Many people have an intuitive sense that time seems to flow only forward.

Hot water cools down gradually, a shattered cup does not reassemble on its own, and the scent of perfume that has diffused into the air is hardly ever able to gather back into the bottle. We experience this “irreversibility” almost every day—time is like an arrow that can only fly forward, rarely turning back.

But interestingly, in modern physics, many of the most fundamental laws of motion do not strictly distinguish the direction of time.

If you play a video of a planet orbiting the Sun in reverse, the footage still conforms to Newtonian mechanics; similarly, reversing a video of two billiard balls colliding doesn’t look particularly unnatural. Indeed, many fundamental equations in classical mechanics, electromagnetism, and even quantum mechanics are mathematically invariant under time reversal. In other words, from the perspective of microscopic laws, both “forward‑going” and “reverse‑going” processes can often be equally valid.

This is “time-reversal symmetry” in physics.

Of course, this does not mean that the real world can actually reverse time. In the macroscopic realm, the “arrow of time” is typically linked to statistical behavior and the increase of entropy. The collective motion of a large number of particles makes it far more likely for a system to evolve from order to disorder. This is also why a broken cup is far more common than an intact one: there are vastly more microscopic configurations corresponding to the “broken state.”

However, time-reversal symmetry remains a crucial concept in modern physics. Particularly in condensed-matter physics and the study of quantum materials, it is not merely a theoretical mathematical tool; it also has a tangible impact on how electrons move and on the properties that materials exhibit.

A typical example is magnetism.

In addition to carrying electric charge, electrons possess a quantum property known as “spin.” Spin gives rise to a magnetic moment; consequently, when the spins of a large number of electrons are aligned, a macroscopic magnetic field emerges. When we perform a time-reversal operation on the system, the angular momentum associated with the electron spins reverses direction, and the magnetic moment likewise changes accordingly.

Therefore, a system with magnetic properties generally does not retain its original state after time reversal. In other words, magnetism often implies the breaking of time-reversal symmetry.

This is not merely an abstract theoretical concept; it directly influences the transport behavior of electrons in materials. Over the past few decades, physicists have come to recognize that symmetry itself can dictate a material’s electronic properties. It is against this backdrop that topological insulators have increasingly attracted the attention of researchers.

Topological insulators are a class of rather special quantum materials. Their bulk is typically non-conductive, yet their surfaces can conduct electricity in a robust manner. More importantly, this surface conduction does not depend solely on the material’s perfection; rather, it is tied to the material’s deeper quantum structure.

Research has shown that these surface states are closely linked to time-reversal symmetry. In many cases, as long as time-reversal symmetry remains unbroken, these surface states can remain stable and exhibit a degree of robustness against ordinary impurity scattering. However, once magnetism is introduced, time-reversal symmetry is broken, and the originally protected surface states may undergo significant changes.

This means that a seemingly abstract “symmetry” can, in fact, determine whether electrons are prone to scattering, whether a material is conductive, and how electrons propagate at the boundaries.

In recent years, similar ideas have also begun to emerge in an increasing number of cutting-edge quantum materials studies. For instance, kagome‑structured materials, two‑dimensional materials, moiré superlattices, and certain superconducting systems are all closely linked to symmetry, topological properties, and collective electronic behavior.

These studies share a common feature: the microstructure of materials often profoundly influences electronic behavior.

At the macroscopic scale, differences on the order of tens of micrometers are hardly noticeable. However, at the nanoscale, structural dimensions, periodic arrangements, and even boundary shapes can all influence the spatial distribution of electronic wavefunctions. Moreover, certain quantum effects may manifest only under specific size regimes and in particular structural configurations.

Therefore, modern research on quantum materials not only relies on theoretical calculations but is also increasingly dependent on micro- and nanofabrication techniques.

In the past, researchers primarily sought exotic materials in nature; today, they have begun to actively “design” electronic behavior. By artificially fabricating periodic structures, micro‑ and nano‑scale patterns, and quantum devices, it is now possible to control, to a certain extent, how electrons move, how they couple, and how different quantum states interact with one another.

