These days, the three-volume masterpiece "Amorphous Matter" by Wang Weihua, a teacher from the Institute of Physics of the Chinese Academy of Sciences (Oh, the Institute of Physics of the Chinese Academy of Sciences), has been published. To this end, Mr. Wei Hua also wrote a preface text ", which expressed his feelings for more than 30 years of hard work, which is admirable. This kind of admiration, from the heart, is a congratulation from old friends, and it is also because of the experience of reading over the years.
At best, I only scratch the surface of "condensed matter physics", but I also want to talk about amorphous or disordered states (as a beginner science, let's consider the two as one category). In my opinion, the biggest difficulty in the study of disordered states of matter is the lack of clear symmetry in this state of matter, breaking the physical and order parameters.
As we all know, the research paradigm of physics mainly relies on measurable order parameters (or thermodynamically measurable as materials people often say) to express them. Without these order parameters, it is difficult to characterize the structural characteristics and evolution of materials, and it is difficult to construct a scientific expression of the relationship between the structure and properties of materials.
In the vernacular, what can you measure against disordered states?! Because any physical quantity measured is most likely pale and trimeculous, lacking clear features (peaks, valleys, singularities, etc.). The feature here refers to the feature that can clearly indicate the change of the order parameters. The very broad and smooth morphological features, such as those of disordered structures in the XRD spectrum, are not discussed here, because broad morphological features do not convey the clear meaning of structural phase transitions.
Since there is a lack of feature, how can we discuss physics in it? From a more thermodynamic or scaled perspective, our understanding is that there is far more than one physical process or state of disordered matter, and that there may be an infinite number of physical processes or states that are close to each other. It is almost impossible to separate them one by one to facilitate individual measurements, characterization, and theoretical modeling.
Since it is impossible, physical humans have long begun to assemble these states of matter, carry out space-time scaling, normalization, and try to find specific pointers. The scale indices and critical relaxation behaviors that we commonly see in books** are also often used to describe the characteristics of disordered states. But the road still looks full of thorns, and the physics behind those scaling indices are not clear. Along these lines, physics has been going on for decades, and progress has not been satisfactory. The lack of features is probably one of the reasons why the progress of disordered states of matter is not as significant as that of other crystalline physical advances. Figure 1 illustrates the results of the measurement and characterization of various physical quantities in disordered states collected by several random isings.
Figure 1Examples of thermodynamic and spectroscopic characterization of various amorphous or disordered states of crystalline structures (interpreting these features is not complicated and will not be verbose here).
a) a. s. rajan et al, energy environ. sci. 7, 1110 (2014),
b) raman spectra of (a) crystalline si, (b) amorphous si, ©crystalline and (d) amorphous si1-xgex with x = 0.38. from p. martin et al, j. appl. phys. 96, 155 (2004),
c) w. wang et al, sr 7, 4084 (2017),
d) i. m, kalogeras et al, j. mater. edu. 34 (3-4), 69 (2012),
Of course, the logic of physical research has always been to develop both connotation and extension: since the excavation of the connotation of disorder is not so smooth, then try extension! One of the concerns of disordered state of matter research is to try to find structural units with short programs, medium programs, and local areas in disordered structures, and then construct the structural properties of materials containing these elements within the solid state physical framework. This kind of extension does have many good results. However, the rigorous mathematical or thermodynamic expression of such a short-range program is itself a problem and a reason why physicists are hesitant. This kind of short-term program is more of an image of an "excited state" or a higher-order physical fluctuation outside of the dominant disordered state of matter. The causes and geometry ahead are still topics of concern.
In this sense, Mr. Wei Hua's contribution lies in the fact that he stopped in this "barren" place that lacks order parameters and explored some methods and models. This is remarkable, but also hard, and worthy of admiration!
Ising is talking about Mr. Wei Hua's amorphous (disordered) state of matter here, hoping to introduce a topic: the disordered state of matter is so difficult to "physics", must it reflect that only long programs are good physics?! Obviously, this is a nonsense, tricky question, because the benefits of long procedures and the profundity of physics have long been closed. However, the amorphous state that Mr. Wei Hua has done well is not an individual case or an exception. In fact, physics is changing, including in other condensed matter fields other than amorphous, and it is also consciously or unconsciously proclaiming that "disordered states of matter" are actually quite good! This article will try to discuss another example to see if it can resonate with Mr. Wei Hua in some way.
Our topic, of course, is quantum materials. The crystal lattice of quantum materials here is strictly periodically ordered. The so-called possible disordered states of matter refer to the disorder of the electron degrees of freedom in the periodic lattice. Therefore, the disordered state here is not a high-energy atomic lattice form, but a much lower scale-down state with an ordered disorder of electrons in all degrees of freedom (charge, spin, orbit). This is different from amorphous matter, which is both epitaxial and connotation.
