Doped Mott Insulator Research Articles

Emergence of quasiparticles in a doped Mott insulator

How a Mott insulator develops into a weakly coupled metal upon doping is a central question to understanding various emergent correlated phenomena. To analyze this evolution and its connection to the high-Tc cuprates, we study the single-particle spectrum for the doped Hubbard model using cluster perturbation theory on superclusters. Starting from extremely low doping, we identify a heavily renormalized quasiparticle dispersion that immediately develops across the Fermi level, and a weakening polaronic side band at higher binding energy. The quasiparticle spectral weight roughly grows at twice the rate of doping in the low doping regime, but this rate is halved at optimal doping. In the heavily doped regime, we find both strong electron-hole asymmetry and a persistent presence of Mott spectral features. Finally, we discuss the applicability of the single-band Hubbard model to describe the evolution of nodal spectra measured by angle-resolved photoemission spectroscopy (ARPES) on the single-layer cuprate La2−xSrxCuO4 (0 ≤ x ≤ 0.15). This work benchmarks the predictive power of the Hubbard model for electronic properties of high-Tc cuprates.

Critical role of the sign structure in the doped Mott insulator: Luther-Emery versus Fermi-liquid-like state in quasi-one-dimensional ladders

Mechanism of superconductivity (SC) in a purely interacting electron system has been one of the most challenging issues in condensed matter physics. In the BCS theory, the Landau's Fermi liquid is a normal state against which an SC instability occurs once an \emph{additional} pairing force is added. We show that in the doped Mott insulator an \emph{intrinsic} SC ground state (specifically a Luther-Emery state in a finite-doping two-leg $t$-$J$ ladder) can be directly turned into a Fermi-gas-like state by merely switching off the hidden statistical sign structure via two schemes. It points to a new pairing paradigm, %beyond the resonating-valence-bond scheme, which is an "Amperean-like pairing" with a "stringlike" pairing force as shown by an adiabatic continuity to a strong anisotropic limit of the model.

Charge transport in the Hubbard model at high temperatures: Triangular versus square lattice

High-temperature bad-metal transport has been recently studied both theoretically and in experiments as one of the key signatures of strong electronic correlations. Here we use the dynamical mean field theory (DMFT) and its cluster extensions, as well as the finite-temperature Lanczos method (FTLM) to explore the influence of lattice frustration on the thermodynamic and transport properties of the Hubbard model at high temperatures. We consider the triangular and the square lattice at half-filling and at 15\% hole-doping. We find that for $T \gtrsim 1.5t$ the self-energy becomes practically local, while the finite-size effects become small at lattice-size $4 \times 4$ for both lattice types and doping levels. The vertex corrections to optical conductivity, which are significant on the square lattice even at high temperatures, contribute less on the triangular lattice. We find approximately linear temperature dependence of dc resistivity in doped Mott insulator for both types of lattices.

Direct Visualization of Ambipolar Mott Transition in Cuprate CuO2 Planes

Identifying the essence of doped Mott insulators is one of the major outstanding problems in condensed matter physics and the key to understanding the high-temperature superconductivity in cuprates. We report real space visualization of Mott insulator-metal transition in Sr_{1-x}La_{x}CuO_{2+y} cuprate films that cover both the electron- and hole-doped regimes. Tunneling conductance measurements directly on the copper-oxide (CuO_{2}) planes reveal a systematic shift in the Fermi level, while the fundamental Mott-Hubbard band structure remains unchanged. This is further demonstrated by exploring the atomic-scale electronic response of CuO_{2} to substitutional dopants and intrinsic defects in a sister compound Sr_{0.92}Nd_{0.08}CuO_{2}. The results may be better explained in the framework of self-modulation doping, similar to that in semiconductor heterostructures, and form a basis for developing any microscopic theories for cuprate superconductivity.

