Fermi Liquid Instabilities Research Articles

Fermiology of Topological Metals

The modern scope of fermiology encompasses not just the classical geometry of Fermi surfaces but also the geometry of quantum wave functions over the Fermi surface. This enlarged scope is motivated by the advent of topological metals—metals whose Fermi surfaces are characterized by a robustly nontrivial Berry phase. We review the extent to which topological metals can be diagnosed from magnetic-field-induced quantum oscillations of transport and thermodynamic quantities. A holistic analysis of the oscillatory wave form is proposed, in which different characteristics of the wave form (e.g., phase offset, high-harmonic amplitudes, temperature-dependent frequency) encode different aspects of a topologically nontrivial Fermi surface. Which characteristic to focus on depends on ( a) the orientation of the magnetic field relative to certain crystallographic axes, ( b) the symmetry class of the topological metal, and ( c) the separation of Fermi-surface pockets in quasimomentum [Formula: see text] space. Closely proximate pockets arise when (1) spin–split pockets are nearly overlapping due to a weak spin–orbit force or when (2) two pockets touch at an isolated [Formula: see text] point, which can be a topological band-touching point or a saddlepoint in the energy-momentum dispersion. The emergence of a pseudospin degree of freedom (in case 1) and the implications of magnetic breakdown (in case 2) are reviewed, with emphasis on new aspects originating from the (nonabelian) Berry connection of the Fermi surface. Future extensions of topofermiology are suggested in the directions of interaction-induced Fermi-liquid instabilities and two-dimensional electron liquids.

Successive phase transitions of the spin–orbit-coupled metal Cd2Re2O7 probed by high-resolution synchrotron x-ray diffraction

The 5d pyrochlore oxide superconductor Cd2Re2O7 (CRO) has attracted significant interest as a spin–orbit-coupled metal (SOCM) that spontaneously undergoes a phase transition to an odd-parity multipole phase by breaking the spatial inversion symmetry due to the Fermi liquid instability caused by strong spin–orbit coupling. Despite the significance of structural information during the transition, previous experimental results regarding lattice deformation have been elusive. We have conducted ultra-high resolution synchrotron radiation x-ray diffraction experiments on a high-quality CRO single crystal. The temperature-dependent splitting of the 0 0 16 and 0 0 14 reflections, which are allowed and forbidden, respectively, in the high-temperature cubic phase I (space group Fd–3m), has been clearly observed and reveals the following significant facts: inversion symmetry breaking and tetragonal distortion occur simultaneously at T s1 = 201.5(1) K; the previously believed first-order transition between phase II (I–4m2) and phase III (I4122) at T s2 ∼120 K consists of two close second-order transitions at T s2 = 115.4(1) K and T s3 ∼ 100 K; there is a new orthorhombic phase XI (F222) in between. The order parameters (OPs) of these continuous transitions are uniquely represented by a two-dimensional irreducible representation Eu of the Oh point group, and the OPs of phase XI are a linear combination of those of phases II and III. Each phase is believed to correspond to a distinct odd-parity multipole order, and the complex successive transitions observed may be the result of an electronic phase transition that resolves the Fermi liquid instability in the SOCM.

Electronic states of metallic electric toroidal quadrupole order in Cd2Re2O7 determined by combining quantum oscillations and electronic structure calculations

Pyrochlore oxide ${\mathrm{Cd}}_{2}{\mathrm{Re}}_{2}{\mathrm{O}}_{7}$ exhibits successive structural transitions upon cooling that break its inversion symmetry. The low-temperature noncentrosymmetric metallic phases are believed to be some odd-parity multipole ordered states that are associated with a Fermi-liquid instability due to the strong spin-orbit interaction (SOI) and electronic correlation. However, their microscopic ordering pictures and the driving force of the phase transitions are still unclear. We determined the electronic structure of the lowest temperature phase of ${\mathrm{Cd}}_{2}{\mathrm{Re}}_{2}{\mathrm{O}}_{7}$ by combining quantum oscillation measurements with electronic structure calculations. The observed Fermi surfaces were well reproduced based on the optimized crystal structure, and we demonstrated the strong influence of the antisymmetric SOI. From the mass enhancement factor, we elucidated the strongly correlated nature of the electronic states. In addition, we visualized the microscopic picture of the $3{z}^{2}\ensuremath{-}{r}^{2}$-type metallic electric-toroidal-quadrupole (ETQ) order characterized by the Re-O bond order. These results corroborate that the metallic ETQ order is driven by a Fermi-liquid instability associated with the strong SOI and electronic correlation, as has been theoretically proposed. Our results provide the basis for exploring unconventional phenomena expected in the metallic ETQ order.

