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Journal of Experimental and Theoretical Physics Letters

Phase diagram of a 2D metal system with a variable number of carriers

V. P. Gusynin, В. М. Локтев, Sergei G. Sharapov

Published Jan 1, 1997• 44 citations
Publisher

Abstract

It is shown that the phase diagram of a 2D metal undergoing a superconducting transition consists of regions of a normal phase where the modulus of the order parameter is absent, an “anomalous normal” phase where the modulus of the order parameter is different from zero but the phase of the order parameter is a random quantity, and a Berezinskii-Kosterlitz-Thouless phase. The characteristic temperatures of transitions between the phases and the behavior of the chemical potential as a function of the fermion density and temperature are found.

DOI
10.1134/1.567308

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It is shown that the phase diagram of a 2D metal undergoing a superconducting transition consists of regions of a normal phase where the modulus of the order parameter is absent, an “anomalous normal” phase where the modulus of the order parameter is different from zero but the phase of the order parameter is a random quantity, and a Berezinskii-Kosterlitz-Thouless phase. The characteristic temperatures of transitions between the phases and the behavior of the chemical potential as a function of the fermion density and temperature are found.
A phase diagram for a 2D metal with variable carrier density has been derived. It consists of a normal phase, where the order parameter is absent: a so-called “abnormal normal” phase where this parameter is also absent but the mean number of composite bosons (bound pairs) exceeds the mean number of free fermions; a pseudogap phase where the absolute value of the order parameter gradually increases but its phase is a random value, and finally a superconducting (here Berezinskii-Kosterlitz-Thouless) phase. The characteristic transition temperatures between these phases are found. The chemical potential and paramagnetic susceptibility behavior as functions of the fermion density and the temperature are also studied. An attempt is made to qualitatively compare the resulting phase diagram with the features of underdoped high-T c superconducting compounds above their critical temperature.
A phase diagram for a two-dimensional metal with variable carrier density has been studied using the modulus-phase representation for the order parameter in fully microscopic treatment. This amounts to splitting the degrees of freedom into neutral fermion and charged boson degrees of freedom. Although true long range order is forbidden in two dimensions, long range order for the neutral fermions is possible since this does not violate any continuous symmetry. The phase fluctuations associated with the charged degrees of freedom destroy long range order in the full system as expected. The presence of the neutral order parameter gives rise to new features in the superconducting condensate formation in low-dimensional systems. The resulting phase diagram contains a new phase which lies above the superconducting (here Berezinskii–Kosterlitz–Thouless) phase and below the normal (Fermi-liquid) phase. We identify this phase with the pseudogap phase observed in underdoped high-T c superconducting compounds above their critical temperature. We also find that the phase diagram persists even in the presence of weak 3-dimensionalisation.
Abstract We discuss the evolution from Bardeen-Cooper-Schrieffer (BCS) to Bose superconductivity vs . carrier density n in two-dimensional (2D) gated superconductors and address the fundamental role that the interaction range plays in the Berezinskii-Kosterlitz-Thouless transition. We investigate the density dependence of the critical temperature ( T c ), superfluid density, order parameter modulus, chemical potential and pair size. Our most important finding is that it is absolutely essential to include classical and quantum phase fluctuations, as well as finite-ranged interactions to explain the non-monotonic behavior of T c vs . n and to guarantee that the upper bound on T c is not exceeded in 2D superconductors, as experimentally observed in (Nakagawa Y. et al. , Science , 372 (2021) 190), a lithium-intercalated layered nitride, and in magic-angle twisted trilayer graphene (Park J. M. et al. , Nature , 590 (2021) 249). Furthermore, we show that we can extract, from measurements of T c and the order parameter modulus, the effective mass of charge carriers and their interaction strength and range.
An attempt is made to analyze the state-of-the-art in the description of the superconducting phase in 2D metals with an arbitrary carrier density. It is shown that a decrease in the density leads to a nontrivial equation for chemical potential μ, in particular, to the inequality μ ≠ εF including μ < 0 (εF is the Fermi energy). In this case, the region of μ ≃ 0 corresponds to a transition (crossover) from Cooper pairing (with strongly overlapping pairs) and from the description of superconductivity in terms of the BCS–Bogoliubov theory to local (nonoverlapping) pairs and their Bose–Einstein condensation. Some examples of such a crossover are discussed.