Emergence of a Novel Pseudogap Metallic State in a Disordered 2D Mott Insulator

We explore the nature of the phases and an unexpected disorder-driven Mott insulator to metal transition in a single crystal of the layered dichalcogenide $1\mathrm{T}\text{−}{\mathrm{TaS}}_2$ that is disordered without changing the carrier concentration by Cu intercalation. Angle resolved photoemission spectroscopy measurements reveal that increasing disorder introduces delocalized states within the Mott gap that lead to a finite conductivity, challenging conventional wisdom. Our results not only provide the first experimental realization of a disorder-induced metallic state but in addition also reveal that the metal is a non-Fermi liquid with a pseudogap with a suppressed density of states that persists at finite temperatures. Detailed theoretical analysis of the two-dimensional disordered Hubbard model shows that the novel metal is generated by the interplay of strong interaction and disorder.

Figure 1

Schematic figure showing the effect of disordering a Mott insulator (without adding carriers). As the disorder strength $V$ is increased relative to the bandwidth, the charge gap ${\mathrm{\Delta }}_{\text{gap}}$ in the Mott insulator vanishes at the quantum phase transition to a metal. The novel metal has a finite dc conductivity ${\sigma }_{\text{dc}}$ and other unusual spectral properties elucidated by angle resolved photoemission spectroscopy experiments reported here. At higher disorder we expect a second quantum phase transition from the metal to a gapless localized insulator. If the Mott insulator has magnetic order $m_q$, it need not be tied to the metal insulator transitions.

Figure 2

Mott phase in $1\mathrm{T}\text{−}{\mathrm{TaS}}_2$: (a) visualization of the CCDW phase and star-of-David clusters on a triangular lattice. (b) The 2D Brillouin zone of the original triangular Ta sheet (red), and the CCDW phase reconstructed reciprocal unit cells (green). (c),(d) TEM diffraction images from a disordered sample in the nearly commensurate CDW phase ($T=223\mathrm{K}$) and the commensurate CDW phase ($T=123\mathrm{K}$), respectively. (e),(f) ARPES data from a disordered sample showing the band dispersion along the $\mathrm{\Gamma }\text{−}M$ direction above and below the CCDW phase transition at 180 K, respectively. The dashed lines are guides to the eye showing the band dispersion. (g) In-plane resistance as a function of temperature for a clean and a disordered sample upon cooling from 300 K down to 2 K and heating back to 300 K. $1\mathrm{T}\text{−}{\mathrm{TaS}}_2$ is quasi-2D with large resistance anisotropy (${\rho }_c/{\rho }_a\approx 500$) [27, 28]. For a discussion of the unusual temperature dependence of the resistivity, see the Supplemental Material [29].

Figure 3

ARPES spectra of a disordered Mott insulator $1\mathrm{T}\text{−}{\mathrm{TaS}}_2$: spectra taken with 22 eV photons along the $\mathrm{\Gamma }\text{−}K$ direction at $T=25\mathrm{K}<T_{\mathrm{CCDW}}$. Panel (a) for a clean system reveals a Mott gap as indicated by the lack of intensity within about 80 meV of the Fermi energy. Panel (b) for a disordered sample shows the presence of significant spectral weight close to the Fermi energy, inside the energy gap. In panels (c)–(f), the scans in black are for a clean system while those in red are for a Cu intercalated disordered system. (c) Comparison of the EDC at the $\mathrm{\Gamma }$ point taken from the scans in (a) and (b). The peak in the disordered $1\mathrm{T}\text{−}{\mathrm{TaS}}_2$ is broadened and shifted towards lower binding energy and there is substantial intensity at zero energy. (d) The same EDCs shown in (c) after symmetrization clearly reveal the closing of the gap in the disordered sample, and the formation of a pseudogap with about 20% of the peak intensity. (e) Reproducibility of the results: EDCs from 13 different samples (seven clean and six disordered) taken in different ARPES systems with different photon energies and polarizations; all reveal the same qualitative behavior. (f) Evolution of the pseudogap at the $\mathrm{\Gamma }$ point as a function of increasing temperature. While at low temperatures the spectral weight at zero energy is much larger in the disordered samples, above the CCDW transition temperature the difference in the spectral functions of the clean and disordered samples disappears.

Figure 4

(a) Theoretical density of states as a function of disorder $V$ (in units of hopping $t$) for interaction $U=6t$. (b) EDC at $k=k_F$ for $U=6t$ showing a well formed gap for weak disorder ($V<U$), which closes for $V\ge U$ with a pseudogap persisting. Inset shows the monotonic increase of spectral weight at $\omega =0$ with disorder. Panels (c) and (d) show the spatial map of the probability density $|\mathrm{\Psi }(i){|}^2$ of the eigenstate at $\omega =0$ for $V=7t$ and $U=0$ (c) and $U=6t$ (d). Remarkably repulsive interactions compete against disorder and delocalize the wave function over the entire lattice. The results in panels (a) and (b) are on $18\times 18$ lattices averaged over 100 disorder realizations, and in (c) and (d) on a $32\times 32$ lattice for a single realization.