Exact theory for superconductivity in a doped Mott insulator

Because the cuprate superconductors are doped Mott insulators, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. We consider the Hatsugai–Kohmoto model1,2, an exactly solvable system that is a prototypical Mott insulator. Upon either doping or reducing the interaction strength, our exact calculations show that the system becomes a non-Fermi liquid metal with a superconducting instability. In the presence of a weak pairing interaction, the instability produces a thermal transition to a superconducting phase, which is distinct from the traditional state described by Bardeen–Cooper–Schrieffer (BCS) theory, as evidenced by a gap-to-transition temperature ratio exceeding the universal BCS limit. The elementary excitations of this superconductor are not Bogoliubov quasiparticles but rather superpositions of doublons and holons, composite excitations that show that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. An unexpected feature of this model is that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies, as seen in the cuprates3, as well as a suppression of the superfluid density relative to that in BCS theory.

Hidden magnetism at the pseudogap critical point of a cuprate superconductor

The mysterious pseudogap phase of cuprate superconductors ends at a critical hole doping level p* but the nature of the ground state below p* is still debated. Here, we show that the genuine nature of the magnetic ground state in La2-xSrxCuO4 is hidden by competing effects from superconductivity: applying intense magnetic fields to quench superconductivity, we uncover the presence of glassy antiferromagnetic order up to the pseudogap boundary p* ~ 0.19, and not above. There is thus a quantum phase transition at p*, which is likely to underlie highfield observations of a fundamental change in electronic properties across p*. Furthermore, the continuous presence of quasi-static moments from the insulator up to p* suggests that the physics of the doped Mott insulator is relevant through the entire pseudogap regime and might be more fundamentally driving the transition at p* than just spin or charge ordering.

Complex phase diagram of doped XXZ ladder: Localization and pairing

How the ground state nature can be dramatically changed by the distinct underlying spin correlation is a central issue of doped Mott insulators. The two-leg XXZ ladder provides a prototypical spin background, which can be tuned from a long-range N\'{e}el order to a short-range ``spin liquid'' via the superexchange anisotropy, giving rise to a complex phase diagram at finite doping. By density matrix renormalization group method, we show that although the charge is always self-localized in the N\'{e}el ordered phase, a second insulating phase emerges, in which the doped holes become paired but remain localized while the transverse spin-spin correlation reduces to short-ranged one to make the N\'{e}el order classical. Only when the N\'{e}el order totally disappears by further reducing anisotropy, does the pairing become truly coherent as characterized by a Luther-Emery state. In sharp contrast, the pairing is totally absent in the in-plane ferromagnetic XXZ regime, where a direct transition from the charge self-localization in the N\'{e}el ordered phase to a Fermi-gas-like state in the spin liquid phase is found. A consistent physical picture is briefly discussed.

Phenomenological single-particle Green's function for the pseudogap and superconducting phases of high- Tc cuprates

We present a phenomenological Green's function to characterize the superconducting and pseudogap phases of the cuprates based on a microscopic theory of doped Mott insulators. In this framework, the "Fermi arc" and "kink" phenomena observed by angle-resolved photoemission spectroscopy (ARPES) experiments in the pseudogap phase can be systematically explained as a function of doping, which is further connected to the two-gap feature in the superconducting phase with dichotomy between the nodal and antinodal physics. We demonstrate that a phase-string-induced fractionalization plays the key role in giving rise to such a peculiar Green's function with a unique two-component structure.

