 Two talks. So since we encourage people to ask a question during the talk, so when you raise the hand, also say the word question. And then it will bring the microphone to you, because otherwise I will not see who is raising the hand. And the first speaker is Eugene Matsuda. And the title of the talk, Myaranda Quantization and Half-Integer Thermal Quantum Whole Effect in a Kitai spin liquid. Thank you very much. So first of all, I'd like to thank the organizer inviting this workshop. So today, I'd like to talk about Myaranda fermions and quantum whole phenomena in quantum magnet. This main player of this work is Kasahara, Onishi, and Ma, and Sugii, in the middle of Tokyo. And the work has been done in collaboration with Takashi Baichi's group. And the single crystals has been grown by Tanaka's group, Tokyo Institute of Technology. And Nassu and Motome gave us many important theoretical suggestions. In my talk, I'd like to start with explaining the Kitai quantum spin liquid quite briefly. Then I talk about detecting Myaranda fermions in insulating magnet. Then I talk about Kitai candidate material, alpha-routinium shield 3. After that, I'll focus on thermal whole effect in alpha-routinium shield 3. In particular, I'll address the issue of half-integer quantized thermal whole conductance and topological phase transition. The Kitai interaction is a bond dependent, ising like interactions. And each bond favors different directions of x, y, and z, x, y, and z. Then the spins cannot satisfy the three different configurations simultaneously, leading to exchange frustrations. In 2D honeycomb lattice and 3D hyper honeycomb lattice, exactly solvable quantum spin liquid grand state appears. In Kitai model, spins can be represented in terms of four Myaranda fermions, a particle is its own antiparticles under this constraint. In Kitai model, this bracket operator commutes with total Hamiltonian. And because WP square is unity, the WP can be taken as plus minus 1. In the grand state, the old bracket takes a value of plus 1. The excited state is a minus 1 state, which is called G2 flux bisome. The Kitai spin rigid has very short spin correlation lengths. But actually, this state is orthogonal to this state. Then the spin correlation length is similar to Bratz spacing. Then the quantum spin rigid state with extremely short spin correlation length appears in the Kitai model. There are two types of Kitai quantum spin rigid state, depending on the anisotropy of J1, Jx, Jy, Jz. The very anisotropic case, the gap spin rigid, appears. And when the small anisotropy, the gap spin rigid with 2D deluxe cone appears. Then today, I'd like to discuss in this region. Two types of excitations in the quantum spin rigid due to the fractionation of quantum spins, namely the Italian and localised minor fermions, G2 flux bisome. At a very high temperature, larger than the Kitai of interactions, system is a parabenetic regime. On the other hand, at a very low temperature regime, system is a quantum spin rigid with deluxe dispersions. And only the Italian and the minor fermions are moving in the bulk. In the intermediate temperature range, the G2 flux are excited and interact with the Italian and the minor fermions. Together, let me discuss how to detect the minor fermions in these initiating magnets. In the absence of magnetic field, as I mentioned, minor fermi-metal state with deluxe cone dispersion appears in the bulk. The magnetic field opens up the gap. And topologically, a non-trivial state with the channel number of unity appears in the bulk. And so this is different from the, in this sense, this state is very different from the graphene. Because in graphene, if you have a magnetic field, the gap does not open. And as a result, the chiral edge current of gap-less neutral minor fermions appears at the edge of the sample. Then how to detect this chiral minor edge current? Because the minor fermions cannot carry the heat, but can carry the heat. The thermal hole effect is a very powerful probe to detect this chiral minor edge current. So let me compare the system with the chiral quantum magnet with two-dimensional electron gas, which shows the quantum hole effect. I would like to remind you, in quantum hole effect, two-dimensional conductivity sigma xy is quantized in the unit of e square over h. In the integer quantum hole effect, nu is 1, 2, 3. And edge current carried by electrons. In the fractional quantum hole effect, the nu is 1, 3, 2, 5. And the denominator is usually odd number. And in this case, the edge current carried by fractional recharged quasi-particles. Also, it is less known that in the quantum hole state, thermal hole conductance is also quantized. Actually, the two-dimensional thermal hole conductance, couple xy 2D divided by temperature, is quantized in units of this quantity. So q is the central charge and n equal 1, 2, 3. Then in the integer quantum hole effect, and the usual fractional quantum hole effect with auto-denominator, the integer thermal hole, integer thermal quantum hole effect is observed. This is recently reported by Weitzman group. Then let me discuss a case for a quantum spin rigid. In the Kitei quantum spin rigid, the edge current of the neutral Mylar fermion carries the heat. Because our degree of freedom of Mylarna is half of the conventional fermion, and q is 1 half, namely the non-Aberian enions. So in this case, two-dimensional thermal hole conductance divided by temperature takes half value of this quantity. So namely, half-integer thermal quantum hole effect is expected. In other words, if we observe this half-integer thermal quantum hole effect, this provides the direct