Mott-Driven BEC-BCS Crossover in a Doped Spin Liquid Candidate $\kappa \text{−}(\mathrm{BEDT}\text{−}\mathrm{TTF}{)}_4{\mathrm{Hg}}_{2.89}{\mathrm{Br}}_8$

The pairing of interacting fermions leading to superfluidity has two limiting regimes: the Bardeen-Cooper-Schrieffer (BCS) scheme for weakly interacting degenerate fermions and the Bose-Einstein condensation (BEC) of bosonic pairs of strongly interacting fermions. While the superconductivity that emerges in most metallic systems is the BCS-like electron pairing, strongly correlated electrons with poor Fermi liquidity can condense into the unconventional BEC-like pairs. Quantum spin liquids harbor extraordinary spin correlation free from order, and the superconductivity that possibly emerges by carrier doping of the spin liquids is expected to have a peculiar pairing nature. The present study experimentally explores the nature of the pairing condensate in a doped spin liquid candidate material and under varying pressure, which changes the electron-electron Coulombic interactions across the Mott critical value in the system. The transport measurements reveal that the superconductivity at low pressures is a BEC-like condensate from a non-Fermi liquid and crosses over to a BCS-like condensate from a Fermi liquid at high pressures. The Nernst-effect measurements distinctively illustrate the two regimes of the pairing in terms of its robustness to the magnetic field. The present Mott tuning of the BEC-BCS crossover can be compared to the Feshbach tuning of the BEC-BCS crossover of fermionic cold atoms.

Popular Summary

Superconductivity—the ability of a material to conduct electricity with zero resistance—arises from peculiar pairings that form among electrons. These pairings have two limiting regimes: barely overlapping small pairs and heavily overlapping large pairs, called Bose-Einstein condensation (BEC)–like and Bardeen-Cooper-Schrieffer (BCS) pairing, respectively. Most superconductors fall under the BCS regime. Here, we report that superconductivity in a material that is supposed to host a quantum spin liquid—no magnetic order even at absolute zero—is BEC-like and changes to the BCS regime by pressure application.

In our experiments, we study an organic superconductor. By gradually ratcheting the pressure on the sample up to about 1 GPa and measuring its resistivity, we identify a clear transition from BEC-like superconductivity to the BCS regime. Because increased pressure reduces the Coulomb interactions among electrons, this result suggests that strong Coulomb interactions prefer the unconventional BEC-like small pairs, and they cross over to the conventional BCS pairs as the interactions are reduced.

The realization of unconventional BEC-like superconductivity in an exotic spin-liquid candidate material widens the ground where superconductivity emerges and will stimulate the quest for novel mechanisms of pair formation. The finding of the interaction-tunable BEC-BCS crossover offers a novel type of pairing control, which adds to the more general physics of pairing instabilities of interacting fermions.

Figure 1

Structure and phase diagram of $\kappa \text{−}{(\mathrm{BEDT}\text{−}\mathrm{TTF})}_4{\mathrm{Hg}}_{2.89}{\mathrm{Br}}_8$. (a) Layered structure consisting of BEDT-TTF conducting layers and ${\mathrm{Hg}}_{2.89}{\mathrm{Br}}_8$ insulating layers. BEDT-TTF denotes bis(ethylenedithio)tetrathiafulvalene. The nonstoichiometry in the Hg composition comes from the fixed incommensurability between the Hg and BEDT-TTF lattices originating from material chemistry, not from extrinsic defects. (b) In-plane structure of the conducting layers. BEDT-TTF molecules form dimers, which constitute a nearly isotropic isosceles triangular lattice with the anisotropy of transfer integrals $t^{\prime }/t$ close to unity. (c) Pressure-temperature phase diagrams of $\kappa \text{−}{(\mathrm{BEDT}\text{−}\mathrm{TTF})}_4{\mathrm{Hg}}_{2.89}{\mathrm{Br}}_8$ and a quantum spin liquid candidate $\kappa \text{−}(\mathrm{BEDT}\text{−}\mathrm{TTF}{)}_2{\mathrm{Cu}}_2{(\mathrm{CN})}_3$. The red area indicates the superconducting phase. The blue area in $\kappa \text{−}{(\mathrm{BEDT}\text{−}\mathrm{TTF})}_4{\mathrm{Hg}}_{2.89}{\mathrm{Br}}_8$ depicts the non-Fermi-liquid region [corresponding to the yellow region in Fig. 2]. The purple area in $\kappa \text{−}{(\mathrm{BEDT}\text{−}\mathrm{TTF})}_2{\mathrm{Cu}}_2{(\mathrm{CN})}_3$ depicts the Mott-insulating spin liquid phase [42, 43]. $T_c$ in $\kappa \text{−}{(\mathrm{BEDT}\text{−}\mathrm{TTF})}_2{\mathrm{Cu}}_2{(\mathrm{CN})}_3$ is taken from Ref. [42], and $T_c$ in $\kappa \text{−}{(\mathrm{BEDT}\text{−}\mathrm{TTF})}_4{\mathrm{Hg}}_{2.89}{\mathrm{Br}}_8$ corresponds to the midpoint of the resistive transition observed in this study. MI, QSL, NFL, and SC represent the Mott insulator, quantum spin liquid, non-Fermi liquid, and superconductivity, respectively. The white broken line indicates the location of the so-called 6 K anomaly observed in $\kappa \text{−}{(\mathrm{BEDT}\text{−}\mathrm{TTF})}_2{\mathrm{Cu}}_2{(\mathrm{CN})}_3$ [12, 41, 42], a possible indication of an instability of QSL.

