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Physical review. B, Condensed matter

Two-dimensional Bose liquid with strong gauge-field interaction

M. V. Feigel’man, V. B. Geshkenbeǐn, L. B. Ioffe, A. I. Larkin

Published Dec 1, 1993• 82 citations
Publisher

Abstract

Two unrelated problems can be reduced to a model of a Bose gas interacting with a gauge field: (i) the effect of thermal fluctuations on a system of vortices in bulk superconductors in fields ${\mathit{H}}_{\mathit{c}1}$\ensuremath{\ll}H\ensuremath{\ll}${\mathit{H}}_{\mathit{c}2}$, and (ii) charged, spinless excitations in two-dimensional (2D) strongly correlated electron systems. Both problems are important for the theory of high-temperature superconductors. We study this model in three regimes: at finite temperatures, assuming that the gauge field is purely transverse; at T=0, for the purely static (2D Coulomb) interaction; and at T=0, for a weak Coulomb interaction and a strong transverse one. Transverse interactions suppress the temperature of the superfluid transition significantly. A sufficiently strong transvese interaction is shown to produce a phase separation as the temperature decreases (in the absence of Coulomb repulsion). If there is Coulomb repulsion, the ground state does not have off-diagonal long-range order but the superfluid density is not zero unless the Coulomb constant exceeds a critical value. Sufficiently strong coupling to the transverse field destroys superfluidity as well. In the normal state formed at large couplings, the translational invariance is intact. We propose a bosonic ground state that is not superfluid at T=0. We discuss the implications of these results both for vortex liquids and strongly correlated electron systems.