evidence of Mylarna particle. So let me introduce the thermal hole effect quite briefly. The thermal hole effect is a? I'm sorry, I don't understand. Do you have the Z2 field applied in your akitaev model? In 2D electron gas quantum hole effect, you apply magnetic field. And in akitaev spin rigid, what plays the role of the magnetic? It is because we apply the magnetic field, perpendicular to the plane. Adjust magnetic field? Yeah, we apply the magnetic field. But it does not act on the Mylarna fermions the same way as magnetic field acts on ordinary fermions. If we apply the magnetic field to the akitaev spin rigid, the gap opens in the bulk. But at the edge, the gapless state appears. They are similar to the quantum hole effect. But in zero field, there is no gap. With a thermal hole effect is a similar analog of the electrical hole effect. And it is a transverse response in the applied current and magnetic field. Let me discuss the further we are measuring. The further we can measure is the Jx and the temperature gradient around the x-axis and y-axis. And using these relations, we determine kappa xx and kappa xy. The far as important is that in contrast to kappa xx, kappa xy does not contain the phonon contribution. Then the kappa xy only contains the spin contributions. Then we have some advantage to measure kappa xy. So let me discuss the akitaev candidate material, alphardenium CL3. The akitaev type interactions arise from partially filled T2G levels in the presence of strongly spin omitted coupling. Then the J equal 1 half motor insulator appears. The material, honeycomb lattice, with 90-degree bound bond by H shared octahedral, can host the akitaev systems, as suggested by Jack Allen and Kalyurin. Actually, in this case, the super exchange pass from this one and this one cancels. Then we can obtain the akitaev interaction. With the recently strongly spin omitted coupled, J equal 1 half motor insulator, alphardenium CL3, has emerged as a prime candidate for hosting a properly approximate akitaev quantum spin rigid. So today I discuss this material. Actually, in this material, the first principle calculation shows that akitaev interaction has dominance. But actually, this material contains the Heisenberg term, but it's very small. But the off-diagonal term, but it's comparable or smaller than the akitaev interaction. Then this material has significant akitaev time. However, because of the non-kitaev interactions, anti-fermented order with zigzag spin structure appears at T equal 7.5 Kelvin. So this model is often discussed by K gamma model. So let me show you some signature of the akitaev spin rigid. The broad magnetic continuum observed by Ravan scattering indicates the presence of ferrebenic, not bosonic excitations up to very high temperature. Moreover, the EN-sq neutrons scattering show that the magnetic continuum appears. This is an experimental result of this simulation. The magnetic continuum appears below the temperature characterized by kitaev interactions. So these results reflect the proximity to the kitaev model. Now let me discuss the thermal whole effect in alpha-alternium CL3. We first measure the thermal conductivity. Actually, thermal conductivity has been measured by many groups here. The thermal conductivity decreases and shows a sharp increase at the nail temperature. And then decrease. We observe the clear anomaly at the nail temperatures. But we need to be careful to study this material. Because in this material, above the nail temperature, the thermal anomaly often appears. For example, mainly the 14 Kelvin due to the stacking fault. So as I discussed later, this stacking fault is a very important rule for the quantum thermal whole conductance, so that we carefully select the sample which does not show the 14 Kelvin anomaly due to the stacking fault. Actually, before the experiment, we carefully selected the sample which shows no anomaly at 14 Kelvin. But this is not enough, because the sample is very easy to bend. So if you bend the sample, the stacking fault is easy to be introduced inside the crystal. And once you introduce the stacking fault inside the crystal, you cannot remove it. Then to check it, after the measurement, we always measure the multisurcerability and the special key and confirm the stacking fault was not introduced by the measurement. And also, we selected high quality single crystal which shows a large couple of x-axis. This is the temperature dependence of the thermal whole effect divided by temperature or two different crystals. We applied the magnetic field perpendicular to the frame. Again, the thermal whole response is very tiny compared to the longitudinal response. It's 0.1% of the longitudinal response. Then special care was taken to measure couple x-y. So we have done the following method to check our result. So we measured two different crystals, shaft 1 and shaft 2, sample 1 and sample 2, by different setup. One sample was measured by our university, Kyoto University. The other sample was measured in University of Tokyo, ISSP. So with different kind of summator, so we used Sanox 1070 and ISSP used Sanox 1050. And in this measurement, calibration of the summator in magnetic field is crucial. Then both summators are calibrated by different method. We calibrated the summator by capacitance method and ISSP calibrated the summator by, I forget it. Maybe the cancellation coil method. And most importantly, the data was analyzed by different persons, female and male. So as far as this figure, we observed the same behavior in sample 1 and sample 2. So we have confidence on the result. Then the finite couple x-y appears, below 70 