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arXiv:2112.14991 · Physical Review Research

Majorana chiral spin liquid in a model for Mott insulating cuprates

Jaime Merino, Arnaud Ralko

Published May 16, 2022• 8 citations
arXivHTMLPDF

Abstract

The large thermal Hall conductivity recently detected in Mott insulating cuprates has been attributed to chiral neutral spin excitations. A quantum spin liquid (QSL) with Majorana excitations, Chern number $\ifmmode\pm\else\textpm\fi{}4$ and large thermal Hall conductivity is found to be an excited state of a frustrated Heisenberg model on the square lattice. Using a Majorana mean-field theory and exact diagonalizations, we explore two possible routes to achieve this chiral QSL, an orbital magnetic-field effect and spin-orbit couplings as present in cuprates. In particular, we show how only the orbital magnetic field allows this topological phase to be the ground state, while it remains an excited state of the Majorana mean field under the Dzyaloshinskii-Moriya terms. A large quantized low-temperature thermal Hall effect can be induced in our model of Mott insulating cuprates by the orbital effect of an applied magnetic field.

DOI
10.1103/physrevresearch.4.023122

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The large thermal Hall conductivity recently detected in Mott insulating cuprates has been attributed to chiral neutral spin excitations. A quantum spin liquid (QSL) with Majorana excitations, Chern number \ifmmode±\else\textpm\fi4\ifmmode\pm\else\textpm\fi{}4\ifmmode±\else\textpm\fi4 and large thermal Hall conductivity is found to be an excited state of a frustrated Heisenberg model on the square lattice. Using a Majorana mean-field theory and exact diagonalizations, we explore two possible routes to achieve this chiral QSL, an orbital magnetic-field effect and spin-orbit couplings as present in cuprates. In particular, we show how only the orbital magnetic field allows this topological phase to be the ground state, while it remains an excited state of the Majorana mean field under the Dzyaloshinskii-Moriya terms. A large quantized low-temperature thermal Hall effect can be induced in our model of Mott insulating cuprates by the orbital effect of an applied magnetic field.
Motivated by recent transport measurements in high-Tc{T}_{c}Tc​ cuprate superconductors in a magnetic field, we study the thermal Hall conductivity in materials with topological order, focusing on the contribution from neutral spinons. Specifically, different Schwinger boson mean-field Ans\"atze for the Heisenberg antiferromagnet on the square lattice are analyzed. We allow for both Dzyaloshinskii-Moriya interactions, and additional terms associated with scalar spin chiralities that break time-reversal and reflection symmetries, but preserve their product. It is shown that these scalar spin chiralities, which can either arise spontaneously or are induced by the orbital coupling of the magnetic field, can lead to spinon bands with nontrivial Chern numbers and significantly enhanced thermal Hall conductivity. Associated states with zero-temperature magnetic order, which is thermally fluctuating at any T>0T>0T>0, also show a similarly enhanced thermal Hall conductivity.
In this work we study the phase diagram of the Kekul\'e-Kitaev model. The model is defined on a honeycomb lattice with bond-dependent anisotropic exchange interactions, making it exactly solvable in terms of Majorana representation of spins, in close analogy to the Kitaev model. However, the energy spectrum of Majorana fermions has a multiband structure characterized by Chern numbers 0, $\ifmmode\pm\else\textpm\fi{}1$, and $\ifmmode\pm\else\textpm\fi{}2$. We obtained the phase diagram of the model in the plane of exchange couplings and in the presence of a magnetic field and found chiral topological and trivial spin-liquid ground states. In the absence of magnetic field most of the phase diagram is a trivial gapped phase continuously connected to an Abelian phase, while in the presence of the magnetic field a topological phase arises. Furthermore, motivated by recent thermal measurements on the spin-liquid candidate $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$, we calculated the thermal Hall conductivity at different regimes of parameters and temperatures and found the latter is quantized over a wide range of temperatures.
