An electronic nematic liquid in BaNi2As2

Abstract

Understanding the organizing principles of interacting electrons and the emergence of novel electronic phases is a central endeavor of condensed matter physics. Electronic nematicity, in which the discrete rotational symmetry in the electron fluid is broken while the translational one remains unaffected, is a prominent example of such a phase. It has proven ubiquitous in correlated electron systems, and is of prime importance to understand Fe-based superconductors. Here, we find that fluctuations of such broken symmetry are exceptionally strong over an extended temperature range above phase transitions in [Formula: see text], the nickel homologue to the Fe-based systems. This lends support to a type of electronic nematicity, dynamical in nature, which exhibits a particularly strong coupling to the underlying crystal lattice. Fluctuations between degenerate nematic configurations cause splitting of phonon lines, without lifting degeneracies nor breaking symmetries, akin to spin liquids in magnetic systems.

Fig. 1. Raman scattering from BaNi₂As₂.

a Raman active phonons of BaNi₂As₂, and room temperature Raman spectra obtained in the different incoming and scattered photon polarizations. Detailed view of the temperature dependencies of the A_1g (b) and E_g,1 (c) phonons above T_Tri in BaNi₂As₂.

Fig. 2. Doping dependence.

a temperature dependence of the resistivity and its derivative measured upon cooling in BaNi₂As₂, b of the integrated intensity of the q_I-CDW = (0.28,0,0) and q_C-CDW = (1/3,0,1/3) superstructure peaks (measured upon cooling) in BaNi₂As₂ (c) temperature dependence of the E_g,2 phonon intensity in BaNi₂As₂ (after background subtraction and Bose-factor correction, Supplementary Note 3) (d) temperature dependence of the E_g,1 phonon intensity in BaNi₂As₂ (after background subtraction and bose correction, Supplementary Note 3). e, f, g, h same as (a, b, c, d) for $\mathrm{Ba}{\mathrm{Ni}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$(x = 3.5%) (i, j, k, l) same as (a, b, c, d) for $\mathrm{Ba}{\mathrm{Ni}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$(x =7.6%) (m, n, o, p) same as (a, b, c, d) for $\mathrm{Ba}{\mathrm{Ni}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$(x = 10%). In each panel we have indicated the position of the triclinic transition (upon cooling) T_Tri, of the local minimum of dR/dT T_rho and of the temperature at which the I-CDW intensity starts to grow T_I-CDW. The shaded area corresponds to the uncertainty on the determination of T^* at which the E_g phonon starts to broaden.

Fig. 3. Electronic Raman scattering.

a B_2g electronic Raman response ${\chi }_{B_{\mathrm{2g}}}^{{}^{″}}\left(\omega ,T\right)$ of $\mathrm{Ba}{\mathrm{Ni}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$(x = 7.6%) as a function of temperature. The inset shows the same data after subtraction of the high-temperature response ${\chi }_{B_{\mathrm{2g}}}^{{}^{″}}\left(\omega ,T\right)$ - ${\chi }_{B_{\mathrm{2g}}}^{{}^{″}}\left(\omega ,T=250\mathrm{K}\right)$. b B_1g electronic Raman response ${\chi }_{B_{\mathrm{1g}}}^{{}^{″}}\left(\omega ,T\right)$ of $\mathrm{Ba}{\mathrm{Ni}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$(x=7.6%) as a function of temperature. The inset shows the same data after subtraction of the high-temperature response ${\chi }_{B_{\mathrm{1g}}}^{{}^{″}}\left(\omega ,T\right)$ - ${\chi }_{B_{\mathrm{1g}}}^{{}^{″}}\left(\omega ,T=250\mathrm{K}\right)$.

Fig. 4. Model calculation.

a Calculation of the E_gRaman response using a simple model of two degenerate harmonic oscillators coupled via λ to a fluctuating nematic degree of freedom. Details of the calculation are laid out in the Supplementary Note 4. Parameters for the B_1g fluctuation frequency and temperature are chosen Ω = ω₀/20, T = ω₀/5. b The weight distribution of the peak splitting depends on the relative energy scales in the problem, as illustrated for two different temperatures T ≪ Ω and Ω ≪ T ≪ ω₀. c In the disordered case with equal peak splitting the degeneracy of the two Raman responses can be lifted by applying a conjugate external strain σ_ext. d Schematic of the allowed transitions that cause the peak splitting of the Raman signal even in the tetragonal state (left panel) and in the strained/orthorhombic state (right panel). e Raman response of BaNi₂As₂stress-free and under uniaxial stress and comparison to local stress dependence (f) of FeSe [Data from ref. , plotted with permission from the authors].

Fig. 5. Phase diagram for BaNi2(As1−xPx)2.

The transition temperatures for the triclinic phases are determined from transport and thermal expansion measurements. We also report the temperature T_ρ of the minimum in dR/dT which corresponds to an orthorhombic transition in the parent compound (Supplementary Note 2). The superconducting transition temperature is measured by specific heat (Supplementary Note 2). The onset of the C-CDW seen with XRD coincides with the triclinic transition, whereas the intensity of the I-CDW satellites increases strongly at T_I-CDW, just above T_ρ (see Fig. 2). The onset of the broadening of the E_g,1 Raman phonons is indicated by T^* (see also Supplementary Note 3). Horizontal error bars correspond to the uncertainty on the P-concentration as determined from EDX (Supplementary Note 1). Vertical error bars reflect the accuracy with which the various temperatures can be determined from Fig. 2.