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Physical review. B, Condensed matter

Superconductivity coupled to density waves

Nobuhiro Mitani, Susumu Kurihara

Published Aug 1, 1993• 4 citations
Publisher

Abstract

We investigate a mechanism of superconductivity on the basis of the nested-Fermi-liquid theory. A set of parquet equations is derived to investigate the instability towards superconductivity and spin- or charge-density-wave states. The phase diagram is examined on the basis of the parquet equations. We find that the polarization mode of the marginal-Fermi-liquid-type is of vital importance to superconductivity. We also discuss the properties of a superconductor on the basis of the nested Fermi liquid.

DOI
10.1103/physrevb.48.3356

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We investigate a mechanism of superconductivity on the basis of the nested-Fermi-liquid theory. A set of parquet equations is derived to investigate the instability towards superconductivity and spin- or charge-density-wave states. The phase diagram is examined on the basis of the parquet equations. We find that the polarization mode of the marginal-Fermi-liquid-type is of vital importance to superconductivity. We also discuss the properties of a superconductor on the basis of the nested Fermi liquid.
We study instabilities occurring in the electron system whose Fermi surface has flat regions on its opposite sides. Such a Fermi surface resembles Fermi surfaces of some high-Tc{\mathrm{T}}_{\mathrm{c}}Tc​ superconductors. In the framework of the parquet approximation, we classify possible instabilities and derive renormalization-group equations that determine the evolution of corresponding susceptibilities with decreasing temperature. Numerical solutions of the parquet equations are found to be in qualitative agreement with a ladder approximation. For the repulsive Hubbard interaction, the antiferromagnetic (spin-density-wave) instability dominates, but when the Fermi surface is not perfectly flat, the d-wave superconducting instability takes over.
We present an analytic theory unraveling the microscopic mechanism of instabilities within interacting DDD-dimensional Fermi liquid. Our model consists of a DDD-dimensional electron gas subject to an instantaneous electron-electron interaction of a finite range exceeding the average interparticle distance. Pair, charge, and spin susceptibilities are evaluated via the one-loop renormalization group theory and via the bosonization approach, giving identical results. In case of a repulsive interaction, we identify an intrinsic Fermi-liquid instability towards insulating spin- and charge-density-wave order when the interaction coupling strength reaches a universal critical value. If both electron and hole pockets of the same size are present, the ground state is an excitonic insulator at arbitrarily small repulsive interaction. If the interaction is attractive, the ground state is a singlet non-BCS superconductor with a uniform condensate. In case if both electron and hole Fermi surfaces are present, we predict an instability towards the interpocket pair-density-wave ordering at the critical coupling. This prediction lends strong theoretical support to the pair-density-wave scenario of superconductivity in cuprate materials. Due to its simple and universal nature, presented microscopic mechanism of intrinsic instabilities of interacting DDD-dimensional Fermi liquids constitutes a solid theoretical ground for understanding quantum phase transitions in a variety of quantum materials, from ultraclean semiconductor quantum wells to high-temperature superconductors.
We study a model of strongly-correlated systems that incorporates phases such as Fermi liquids, non-Fermi liquids, and superconductivity, in addition to potential intertwined orders. The model describes Fermi surfaces of spinful electron gas or electron liquid coupled to bosons via an intermediate gauge field. Effectively, the coupling imposes constraints and interactions between the fermion spin and the local boson density. This grants the bosons the meaning as the Schwinger boson of the magnetic order and allows us to probe a larger phase space, rather than around the quantum critical point. We design the initial model so that after the boson and gauge fields are integrated out exactly, the resulting fermion-only effective theory only consists of several local interactions, allowing controlled weak-coupling interpretation for certain parameter regions. Consequently, we find a non-Fermi liquid whose degrees of freedom in the effective theory take the form of an \emph{emergent} Fermi surface that has a different Luttinger volume from the original fermions, therefore explicitly violates the Luttinger theorem. Further, this allows a ddd-wave superconducting instability if the effective interacting induced by boson coupling is in the relevant pairing channel. When the emergent Fermi surface undergoes a Lifshitz transition, the carrier type changes. In addition, we attribute the Mott insulating behavior in the strong coupling limit to the loss of emergent Fermi surface and argue the possibility of coexisting magnetic order. Our effective theory also suggests the possibility of charge density waves as a consequence of \emph{effective} strong repulsion and is independent of the Fermi-surface-nesting scenario. We discuss the possible optimal conditions for higher superconducting transition temperature and potential relevances and implications for realistic materials.
We will take the low- T Fermi liquid state of Section 11.2.2 in dimensions d ≥ 2 (or its spinful generalization) and examine the nature of its instabilities to other ground states of a dense gas of fermions. Possibilities include ferromagnets, states in which there is spin or charge density wave order (to be defined more precisely below), or various types of superconductors. All of these cases are of considerable practical importance and have numerous experimental applications. A theoretical treatment of the quantum transition between a Fermi liquid and a magnetically or charge ordered state was given in a paper by Hertz, although many important points were anticipated in earlier work. We shall present Hertz's basic arguments in Section 12.1 for the case of a transition between a Fermi liquid and a spin density wave state. We shall not treat the other cases here and will, instead, refer the reader to the literature. There are a number of reasons for this neglect: (i) Many aspects of these transitions are not fully understood (we will note some below) and are the subject of considerable debate in the literature; it is therefore inappropriate to include them in this introductory treatment. (ii) We shall only consider systems in spatial dimensions d ≥ 2 here (the d = 1 case requires a separate treatment appropriate to Tomonaga–Luttinger liquids and will be addressed in Chapter 14). […]
The aim of this thesis it to contribute to three open problems in the theory of itinerant electron systems in two spatial dimensions. Firstly, the mechanism for charge density wave formation in the transition metal dichalcogenides is a debated subject. In this thesis it is shown that charge density wave formation is possible via a purely electronic mechanism in monolayer vanadium diselenide. The competition of superconductivity and density wave formation is taken into account using the renormalisation group. As the Fermi surface is tuned to perfect nesting, a charge density wave phase emerges when the Heisenberg exchange interaction is of the order of the contact Coulomb repulsion. Secondly, the search for materials which exhibit topological superconductivity is ongoing. Possible candidates are strongly spin-orbit-coupled metals. In this thesis a square-lattice Hubbard model with strong Rashba spin-orbit coupling and one of the Fermi surfaces close to a Lifshitz transition is examined. The metal is shown to be generically unstable to the formation of mixed-parity superconductivity with a helical triplet component via a renormalisation group analysis. Thirdly, the breakdown of Fermi liquid theory close to a quantum critical point is still not well understood. In this thesis a functional renormalisation group analysis is presented using a soft frequency cutoff, investigating a general class of Pomeranchuk instabilities with 𝑁_𝑏 flavours of boson. At small 𝑁_𝑏 the theory is characterised by weakly non-Fermi-liquid behaviour of the electrons and 𝑧≈2 dynamics for the order parameter fluctuations. For large 𝑁_𝑏, the theory crosses over to 𝑧≈1 scaling and non-Fermi-liquid behaviour.
We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |∆|, where ∆ is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the |∆|2 shift predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by copper based high temperature superconductors. Based on spin and charge fractionalization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductivity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractionalization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as “nodal-antinodal dichotomy” at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such universal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs.