Anomalous thickness dependence of the vortex pearl length in few-layer NbSe2

The coexistence of multiple types of orders is a common thread in condensed matter physics and unconventional superconductors. The nature of superconducting orders may be unveiled by analyzing local perturbations such as vortices. For thin films, the vortex magnetic profile is characterized by the Pearl-length <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> , which is inversely proportional to the 2D superfluid density; hence, normally, also inversely proportional to the film thickness, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math> . Here we employ the scanning SQUID-on-tip microscopy to measure <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> in NbSe₂ flakes with thicknesses ranging from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn></mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>53</mml:mn></mml:math> layers. For <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi> <mml:mspace></mml:mspace> <mml:mo>></mml:mo> <mml:mspace></mml:mspace> <mml:mn>10</mml:mn></mml:math> , we find the expected dependence <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi> <mml:mo>∝</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mi>d</mml:mi></mml:math> . However, six-layer films show a sharp increase of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> deviating by a factor of three from the expected value. This value remains fixed for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn></mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>6</mml:mn></mml:math> . This unexpected behavior suggests the competition between two orders; one residing only on the first and last layers of the film while the other prevails in all layers.