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arXiv:2406.15553 · Physical review. B./Physical review. B

Electric transport in doped Mott insulators dictated by a non-Ioffe-Larkin composition rule and spinons

Chuan Chen, Jiaxin Zhang, Zhi-Jian Song, Zheng-Yu Weng

Published Apr 21, 2025• 3 citations
arXivHTMLPDF

Abstract

Electric resistivity is examined in the constrained Hilbert space of a doped Mott insulator, which is dictated by a non-Ioffe-Larkin composition rule due to the underlying mutual Chern-Simons topological gauge structure. In the low-temperature pseudogap phase, where holons remain condensed while spinons proliferate, charge transport is governed by chiral spinon excitation, comprising a bosonic spin-$\frac{1}{2}$ at the core of a supercurrent vortex. It leads to vanishing resistivity with the confinement of the spinons in the superconducting phase but low-$T$ divergence of the resistivity once the spinon confinement is disrupted by external magnetic fields. In the latter, the chiral spinons will generate a Hall number ${n}_{H}=$ doping concentration $\ensuremath{\delta}$ and a Nernst effect to signal underlying long-range entanglement between the charge and spin degrees of freedom. Their presence is further reflected in thermodynamic quantities such as specific heat and spin susceptibility. Finally, in the high-temperature spin-disordered phase, it is shown that the holons exhibit linear-$T$ resistivity by scattering with the spinons acting as free local moments, which generate randomized gauge fluxes as perceived by the charge degree of freedom.

