Direct evidence for two-gap superconductivity in hydrogen-intercalated titanium diselenide

Abstract

Transition-metal dichalcogenides (TMDs) offer an extremely rich material platform in the exploration of unconventional superconductivity. The unconventional aspects include exotic coupling mechanisms such as the Ising pairing, a complex interplay with other electronic orders such as charge-density waves (CDWs), symmetry-breaking and topological effects, and non-trivial gap structures such as multi-gap and possible nodal phases. Among TMDs, titanium diselenide (1$T$-TiSe$_2$) is one of the most studied and debated cases. Hints to an anomalous structure of its superconducting order parameter have emerged over the years, possibly linked to its spatial texturing in real and reciprocal space due to the presence of a 2$\times$2$\times$2 CDW phase, or to a pressure-driven multi-band Fermi surface. However, a direct evidence for a non-trivial structure of the superconducting gap in this material is still lacking. In this work, we bring the first evidence for a two-gap structure in the recently-discovered H-intercalated TiSe$_2$ superconductor (with T$_c \simeq 3.6$ K) by an extensive experimental study that combines magnetotransport measurements, point-contact spectroscopy and scanning tunnel spectroscopy. We show that the temperature dependence of the upper critical field (for $\vec B \parallel c$) as well as the shape of the point-contact and tunneling spectra strongly suggest the existence of two distinct superconducting gaps, and can indeed all be fitted in a self-consistent way with the same gap amplitudes $Δ_1 = 0.26 \pm 0.12$ meV and $Δ_2 =0.62 \pm 0.18$ meV.

Figures (5)

