Pressure-induced enhancement of superfluid density in transition metal dichalcogenides with and without charge density wave

Gaining a deeper understanding of the interplay between charge density wave (CDW) order and superconductivity in transition metal dichalcogenides (TMDs), particularly within the (4H/2H)-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mrow><a:mi>Nb</a:mi><a:mi>X</a:mi></a:mrow><a:mn>2</a:mn></a:msub><a:mo> </a:mo><a:mrow><a:mo>(</a:mo><a:mi>X</a:mi><a:mo>=</a:mo><a:mi>Se</a:mi></a:mrow></a:math> and S) family, remains an open and intriguing challenge. A systematic microscopic study across various compounds in this family is therefore required to unravel this complex interplay. Here, we report on muon spin rotation (µSR) and magnetotransport experiments investigating the effects of hydrostatic pressure on the superconducting transition temperature (<b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>T</b:mi><b:mi mathvariant="normal">c</b:mi></b:msub></b:math>), the temperature-dependent magnetic penetration depth (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>λ</d:mi><d:mi>eff</d:mi></d:msub></d:math>), and the charge density wave order (CDW) in two layered chalcogenide superconductors: 4H-<e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi>NbSe</e:mi><e:mn>2</e:mn></e:msub></e:math>, which exhibits CDW order, and 2H-<f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi>NbS</f:mi><f:mn>2</f:mn></f:msub></f:math>, which lacks such order. Our observations reveal a substantial <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mn>75</g:mn><g:mo>%</g:mo></g:mrow></g:math> enhancement of the superfluid density (<h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:msub><h:mi>n</h:mi><h:mi>s</h:mi></h:msub><h:mo>/</h:mo><h:msup><h:mi>m</h:mi><h:mo>*</h:mo></h:msup></h:mrow></h:math>) in 4H-<i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:msub><i:mi>NbSe</i:mi><i:mn>2</i:mn></i:msub></i:math> upon the maximum applied pressure of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mo>∼</j:mo><j:mn>2</j:mn></j:math> GPa, surpassing that of 2H-<k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:msub><k:mi>NbSe</k:mi><k:mn>2</k:mn></k:msub></k:math>. Despite the absence of CDW order, a sizable <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:mn>20</l:mn><l:mo>%</l:mo></l:mrow></l:math> growth in superfluid density is also observed for 2H-<m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub><m:mi>NbS</m:mi><m:mn>2</m:mn></m:msub></m:math> under an applied pressure of 1.8 GPa. Notably, the evaluated superconducting gaps in all these TMDs remain largely unaffected by changes in applied pressure, irrespective of pressure-induced partial suppression of CDW order in (4H/2H)-<n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:msub><n:mi>NbSe</n:mi><n:mn>2</n:mn></n:msub></n:math> or its general absence in 2H-<o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:msub><o:mi>NbS</o:mi><o:mn>2</o:mn></o:msub></o:math>. These results underscore the complex nature of pressure-induced behaviors in these TMDs, challenging a simplistic view of competition solely between CDW order and superconductivity. Remarkably, the relationship between <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"><p:mrow><p:msub><p:mi>n</p:mi><p:mi>s</p:mi></p:msub><p:mo>/</p:mo><p:msup><p:mi>m</p:mi><p:mo>*</p:mo></p:msup></p:mrow></p:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"><q:msub><q:mi>T</q:mi><q:mi mathvariant="normal">c</q:mi></q:msub></q:math> exhibits an unconventional correlation, indicating a noteworthy similarity with the behavior observed in cuprate, kagome, and iron-based superconductors.