It is useful to briefly illustrate this epitaxial and connotation inheritance between amorphous and spin liquid states by using "quantum spin liquid (QSL)", a well-known problem in the current research of quantum materials. The so-called quantum liquid here is a spin disorder state in which the spin has some antiferromagnetic correlation in space. If far-fetched, there are some commonalities that can be found in the amorphous state and the QSL here: (1) a completely spin-disordered state. Conventional state measurement techniques are used to detect the situation, which is close to "no feature", as shown in the two examples shown in Figure 2. (2) In the amorphous state of matter, many people pay attention to the short-range and long-term procedures. QSL also focuses on the antiferromagnetic correlation of wave vector space and the spin flip process. Moreover, it is precisely this antiferromagnetic correlation that forms the basis of the Cooper pair pairing of electron spin single states, which is one of the essences of superconducting physics.
So, there doesn't seem to be much to be said about pure, idealized disorder itself (or we don't yet know what its significance), but those associations or localized states that quietly deviate from ideal disorder can be significant. It seems to be physical fate, and it's hard to stay out of fate!
Figure 2Thermodynamic and spectroscopic characteristics of some candidate systems for quantum spin liquids (almost no features).
a) signatures of specific heat and magnetism for qsl candidate li4cuteo6, from j. khatua et al, communi. phys. 5, 99 (2922),b) 19f nmr spectra under 3 t at different temperatures. the vertical dash line f0 = 120.199 mhz, corresponding to the chemical shift, is a guide to the eyes, for qsl compound cu3zn(oh)6fbr, from z. feng et al, cpl 34, 077502 (2017),
Starting from this example, in order to pursue the core application goals of quantum materials, we can describe why long programs are not so popular with quantum materials from the following levels:
1) First of all, look at the energy mark. The long programs of each degree of freedom of the electrons, whether they are (anti)ferroelectric, (anti)ferromagnetic, or orbitally ordered (charge order), are at the bottom of a well well deep enough. To excite them, or disordering or flipping, the corresponding energy scales are very large, and non-quantum materials are future-oriented subjects, or they are not the main carriers of quantum technology in the future. Please allow the word "subject" to be used here, but I don't want to be absolute, although that's pretty much it. To be a little more specific, these ordered states involve energy labels (100 ev 100 EV) is much larger than the energy standard (100 MEV or less) of quantum technology. So, if there are these long programs, the quantum effects that we're interested in are buried so deep that they don't manifest themselves for my use. It is only when these long programs are disrupted that the quantum states of the higher-order interaction can be highlighted, and the physical basis of quantum technology is noted. Figure 3 attempts to illustrate this naïve idea from a phase diagram perspective.
2) Second, look at examples. Some of the correlation effects and their consequences that quantum materials are concerned about, such as superconducting Cooper pairs, majorana fermions, quantum entanglement, qubits, spin-wave magnons, quantum paraelectricity, magnetoelectric sigmions, etc., do not seem to depend on or do not want to depend on long-range ordered states with each degree of freedom of electrons. Long-range quantum sequences, such as charge-ordered states, ferroelectric states, antiferromagnetic ordered states, and orbital ordered states, may serve as the matrix and starting point of quantum effects. Phase diagrams such as these clearly show that long program parameters are destroyed in order to produce the required quantum state. What destroys this long program is nothing more than the action of carriers and other regulated bands, as shown in the example in Figure 3. The consequence of this amount of action is the introduction of disordered fluctuations (kinetic energy) and disordered states of matter (driving fields). Conventional superconductivity is spin single-state, and unconventional superconductivity does not allow long-range magnetism, and even future triplet superconductivity will not allow long-range magnetic sequences in real space. Quantum magnetism also rarely discusses long procedures, all of which are dealing with some "crooked melons and cracked dates" under high magnetic resistance. Novel quantum excitations such as spin w**e (magnon) and topological vortex (vortex antivortex) are probably relevant to future applications of quantum information, both of which are mutually exclusive to long-range magnetism. The real space sigmions shown in Figure 3(c) have no intersection with the long program, and even the boundaries of the phase diagram must be clearly zoned with the long-range ordered phase. Even when it is extended to ferroelectricity, which is still thousands of miles away from quantum information or computing, with new effects such as quantum paraelectric states, ferroelectric metals, ferroelectric topologies, and two-dimensional slip ferroelectricity, electropolarized quantum states are also brewing, and they are all contrary to ferroelectric long programs.
3) Again, look at the characterization. The characterization methods of new effects in quantum materials are more or less intimidating to the long procedures of electronic states. No matter which degree of freedom of the electron or lattice phonon fluctuates in real space or wave vector space to characterize, as long as these degrees of freedom are hidden in the long-range ordered state, most of them require strong internal and external excitation to make them reveal their true colors. In the foreseeable future, these "strong enough" will probably be difficult to achieve, and it is unlikely that they will be used in practice. Therefore, the countermeasures of physical humans are always to carry out characterization detection near the critical point or phase transition point. Near the tipping point, a clean, manipulable single representation presents a number of challenges.