Kelvin, nearly 70 Kelvin, which corresponds to Kitter-Fm interaction. This indicates couple x-y detects excitations inherent to the skewered state. This is consistent with the numerical result. And that is the absolute value of couple x-y of this material is called this behavior. Yeah, yeah, yeah, yeah. So the red points indicate the maximum around between 60 and 70 K. And the blue just goes slowly. Can you comment this? This is the error bar. Because as I mentioned, the sum of response is very tiny. Then at high temperature, we have the blue error bar. So we repeated many times in these regions, but still we have some error bars like this one. But below 50 Kelvin error bars are just like this. So the absolute value of couple x-y of this material is really large. It's one or two thousand magnitude larger than other materials, like the Triangular and Kagome and the Paracolar lattice. So with decreasing temperature, couple x-y divided by temperature increase and show the maximum and then decrease. Yeah, I probably miss it, but why does the conductivity changes sign twice, right? I mean, at low temperature, it is negative and it is negative again at the higher temperature. Is it? Yes, why is it changing sign? That's an interesting question, but at least now that we don't have any explanation, why is it changing? But what is important is at low temperature, it goes to zero. And then at low temperature, it changes sign. And even at very low temperature, they have some finite couple x-y, but it's negative. But I think that this comes from the summer gel-synx-molier interaction. Gel-synx-molier interaction of this material is the order of five Kelvin. Then if we take into account the gel-synx-molier interaction, we can observe the couple x-y even in the order of state. But again, we don't have the satisfactory explanation for this behavior. Okay, then the, so in this figure, the right figure represents a couple x-y, two-dimensional summer-hole conductance divided by temperature, which is plotted in the unit of this one. So one half corresponds to the half quantization. So unfortunately, the couple x-y is, okay, the couple x-y reaches close to the half of the quantized value, but the quantization is not attained. This is because the low temperature properties are masked by finite order. Then we could not observe the half quantized summer-hole conductance in this geometry. So we almost gave up the experiment. So we are in the dead end. But we can escape this problem by the following method. Actually, in this material, if we apply the magnetic field parallel to AB plane, the net order is strongly suppressed. And at nearly seven or eight Tesla, net temperature goes to zero. Actually, this shows the in-earth-neutron scattering result. So in this regions, above the, in zero field, the magnetic continuance is observed. But in this regions, the speed wave-like excitation is observed. But in this regions, again the continuance of excitation is observed here. And this is the gap, okay. So this indicates the magnetic continuance at high energy above H star perpendicular. So indicating the appearance of angel-spin-legged state above H star, namely in this regions. Then we measure the summer-hole conductance in tilted magnetic field. So in this case, the magnetic field parallel component separates the antifreeze order and phase transition is tuned by H parallel. But the summer-hole response is induced by perpendicular component, H perpendicular. So we have done this measurement. Together, I skipped the detailed argument, but this is a phase diagram in tilted magnetic field. So cross is a phase diagram in parallel field. And these are the data for 60 degree. This is a TN at 60, 60 degree agree well with that for parallel field case. And the vanishes at the same H parallel. And the 45 degree case, slightly reduced. But anyway, these indicates the quasi-2D nature of magnetic properties. Actually, this is a van der Waals coupled compound. Together, this is a field of dependence of a couple of xy divided by temperature. So in this region, the system is in the anti-parametric order here. But once entering the spinic heat state, summer conductivity simply increase. So in these regions, the couple of xy divided by temperature shows a plot of behavior here. And this is the right figure. Again, two-dimensional couple of xy divided by temperature is plotted in the units of these quantities. Vijay, I have a question. So in this plot for couple of xy, you have only one point which is negative. And before you were showing the whole tail which was negative couple of xy. Is it just how we can understand this? Because you see that for very small field, the first two points show positive. But actually, that data, we apply the magnetic field of 14 Tesla. Then the resolution is very good. But in this case, the magnetic field applied is only two or three Tesla. So resolution is not so good compared to the previous data. But it shows the negative. If you take the, so in these regions, as you see, the two-dimensional couple of xy over T is nearly half quantized. Actually, in these regions, we take the data many times and the data is quite reproducible. And that means the quantum, whole plateau appears in the quantum speed limit state. And the value is half of this value, namely the half of the quantized value of the quantum whole effect is observed. So again, this is half of the that expected integer quantum whole effect. So this is our temperature dependence of the thermal whole conductance for the 60 degree with tilted angle. In this case of 4.9 Kelvin and 3.7 Kelvin. So in all temperatures, we observe the plateau behavior