Physical limitations of the Hohenberg–Mermin–Wagner theorem

Scientific paper - Original scientific paper

• Author: Grgur Palle
• Author: Denis Karl Sunko
• Author's institution: University of Zagreb; Faculty of Science; (Department of Physics)
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract (english)

The Hohenberg–Mermin–Wagner (HMW) theorem states that infrared (IR) fluctuations prevent long-range order which breaks continuous symmetries in two dimensions (2D), at finite temperatures. We note that the theorem becomes physically effective for superconductivity (SC) only for astronomical sample sizes, so it does not prevent 2D SC in practice. We systematically explore the sensitivity of the magnetic and SC versions of the theorem to finite-size and disorder effects. For magnetism, finite-size effects, disorder, and perpendicular coupling can all restore the order parameter at a non-negligible value of Tc equally well, making the physical reason for finite Tc sample-dependent. For SC, an alternative version of the HMW theorem is presented, in which the temperature cutoff is set by Cooper pairing, in place of the Fermi energy in the standard version. It still allows 2D SC at 2–3 times the room temperature when the interaction scale is large and Cooper pairs are small, the case with high-Tc SC in the cuprates. Thus IR fluctuations do not prevent 2D SC at room temperatures in samples of any reasonable size, by any known version of the HMW argument. A possible approach to derive mechanism-dependent upper bounds for SC Tc is pointed out.

• Keywords (english): Mermin-Wagner theorem; infrared fluctuations; 2D systemssuperconductivity; disorder; finite-size effects
• Language: english
• Publication type: Scientific paper - Original scientific paper
• Publication status: Published
• Peer review: Peer review - international
• Publication version: Published version
• Journal title: Journal of Physics A: Mathematical and Theoretical
• Numbering: vol. 54, no. 31, 315001
• p-ISSN: 1751-8113
• e-ISSN: 1751-8121
• DOI: https://doi.org/10.1088/1751-8121/ac0a9d
• URN:NBN: urn:nbn:hr:217:896476
• Publication: 2021-07-01
• Project: Number: IP-2018-01-7828; Title (croatian): Sulfasoli: nova generacija kompleksnih funkcionalnih materijala; Title (english): Sulfosalts: new generation of complex fuctional materials; Acronym: SulfNewFunMat; Leader: Denis Sunko; Jurisdiction: Croatia; Funding stream: Research Projects
• Document URL: https://iopscience.iop.org/article/10.1088/1751-8121/ac0a9d
• Type of resource: Text
• Access conditions: Open access
• Public note: © 2021 The Author(s). Published by IOP Publishing Ltd. Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 24 February 2021. Revised 20 May 2021. Accepted for publication 11 June 2021. Published 1 July 2021.
• Created on: 2024-09-29 11:23:52