DOI
10.1103/physrevb.48.16641

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Two unrelated problems can be reduced to a model of a Bose gas interacting with a gauge field: (i) the effect of thermal fluctuations on a system of vortices in bulk superconductors in fields Hc1{\mathit{H}}_{\mathit{c}1}Hc1​\ensuremath{\ll}H\ensuremath{\ll}Hc2{\mathit{H}}_{\mathit{c}2}Hc2​, and (ii) charged, spinless excitations in two-dimensional (2D) strongly correlated electron systems. Both problems are important for the theory of high-temperature superconductors. We study this model in three regimes: at finite temperatures, assuming that the gauge field is purely transverse; at T=0, for the purely static (2D Coulomb) interaction; and at T=0, for a weak Coulomb interaction and a strong transverse one. Transverse interactions suppress the temperature of the superfluid transition significantly. A sufficiently strong transvese interaction is shown to produce a phase separation as the temperature decreases (in the absence of Coulomb repulsion). If there is Coulomb repulsion, the ground state does not have off-diagonal long-range order but the superfluid density is not zero unless the Coulomb constant exceeds a critical value. Sufficiently strong coupling to the transverse field destroys superfluidity as well. In the normal state formed at large couplings, the translational invariance is intact. We propose a bosonic ground state that is not superfluid at T=0. We discuss the implications of these results both for vortex liquids and strongly correlated electron systems.
We study an effective action of bosons interacting with a gauge field, which is derived from the t-J model in the slave-boson approach. We use a renormalization-group (RG) scheme to calculate the temperature TBE{\mathit{T}}_{\mathrm{BE}}TBE​ below which the bosons start to condense in a superfluid state. One expects that a strongly fluctuating gauge field tends to destroy this superfluid state. Our numerical calculations indeed show that the presence of a gauge field suppresses the onset of superfluidity. This suppression is partly due to quantum fluctuations, and partly due to thermal excitations of the gauge field. An analytical calculation of the flow in the classical regime T(l)\ensuremath{\gg}1 shows that our perturbative RG scheme provides an expansion of the suppression of TBE{\mathit{T}}_{\mathrm{BE}}TBE​ in powers of q002{\mathit{q}}_{00}^{2}q002​/u0{\mathit{u}}_{0}u0​, where q002{\mathit{q}}_{00}^{2}q002​ is the coupling constant of the gauge field, and u0{\mathit{u}}_{0}u0​ is the short-range repulsion between the bosons. The RG scheme breaks down if q002{\mathit{q}}_{00}^{2}q002​/u0{\mathit{u}}_{0}u0​\ensuremath{\gtrsim}1, in which case one gets into the strong-coupling limit. Thus unfortunately the RG scheme is not reliable for the strong-coupling problem, which is appropriate for the t-J model with t/J\ensuremath{\sim}1.
A simple model of a degenerate two-dimensional Bose liquid interacting with a fluctuating gauge field is investigated as a possible candidate to describe the charge degree of freedom in the normal state of the cuprate superconductors. We show that the fluctuating gauge field efficiently destroys superfluidity even in the Bose degenerate regime. We discuss the nature of the resulting normal state in terms of the geometric properties of the imaginary-time paths of the bosons. We will also present numerical results on the transport properties and the density correlations in the system. We find a transport scattering rate of \ensuremath{\hbar}/${\mathrm{\ensuremath{\tau}}}_{\mathrm{}\mathrm{tr}}$\ensuremath{\sim}2kB{2\mathrm{k}}_{\mathrm{B}}2kB​T, consistent with the experiments on the cuprates in the normal state. We also find that the density correlations of our model resemble the charge correlations of the t-J model.
This review gives a rather general discussion of high temperature superconductors as an example of a strongly correlated material. The argument is made that in view of the many examples of unconventional superconductors discovered in the past twenty years, we should no longer be surprised that superconductivity emerges as a highly competitive ground state in systems where Coulomb repulsion plays a dominant role. The physics of the cuprates is discussed, emphasizing the unusual pseudogap phase in the underdoped region. It is argued that the resonating valence bond picture, as formulated using gauge theory with fermionic and bosonic matter fields, gives an adequate physical understanding, even though many details are beyond the powers of current calculational tools. The recent discovery of quantum oscillations in a high magnetic field is discussed in this context. Meanwhile, the problem of the quantum spin liquid (a spin system with antiferromagnetic coupling which refuses to order even at zero temperature) is a somewhat simpler version of the high T c problem where significant progress has been made recently. It is understood that the existence of matter fields can lead to deconfinement of the U (1) gauge theory in 2 + 1 dimensions, and novel new particles (called fractionalized particles), such as fermionic spinons which carry spin and no charge, and gapless gauge bosons can emerge to create a new critical state at low energies. We even have a couple of real materials where such a scenario may be realized experimentally. The paper ends with answers to questions such as: What limits T c if pairing is driven by an electronic energy scale? Why is the high T c problem hard? Why is there no consensus? And why is the high T c problem important?
A square-lattice gauge-theory model for the holon liquid existing in the unconventional metallic phases of strongly interacting two-dimensional electron liquids is introduced. The phase of the holon order parameter couples in a gauge-invariant way to a statistical gauge field, which arises from strong-interaction physics. We find that the superfluid transition that exists in the absence of statistical gauge-field excitations in the holon liquid turns into a crossover phenomenon in the presence of such fluctuations. The corresponding high-temperature phase shows a T-linear resistance, while the low-temperature phase exhibits a T2{\mathit{T}}^{2}T2 dependence for the resistance. The crossover temperature scale Tc0{\mathit{T}}_{\mathit{c}0}Tc0​ vanishes, however, in the limit of maximum statistical fluctuations. While we find that statistical gauge-field excitations are strictly gapless, the residue of the pole corresponding to such excitations becomes exponentially small at temperatures small in comparison to Tc0{\mathit{T}}_{\mathit{c}0}Tc0​.
The properties of phase transitions and the types of order present in the low-temperature states of matter are fundamentally dependent on the dimensionality of physical systems. Generally, highly ordered states are more robust in higher dimensions, while thermal and quantum fluctuations, which favour disordered states, play a more important role in lower dimensions. The case of a two-dimensional (2d) Bose fluid is particularly fascinating because of its "marginal" behaviour. In an infinite uniform 2d fluid thermal fluctuations at any non-zero temperature are strong enough to destroy the fully ordered state associated with Bose--Einstein condensation, but are not strong enough to suppress superfluidity in an interacting system at low, but non-zero temperatures. Further, the presence of residual "quasi-long-range" order at low temperatures leads to an interesting interplay between superfluidity and condensation in all experimentally relevant finite-size systems. In these notes we give an introduction to the physics of 2d Bose fluids from an atomic physics perspective. Our goal is to summarize the recent progress in theoretical understanding and experimental investigation of ultra-cold atomic gases confined to 2d geometry, and we also hope to provide a useful introduction to these systems for researchers working on related topics in other fields of physics.
In this thesis, we study various issues arising from the QED theory of underdoped, high temperature superconductors in 2+1 dimensions. The theory breaks up roughly into two sectors: fermionic and bosonic. With regard to the fermionic sector, we consider confinement of the emergent gauge field which we take to be compact. In the absence of fermions, the interaction between monopoles is Coulombic and the well known result is that the pure gauge theory is permanently confining. With the addition of fermions, the interaction becomes logarithmic, and an analogy with the usual Kosterlitz-Thouless transition suggests a deconfinement transition for the fermions. We show, however, that, when screening is taken into account, the deconfined phase is destabilized and fermions remain permanently confined. The bosonic sector models Cooper pair phase fluctuations, whose effect on the depletion of the superfluid density we examine in two separate studies. In the first of these, we study the quantum XY model, and show that the quasi-two dimensionality, low critical temperatures and large d-wave gap characteristic of underdoped cuprates severely constrain the form of the superfluid density. Under these assumptions, we find that phase fluctuations alone are insufficient to account for recent observations of deviations from Uemura scaling, and that the quasiparticle contribution is a necessity. We use our results to satisfactorily fit the recent data. In the second study, we model the cuprates by a layered system of interacting bosons and examine the collective excitations in this system. Depending on the anisotropy and the interaction strength, we find find four different regimes of temperature dependence of the superfluid density. We argue that interactions in the underdoped cuprates are effectively short-ranged and weak. Finally, we study the related issue of disordered, interacting bosons in the large-N limit and 2 strong commensuration. Perturbatively at weak disorder and numerically at strong, we show that th screening of the random potential due to interactions is insufficient to delocalize the single-particl states so that no superfluid transition occurs from the Mott insulator.