{"id":41764,"date":"2025-07-05T21:55:13","date_gmt":"2025-07-05T21:55:13","guid":{"rendered":"https:\/\/www.europesays.com\/us\/41764\/"},"modified":"2025-07-05T21:55:13","modified_gmt":"2025-07-05T21:55:13","slug":"correlation-between-the-dome-shaped-superconducting-phase-diagram-charge-order-and-normal-state-electronic-properties-in-laru3si2","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/us\/41764\/","title":{"rendered":"Correlation between the dome-shaped superconducting phase diagram, charge order, and normal-state electronic properties in LaRu3Si2"},"content":{"rendered":"

Figure\u00a03<\/a> a presents the temperature dependence of resistivity (see also Supplementary Figs.\u00a0S1<\/a> and S2<\/a>) for LaRu3Si2, focusing on the low-temperature range, measured at ambient pressure and under applied pressures up to 38 GPa. At ambient pressure, the system displays a well-defined superconducting transition, with an onset temperature \\({T}_{c}^{{{{\\rm{onset}}}}}\\) of 6.5 K, and reaching zero resistance below 6 K, indicating a robust superconducting phase. With an applied pressure of 1 GPa, Tc,onset increases noticeably to 9 K, although the transition becomes relatively broader, suggesting pressure-induced modifications in the superconducting properties. As the pressure increases further, up to 10 GPa, \\({T}_{c}^{{{{\\rm{onset}}}}}\\) remains at 9 K; however, the superconducting transition sharpens, indicating an enhancement in phase coherence or homogeneity in the superconducting state under moderate pressures. This stability in the superconducting onset up to 10 GPa reflects the systems resilience to pressure within this range. Beyond 10 GPa, the onset of superconductivity begins to decrease gradually, signifying a pressure-induced suppression of superconductivity. By 38 GPa, the onset temperature has decreased significantly, reaching 2 K, pointing to a diminishing superconducting state at high pressures. Figure\u00a03<\/a>d\u2013i illustrate the suppression of the transitions under magnetic fields at selected pressures, confirming the superconducting nature of the transitions. Additionally, they demonstrate a decrease in the critical field as pressure is reduced.<\/p>\n

Fig. 3: Pressure tuning of superconductivity.<\/b>\"figure<\/a><\/p>\n

a<\/b> Temperature dependence of resistivity, normalized to the value at 15 K, focusing on the low-temperature region to highlight the superconducting transitions recorded at ambient pressure and under pressures up to 38 GPa. b<\/b>, c<\/b> Temperature dependence of resistivity, normalized to the value at 300 K, measured over a wide temperature range at various pressures within 0-10 GPa and 13.6-51 GPa. d<\/b>\u2013i<\/b> Temperature dependence of resistivity below 10 K, measured under different applied magnetic fields at selected pressures: (d<\/b>) 1\u2009GPa, (e<\/b>) 6.7\u2009GPa, (f<\/b>) 10\u2009GPa, (g<\/b>) 15.4\u2009GPa, (h<\/b>) 20.2\u2009GPa, and (i<\/b>) 31.4\u2009GPa.<\/p>\n

For clarity in interpreting these observations, we define three characteristic temperatures: the onset temperature \\({T}_{c}^{{{{\\rm{onset}}}}}\\), the midpoint temperature \\({T}_{c}^{{{{\\rm{midpoint}}}}}\\) (where resistivity decreases by 50%), and the temperature \\({T}_{c}^{{{{\\rm{zero}}}}}\\) below which resistivity reaches zero. These defined temperatures are illustrated in the phase diagram shown in Fig.\u00a01<\/a>c, which captures the overall pressure-dependent superconducting behavior. The phase diagram exhibits a dome-shaped superconducting region, indicating an optimal pressure range where superconductivity is most robust, with suppression occurring beyond this optimal range. This dome-shaped behavior highlights the intricate interplay between pressure and superconductivity in LaRu3Si2, potentially revealing insights into the underlying mechanisms of superconductivity in this system.<\/p>\n