Figure 3Phase diagrams of several quantum materials. Their common feature is that through various intrinsic or external actions (carriers, quantum manipulation parameters, interaction regulation, etc.), the long-range ordered states of various degrees of freedom of electrons are destroyed, and new quantum states are generated from them.
a) phase diagram of cuprate superconductors as a function of hole doping p, from l. taillefer, annual review of condensed matter physics1, 51 (2010), 104117。
c) phase diagram in square lattice frustrated magnet with a weak magnetic anisotropy, from y. k. kharkov et al, phys. rev. lett. 119, 207201 (2017),
ISING's "blind man's reading" theory only wants to express that the functions and properties carried by those long-range ordered states in quantum condensed matter (such as ferroelectric, ferromagnetic, nonlinear optics, etc.) have been widely used in classical technology. In the so-called quantum era in the future, disordered states of matter may be the source and carrier of contained applications. The quantum effects we expect exist in the higher-order fluctuations, entanglements, and correlations of the degrees of freedom or order parameters of electrons on the basis of disordered ground states. Because of this, quantum materials research is increasingly moving towards those higher-order quantum effects. This is true both from the scale of the energy standard and from the perspective of specific effects. In this case, the best, and most brutal and direct approach, is to kill many of the long electronic programs, so that the quantum physics behind them can be better highlighted. This is a thread of quantum materials, albeit a little confusing and overwhelming!
At this point, the topic to be rendered by ising is about to come out: since there is no long program, including no long-range magnetism, how can the behavior of electrons in quantum materials be detected, characterized, and exploited (without clear detection, of course, it is impossible to talk about quantum information, computing, and applications)? We finally come back to the problem that Wei Hua often faces when studying amorphous states: how to reveal the physics without long procedures and macroscopic effects corresponding to conventional measurable quantities? It seems that most thermodynamic characterization methods have to be hesitant to move forward here. For example, what features can be detected by squid, the most sensitive method for detecting magnetism? Note that the working principle of squid is inherently quantum, albeit by taking advantage of superconductivity, an extremely rare macroscopic quantum effect. Quantum materials people are more fortunate than Wei Hua in that physics has both quantum mechanics as a powerful weapon, and has developed several methods to detect quantum states at the edge of disordered states, which seems to be very effective, although they also face great difficulties. This difficulty has always existed in the chase of various quantum effects, including QSL!
There are also many characterization methods to detect electron degrees of freedom or correlated physical quantities, and there are two most commonly used types of quantum materials: neutron scattering spectroscopy (NS) and X-ray scattering spectroscopy (XS). X-rays directly excite electrons in the extranuclear orbit and record the non-equilibrium excitation and relaxation processes of electrons. Essentially, the interaction of X-ray photons with extranuclear electrons has the potential to capture a wide range of quantum processes in quantum materials, including charge transitions and relaxation, spin flipping, etc., and more recently, magnon excitation and multi-spin chiral excitation. Neutrons are not charged, making it difficult to excite and detect electron charge fluctuations, but they are unique in that neutrons carry spins, which are indispensable for detecting spin sequences and their fluctuations. However, considering that the energy carried by the electron spin is much smaller than that carried by the electric charge, there seems to be a huge obstacle in trying to manipulate the charge excitation event by excitation and flipping of the spin (it is difficult for a small energy event to shake a large energy event unless the latter is in a critical state of instability). From this point of view, it seems that neutrons are not sufficient for the all-round role of detecting electron degrees of freedom.
Indeed, X-ray scattering spectroscopy-based techniques are becoming increasingly important and general in the development of advanced quantum materials characterization methods. First, there is no need to detect long-range spin sequences, so the uniqueness of neutron scattering is less important here. Secondly, the acquisition of neutron sources, even the spallation neutron source in Dongguan, is still more difficult than the high-energy X-ray (synchrotron radiation) source (there is absolutely no intention to offend the "Dongguan Spallation Source" Thirdly, the accumulation of more than 100 years of photoelectron spectroscopy physics has indeed given X-ray detection of some possibilities for the fluctuation, entanglement and correlation of various degrees of freedom of electrons. This is why X-ray scattering spectroscopy has such a multicolored branch.
It is interesting to note that theoretical computational physicists seem to be leading the way in the development of new quantum effects in solid-state using X-ray de-excitation and spectroscopy. For example, Professor Yao Daoxin of the School of Physics at Sun Yat-sen University has been working on the theory of X-ray scattering spectroscopy of quantum materials. He has also written a critically acclaimed popular science article for Quantum Materials** (click to read). Interested readers can visit the Imperial Tour.
