Pressure induced transition from chiral charge order to time-reversal symmetry-breaking superconducting state in Nb-doped CsV3Sb5

Abstract

Understanding how time-reversal symmetry (TRS) breaks in quantum materials is key to uncovering new states of matter and advancing quantum technologies. However, unraveling the interplay between TRS breaking, charge order, and superconductivity in kagome metals continues to be a compelling challenge. Here, we investigate the kagome metal Cs(V_1-x Nb _x )₃Sb₅ with x = 0.07 using muon spin rotation (μSR), alternating current (AC) magnetic susceptibility, and scanning tunneling microscopy (STM), under combined tuning by chemical doping, hydrostatic pressure, magnetic field, and depth from the surface. We find that TRS breaking in the bulk emerges below 40 K-lower than the charge order onset at 58 K-while near the surface, TRS breaking onsets at 58 K and is twice as strong. Niobium doping raises the superconducting critical temperature from 2.5 K to 4.4 K. Under pressure, both the critical temperature and superfluid density double, with TRS-breaking superconductivity appearing above 0.85 GPa. These findings reveal a depth-tunable TRS-breaking state and unconventional superconducting behavior in kagome systems.

Keywords: Magnetic properties and materials; Superconducting properties and materials.

Fig. 1. Scanning tunnelling microscopy measurements of Cs(V_0.93Nb_0.07)₃Sb₅.

a Topographic image with high bias voltage showing the individual Nb dopants (dark spots). b Topographic image with low bias voltage at the same atomic location. The inset shows its Fourier transform, demonstrating the 2 × 2 charge order vector peaks (red circles). c Differential tunnelling spectrum showing a gap of 20 meV caused by the charge order. The spectrum is measured over a wide energy scale with a low energy resolution; the excitation voltage of the lock-in is set to be large, so that it smears out the superconducting gap structure. d Differential tunnelling spectrum showing superconducting gap of 0.64 meV. The density of states does drop to zero at zero bias. All the data were collected at a lattice temperature of 30 mK.

Fig. 2. Summary of muon-spin rotation (μSR) experiments in the normal state of Cs(V_0.93Nb_0.07)₃Sb₅ (Nb_0.07-CVS).

a Zero-field (ZF) and longitudinal-field (LF) μSR spectra measured at 5 K in various fields up to 20 mT. The error bars are the standard error of the mean (s.e.m.) in about 10⁶ events. b Evolution of σ (red triangles) and Γ (purple diamonds) relaxation rates as a function of temperature in the normal state. An increase in the Γ relaxation below T_CO implies time-reversal symmetry (TRS) breaking is present in Nb_0.07-CVS. The error bars represent the standard deviation of the fit parameters. c Evolution of σ relaxation rate under applied fields of 0.01 T (blue squares), 4 T (yellow triangles) and 8 T (red circles). Inset shows the Fourier transform of the 8 T data at 5 K, which has been fit with two components; the sample (red) and the silver holder (grey).

Fig. 3. Depth-dependent magnetism in Cs(V_0.93Nb_0.07)₃Sb₅ (Nb_0.07-CVS).

a Muon implantation profile simulated for several energies. b Zero-field (ZF) muon-spin rotation (μSR) spectra for Nb_0.07-CVS. obtained at 5 K at the surface (mean implantation depth, $\overline{z}=10\mathrm{nm}$, green) and in the bulk ($\overline{z}=100\mathrm{nm}$, purple). The error bars are the standard error of the mean (s.e.m.) in about 10⁶ events. c Temperature dependence of the relaxation rate, Γ measured in 50 G and zero-field at the surface ($\overline{z}=10\mathrm{nm}$, green), and zero-field in the bulk ($\overline{z}=100\mathrm{nm}$, purple). The high-temperature relaxation rate has been subtracted to put all data on a comparable scale. The error bars represent the standard deviation of the fit parameters. d The zero-field muon-spin relaxation rate measured at 5K in an applied field of 5 mT as a function of muon implantation energy, E. Top axis shows the mean implantation depth, $\overline{z}$. Green to purple shading depicts the transition from near-surface to bulk behaviour.

Fig. 4. Summary of muon-spin rotation (μSR) experiments in the superconducting state of Cs(V_0.93Nb_0.07)₃Sb₅.

a Transverse-field (TF) μSR spectra collected above (10 K, purple) and below (1.5 K, red) T_C after field-cooling the sample from above T_C in an applied field of 10mT. The error bars are the standard error of the mean (s.e.m.) in about 10⁶ events. b Fourier transforms of the data from (a). c Temperature dependence of the superconducting muon spin depolarisation rate, σ_sc and inverse squared penetration depth, λ⁻² measured in 10 mT. The red and green solid lines show the fit of a nodeless s-wave gap and dirty-d wave model, respectively. The inset shows λ⁻² against the low-temperature data on a log–log scale. The error bars represent the standard deviation of the fit parameters. d Response of the internal magnetic field, μ₀H_int, in the superconducting state has the expected diamagnetic shift.

Fig. 5. Tuning superconductivity in Cs(V_0.93Nb_0.07)₃Sb₅ with pressure.

a AC magnetic susceptibility, χ under various applied hydrostatic pressures. Data is normalised between  −1 and 0. b Temperature dependence of normalised superconducting muon spin depolarisation rates, σ_sc measured in an applied field of μ₀H = 10 mT at ambient and various applied hydrostatic pressures. The superconducting gap symmetries have been determined as single nodeless s-wave (solid lines) with the exception of 0.8 GPa, which sits on the boundary between the two phases and was subsequently modelled with two s-wave gaps (dashed line). The error bars represent the standard deviation of the fit parameters.

Fig. 6. Cs(V_0.93Nb_0.07)₃Sb₅ pressure phase diagram and comparison of time-reversal symmetry (TRS) breaking in CsV₃Sb₅ derived compounds.

a AC susceptibility measurements as a function of applied hydrostatic pressure (0–2.2 GPa) have been normalised between −1 and 0 as described by the colour bar. The phase diagram is divided into three clear regions. Open circles show the inverse penetration depth squared, λ⁻² (right axis), determined from the gap structure analysis of the muon-spin rotation data. b Comparison of TRS breaking across T_C for pure and doped CsV₃Sb₅ compounds. Single-crystal and polycrystalline samples are shown by closed and open markers, respectively. The x-axis has been scaled by a factor of T_C for each compound at that pressure. The error bars represent the standard deviation of the fit parameters.