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arXiv:2212.08768 · Physical review. B./Physical review. B

Electronic density of states of a U(1) quantum spin liquid with spinon Fermi surface. II. Zeeman magnetic field effects

Wen‐Yu He, Patrick A. Lee

Published May 31, 2023• 10 citations
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Abstract

This work studies the Zeeman magnetic field effect on a quantum spin liquid with a spinon Fermi surface. In the absence of gauge binding, the quantum spin liquid electronic density of states exhibits no Zeeman shift in the threshold energy. As the gauge binding increases, the band edge resonance peaks exhibit a reduced Zeeman shift and eventually have the Zeeman shift direction reversed for a sufficiently large gauge binding. The authors further suggest to use such anomalous Zeeman response to identify the gapless quantum spin liquid phase.

DOI
10.1103/physrevb.107.195156

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This work studies the Zeeman magnetic field effect on a quantum spin liquid with a spinon Fermi surface. In the absence of gauge binding, the quantum spin liquid electronic density of states exhibits no Zeeman shift in the threshold energy. As the gauge binding increases, the band edge resonance peaks exhibit a reduced Zeeman shift and eventually have the Zeeman shift direction reversed for a sufficiently large gauge binding. The authors further suggest to use such anomalous Zeeman response to identify the gapless quantum spin liquid phase.
The authors study the orbital magnetic field induced Landau quantization of a quantum spin liquid with spinon Fermi surface. In the electronic density of states of the quantum spin liquid, the Landau quantization is found to induce a set of band-edge steps, band-edge resonance peaks, or in-gap bound states when the gauge-field fluctuations are negligible, weak, or strong, respectively. The results indicate that the Landau quantization of the spinon Fermi surface can be detected through scanning tunneling microscope measurements.
Electronic Density of States of a U(1)U\left(1\right)U(1) Quantum Spin Liquid with Spinon Fermi Surface. I. Orbital Magnetic Field Effects
Quantum spin liquid (QSL) with spinon Fermi surface is an exotic insulator that hosts neutral Fermi surfaces inside the gap. In an external magnetic field, it has been pointed out that the neutral Fermi surfaces are Landau quantized to form Landau levels (LLs) due to the induced emergent gauge magnetic field. In this work, we calculate the electronic density of states (DOS) of the QSL in an orbital magnetic field. We find that the LLs from the neutral Fermi surfaces give rise to a set of steps emerging at the upper and lower Hubbard band edges. Each of the Hubbard band edge steps further develop into a band edge resonance peak when a weak gauge binding from the gauge field fluctuations is taken into account. Importantly, each Hubbard band edge step and its resulting resonance peak in the weak gauge binding are found to have a correspondence LL from the neutral Fermi surfaces, so the Hubbard band edge steps and the band edge resonance peaks are the unique features that characterize the Landau quantization of the in-gap neutral Fermi surfaces. We further consider the strong gauge binding regime where the band edge resonance peaks move into the Mott gap and develop into true in-gap bound states. In the strong gauge binding regime, we solve the bound state LL spectrum. For the bound state with a Mexican hat like band dispersion, we find that the envelop energy to have a state excited from the bound state LL decreases quadratically with the magnetic field. The quadratic decrease behavior of the envelop energy is consistent with the intuition that applying magnetic field localizes the states and energetically promotes the in-gap bound states formation. Finally, we connect our results to the electronic DOS spectra measured in the layered 1T-TaS2_22​. We point out that a QSL with a quasi-bound state in the upper Hubbard band can give the DOS spectra similar to the one measured in the experiment.
We study the transverse dynamical spin susceptibility of the two-dimensional U(1) spinon Fermi-surface spin liquid in a small applied Zeeman field. We show that both short-range interactions, present in a generic Fermi liquid, as well as gauge fluctuations, characteristic of the U(1) spin liquid, qualitatively change the result based on the frequently assumed noninteracting spinon approximation. The short-range part of the interaction lead to a collective ``spinon spin wave'' mode, which splits off from the two-spinon continuum at a small momentum and disperses downward. Gauge fluctuations renormalize the susceptibility, providing nonzero power-law weight in the region outside the spinon continuum and giving the spin wave a finite lifetime, which scales as momentum squared. We also study the effect of Dzyaloshinskii-Moriya anisotropy on the zero momentum susceptibility, which is measured in electron spin resonance (ESR), and obtain a resonance linewidth linear in temperature and varying as B2/3{B}^{2/3}B2/3 with magnetic field BBB at low temperatures. Our results form the basis for a theory of inelastic neutron scattering, ESR, and resonant inelastic x-ray scattering studies of this quantum spin-liquid state.
We solve the problem of a magnetic impurity coupled to a U(1)U(1)U(1) quantum spin liquid with a spinon Fermi surface, and we compute the impurity spectral function. Using the slave rotor mean-field approach combined with gauge field fluctuations, we find that a peak located at the top of the lower Hubbard band and one at the bottom of the upper Hubbard band can emerge in the impurity spectral function. The peaks at the Hubbard band edges arise from the gauge field fluctuation-induced spinon-chargon binding inside the spinon Kondo screening cloud of the magnetic impurity. For a magnetic impurity embedded in a Mott insulator, our findings suggest that the emergence of a pair of peaks at the Hubbard band edges in the impurity density of states spectra provides strong evidence that the host Mott insulator is a U(1)U(1)U(1) quantum spin liquid with a spinon Fermi surface.
We address the problem of a magnetic impurity in a two-dimensional U(1)U(1)U(1) spin liquid where the spinons have gapless excitations near the Fermi surface and are coupled to an emergent gapless gauge field. Using a large N expansion, we analyze the strong coupling behavior and obtain the Kondo temperature which was found to be the same as for a Fermi liquid. In this approximation, we also study the specific heat and the magnetic susceptibility of the impurity. These quantities present no deviations from the Fermi liquid ones, consistent with the notion that the magnetic impurity is only sensitive to the local density of fermionic states.
The Kitaev model with an applied magnetic field in the [Formula: see text] direction shows two transitions: from a nonabelian gapped quantum spin liquid (QSL) to a gapless QSL at [Formula: see text] and a second transition at a higher field [Formula: see text] to a gapped partially polarized phase, where K is the strength of the Kitaev exchange interaction. We identify the intermediate phase to be a gapless U(1) QSL and determine the spin structure function [Formula: see text] and the Fermi surface [Formula: see text] of the gapless spinons using the density matrix renormalization group (DMRG) method for large honeycomb clusters. Further calculations of static spin-spin correlations, magnetization, spin susceptibility, and finite temperature-specific heat and entropy corroborate the gapped and gapless nature of the different field-dependent phases. In the intermediate phase, the spin-spin correlations decay as a power law with distance, indicative of a gapless phase.