Pressure-modulated competition between dual charge density waves in NbS e 3

Controlling collective electronic states through clean and reversible external stimuli is crucial for realizing functional quantum materials. Here, we report a study on temperature ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>T</a:mi> </a:mrow> </a:math> ) and pressure ( <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>P</b:mi> </b:mrow> </b:math> )-tuned charge-density-wave (CDW) orders in the quasi-one-dimensional system of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>NbS</c:mi> <c:msub> <c:mi mathvariant="normal">e</c:mi> <c:mn>3</c:mn> </c:msub> </c:mrow> </c:math> , through single-crystal x-ray diffraction, and electric and magnetotransport measurements. A refined and extended phase diagram is presented, prompting a reevaluation of earlier claims regarding the coexistence of CDW and superconductivity (SC). Here, SC is found to emerge only once all long-range CDWs are suppressed. Notably, the anomalous Hall and magnetoresistance (MR) effects observed at low pressure ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>LP</e:mi> <e:mo>∼</e:mo> <e:mn>0.8</e:mn> <e:mspace width="0.16em"/> <e:mi>GPa</e:mi> </e:mrow> </e:math> ) may arise from distinct carrier types associated with the two competing CDWs, CDW1 and CDW2. These two coexisting CDWs, characterized by distinct modulation vectors, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msub> <g:mi mathvariant="bold-italic">q</g:mi> <g:mn mathvariant="bold">1</g:mn> </g:msub> </g:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:msub> <j:mi mathvariant="bold-italic">q</j:mi> <j:mn mathvariant="bold">2</j:mn> </j:msub> </j:math> , show pressure-induced opposing shifts in their <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>b</m:mi> </m:mrow> <m:mo>*</m:mo> </m:msup> </m:math> axis projections (denoted as <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:msubsup> <n:mi>q</n:mi> <n:mn>1</n:mn> <n:mrow> <n:mi>b</n:mi> <n:mo>*</n:mo> </n:mrow> </n:msubsup> </n:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:msubsup> <o:mi>q</o:mi> <o:mn>2</o:mn> <o:mrow> <o:mi>b</o:mi> <o:mo>*</o:mo> </o:mrow> </o:msubsup> </o:math> ), while preserving a phase-coupling relationship 2( <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:mrow> <p:msub> <p:mi mathvariant="bold-italic">q</p:mi> <p:mn mathvariant="bold">1</p:mn> </p:msub> <p:mo>+</p:mo> <p:msub> <p:mi mathvariant="bold-italic">q</p:mi> <p:mn mathvariant="bold">2</p:mn> </p:msub> </p:mrow> </p:math> ) <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"> <u:mrow> <u:mo>∼</u:mo> <u:mo>[</u:mo> <u:mn>111</u:mn> <u:mo>]</u:mo> </u:mrow> </u:math> . Upon gradual suppression of the long range order CDW2 order, <v:math xmlns:v="http://www.w3.org/1998/Math/MathML"> <v:msubsup> <v:mi>q</v:mi> <v:mn>1</v:mn> <v:mrow> <v:mi>b</v:mi> <v:mo>*</v:mo> </v:mrow> </v:msubsup> </v:math> of CDW1 stabilizes and enters a decoupled regime within <w:math xmlns:w="http://www.w3.org/1998/Math/MathML"> <w:mrow> <w:mo>∼</w:mo> <w:mn>0.8</w:mn> <w:mo>−</w:mo> <w:mn>1.3</w:mn> </w:mrow> </w:math> GPa, followed by a pronounced change in its periodicity between <x:math xmlns:x="http://www.w3.org/1998/Math/MathML"> <x:mrow> <x:mo>∼</x:mo> <x:mn>1.3</x:mn> </x:mrow> </x:math> and 2.9 GPa. Above 2.9 GPa, all long-range CDW orders vanish, giving way to emergent superconductivity (SC).