This also constitutes one of the key contextual factors underlying the sustained advancement of micro- and nanomanufacturing technologies in recent years.

Take ZEPTOOLS DMD maskless lithography system as an example: it uses a digital micromirror device to directly project patterns, eliminating the need for traditional fixed photomasks, and enabling rapid realization of exposure and iterative patterning for diverse structures. In certain research settings, this approach can significantly reduce the time required for pattern modification and process validation, making it particularly well-suited for early-stage experimental exploration.

For example, in microfluidic chips, two-dimensional material electrodes, and certain in-situ patterning processes, researchers often need to frequently refine their structural designs. However, ZEPTOOLS DMD maskless lithography system enables in-situ writing and overlay alignment directly from microscopic images, ensuring that the patterns precisely correspond to the spatial relationships on the sample surface.

As research delves further into the nanoscale, relying solely on conventional optical lithography often runs into the diffraction limit. At this point, the significance of electron-beam lithography becomes increasingly apparent.

Electron-beam lithography does not rely on light; instead, it uses a focused electron beam to directly expose an electron-beam resist. Because the de Broglie wavelength of electrons is much shorter than that of visible light, it enables the fabrication of micro- and nanostructures with significantly higher resolution.

In some studies, structural changes at the scale of tens of nanometers or even smaller can significantly influence electronic transport properties. Consequently, fabrication accuracy, alignment precision, and pattern‑correction capabilities directly determine the device’s ultimate performance.

For example, the “proximity effect,” a common issue in electron-beam lithography, causes electron scattering in adjacent regions to interfere with one another, leading to distortions at the pattern edges. ZEPTOOLS electron-beam lithography systems mitigate this effect through dose correction and other techniques.

In a sense, the significance of these technologies extends beyond merely “miniaturizing fabrication.” More importantly, they are enabling humanity to progressively develop the capability to actively engineer microscopic environments that can host specific quantum phenomena.

Time-reversal symmetry, once merely a concept in theoretical physics, has now become intimately connected with real materials, actual devices, and concrete experiments. How electrons move, whether surface states are stable, and whether topological structures can emerge—all may be closely tied to these symmetries.

Meanwhile, micro- and nanofabrication technologies are emerging as a bridge between “theory” and “reality.”

Today’s research on quantum materials no longer confines itself to observing phenomena already present in nature. Increasingly, researchers are turning to the deliberate design of artificial structures to induce specific quantum behaviors under tailored conditions. Periodic arrangements in two-dimensional materials, electron coupling in artificial lattices, and boundary states in topological devices all, at their core, fall within this conceptual framework.

This, perhaps, is also one of the most intriguing aspects of modern condensed matter physics.

Researchers no longer focus solely on “what the world is like”; they have also begun to ask: if we alter the structure, break the symmetry, or modify the boundary conditions, will electrons exhibit new behaviors?

Behind these questions lie both fundamental physics—concerning time, symmetry, and quantum states—and increasingly sophisticated micro‑ and nanofabrication capabilities. In a sense, the value of modern micro‑ and nanotechnology extends beyond merely shrinking dimensions to the nanoscale; it is helping humanity inch closer to a new stage: moving from an understanding of microscopic laws toward the limited ability to design and construct environments in which those laws can operate.

Reference materials 
1. Hu Jiangping. (2026). The Arrow of Time: From the Cosmic Beginning to Quantum Materials. Chinese Academy of Sciences Institute of Physics Official Account. 
2. QuarX. (2015, January 5). Thermodynamics and entropy – Our irreversible universe. Naturphilosophie. 
3. Berkeley Lab. (2025, March 24). Moiré than meets the eye. Berkeley Lab News Center. 
4. Ingrid Fadelli. (2026, March 18). 2D topological Kondo insulator observed in a moiré superlattice. Phys.org.