The search for exotic states of matter continues to be a central theme in condensed matter physics. Among these, quantum spin liquids (QSLs) represent a profound challenge and opportunity, characterized by long-range entanglement and fractionalized excitations without conventional magnetic order even at absolute zero temperature. Frustrated quantum magnets are prime candidates for hosting such states, where competing interactions prevent classical ground states. This paper reports the theoretical and experimental signatures that would lead to the discovery of a chiral bosonic liquid (CBL) in a novel frustrated quantum magnet. A CBL is a particularly elusive type of QSL characterized by elementary excitations that behave as bosons and exhibit a distinct chirality, manifesting as a non-zero thermal Hall effect in the absence of a magnetic field. We outline a comprehensive strategy involving advanced material synthesis, precise low-temperature thermodynamic measurements, inelastic neutron scattering, and numerical simulations to identify the unique fingerprints of this novel state. Key indicators include a gapless or nearly gapless excitation spectrum, a specific heat scaling characteristic of bosonic excitations, and, most critically, a quantized or near-quantized thermal Hall conductivity directly reflecting the chiral nature of the bosonic fractional excitations. The implications of this discovery extend to fundamental understanding of quantum entanglement, topological states of matter, and potential applications in robust quantum information processing.
We study quantum phase transitions in the honeycomb Kitaev model under a magnetic field, focusing on the topological nature of Majorana fermion excitations. We find a gapless phase between the low-field gapless quantum spin liquid and the high-field gapped forced-ferromagnetic state for the antiferromagnetic Kitaev model in the [001] field by using the Majorana mean-field theory, in conjunction with the exact diagonalization and the spin-wave theory supporting the validity of this approach. The transition between the two gapless phases is driven by a topological change of the Majorana spectrum---line node formation interconnecting two Majorana cones. The peculiar change of the Majorana band topology is rationalized by a sign change of the effective Kitaev coupling by the magnetic field, which does not occur in the ferromagnetic Kitaev case. Upon tilting the magnetic field away from [001], the two gapless phases become gapped and topologically nontrivial, characterized by nonzero Chern numbers with different signs. The sign change of the Chern number leads to a reversal of the thermal edge current in the half-quantized thermal Hall effect.
The competition between fractionalized spin-liquid states and magnetically ordered phases is an important paradigm in frustrated magnetism. Spin-orbit coupled Mott insulators with Ising-like magnetic anisotropies, such as Kitaev materials, are a particularly rich playground to explore this competition. In this work, we use effective field theory methods to show that a direct quantum phase transition can occur in two-dimensional (2D) Ising spin systems between a topologically ordered chiral spin liquid and a phase with magnetic long-range order. Such a transition can be protected by lattice symmetries and is described by a theory of massless Majorana fields coupled to non-Abelian SO(N)\text{SO}(N)SO(N) gauge fields with a Chern-Simons term. We further show that Euclidean Majorana zero modes bound to Z2{\mathbb{Z}}_{2}Z2​ monopole-instantons in the emergent non-Abelian gauge field are key to understanding spontaneous symmetry breaking in the ordered phase.
Abstract Quantum spin liquid (QSL) has become an exciting topic in interacting spin systems that do not order magnetically down to the lowest experimentally accessible temperature; however, conclusive experimental evidence remains lacking. Motivated by the recent surge of theoretical and experimental interest in a half-filled Hubbard model on the triangular lattice, where chiral QSL can be stabilized, we investigate the electromagnetic signature of the chiral QSL to aid experimental detection. We systematically studied the electrical charge and orbital electrical current associated with a spinon excitation in the chiral QSL based on parton mean-field theory and unbiased density-matrix renormalization group calculations. We then calculated both longitudinal and transverse optical conductivities below the Mott gap. We also conduct quantum field theory analysis to unravel the connection between spinon excitation and emergent and physical gauge fields. Our results show that the chiral QSL phase has a clear electromagnetic response even in a Mott insulator regime, which can facilitate the experimental detection of this long-sought-after phase.