DOI
10.1103/physrevb.111.165138

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Electric resistivity is examined in the constrained Hilbert space of a doped Mott insulator, which is dictated by a non-Ioffe-Larkin composition rule due to the underlying mutual Chern-Simons topological gauge structure. In the low-temperature pseudogap phase, where holons remain condensed while spinons proliferate, charge transport is governed by chiral spinon excitation, comprising a bosonic spin-12\frac{1}{2}21​ at the core of a supercurrent vortex. It leads to vanishing resistivity with the confinement of the spinons in the superconducting phase but low-TTT divergence of the resistivity once the spinon confinement is disrupted by external magnetic fields. In the latter, the chiral spinons will generate a Hall number nH={n}_{H}=nH​= doping concentration \ensuremathδ\ensuremath{\delta}\ensuremathδ and a Nernst effect to signal underlying long-range entanglement between the charge and spin degrees of freedom. Their presence is further reflected in thermodynamic quantities such as specific heat and spin susceptibility. Finally, in the high-temperature spin-disordered phase, it is shown that the holons exhibit linear-TTT resistivity by scattering with the spinons acting as free local moments, which generate randomized gauge fluxes as perceived by the charge degree of freedom.
In the pseudogap phase of the cuprate, a thermal Hall response of neutral objects has been recently detected experimentally, which continuously persists into the antiferromagnetic insulating phase. In this paper, we study the transport properties of neutral spinons as the elementary excitation of a doped Mott insulator, which is governed by a mutual Chern-Simons topological gauge structure. We show that such a chiral spinon as a composite of an S = 1 / 2 spin sitting at the core of a supercurrent vortex, can contribute to the thermal Hall effect, thermopower, and Hall effect due to its intrinsic transverse (cyclotron) motion under internal fictitious fluxes. In particular, the magnitudes of the transport coefficients are phenomenologically determined by two basic parameters: the doping concentration and T c , quantitatively consistent with the experimental measurements including the signs and qualitative temperature and magnetic-field dependence. Combined with the predictions of the spinon longitudinal transport properties, including the Nernst and spin Hall effects, a phenomenological description of the pseudogap phase is established as characterized by the neutral spinon excitations, which eventually become “confined” with an intrinsic superconducting transition at T c . Finally, within this theoretical framework, the “order to order” phase transition between the superconducting and antiferromagnetic insulating phases are briefly discussed, with the thermal Hall monotonically increasing into the latter. Published by the American Physical Society 2024
The pseudogap phase is considered to be a new state of matter in the phase string model of the doped Mott insulator, which is composed of two distinct regimes known as the upper and lower pseudogap phases, respectively. The former corresponds to the formation of spin-singlet pairing, the magnetic characterizations of which have been recently studied [Phys. Rev. B 72, 104520 (2005)]. The latter, as a low-temperature regime of the pseudogap phase, is systematically explored in this work, which is characterized by the formation of the Cooper pair amplitude and described by a generalized Ginzburg-Landau theory. Elementary excitation in this phase is a charge-neutral object carrying spin-1∕21∕21∕2 and locking with a supercurrent vortex, known as a spinon-vortex composite. Such a lower pseudogap phase can be regarded as a vortex liquid state due to the presence of free spinon vortices. Here thermally excited spinon vortices destroy the phase coherence and are responsible for the nontrivial Nernst effect and diamagnetism. The transport entropy and core energy associated with a spinon vortex are determined by the spin degrees of freedom. Such a spontaneous vortex liquid phase can be also considered as a spin liquid with a finite correlation length and gaped S=1∕2S=1∕2S=1∕2 excitations, where a resonancelike nonpropagating spin mode emerges at the antiferromagnetic wavevector $(\ensuremath{\pi},\ensuremath{\pi})$ with a doping-dependent characteristic energy. The superconducting phase is closely related to the lower pseudogap phase by a topological transition with spinon vortices and antivortices forming bound pairs and the emergence of fermionic quasiparticles as holon-spinon-vortex bound objects. A quantitative phase diagram in the parameter space of doping, temperature, and magnetic field is determined. Comparisons with experiments are also made.
A phenomenological description for confinement of fractionalized excitations is proposed in the gauge theory approach for doped Mott insulators. Introducing the Polyakov-loop parameter into an SU(2) gauge theory for the t-J model, we show that electron excitations emerge below the so-called coherence temperature, resulting from confinement of spinons and holons via the formation of the Polyakov loop. Remarkably, such confined electrons turn out to exhibit non-Fermi liquid physics without quantum criticality, yielding the electric resistivity in quantitative agreement with experimental data. The Higgs phase is not allowed due to confinement, suggesting a possible novel mechanism of superconductivity in the strong coupling approach.
A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a T2{\mathit{T}}^{2}T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.
We propose an explanation of several experimental features related to the "pseudogap" in high Tc cuprates in terms of a spin-charge gauge theory. In this approach, based on a formal spin-charge separation applied to the t-J model, the low energy effective action describes gapful spinons (with a theoretically derived doping dependence of the gap ms~J(δ| ln δ|)1/2, where δ is the doping concentration) and holons with "small" Fermi surface (∊F~tδ) interacting via a gauge field. The main effect of gauge fluctuations is to introduce a dissipation ~T/χ, where χ is the diamagnetic susceptibility. The competition between the two energy scales, ms and T/χ, is the root in our approach of many phenomena peculiar to in-plane transport properties of the "pseudogap phase". Furthermore the gauge interaction induces binding of spinon and holon into an "electron" resonance. This binding introduces another energy scale, the recombination rate, which dominates the out-of-plane resistivity, yielding an insulating behavior. A good agreement is found between the experimental data and theoretically derived doping and temperature dependence of resistivity, both in-plane and out-of-plane, and spin relaxation.
In this work, we present a topological characterization of superconductivity in a prototype electron fractionalization model for doped Mott insulators. In this model, spinons and holons are coupled via the mutual Chern-Simons gauge fields. We obtain a low-lying effective description of the collective current fluctuations by integrating out the matter fields, which replaces the conventional Ginzburg-Landau action to describe the generalized rigidity of superconductivity. The superconducting phase coherence is essentially characterized by a topological order parameter related to a Gaussian linking number, and an experiment is proposed to probe this topological property. We further show that a gauge-neutral fermionic mode can naturally emerge in this model, which behaves like a Bogoliubov quasiparticle.