Next, we discuss the normal-state response observed in the resistivity data. Notably, no anomaly is detected across Tco,II either at ambient pressure or under applied pressure. However, an anomaly is evident across T*, which is weak at ambient pressure but becomes clear in the first derivative of the resistivity, as shown in Fig.\u00a04<\/a>a. Interestingly, applying pressure enhances the prominence of this anomaly, particularly in the pressure range between 2.2 GPa and 15.4 GPa. In this range, the anomaly is clearly visible in the resistivity data and is further accentuated in the first derivative, where sharper and more intense peaks are observed. Above 15.4 GPa, the anomaly progressively weakens, and the peaks in the first derivative become less intense and broader. To characterize the pressure evolution of this anomaly, we calculated the difference in the first derivative dR\/dT between its maximum value at T* and its value at 120 K. This difference serves as a measure of the anomaly\u2019s strength and is plotted as a function of pressure in Fig.\u00a01<\/a>d. Remarkably, the anomaly exhibits a dome-shaped pressure dependence, with its maximum occurring in the pressure range of 1-15.4 GPa, coinciding with the pressure range where the superconducting transition temperature Tc reaches its peak. To highlight this, we plot the anomaly strength as a function of Tc, revealing a clear linear correlation (Fig.\u00a01<\/a>f). This indicates that the anomaly at T* becomes most pronounced when superconductivity is optimal. This correlation implies an intimate connection between Tc and T*, the latter being the temperature below which muon-spin rotation experiments detect time-reversal symmetry breaking and magnetotransport measurements show enhanced magnetoresistance. In Fig.\u00a01<\/a>e, the pressure dependence of T*, determined as the peak position in the first derivative, is presented. While the absolute value of T* changes slightly with pressure, it exhibits a dip around 12 GPa, aligning with the maximum Tc.<\/p>\n

Fig. 4: Pressure tuning of normal state transport in LaRu3Si2.<\/b>\"figure<\/a><\/p>\n

a<\/b> The temperature dependence of the derivative of resistivity dR\/dT, measured under various pressures up to 51 GPa. b<\/b> The temperature dependence of magnetoresistance, measured at selected pressures of p=0\u2009GPa, 2.2\u2009GPa, 20.2\u2009GPa and 41.8\u2009GPa.<\/p>\n

Both temperature scales, T* and Tco,II, in LaRu3Si2, are also reflected in magnetoresistance (MR) measurements. Magnetotransport techniques34<\/a>,35<\/a>,36<\/a>,37<\/a>,38<\/a>,39<\/a>,40<\/a>, known for their sensitivity to charge-order transitions, utilize MR as an indicator of the mean free path integrated over the Fermi surface37<\/a>. This approach is particularly effective in detecting changes in scattering anisotropy and Fermi surface reconstructions. Figure\u00a05<\/a>a\u2013d present the MR in LaRu3Si2 under a perpendicular magnetic field across the temperature range of 10 K to 80 K, measured at p\u2009=\u20090\u2009GPa and at selected pressures of p\u2009=\u20092.2\u2009GPa, 20.2\u2009GPa, and 41.8\u2009GPa. Additionally, Fig.\u00a04<\/a>b shows the temperature dependence of MR at 9 T, recorded under various pressures. Within the primary 1\/4 charge-ordered state, the MR remains negligible and only begins to appear below the 1\/6 charge ordering temperature Tco,II. At p\u00a0=\u00a00 GPa, the MR starts to increase at Tco,II, with a steeper rise occurring below T* (see Figs.\u00a04<\/a>b and 5<\/a>a). Under a pressure of 2.2 GPa, both the onset of MR and its base-temperature value at 9 T remain unchanged down to T*, below which the MR increases significantly (see Figs.\u00a04<\/a>b and 5<\/a>b). Notably, the MR(9T) value at 10 K reaches 14 %, nearly twice the value observed at ambient pressure. However, when pressure exceeds 15\u2009GPa, the MR decreases and eventually becomes smaller than the value recorded at ambient pressure (see Fig.\u00a05<\/a>c and d). Despite these changes, the onset of charge order at Tco,II remains nearly unaffected. These MR experiments reveal that the absolute value of MR is maximized within the pressure range where superconductivity is optimal, highlighting a strong connection between charge order, magnetotransport properties, and superconductivity in LaRu3Si2.<\/p>\n

Fig. 5: Pressure tuning of magnetotransport characteristics in LaRu3Si2.<\/b>\"figure<\/a><\/p>\n

The magnetoresistance measured at various temperatures across the charge ordering temperature TCO,II \u2243 80 K at ambient pressure (a)<\/b> and under various pressures of (b<\/b>) p=2.2 GPa, (c<\/b>) p\u2009=\u200920.2\u2009GPa and (d<\/b>) p\u2009=\u200941.8\u2009GPa.<\/p>\n