Quasi-particle functional Renormalisation Group calculations in the two-dimensional half-filled Hubbard model at finite temperatures

We present a highly parallelisable scheme for treating functional Renormalisation Group equations which incorporates a quasi-particle-based feedback on the flow and provides direct access to real-frequency self-energy data. This allows to map out the boundaries of Fermi-liquid regimes and to study the effect of quasi-particle degradation near Fermi liquid instabilities. As a first application, selected results for the two-dimensional half-filled perfectly nested Hubbard model are shown.

Domain Control by Adjusting Anisotropic Stress in Pyrochlore Oxide Cd2Re2O7

The 5d pyrochlore oxide Cd2Re2O7 exhibits successive phase transitions from a cubic pyrochlore structure (phase I) to a tetragonal structure without inversion symmetry below Ts1 of ~200 K (phase II) and further to another noncentrosymmetric tetragonal structure below Ts2 of ~120 K (phase III). The two low-temperature phases may be characterized by odd-parity multipolar orders induced by the Fermi liquid instability of the spin-orbit-coupled metal. To control the tetragonal domains generated by the transitions and to obtain a single-domain crystal for the measurements of anisotropic properties, we prepared single crystals with the (0 0 1) surface and applied biaxial and uniaxial stresses along the plane. Polarizing optical microscopy observations revealed that inducing a small strain of approximately 0.05% could flip the twin domains ferroelastically in a reversible fashion at low temperatures, which evidences that the tetragonal deformation switches at Ts2 between c > a for phase II and c < a for phase III. Resistivity measurements using single-domain crystals under uniaxial stress showed that the anisotropy was maximum at around Ts2 and turned over across Ts2: resistivity along the c axis is larger (smaller) than that along the a axis by ~25% for phase II (III) at around Ts2. These large anisotropies probably originate from spin-dependent scattering in the spin-split Fermi surfaces of the cluster electric toroidal quadrupolar phases of Cd2Re2O7.

Spin–orbit-coupled metal candidate PbRe2O6

We study the lead rhenium oxide PbRe2O6 as a candidate spin–orbit-coupled metal (SOCM), which has attracted much attention as a testing ground for studying unconventional Fermi liquid instability associated with a large spin–orbit interaction. The compound comprises a stack of modulated honeycomb lattices made of Re5+ (5d2) ions in a centrosymmetric R–3m structure at room temperature. Resistivity, magnetic susceptibility, and heat capacity measurements using single crystals reveal two successive first-order phase transitions at Ts1 ​= ​265 ​K and Ts2 ​= ​123 ​K. At Ts1, the magnetic susceptibility is enormously reduced and a structural transition to a monoclinic structure takes place, while relatively small changes are observed at Ts2. Surprisingly, PbRe2O6 bears a close resemblance to another SOCM candidate Cd2Re2O7 despite crucial differences in the crystal structure and probably in the electronic structure, suggesting that PbRe2O6 is an SOCM.

Pyrochlore Oxide Superconductor Cd2Re2O7Revisited

The superconducting pyrochlore oxide Cd2Re2O7 is revisited with a particular emphasis on the sample-quality issue. The compound has drawn attention as the only superconductor (Tc = 1.0 K) that has been found in the family of {\alpha}-pyrochlore oxides since its discovery in 2001. Moreover, it exhibits two characteristic structural transitions from the cubic pyrochlore structure, with the inversion symmetry broken at the first one at 200 K. Recently, it has attracted increasing attention as a candidate spin-orbit coupled metal (SOCM), in which specific Fermi liquid instability is expected to lead to an odd-parity order with spontaneous inversion-symmetry breaking [L. Fu, Phys. Rev. Lett. 115, 026401 (2015)] and parity-mixing superconductivity [V. Kozii and L. Fu: Phys. Rev. Lett. 115 (2015) 207002; Y. Wang et al., Phys. Rev. B 93 (2016) 134512]. We review our previous experimental results in comparison with those of other groups in the light of the theoretical prediction of the SOCM, which we consider meaningful and helpful for future progress in understanding this unique compound.

Hund's Induced Fermi-Liquid Instabilities and Enhanced Quasiparticle Interactions.

Hund's coupling is shown to generally favor, in a doped half-filled Mott insulator, an increase in the compressibility culminating in a Fermi-liquid instability towards phase separation. The largest effect is found near the frontier between an ordinary and an orbitally decoupled ("Hund's") metal. The increased compressibility implies an enhancement of quasiparticle scattering, thus favoring other possible symmetry breakings. This physics is shown to happen in simulations of the 122 Fe-based superconductors, possibly implying the relevance of this mechanism in the enhancement of the critical temperature for superconductivity.

