Using an asymmetric two-leg ladder comprising pairing and metallic chains, this Letter proves the striking power of reservoir-mediated boosting of superconductivity. Using many-body numerics on large systems at zero and finite temperature, we unravel the processes by which the metal parameters can impact the effective pairing strength and the ranged pair-pair coupling mediated by the metal. These then enhance key superconducting properties far above those of the isolated system. Thus, our Letter identifies a general mechanism by which reservoirs can strongly suppress the effects of the Mermin-Wagner theorem in finite-sized systems, allowing even large one-dimensional systems to appear practically ordered.
Using an asymmetric two-leg ladder comprising pairing and metallic chains, this Letter proves the striking power of reservoir-mediated boosting of superconductivity. Using many-body numerics on large systems at zero and finite temperature, we unravel the processes by which the metal parameters can impact the effective pairing strength and the ranged pair-pair coupling mediated by the metal. These then enhance key superconducting properties far above those of the isolated system. Thus, our Letter identifies a general mechanism by which reservoirs can strongly suppress the effects of the Mermin-Wagner theorem in finite-sized systems, allowing even large one-dimensional systems to appear practically ordered.
In this letter we consider D-dimensional interacting Fermi liquids, and demonstrate that an attractive interaction with a finite range Rs that is much greater than the Fermi wavelength λF breaks the conventional BCS theory of superconductivity. In contrast to the BCS prediction of a finite superconducting gap for all attractive contact interactions, we show that a finite-range interaction does not induce a superconducting gap. Instead, the pair susceptibility develops a power-law singularity at zero momentum and zero frequency signaling quantum critical behavior without long-range ordering. Starting from this, we show that superconductivity can be stabilized by adding a short-range attractive interaction, which is always present in real electronic systems. As an example, we consider a layered quasi-two-dimensional material with attractive electron-electron interactions mediated by optical phonons. We demonstrate a dome shape of the critical temperature Tc versus doping, strongly suppressed isotope effect, and a weak dependence of the optimal doping and maximal Tc∗∼0.1EF on the interaction range at Rs≫λF, EF is the Fermi energy. We believe that these results could be relevant to high-temperature superconductors.
In this Letter we consider D-dimensional interacting Fermi liquids, and demonstrate that an attractive interaction with a finite range R_{s} that is much greater than the Fermi wavelength λ_{F} breaks the conventional BCS theory of superconductivity. In contrast to the BCS prediction of a finite superconducting gap for all attractive contact interactions, we show that a finite-range interaction does not induce a superconducting gap. Instead, the pair susceptibility develops a power-law singularity at zero momentum and zero frequency signaling quantum critical behavior without long-range ordering. Starting from this, we show that superconductivity can be stabilized by adding a short-range attractive interaction, which is always present in real electronic systems. As an example, we consider a layered quasi-two-dimensional material with attractive electron-electron interactions mediated by optical phonons. We demonstrate a dome shape of the critical temperature T_{c} versus doping, strongly suppressed isotope effect, and a weak dependence of the optimal doping and maximal T_{c}^{*}∼0.1E_{F} on the interaction range at R_{s}≫λ_{F}, E_{F} is the Fermi energy. We believe that these results could be relevant to high-temperature superconductors.
Decades after the discovery of high-temperature superconductivity, understanding the effects of doping a Mott insulator remains a topic of great relevance, since the fundamental excitations in the normal state are not known, nor the precise origin of the pairing mechanism. In particular, the nature of the pseudogap phase at finite temperatures, above the superconducting dome, or the redistribution of spectral weight observed in experiments indicate that our knowledge is incomplete and theories may be missing some key ingredients.Due to the two-dimensionality of the problem and the limitations imposed by the Mermin-Wagner theorem, the numerical study of these questions is remarkably difficult: most treatments are either limited to small or quasi one-dimensional systems at zero temperature, or simulations may be carried out at finite temperature, completely missing the possibility for long-range order. In this dissertation, we tackle paradigmatic problems in condensed matter from a fundamentally new perspective. We numerically study interacting chains and ladders introducing RKKY-like SU(2)-symmetric long-range interactions that allow one to realize actual spontaneous symmetry breaking and true antiferromagnetic order. We shed new light on problems such as the role of magnetic order on quasi-particle formation and fractionalization, and pairing instabilities in generalized Hubbard-like models. In particular, we address questions of a very fundamental nature: (i) How do spinons evolve into magnons and what are their signatures in the excitation spectrum? (ii) how do coherent quasi-particles form in the presence of long range order? Will we still observe signatures of spin-charge separation in the spectrum? (iii) what is the interplay between long-range antiferromagnetic order and pairing? Our work offers new insight onto the role played by long-range antiferromagnetism in quasi-particle formation and pairing in the context of new toy-models that realize much of the phenomenology of their higher dimensional counterparts.--Author's abstract
Using computational techniques, it is shown that pairing is a robust property of hole-doped antiferromagnetic insulators. In one dimension and for two-leg ladder systems, a BCS-like variational wave function with long-bond spin singlets and a Jastrow factor provides an accurate representation of the ground state of the t-J model, even though strong quantum fluctuations destroy the off-diagonal superconducting long-range order in this case. However, in two dimensions it is argued-and numerically confirmed using several techniques, especially quantum Monte Carlo-that quantum fluctuations are not strong enough to suppress superconductivity.
After a brief discussion of the Bogoliubov inequality and possible generalizations thereof, we present a complete review of results concerning the Mermin-Wagner theorem for various many-body systems, geometries and order parameters. We extend the method to cover magnetic phase transitions in the periodic Anderson model as well as certain superconducting pairing mechanisms for Hubbard films. The relevance of the Mermin-Wagner theorem to approximations in many-body physics is discussed on a conceptual level.
Abstract Conventional superconductivity emerges from pairing of charge carriers—electrons or holes—mediated by phonons 1 . In many unconventional superconductors, the pairing mechanism is conjectured to be mediated by magnetic correlations 2 , as captured by models of mobile charges in doped antiferromagnets 3 . However, a precise understanding of the underlying mechanism in real materials is still lacking and has been driving experimental and theoretical research for the past 40 years. Early theoretical studies predicted magnetic-mediated pairing of dopants in ladder systems 4–8 , in which idealized theoretical toy models explained how pairing can emerge despite repulsive interactions 9 . Here we experimentally observe this long-standing theoretical prediction, reporting hole pairing due to magnetic correlations in a quantum gas of ultracold atoms. By engineering doped antiferromagnetic ladders with mixed-dimensional couplings 10 , we suppress Pauli blocking of holes at short length scales. This results in a marked increase in binding energy and decrease in pair size, enabling us to observe pairs of holes predominantly occupying the same rung of the ladder. We find a hole–hole binding energy of the order of the superexchange energy and, upon increased doping, we observe spatial structures in the pair distribution, indicating repulsion between bound hole pairs. By engineering a configuration in which binding is strongly enhanced, we delineate a strategy to increase the critical temperature for superconductivity.