Figure 2

Temperature dependence of resistivity under pressures. (a) Temperature variation of the in-plane resistivity $\rho (T)$ at 0 T and a perpendicular field of 9 T. (b) Logarithmic plot of the temperature-dependent part of resistivity, $\rho (T)-{\rho }_0$, with ${\rho }_0$ being the residual resistivity (see main text for its determination). The solid and dashed lines indicate the resistivity at $H=0$ and 9 T, respectively. (c) Contour plot of the exponent $\alpha$ in fits of the form $A{T}^{\alpha }$ to the temperature-dependent part of the experimental in-plane resistivity $\rho (T)-{\rho }_0$; $\alpha$ is determined by $\alpha (T)\equiv d\log [\rho (T)-{\rho }_0]/d\log T$. The yellow region ($\alpha \approx 1$) corresponds to a non-Fermi-liquid phase, and the blue region ($\alpha \approx 2$) corresponds to the Fermi-liquid (FL) phase.

Figure 3

Resistivity under magnetic field. (a) In-plane resistivity as a function of magnetic field $H$ applied perpendicular to the layers under the pressure of 0.32 GPa. The temperature was set to the temperatures between 1.8 and 6.6 K at 0.3 K intervals and to 10.0 K. (b)–(j) Contour plots of the normalized in-plane resistivity, $\rho (T,H)/{\rho }_n(T)$, in the temperature–magnetic-field ($T\text{−}H$) plane for the pressure of 0.24, 0.27, 0.32, 0.39, 0.52, 0.58, 0.73, 0.83, and 1.0 GPa, where $\rho (T,H)$ is the in-plane resistivity at $T$ and $H$ and ${\rho }_n(T)$ is the normal resistivity with the form of (${\rho }_0+A{T}^{\alpha }$) fitting the high-field data (see text). The solid lines indicate the contours of $\rho (T,H)/{\rho }_n(T)=0.1$, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9.

Figure 4

Upper critical field and superconducting coherence length. The in-plane Ginzburg-Landau coherence length ${\xi }_{\parallel }$ calculated from the slope of the upper critical field, $d{H_{c2}}_{\perp }/dT$ near $T_c$, where the ${H_{c2}}_{\perp }$ is determined from the line at $\rho (T,H)/{\rho }_n(T)=0.8$, 0.9 (80% and 90% of the normal-state resistivity) in Fig. 3. The squares and diamonds are the values determined for $\rho (T,H)/{\rho }_n(T)=0.8$ and 0.9, respectively.

Figure 5

Pressure dependence of $k_F{\xi }_{\parallel }$ and BEC-BCS crossover. Superconducting transition temperature $T_c$ and $k_F{\xi }_{\parallel }$ as a function of temperature, where $k_F$ is the Fermi wave number determined by the Hall coefficient [37]. The value of $k_F{\xi }_{\parallel }$ is $\sim 3$ at low pressures and increases up to $\sim 50$ at 1 GPa with pressure, pointing to a BEC-BCS crossover. Schematics drawn underneath the main panel depict the BEC- and BCS-like pairs on the low- and high-pressure sides.

Figure 6

Temperature dependence of the Nernst signal $e_N$ under a pressure of 0.30 GPa. The measurements were made at the magnetic fields of 0.2, 0.5, 1, 3, 5, 7, and 9 T applied perpendicular to the conducting layers. The arrow indicates the zero-field $T_c$ determined by the simultaneously measured thermopower. The geometry of the measurement setup is depicted in the inset.

Figure 7

Magnetic-field–temperature profile of the Nernst signal $e_N$ under different pressures. (a)–(d) Nernst signal $e_N$ traced upon sweeping the perpendicular magnetic field at several fixed temperatures under the pressures studied: 0.3, 0.5 0.65, and 0.9 GPa. (e)–(h) Contour plots of the Nernst signal $e_N$ in the temperature–magnetic-field plane at the pressures of 0.3, 0.5 0.65, and 0.9 GPa. The red areas indicate hot Nernst regions. The arrows indicate the zero-field $T_c$.

Figure 8

Temperature-pressure profile of the Nernst signal $e_N$. The contour plot of the Nernst signal $e_N$ at a field of 9 T is shown in the temperature-pressure plane. The white circles indicate the zero-field $T_c$.