Fulde-Ferrell-Larkin-Ovchinnikov pairing as leading instability on the square lattice

We study attractively interacting spin-1/2 fermions on the square lattice subject to a spin population imbalance. Using unbiased diagrammatic Monte Carlo simulations we find an extended region in the parameter space where the Fermi liquid is unstable towards formation of Cooper pairs with non-zero center-of-mass momentum, known as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. In contrast to earlier mean-field and quasi-classical studies we provide quantitative and well-controlled predictions on the existence and location of the relevant Fermi-liquid instabilities. The highest temperature where the FFLO instability can be observed is about half of the superfluid transition temperature in the unpolarized system.

Universality and Scaling in a Charge Two-Channel Kondo Device.

We study a charge two-channel Kondo model, demonstrating that recent experiments [Z. Iftikhar etal, Nature (London) 526, 233 (2015)] realize an essentially perfect quantum simulation-not just of its universal physics, but also nonuniversal effects away from the scaling limit. Numerical renormalization group (RG) calculations yield conductance line shapes encoding RG flow to a critical point involving a free Majorana fermion. By mimicking the experimental protocol, the experimental curve is reproduced quantitatively over 9 orders of magnitude, although we show that far greater bandwidth/temperature separation is required to obtain the universal result. Fermi liquid instabilities are also studied: In particular, our exact analytic results for nonlinear conductance provide predictions away from thermal equilibrium, in the regime of existing experiments.

Functional renormalization and mean-field approach to multiband systems with spin-orbit coupling: Application to the Rashba model with attractive interaction

The functional renormalization group (RG) in combination with Fermi surface patching is a well-established method for studying Fermi liquid instabilities of correlated electron systems. In this article, we further develop this method and combine it with mean-field theory to approach multiband systems with spin-orbit coupling, and we apply this to a tight-binding Rashba model with an attractive, local interaction. The spin dependence of the interaction vertex is fully implemented in a RG flow without SU(2) symmetry, and its momentum dependence is approximated in a refined projection scheme. In particular, we discuss the necessity of including in the RG flow contributions from both bands of the model, even if they are not intersected by the Fermi level. As the leading instability of the Rashba model, we find a superconducting phase with a singlet-type interaction between electrons with opposite momenta. While the gap function has a singlet spin structure, the order parameter indicates an unconventional superconducting phase, with the ratio between singlet and triplet amplitudes being plus or minus one on the Fermi lines of the upper or lower band, respectively. We expect our combined functional RG and mean-field approach to be useful for an unbiased theoretical description of the low-temperature properties of spin-based materials.

Parity-Breaking Phases of Spin-Orbit-Coupled Metals with Gyrotropic, Ferroelectric, and Multipolar Orders.

We study Fermi liquid instabilities in spin-orbit-coupled metals with inversion symmetry. By introducing a canonical basis for the doubly degenerate Bloch bands in momentum space, we derive the general form of Landau interaction functions. A variety of time-reversal-invariant, parity-breaking phases is found, whose Fermi surface is spontaneously deformed and spin split. In terms of symmetry, these phases possess gyrotropic, ferroelectric, and multipolar orders. The ferroelectric and multipolar phases are accompanied by structural distortions, from which the electronic orders can be identified. The gyrotropic phase exhibits a unique nonlinear optical property. We identify correlated electron materials that exhibit these parity-breaking phases, including LiOsO(3) and Cd(2)Re(2)O(7).

Marginal Fermi liquid versus excitonic instability in three-dimensional Dirac semimetals

We study the different phases in the Quantum Electrodynamics of three-dimensional Dirac semimetals depending on the number $N$ of Dirac fermions, using renormalization group methods and the self-consistent resolution of the Schwinger-Dyson equation. We find that, for $N&lt;4$, a phase with dynamical generation of mass prevails at sufficiently strong coupling, sharing the same physics of the excitonic instability in two-dimensional Dirac semimetals. For $N\ensuremath{\ge}4$, we show that the phase diagram has instead a line of critical points characterized by the suppression of the quasiparticle weight at low energies, making the system fall into the class of marginal Fermi liquids. Such a boundary marks the transition to a kind of strange metal which can still be defined in terms of electron quasiparticles, but with parameters that have large imaginary parts implying an increasing deviation from the conventional Fermi liquid picture.

Sublattice interference in the kagome Hubbard model

We study the electronic phases of the kagome Hubbard model (KHM) in the weak coupling limit around van Hove filling. Through an analytic renormalization group analysis, we find that there exists a sublattice interference mechanism where the kagome sublattice structure affects the character of the Fermi surface instabilities. It leads to major suppression of Tc for d+id superconductivity in the KHM and causes an anomalous increase of Tc upon addition of longer-range Hubbard interactions. We conjecture that the suppression of conventional Fermi liquid instabilities makes the KHM a prototype candidate for hosting exotic electronic states of matter at intermediate coupling.

