No Arabic abstract
The exactly-solvable Kitaev model of two-dimensional honeycome magnet leads to a quantum spin liquid (QSL) characterized by Majorana fermions, relevant for fault-tolerant topological quantum computations.In the high-field paramagnetic state of $alpha$-RuCl$_3$, half-integer quantization of thermal Hall conductivity has been reported as a signature of Majorana fermions, but the bulk nature of this state remains elusive.Here, from high-resolution heat capacity measurements under in-plane field rotation, we find strongly angle-dependent low-energy excitations in the bulk of $alpha$-RuCl$_3$. The excitation gap has a sextuple node structure, and the gap amplitude increases with field, exactly as expected for itinerant Majorana fermions in the Kitaev model.Our thermodynamic results are fully linked with the transport quantization properties, providing the first demonstration of the bulk-edge correspondence in a Kitaev QSL.
Recently, the resistance saturation at low temperature in Kondo insulator SmB6, a long-standing puzzle in condensed matter physics, was proposed to originate from topological surface state. Here,we systematically studied the magnetoresistance of SmB6 at low temperature up to 55 Tesla. Both temperature- and angular-dependent magnetoresistances show a similar crossover behavior below 5 K. Furthermore, the angular-dependent magnetoresistance on different crystal face confirms a two-dimensional surface state as the origin of magnetoresistances crossover below 5K. Based on two-channels model consisting of both surface and bulk states, the field-dependence of bulk gap with critical magnetic field (Hc) of 196 T is extracted from our temperature-dependent resistance under different magnetic fields. Our results give a consistent picture to understand the low-temperature transport behavior in SmB6, consistent with topological Kondo insulator scenario.
The ruthenium halide $alpha$-RuCl$_{3}$ is a promising candidate for a Kitaev spin liquid. However, the microscopic model describing $alpha$-RuCl$_{3}$ is still debated partly because of a lack of analogue materials for $alpha$-RuCl$_{3}$, which prevents tracking of electronic properties as functions of controlled interaction parameters. Here, we report a successful synthesis of RuBr$_{3}$. The material RuBr$_{3}$~possesses BiI$_3$-type structure (space group: $Roverline{3}$) where Ru$^{3+}$ form an ideal honeycomb lattice. Although RuBr$_{3}$ has a negative Weiss temperature, it undergoes a zigzag antiferromagnetic transition at $T_mathrm{N}=34$ K, as does $alpha$-RuCl$_{3}$. Our analyses indicate that the Kitaev and non-Kitaev interactions can be modified in ruthenium trihalides by changing the ligand sites, which provides a new platform for exploring Kitaev spin liquids.
Effects of bond randomness and site dilution are systematically investigated for the Kitaev model describing a quantum spin liquid with fractional excitations of itinerant Majorana fermions and localized fluxes. We find that, in the high-temperature region where the itinerant Majorana fermions release their entropy, both types of disorders suppress the longitudinal thermal conductivity while keeping the specific heat almost unchanged. This suggests that both disorders reduce the mean-free path of the Majorana fermions. On the other hand, in the low-temperature region, the other specific heat peak associated with the entropy release from the localized fluxes is suppressed for both cases, but it is broadened and shifted to the lower-temperature side by the bond randomness, while the position and the width are almost unchanged against the site dilution. Contrasting behavior is also found in the thermal Hall effect under a magnetic field; the half quantization of the thermal Hall conductivity is fragile against the site dilution, while it remains for the bond randomness despite the reduced onset temperature. We discuss the contrasting behavior from the stability of the topological nature by calculating flux condensation and Majorana excitation gap.
We report a comprehensive investigation of the magnetism of the $S$ = 3/2 triangular-lattice antiferromagnet, $alpha$-CrOOH(D) (delafossites green-grey powder). The nearly Heisenberg antiferromagnetic Hamiltonian ($J_1$ $sim$ 23.5 K) with a weak single-ion anisotropy of $|D|$/$J_1$ $sim$ 4.6% is quantitatively determined by fitting to the electron spin resonance (ESR) linewidth and susceptibility measured at high temperatures. The weak single-ion anisotropy interactions, possibly along with other perturbations, e.g. next-nearest-neighbor interactions, suppress the long-range magnetic order and render the system disordered, as evidenced by both the absence of any clear magnetic reflections in neutron diffraction and the presence of the dominant paramagnetic ESR signal down to 2 K ($sim$ 0.04$J_1$$S^2$), where the magnetic entropy is almost zero. The power-law behavior of specific heat ($C_m$ $sim$ $T^{2.2}$) observed below the freezing temperature of $T_f$ = 25 K in $alpha$-CrOOH or below $T_f$ = 22 K in $alpha$-CrOOD is insensitive to the external magnetic field, and thus is consistent with the theoretical prediction of a gapless U(1) Dirac quantum spin liquid (QSL) ground state. At low temperatures, the spectral weight of the low-energy continuous spin excitations accumulates at the K points of the Brillouin zone, e.g. $|mathbf{Q}|$ = 4$pi$/(3$a$), and the putative Dirac cones are clearly visible. Our work is a first step towards the understanding of the possible Dirac QSL ground state in this triangular-lattice magnet with $S$ = 3/2.
Magnetic fields can give rise to a plethora of phenomena in Kitaev spin systems, such as the formation of non-trivial spin liquids in two and three spatial dimensions. For the original honeycomb Kitaev model, it has recently been observed that the sign of the bond-directional exchange is of crucial relevance for the field-induced physics, with antiferromagnetic couplings giving rise to an intermediate spin liquid regime between the low-field gapped Kitaev spin liquid and the high-field polarized state, which is not present in the ferromagnetically coupled model. Here, by employing a Majorana mean-field approach for a magnetic field pointing along the [001] direction, we present a systematic study of field-induced spin liquid phases for a variety of two and three-dimensional lattice geometries. We find that antiferromagnetic couplings generically lead to (i) spin liquid phases that are considerably more stable in field than those for ferromagnetic couplings, and (ii) an intermediate spin liquid phase which arises from a change in the topology of the Majorana band structure. Close inspection of the mean-field parameters reveal that the intermediate phase occurs due to a field-driven sign change in an effective $z$-bond energy parameter. Our results clearly demonstrate the richness of the Majorana physics of the antiferromagnetic Kitaev models, in comparison to their ferromagnetic counterparts.