which is quantized nearly half of the quantized value. Unfortunately, we could not go down to below this temperature because below this temperature, the thermal response is become very tiny. So the error increase. And at the high temperature, the deviation from the quantized value is observed. And at 15 Kelvin, we never observed the plateau like behavior. So we also measure the different angle. At 45 degree, we again observe the half quantized thermal whole conductance at all temperatures. Interestingly, at 60 degree, we observed some enhancement enhancement from the plateau value. But at 45 degree, we never observed such a behavior. Actually the origin of such enhancement is unknown. But in both case, in the case, the thermal whole conductance suddenly go to zero at high temperatures. So I would like to emphasize. So as I mentioned, this is a response of the insulator. So this thermal whole conductance arise from the response of neutral quasi particle. The second point is the plateau indicates the topological protectant. Degree of freedom is half of conventional of elements because one half quantized. So these are the, provide the evidence of the Mylana-Phermium. So let me discuss the temperature dependence of plateau behavior at this point. Here the temperature dependence of couple x over t, and here's the counter value. The half integer thermal whole conductance is preserved nearly up to five Kelvin. Above five Kelvin, up term of couple x over t is observed. And this is a high temperature regime. So it increase and show the peak at 20 Kelvin, then decrease and burnish nearly 60 Kelvin. So in the conventional quantum whole system, the quantum whole plateau is observed at very low temperatures, usually the very 100 millimeter Kelvin. But in this case, the concentration preserved up to five Kelvin. This indicates the Mylana gap is very large. So this is the NMR result. The NMR one over T1T has been measured four group. And the three groups observe the similar result. And three groups report in the region we observe the plateau, the large gap nearly 30 Kelvin is reported. On the hand, these group show the gap less. But if you believe this result, this is consistent with the plateau up to five Kelvin. Recently the neutron scattering experiment also shows a gap of 10 Kelvin. Okay, the next important question is what is the origin of up term of couple x over t from the quantized value, this one. Actually there are two theories has been proposed. First one is the phonon by Atchim Rosch. And in this case, couple xy increase as a function of t squared. And recently the Young-Goomers group Kaisto also claims that this enhancement come from the delocalized bisons due to the presence of next to the nearest neighbor interactions. Unfortunately our experimental result cannot check which is correct because of the resolution. Okay, another important point is the effect of the phonon. So recently the Atchim Rosch and Valence proposed the effect of the phonon. They proposed a similar theory. The according to their theory, the thermal hole conductance quantized when the phonon and H current are equally summarized. On the hand at very low temperature when the phonon become ballistic the decoupling of phonon and H occurs. So in this case, we never expect a quantized thermal hole conductance. But at t called zero we can expect a thermal hole conductance. So unfortunately we could not check it because we cannot go down to very low temperatures. But anyway this are consistent with our experiment. Okay, let me discuss the sample dependence. Until now we measured four crystals. There are sample one, two, three and now sample three is now we are measuring. So I did not show this later. And sample one and two which shows a very large kappa xx we observe the plateau. But we also measure the sample with low quality, the sharp sharp three crystal. In this crystal we observe the large anomaly at 14 Kelvin is stuck in fault. In such a crystal we never observe the thermal hole conductance, quantized thermal hole conductance. Also the some kind of plateau behavior is observed. Okay, let me discuss the topological phase transitions. Okay, so I summarized the data as there are three regions. In these regions kappa xy is very small and in these regions half integer plateau appears. And in these regions parallel edge current of neutral parallel element flowing at the edge. And in these regions kappa xy suddenly goes to zero. And in these regions the topological phase transition to force the ferromagnetic space for a new contact of the state. The name is anyway this topological phase transition point located in these regions. But actually there are recently there are a special key to show the clear anomaly at this point. So this indicates the suggest the presence of contact critical point which I skipped the kappa xy color plot. Okay. One minute, one minute. Okay, the recently minor edge current has been observed fractional quantum hole effect. The half integer thermal hole conductance of the five half state appears in the fractional quantum hole effect. But question, but the point is the origin of five half state in fractional quantum hole effect is controversial. And also the minor edge current induced by a proximal effect has been also reported in quantum anomalous hole insulator superconducting hybrid systems. So as they observe the half integer of sigma xx, not xy, longitudinal effect conductance. But soon after this experiment, different interpretations other than minor has been proposed. So this effect is still controversial. Okay, this is a summary of my talk. Thank you very much. Thanks a lot for very nice talk.