To complement the resistivity experiments, we conducted X-ray diffraction measurements41<\/a> up to 20 GPa, providing direct insight into both the 1\/4 and 1\/6 charge orders. In Fig.\u00a06<\/a>a\u2013d, we present reconstructed reciprocal-space patterns along the (hk1) direction for 300 K at selected pressures for a single crystal of LaRu3Si2. At higher temperature (T = 300K) T (see\u00a0Fig.\u00a06<\/a>a), the diffraction pattern reveals fundamental Bragg peaks \u03c4 and superlattice peaks at Q\u00a0=\u00a0\u03c4\u00a0+\u00a0qi with q1 = (\\(\\frac{1}{4}\\),0,0) and q2 = (0,\\(\\frac{1}{4}\\),0). The application of pressure suppresses the onset temperature of the primary charge order (Tco,I) such that already at 7 GPa charge order peaks are not visible (Fig.\u00a06<\/a>b\u2013d). As the temperature decreases below Tco,II \u2243 80 K (see Fig. 6<\/a>e, i), an additional set of reflections emerges at positions corresponding to \\(q^{\\prime}_{1}\\)=(\\(\\frac{1}{6},0,0\\)), \\(q^{\\prime}_{2}\\)=(0, \\(\\frac{1}{6},0\\)), and \\(q^{\\prime}_{3}\\)=(\\(\\frac{1}{6},\\frac{-1}{6},\\,0\\)). Significantly, both \\(\\frac{1}{4}\\) and \\(\\frac{1}{6}\\) charge orders coexist below 80 K, persisting into the superconducting state33<\/a>. While the application of pressure suppresses the onset temperature of the primary charge order (Tco,I), the onset temperature (Tco,II) below which 1\/4 and 1\/6 charge orders coexist remains nearly unaffected (see Fig.\u00a06<\/a>e\u2013g). At approximately 12.5\u2009GPa, Tco,I and Tco,II converge, beyond which broad, diffuse scattering intensity emerges at the same onset temperature (Tco,II) (see Fig.\u00a06<\/a>g, h), and it does not coalesce into sharp Bragg diffraction peaks down to base temperature. We note that the crossover from long-range to short-range charge order above 12.5 GPa begins around 80 K and persists down to 3 K, even in the superconducting state. As an example, we present data taken well below 80 K (see Fig.\u00a06<\/a>i\u2013k). Notably, the transition from long-range charge order to a short-range state at 12.5\u2009GPa coincides with the pressure at which the superconducting transition temperature begins to decrease. This correlation suggests a positive relationship between charge order and superconductivity in LaRu3Si2.<\/p>\n

Fig. 6: Pressure tuning of charge orders in LaRu3Si2.<\/b>\"figure<\/a><\/p>\n

a<\/b>\u2013d<\/b> Reconstructed reciprocal space in the (h k 1) plane, measured at T=300 K for various pressures (a<\/b>) p=0.3 GPa, (b<\/b>) 7\u2009GPa, (c<\/b>) 12\u2009GPa, and (d<\/b>) 18\u2009GPa. Panels b,c,d correspond to the same area in reciprocal space as the other panels but reflections are indexed with a and b lattice parameters doubled. e<\/b>\u2013h<\/b> Reconstructed reciprocal space in the (h k 1) plane, measured at T \u2243 70 K for various pressures p=0.4 GPa (e<\/b>), 6.4 GPa (f<\/b>), 12.5 GPa (g<\/b>), and 19.8\u2009GPa (h<\/b>). i<\/b>\u2013k<\/b> Reconstructed reciprocal space in the (h k 1) plane, measured at T \u2243 10 K for various pressures p=0.3\u2009GPa (i<\/b>), 6.5\u2009GPa (j<\/b>), 12.8\u2009GPa (k<\/b>). Green circles indicate Bragg peaks. Red and orange circles indicate the charge order peaks with a propagation vectors of (\\(\\frac{1}{4}\\), 0, 0) and (\\(\\frac{1}{6}\\), 0, 0), respectively. The bright reflection visible in (j<\/b> and k<\/b>) corresponds to a diamond reflection from one of the anvils.<\/p>\n","protected":false},"excerpt":{"rendered":"Figure\u00a03 a presents the temperature dependence of resistivity (see also Supplementary Figs.\u00a0S1 and S2) for LaRu3Si2, focusing on…\n","protected":false},"author":3,"featured_media":41765,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25],"tags":[16443,10046,10047,492,159,27577,67,132,68],"class_list":{"0":"post-41764","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-electronic-properties-and-materials","9":"tag-humanities-and-social-sciences","10":"tag-multidisciplinary","11":"tag-physics","12":"tag-science","13":"tag-superconducting-properties-and-materials","14":"tag-united-states","15":"tag-unitedstates","16":"tag-us"},"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@us\/114802860120876803","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/posts\/41764","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/comments?post=41764"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/posts\/41764\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/media\/41765"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/media?parent=41764"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/categories?post=41764"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/tags?post=41764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}