Scaling theory for Mott–Hubbard transitions-II: quantum criticality of the doped Mott insulator

We present a T = 0 K renormalization group (RG) phase diagram for the hole-doped 2D Hubbard model on the square lattice. The RG method employed is nonperturbative in treating quantum fluctuations of the single-particle occupation number via the unitarily decoupling of one electronic state at every RG step. As a result, the RG phase diagram possesses the quantum fluctuation energy scale (ω) as one of its axes. Using effective Hamiltonians and wavefunctions for the low-energy many-body eigenstates for the doped Mott liquid obtained from the stable fixed point of the RG flows, we demonstrate the collapse of the pseudogap for charge excitations (Mottness) at a quantum critical point (QCP) possessing a nodal non-Fermi liquid with superconducting fluctuations, and spin-pseudogapping near the antinodes. The QCP is characterised using both thermodynamic and quantum information-theoretic measures. d-wave superconducting order is shown to arise from this quantum critical state of matter. The pseudogap phase possesses a variety of fluctuations that lead to several symmetry-broken phases at low-energies. Benchmarking of the ground state energy per particle and the double-occupancy fraction obtained from a finite-size scaling analysis against existing numerical results yields excellent agreement. We present detailed insight into the T = 0 origin of several experimentally observed findings in the cuprates, including Homes law and Planckian dissipation. We also establish that the heirarchy of temperature scales for the pseudogap (TPG), onset temperature for pairing (Tons), formation of the Mott liquid (TML) and superconductivity (TC) obtained from our analysis is quantitatively consistent with that observed experimentally for some members of the cuprates. Our results offer insight on the ubiquitous origin of superconductivity in doped Mott insulating states, and pave the way towards a systematic search for higher superconducting transition temperatures in such systems.

A substantial hybridization between correlated Ni-d orbital and itinerant electrons in infinite-layer nickelates

The discovery of unconventional superconductivity in hole doped NdNiO2, similar to CaCuO2, has received enormous attention. However, different from CaCuO2, RNiO2 (R = Nd, La) has itinerant electrons in the rare-earth spacer layer. Previous studies show that the hybridization between Ni-{d}_{{x}^{2}-{y}^{2}} and rare-earth-d orbitals is very weak and thus RNiO2 is still a promising analog of CaCuO2. Here, we perform first-principles calculations to show that the hybridization between Ni-{d}_{{x}^{2}-{y}^{2}} orbital and itinerant electrons in RNiO2 is substantially stronger than previously thought. The dominant hybridization comes from an interstitial-s orbital rather than rare-earth-d orbitals, due to a large inter-cell hopping. Because of the hybridization, Ni local moment is screened by itinerant electrons and the critical UNi for long-range magnetic ordering is increased. Our work shows that the electronic structure of RNiO2 is distinct from CaCuO2, implying that the observed superconductivity in infinite-layer nickelates does not emerge from a doped Mott insulator.

Quantum entanglement in the t−J chain: From charge-spin separation to recombination

In contrast to the conventional von Neumann bipartite entanglement entropy (bEE), we show that a more appropriate description of the one-dimensional doped Mott insulator is a new kind of mutual entanglement entropy (mEE) between the charge and spin degrees of freedom. Such a charge-spin mEE can clearly distinguish the important and distinct features between the $t$-$J$ model and the so-called $\sigma\cdot{t}$-$J$ model. In the latter, the phase string sign structure is switched off such that a single doped hole always behaves like a Bloch wave in the whole regime of $J/t$, whereas in the former it exhibits a series of level crossing with the total momentum jumps in the single-hole ground state from spin-charge separation at $J/t\rightarrow{0}$ to spin-charge recombination at large $J/t$, which are failed to be detected by bEE. We further show that the distinctions between the two models persist to finite energy density, which can be similarly well characterized by mEE but not by bEE. By studying the dynamic time evolution of the states set out of equilibrium at the beginning, we show that mEE indeed always increases with the time, satisfying the common characteristic of entropy.

Thermoelectric properties of Mott insulator with correlated hopping at microdoping

An influence of the localization of itinerant electrons induced by correlated hopping on the electronic charge and heat transport is discussed for the lightly doped Mott insulator phase of the Falicov-Kimball model. The case of strongly reduced hopping amplitude between the sites with occupied f-electron levels, when an additional band of localized d-electron states could appear on the DOS in the Mott gap, is considered. Due to the electron-hole asymmetry and anomalous features on the DOS and transport function induced by correlated hopping, a strong enhancement of the Seebeck coefficient is observed at low temperatures, when the flattened dependence is displayed in a wide temperature range.