• Figure 1: Gate-driven H intercalation and superconductivity in TiSe$_{\rm 2}$. a, Schematic depiction of the experimental setup used in the gate-driven H intercalation process. The voltage $V_{\rm G}$ applied between the Pt gate electrode and the TiSe$_{\rm 2}$ crystal splits the water molecules absorbed by the EMIM-BF$_{\rm 4}$ ionic liquid and drives the H$^{\rm +}$ ions inside the TiSe$_{\rm 2}$ structure. b, Resistivity $\rho$ vs temperature $T$ in pristine and H-intercalated TiSe$_{\rm 2}$ at zero magnetic field. c, $\rho(T)$ curves of H-intercalated TiSe$_{\rm 2}$ across the SC transition for increasing perpendicular magnetic fields $B$. d, same as c plotted in semilogarithmic scale against $T^{-1}$. Dashed lines are linear fits to the data which highlight the TAFF scaling. Arrows indicate the temperatures $T_{\rm a}$ where a crossover to pinning-free vortex motion occurs. e, $\rho(T)$ curve at $B=0.25$ T with three characteristic $T$ scales explicitly indicated: The zero-resistance state temperature $T_{\rm a}$, the mean-field critical temperature $T_{\rm c}^{\rm mf}$, and the onset temperature $T_{\rm on}$. The error bar represents the uncertainty on $T_{\rm on}$ due to the experimental resolution on the condition $d\rho/dT=0$. The dashed line is a linear fit to the data in the flux-flow regime. The normal-state $\rho(T)$ curve at $B=1$ T is also reported. f, $B$ dependence of the activation barrier for vortex motion $U$ in semilogarithmic scale, obtained from the slope of the linear fits shown in d. The corresponding statistical uncertainties are reported as error bars. The dashed line is a linear fit to the data.
• Figure 2: Magnetic field-temperature ($B{-}T$) phase diagram of H-intercalated TiSe$_{\rm 2}$ determined from the magneto-transport measurements. $T_{\rm zrs}$ (green diamonds) are the temperatures below which zero resistance is observed. $T_{\rm a}$ (orange triangles) mark the boundary for the dissipative state due to pinning-free vortex motion. $T_{\rm on}$ and $B_{\rm on}$ (filled and open red pentagons) show the SC onset as defined by $d\rho/dT=0$ and the crossing points of the $\rho(B)$ isotherms, respectively. $T_{\rm c}^{\rm mf}$ and $B_{\rm c2}^{\rm mf}$ (filled and open blue circles) represent the mean-field upper critical field determined by linear extrapolation to the normal state of the $\rho(T)$ and $\rho(B)$ curves, respectively Berghuis1993PRB. Error bars are the resolution on the definitions due to the experimental noise level. The black dashed line shows the expected mean-field line according to the one-band Ginzburg-Landau model Tinkham1963PR. The truly dissipationless SC state is observed for $T \leq T_{\rm zrs}$ (green region). Dissipation develops due to thermal creep at moderate $B$ below the mean-field line (blue region) and free vortex motion at large $B$ where the pinning potential is suppressed at low $T$ (orange region). Inhomogeneity and amplitude fluctuations dominate between the mean-field line and the SC onset (red region).
• Figure 3: Directional PCARS measurements in H$_x$TiSe$_{\rm 2}$. a-d, Examples of symmetrized differential conductance curves ($dI/dV$ vs. $V$) measured in $ab$-plane (a,b) and $c$-axis (c,d) contacts. Normal-state resistance $R_{\rm N}$ and temperature $T$ are indicated in the labels. Green, violed and red arrows highlight the spectral features associated to the small gap $\Delta_1$, large gap $\Delta_2$, and critical current "dips". e,f, $T$ dependence of the $dI/dV$ spectra displayed in panels b,d. g, Same curves of panel e after normalization (symbols) and the best-fitting curves (line) according to the two-band BTK model. h, $T$ dependence of $\Delta_1$ (purple circles) and $\Delta_2$ (green circles) extracted from the fits in panel g. Dashed lines are functions of the form $\Delta_i(T) = \Delta_i(0)\tanh \left(1.74 \sqrt{ T_{\rm c}^{\rm A}/T-1}\right)$. i,l, Same as g,h for the curves of panel f.
• Figure 4: Tunneling spectroscopy measurements in H$_x$TiSe$_{\rm 2}$. a, Example of an as-measured current-voltage ($I-V$) curve measured by biasing the sharp Au tip. b, Color plot of typical normalized STM tunneling spectra ($dI/dV$ vs. $V$) measured at different temperatures $T$ in zero magnetic field. c, Selected spectra from panel b (symbols) and best-fitting curves (lines) according to the two-band BTK model. d, $T$ dependence of the superconducting gaps (symbols) extracted from the fits in panel c. Dashed lines are functions of the form $\Delta_i(T) = \Delta_i(0)\tanh \left(1.74 \sqrt{ T_{\rm c}^{\rm A}/T-1}\right)$.
• Figure 5: Two-gap superconductivity in H$_x$TiSe$_{\rm 2}$. a, Energy gaps measured by PCARS (filled symbols) and STS (hollow symbols) as a function of the contact resistance $R_{\rm N}$. Error bars are the spread of gap values obtained by using different normalization choices in the fitting procedure (Methods). b, Energy gaps as a function of normalized temperature ($T/T_{\rm c}$). Symbols are the mean values obtained by averaging the data measured on all contacts at each $T$. Error bars are the corresponding spread between the different measurements. Solid and dashed lines are the fits with the SMW Suhl1959PRL and Eliashberg Ummarino2009PRBUmmarino2004PCTorsello2019PRB two-band models. c, Upper critical field $B_{\rm c2}$ as a function of $T/T_{\rm c}$. Symbols are the mean-field data shown in Fig. \ref{['fig:phase_diagram']}. Lines are fits to the one-band Ginzburg-Landau model Tinkham1963PR (solid gray line), the two-band Gurevich model Gurevich2003PRBXing2017SciRepDing2022NL (solid black line) and the two-band Eliashberg model Mansor2005PRBUmmarino2011JSNM (dashed black line). Inset shows $B_{\rm c2}$ vs. $T/T_{\rm c}$ for Cu$_x$TiSe$_{\rm 2}$ (grey squares, Ref. Morosan2006NatPhys) and ion-gated TiSe$_{\rm 2}$ (red circles, Ref. Li2016Nature) and the corresponding fits (solid lines) to the one-band Ginzburg-Landau model Tinkham1963PR.