closed flow equation for the fermionic self-energy we also propose a new scheme of truncation of the functional renormalization group flow equations using Dyson-Schwinger equations to express bosonic vertex functions in terms of fermionic ones.

Local defect in metallic quantum critical systems

We present a theory of a single point, line, or plane defect coupling to the square of the order parameter in a metallic system near a quantum critical point at or above its upper critical dimension. At criticality, a spin droplet is nucleated around the defect with its core size determined by the strength of the defect potential. Outside the core a universal slowly decaying tail of the droplet is found, leading to many dissipative channels coupling to the droplet and to a complete suppression of quantum tunneling. We propose an NMR experiment to measure the impurity-induced changes in the local spin susceptibility.