Effective Hamiltonian for nickelate oxides Nd1−xSrxNiO2

We derive the effective single-band Hamiltonian in the flat NiO$_2$ planes for nickelate compounds Nd$_{1-x}$Sr$_x$NiO$_2$. We first implement the first-principles calculation to study electronic structures of nickelates using the Heyd-Scuseria-Ernzerhof hybrid density functional and derive a three-band Hubbard model for Ni-O $pd\sigma$ bands of Ni$^+$ $3d_{x^2-y^2}$ and O$^{2-}$ $2p_{x/y}$ orbitals in the NiO$_2$ planes. To obtain the effective one-band $t$-$t'$-$J$ model Hamiltonian, we perform the exact diagonalization of the three-band Hubbard model for the Ni$_5$O$_{16}$ cluster and map the low-energy spectra onto the effective one-band models. We find that the undoped NiO$_2$ plane is a Hubbard Mott insulator, and the doped holes primarily locate on Ni sites. The physics of the NiO$_2$ plane is a doped Mott insulator, described by the one-band $t$-$t'$-$J$ model with $t=265$~meV, $t'=-21$~meV and $J=28.6$~meV. We also discuss the electronic structure for the "self-doping" effect and heavy fermion behavior of electron pockets of Nd$^{3+}$ $5d$ character in Nd$_{1-x}$Sr$_x$NiO$_2$.

Light-induced evaporative cooling of holes in the Hubbard model

An elusive goal in the field of driven quantum matter is the induction of long-range order. Here, we propose a mechanism based on light-induced evaporative cooling of holes in a correlated fermionic system. Since the entropy of a filled narrow band grows rapidly with hole doping, the isentropic transfer of holes from a doped Mott insulator to such a band results in a drop of temperature. Strongly correlated Fermi liquids and symmetry-broken states could thus be produced by dipolar excitations. Using nonequilibrium dynamical mean field theory, we show that suitably designed chirped pulses may realize this cooling effect. In particular, we demonstrate the emergence of antiferromagnetic order in a system which is initially in a weakly correlated state above the maximum Néel temperature. Our work suggests a general strategy for inducing strong correlation phenomena in periodically modulated atomic gases in optical lattices or light-driven materials.

Anomalous magnetoresistance due to longitudinal spin fluctuations in a Jeff\u2009=\u20091/2 Mott semiconductor

As a hallmark of electronic correlation, spin-charge interplay underlies many emergent phenomena in doped Mott insulators, such as high-temperature superconductivity, whereas the half-filled parent state is usually electronically frozen with an antiferromagnetic order that resists external control. We report on the observation of a positive magnetoresistance that probes the staggered susceptibility of a pseudospin-half square-lattice Mott insulator built as an artificial SrIrO3/SrTiO3 superlattice. Its size is particularly large in the high-temperature insulating paramagnetic phase near the Néel transition. This magnetoresistance originates from a collective charge response to the large longitudinal spin fluctuations under a linear coupling between the external magnetic field and the staggered magnetization enabled by strong spin-orbit interaction. Our results demonstrate a magnetic control of the binding energy of the fluctuating particle-hole pairs in the Slater-Mott crossover regime analogous to the Bardeen-Cooper-Schrieffer-to-Bose-Einstein condensation crossover of ultracold-superfluids.

Spectroscopic Evidence for Electron-Boson Coupling in Electron-Doped Sr_{2}IrO_{4}.

