Multiband One-Dimensional Electronic Structure and Spectroscopic Signature of Tomonaga-Luttinger Liquid Behavior in ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$

We present angle-resolved photoemission spectroscopy measurements of the quasi-one-dimensional superconductor ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$. We find that the Fermi surface contains two Fermi surface sheets, with linearly dispersing bands not displaying any significant band renormalizations. The one-dimensional band dispersions display a suppression of spectral intensity approaching the Fermi level according to a linear power law, over an energy range of $\sim 200\mathrm{meV}$. This is interpreted as a signature of Tomonoga-Luttinger liquid physics, which provides a new perspective on the possibly unconventional superconductivity in this family of compounds.

Figure 1

(a) Crystal structure of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ viewed down the $c$ axis. (b) Angle-integrated photoemission spectrum obtained at 10 K (upper half), compared with the density of states calculated from DFT (lower half). The experimental and calculated Cr $3d$-band width are in good agreement. (c) ARPES measurements of Cr $3d$ valence band dispersions, obtained with horizontal (LH) and vertical (LV) linear polarizations of the incident photons. The spectra are overlaid with DFT calculations along the $\mathrm{\Gamma }\text{−}A$ for reference, which show broad agreement. The calculated bands are colored by the primary orbital character of the band as indicated. (d) Experimental Fermi surface map of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ constructed by integrating spectral weight within 50 meV of the Fermi level, consisting of two pairs of Q1D bands. (e), (f) Calculated Fermi surface of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$; here spin-orbit coupling is included and colors represent different bands not orbital characters.

Figure 2

(a) ARPES dispersion obtained at 10 K for a cut along the $k_z$ direction. Vertical red lines indicate the Brillouin zone center and boundary. (b) Detailed dispersions close to the Fermi level, and (c) selected momentum distribution curves stacked according to binding energy, showing the suppression of spectral weight approaching the Fermi level. (d) Band positions and (f) fit amplitude of the outer and inner bands. (e) Integrated spectral weight for this cut, compared to a polycrystalline Au reference.

Figure 3

Integrated spectral weight within in the range $-0.5<k_z<0.5{\AA }^{-1}$. Data are normalized in the range $250<E_B<200\mathrm{meV}$. (b) Logarithmic plot of (a), after subtraction of constant offset from background (taken well above $E_F$). A black line is a linear fit of logarithmic data in range $20<E_B<200\mathrm{meV}$ at 10 K, implying a power law of $\alpha =0.974$. (c) Fits to TLL spectral function at selected temperatures, obtaining very similar values of $\alpha$. Data are offset for clarity. (d) Scaling plot, showing that the data at various temperatures collapse onto one curve for $\alpha =1$.