In the field of quantum materials, there are many physicists like Yao Daoxin. Here's another example that's impressive. Since it is possible to encompass various quantum processes in quantum materials through the interaction of X-ray photons with extranuclear electrons, can we also include processes such as orbital angular momentum and Berry curvature, which are deeply related to topological quantum materials but have not yet been easily revealed?
Professor Michael Schuler, a renowned scholar in condensed matter theory from the renowned Paul Scherrer Institute (PSI) and the University of Fribourg in Switzerland, worked closely with Dr. Thorsten Schmitt, a leading scholar in the field at the PSI Light Source Division, to propose a resonant inelastic X-ray scattering spectroscopy based on resonant inelastic X Ray Scattering (RIXS) technique is used to detect the theoretical schemes of magnetic orbitals or orbital angular momentum (OAM) and berry curvature. In his article, Daoxin Yao has clearly demonstrated the RIXS method and its ability to detect the degrees of freedom of electrons, including the potential of higher-order magnetic dipole moments in magnetoresistive frustration systems. In particular, neutron scattering, because neutrons carry spins, may mask the weak magnetic signals generated by higher-order excitation! In turn, RIXS technology uses photons without magnetic moments, which can detect higher-order spin fluctuations and higher-order interaction signals. This is called the absence of tigers in the mountains, and the monkeys are the overlords.
Figure 4Professor Michael Schuler of PSI in Switzerland for their RIXS probe scheme for orbital angular momentum OAM and Berry curvature of topological quantum materials**. The upper part is the schematic; The lower part is the result of the calculation for 1t' mos2, especially the results of the Berry curvature, which is expected.
Of course, Yao Daoxin showed that measuring magnetic excitation with RIXS is not trivial, and involves complex many-body, short-term non-equilibrium processes. As a result, RIXS was able to measure at least four spin correlations, including spin chirality in highly magnetoresistive frustration systems. Perhaps based on the fact that RIXS was able to measure multiple spins and higher-order coupled images, Professor Schuler came up with the ingenuity to extend the representation to orbital angular momentum (which has surpassed spin) and the Berry curvature that characterizes the magnetic field of wave vector space, with some of the schematics and results integrated in Figure 4. This is a meaningful and solid step towards topological quantum magnetic characterization, although it has yet to be experimentally confirmed. As a reading note, it is recorded as follows:
1) In topological quantum materials, the core goal is to establish the connection between the Berry curvature of the wave vector space and various evolved topological quantum effects. Berry curvature is closely related to band topology and intrinsic electromagnetic field, which constitute a new physical mechanism behind quantum transport, harmonic excitation, valley electronics effect and higher-order Hall effect.
2) To characterize band topology and Berry curvature, the most common method is angle-resolved photoelectron spectroscopy (ARPES) of circular polarization. Circularly polarized photons, coupled with the orbital angular momentum (OAM) of the wave function, make it possible to detect OAM and Berry curvature. However, there are still great difficulties in the actual measurement, and the main challenge is that the determination of the photoexcitation matrix element of the circularly polarized ARPES is difficult and technically complex. The details are determined not only by the circular polarization properties of the light source, the orbital angular momentum, etc., but also by the parameter adjustment of the measurement itself. Many of these measurements are "unattained by thousands of rivers and mountains".
3) RixS polarized photons carry both spin excitation and orbital excitation when they excite the electron transition near the Fermi surface and the subsequent spin flip process. By analyzing the choice rule of spin flip, the change of orbital angular momentum oam can also be deconstructed, as explained by Yao Daoxin's Xiongwen. In this sense, RIXs are similar to X-ray absorption of magnetic circular dichroism.
However, the most interesting thing here is that Professor Michael Schuler has proposed that in transition metal compound systems, even if there is no magnetism, the Berry curvature can still be linked to the local orbital angular momentum (local oam) by circular dichroism (CD) rixs detection. This work demonstrates that CD RIXs are a powerful means of measuring orbital magnetic excitation and topological physics. Using 2D MOSE2 and 1T' MOS2 as the subjects of study (note that neither of them is magnetic, and 1T' MOS2 has a peculiar, huge linear magnetoresistance due to its topological properties), they theoretically demonstrated the principle and scheme of measuring orbital angular momentum and Berry curvature of RIXs, which is impressive. It is believed that this scheme will be noticed and experimentally verified.
The end of the thunder that can't be moved: ising is a layman, and I apologize for not describing it. If you are interested, please go to the original text. The original link information is as follows:
probing magnetic orbitals and berry curvature with circular dichroism in resonant inelastic x-ray scattering
michael schüler, thorsten schmitt & philipp werner
npj quantum materials 8, article number: 6 (2023)