The pseudogap, d-wave superconductivity and electron-boson coupling are three intertwined key ingredients in the phase diagram of the cuprates. Sr_{2}IrO_{4} is a 5d-electron counterpart of the cuprates in which both the pseudogap and a d-wave instability have been observed. Here, we report spectroscopic evidence for the presence of the third key player in electron-doped Sr_{2}IrO_{4}: electron-boson coupling. Akink in nodal dispersion is observed with an energy scale of ∼50 meV. The strength of the kink changes with doping, but the energy scale remains the same. These results provide the first noncuprate platform for exploring the relationship between the pseudogap, d-wave instability, and electron-boson coupling in doped Mott insulators.

The analytical description of a doped Mott insulator

With the hierarchical Green’s function approach, we study a doped Mott insulator described with the Hubbard model by analytically solving the equations of motion of an one-particle Green’s function and related multiple-point correlation functions, and find that the separation of the spin and charge degrees of freedom of the electrons is an intrinsic character of the doped Mott insulator. For enough of large on-site repulsive Coulomb interaction, we show that the spectral weight of the one-particle Green’s function is proportional to the hole doping concentration that is mainly produced by the charge fluctuation of electrons, while the excitation spectrum of the electrons is composed of two parts: One is contributed by the spin fluctuation of the electrons, which is proportional to the hole doping concentration, and another one is coming from the coupling between the charge and spin fluctuations of the electrons that takes the maximum at undoping. All of these low energy/temperature physical properties originate from the strong on-site Coulomb interaction. The present results are consistent with the spectroscopy observations of the cuprate superconductors and the numerical calculations in normal state above the pseudogap regime.

Evidence for a universal Fermi-liquid scattering rate throughout the phase diagram of the copper-oxide superconductors

The phase diagram of the cuprate superconductors continues to pose formidable scientific challenges. While these materials are typically viewed as doped Mott insulators, it is well known that they are Fermi liquids at high hole-dopant concentrations. It was recently demonstrated that at moderate doping, in the pseudogap (PG) region of the phase diagram, the charge carriers are also best described as a Fermi liquid. Nevertheless, the relationship between the two Fermi-liquid (FL) regions and the nature of the strange-metal (SM) state at intermediate doping have remained unsolved. Here we show for the case of the model cuprate superconductor HgBa2CuO4+δ that the normal-state transport scattering rate determined from the cotangent of the Hall angle remains quadratic in temperature across the PG temperature, upon entering the SM state, and that it is doping-independent below optimal doping. Analysis of prior transport results for other cuprates reveals that this behavior is universal throughout the entire phase diagram and points to a pervasive FL transport scattering rate. These observations can be reconciled with a variety of other experimental results for the cuprates upon considering the possibility that the PG phenomenon is associated with the gradual, non-uniform localization of one hole per planar CuO2 unit.

Quantum Correlated Plasmons and Their Tunability in Undoped and Doped Mott-Insulator Cuprates

Plasmons, collective excitations of charge density, have attracted much interest in fundamental science and applications. While plasmons have been observed in metal-like phase of high-Tc supercondu...

Atomic-scale fragmentation and collapse of antiferromagnetic order in a doped Mott insulator

Disentangling the relationship between the insulating state with a charge gap and the magnetic order in an antiferromagnetic (AF) Mott insulator remains difficult due to inherent phase separation as the Mott state is perturbed. Measuring magnetic and electronic properties at the atomic length scales would provide crucial insight, but this is yet to be experimentally achieved. Here we use spectroscopic-imaging spin-polarized scanning tunneling microscopy (SP-STM) to visualize periodic spin-resolved modulations originating from the AF order in a relativistic Mott insulator Sr2IrO4, and study these as a function of doping. We find that near insulator-to-metal transition (IMT), the long-range AF order melts into a fragmented state with short-range AF correlations. Crucially, we discover that the short-range AF order is locally uncorrelated with the observed spectral gap magnitude. This strongly suggests that short range AF correlations are unlikely to be the culprit behind inhomogeneous gap closing and the emergence of pseudogap regions near IMT. Our work establishes SP-STM as a powerful tool for revealing atomic-scale magnetic information in complex oxides.