Constraints on superconducting pairing in altermagnets
Debmalya Chakraborty, Annica M. Black‐Schaffer
Abstract
Superconductivity in the recently discovered altermagnetic materials hosts large prospects for both fundamental physics and technological applications. In this work, we show that a characteristic spin-sublattice locking in altermagnets puts severe constraints on possible superconducting pairing. In particular, by considering the archetypical two-band model for a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>d</a:mi> <a:mrow> <a:msup> <a:mi>x</a:mi> <a:mn>2</a:mn> </a:msup> <a:mo>−</a:mo> <a:msup> <a:mi>y</a:mi> <a:mn>2</a:mn> </a:msup> </a:mrow> </a:msub> </a:math> -wave altermagnet on a square lattice, we uncover that the most common form of superconductivity, uniform <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>s</b:mi> </b:math> -wave spin-singlet pairing is not possible to achieve in altermagnets. Instead, we find that the most likely forms of spin-singlet pairing have <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msub> <c:mi>d</c:mi> <c:mrow> <c:msup> <c:mi>x</c:mi> <c:mn>2</c:mn> </c:msup> <c:mo>−</c:mo> <c:msup> <c:mi>y</c:mi> <c:mn>2</c:mn> </c:msup> </c:mrow> </c:msub> </c:math> - or extended <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>s</d:mi> </d:math> -wave symmetry. We also find that the simplest form of equal-spin-triplet <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>p</e:mi> </e:math> -wave pairing is not allowed, but only a mixed-spin-triplet <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi>p</f:mi> </f:math> -wave state can exist. We verify these constraints on the superconducting pairing also within an interaction-induced model of altermagnetism, where we further establish their validity for finite-momentum pairing. Additionally we discuss the possible pairing symmetries for odd-frequency superconducting pairing. Due to the generality of our results, they are applicable to both intrinsic superconductivity and proximity-induced superconductivity in altermagnet-superconductor hybrid junctions.