Ultracold gases of ytterbium: ferromagnetism and Mott states in an SU(6) Fermi system

It is argued that an ultracold quantum degenerate gas of ytterbium 173Yb atoms having nuclear spin I=5/2 exhibits an enlarged SU(6) symmetry. Within the Landau Fermi liquid theory, stability criteria against Fermi liquid (Pomeranchuk) instabilities in the spin channel are considered. Focusing on the SU(n>2) generalizations of ferromagnetism, it is shown within mean-field theory that the transition from the paramagnet to the itinerant ferromagnet is generically first order. On symmetry grounds, general SU(n) itinerant ferromagnetic ground states and their topological excitations are also discussed. These SU(n>2) ferromagnets can become stable by increasing the scattering length using optical methods or in an optical lattice. However, in an optical lattice at current experimental temperatures, Mott states with different filling are expected to coexist in the same trap, as obtained from a calculation based on the SU(6) Hubbard model.

Fermi liquid instabilities in two-dimensional lattice models

We develop a procedure for detecting Fermi liquid instabilities by extending the analysis of Pomeranchuk to two-dimensional lattice systems. The method is very general and straightforward to apply, thus, provides a powerful tool for the search of exotic phases. We test it by applying it to a lattice electron model with interactions leading to $s$- and $d$-wave instabilities.

Fermi-liquid instabilities at magnetic quantum phase transitions

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part, experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

Fermi liquid instabilities in the spin channel

We study the Fermi-surface instabilities of the Pomeranchuk type [Sov. Phys. JETP 8, 361 (1959)] in the spin-triplet channel with high orbital partial waves $[{F}_{l}^{a}(l&gt;0)]$. The ordered phases are classified into two classes, dubbed the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ phases by analogy to the superfluid $^{3}\mathrm{He}$ A and B phases. The Fermi surfaces in the $\ensuremath{\alpha}$ phases exhibit spontaneous anisotropic distortions, while those in the $\ensuremath{\beta}$ phases remain circular or spherical with topologically nontrivial spin configurations in momentum space. In the $\ensuremath{\alpha}$ phase, the Goldstone modes in the density channel exhibit anisotropic overdamping. The Goldstone modes in the spin channel have a nearly isotropic underdamped dispersion relation at small propagating wave vectors. Due to the coupling to the Goldstone modes, the spin-wave spectrum develops resonance peaks in both the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ phases, which can be detected in inelastic neutron-scattering experiments. In the $p$-wave channel $\ensuremath{\beta}$ phase, a chiral ground-state inhomogeneity is spontaneously generated due to a Lifshitz-like instability in the originally nonchiral systems. Possible experiments to detect these phases are discussed.

FUNCTIONAL RENORMALIZATION GROUP IN THE 2D HUBBARD MODEL

We review recent developments in functional renormalization group (RG) methods for interacting fermions. These approaches aim at obtaining an unbiased picture of competing Fermi liquid instabilities in the low-dimensional models like the two-dimensional Hubbard model. We discuss how these instabilities can be approached from various sides and how the fermionic RG flow can be continued into phases with broken symmetry.

Fermi liquid instabilities and superconductivity near quantum critical points in f-electron materials

ABSTRACTRecent experiments on single crystals of the compounds CeRh1−xCoxIn5 and PrOs4Sb12 are briefly reviewed. The temperature-composition (T-x) phase diagram of the heavy fermion pseudoternary system CeRh1−xCoxIn5, delineating the regions in which superconductivity, antiferromagnetism, and the coexistence of these two phenomena occur, has been established. Entropy vs x isotherms and residual resistivity vs x plots exhibit peaks near the critical concentration xcr ≈ 0.8 at which the Néel temperature appears to vanish (quantum critical point). The filled skutterudite compound PrOs4Sb12 exhibits unconventional superconductivity below Tc = 1.85 K that involves heavy fermion quasiparticles with an effective mass m* ≈ 50 me, where me is the mass of the free electron. The unconventional superconducting state appears to consist of several distinct superconducting phases and to break time reversal symmetry. A high field ordered phase occurs below ∼ 1 K and between ∼ 4.5 T and ∼ 15 T that appears to be associated with quadrupolar order. The heavy fermion state and superconductivity in PrOs4Sb12 may originate from the interaction between Pr3+ electric quadrupole moments and the charges of the conduction electrons. When Ru is substituted for Os in PrOs4Sb12, a minimum in Tc occurs at Pr(Os0.4Ru0.6)4Sb12, suggesting a competition between two types of superconductivity.