# The Emergence of Mem-Emitters

Victor Lopez-Richard<EMAIL_ADDRESS>Departamento de Física, Universidade
Federal de São Carlos, 13565-905, São Carlos, SP, Brazil  Igor Ricardo
Filgueira e Silva  Departamento de Física, Universidade Federal de São Carlos,
13565-905, São Carlos, SP, Brazil  Alessandra Ames  Departamento de Física,
Universidade Federal de São Carlos, 13565-905, São Carlos, SP, Brazil
Frederico B. Sousa  Departamento de Física, Universidade Federal de São
Carlos, 13565-905, São Carlos, SP, Brazil  Marcio Daldin Teodoro  Departamento
de Física, Universidade Federal de São Carlos, 13565-905, São Carlos, SP,
Brazil  Ingrid David Barcelos  Brazilian Synchrotron Light Laboratory (LNLS),
Brazilian Center for Research in Energy and Materials (CNPEM), Campinas, SP
13083-100, Brazil  Raphaela de Oliveira  Brazilian Synchrotron Light
Laboratory (LNLS), Brazilian Center for Research in Energy and Materials
(CNPEM), Campinas, SP 13083-100, Brazil  Alisson Ronieri Cadore  Brazilian
Nanotechnology National Laboratory (LNNano), Brazilian Center for Research in
Energy and Materials (CNPEM), Campinas, SP 13083-100, Brazil

###### Abstract

The advent of memristors and resistive switching has transformed solid state
physics, enabling advanced applications such as neuromorphic computing.
Inspired by these developments, we introduce the concept of Mem-emitters,
devices that manipulate light emission properties of semiconductors to achieve
memory functionalities. Mem-emitters, influenced by past exposure to stimuli,
offer a new approach to optoelectronic computing with potential for enhanced
speed, efficiency, and integration. This study explores the unique properties
of transition metal dichalcogenides-based heterostructures as a promising
platform for Mem-emitter functionalities due to their atomic-scale thickness,
tunable electronic properties, and strong light-matter interaction. By
distinguishing between population-driven and transition rate-driven Mem-
emitters, we highlight their potential for various applications, including
optoelectronic switches, variable light sources, and advanced communication
systems. Understanding these mechanisms paves the way for innovative
technologies in memory and computation, offering insights into the intrinsic
dynamics of complex systems.

###### keywords:

American Chemical Society, LaTeX

IR,NMR,UV

In recent decades, the field of solid state physics has been revolutionized by
the emergence of memristors and the phenomenon of resistive switching 1. First
theorized in the 1970s, 2 memristors are circuit elements whose resistance can
be altered based on their history. The underlying mechanism for resistive
switching involves changes in a material’s conductance in response to
electrical or other stimuli that interfere with internal state variables. 3
This capability to modulate resistance has unlocked exciting possibilities for
neuromorphic computing, 4 and other advanced applications in the realm of
miniaturized solid state devices characterized by greater efficiency, density,
and a variety of functionalities. 5, 6, 7, 8

Inspired by the concept of resistive switching in memristors, we propose a
paradigm shift in optoelectronics. This approach focuses on manipulating the
light emission properties of semiconductors to achieve memory functionalities
using through methods such as electromagnetic field modulation and proximity
effects. We will refer to these devices as Mem-emitters where past exposure to
light or other stimuli controls the characteristics of their emitted light.
This enables a memory scheme where distinct light emission patterns represent
different information states.

The exploration of Mem-emitters holds potential for the development of light-
based memory devices. This technology could open up possibilities in
optoelectronic computing, paving the way for advancements in speed,
efficiency, and seamless integration with existing technologies.

The main observables in the optical response of the Mem-emitter are the
emission intensity and its energy position. To better frame, qualify, and
quantify the light emission intensity, we can reduce it to its fundamental
components: the population of the initial state, $N$, and the optical
transition rate, $1/\tau$. The intensity $Q$ can be expressed as

$Q=\frac{N}{\tau}.$ (1)

In the simplest approximation, the optical transition rate can be expressed as

$\frac{1}{\tau}=K_{f,i}\cdot D\left(\Delta E_{f,i}-\hbar\omega\right),$ (2)

where $K_{f,i}$ is proportional to the optical transition matrix elements
between the initial (i) and final state (f); and $D\left(\Delta
E_{f,i}-\hbar\omega\right)$ represents the energy conservation factor, which
peaks when the photon energy ($\hbar\omega$) approaches the energy difference
between these two states ($\Delta E_{f,i}$), i.e, $\hbar\omega\simeq\Delta
E_{f,i}$.

For the mem-emitting ability to emerge, the functions in Eqs. 1 and 2 must
depend not only on the external electromagnetic fields, $\vec{F}$, but also on
a set of internal state variables, denoted as a vector of factors, $\vec{x}$.
These internal state variables may include the density of activated or trapped
carriers, internal electric polarization, redox reaction rates at the
interfaces, filament formation rates, and other dynamic factors. Note that, in
the presence of magnetic interactions, the spin degree of freedom must be
considered. If the external fields vary, the time evolution of each emission
intensity component: $K_{f,i}(\vec{F},\vec{x},t)$, $\Delta
E_{f,i}(\vec{F},\vec{x},t)$, and $N(\vec{F},\vec{x},t)$ must be affected by
dynamic relationships, that can be reduced in general terms to

$\frac{d\vec{x}}{dt}=f\left(\vec{F},\vec{x},t\right).$ (3)

This dependence ensures that the light emission intensity, $Q$, and energy
position are influenced by both external fields and the internal state of the
system, allowing for an adaptive emission behavior. Given that the optical
emission rate of the Mem-emitter at any given time is influenced by the entire
history of the external field evolution, its behavior is inherently non-
Markovian. The future state depends not only on the present state but also on
the sequence of past states. This characteristic allows Mem-emitters to be
used in applications that require memory of past conditions, such as in
neuromorphic computing and adaptive circuits. A key signature of this behavior
is the appearance of stable hysteresis in either (or both) the emission
intensity and energy position under periodic external driving, as depicted in
Fig. 1.

Figure 1: (a)-(d) Illustrative depiction of potential hysteresis loops of a
Mem-emitter under periodic stimulus, showcasing various possible topological
shapes: solid and dashed lines highlight contrasting loop configurations, and
the arrows in panel (c) indicate a pinched, non-crossing loop. (e)
Representation of a Mem-emitter consisting of a heterostructure based on a TMD
monolayer of width $d_{TMD}$ on its dielectric substrate of width $d_{D}$,
connected to two electrodes. The nonequilibrium carriers activated in the
substrate and reaching the TMD layer are represented by $\delta n$ along with
the electric polarization fluctuation, $\delta P$, also occurring within the
substrate. Time resolved dynamics of either carrier or polarization
fluctuations in the presence of two independent mechanisms with (f) monotonic
and (g) non-monotonic transients

The conditions under which these hysteresis loops appear and evolve by tuning
external factors, along with their symmetry and the number and positions of
intersection points, are crucial elements for mapping the internal processes
that generate them. Although a comprehensive classification of the topology of
these shapes has yet to be presented, we can identify several classes based on
specific criteria. According to the presence of an opening around the origin
at $F=0$, loops can be classified as (i) open loops (a,b,d), (ii) x-cross
loops [3 (c)-solid line], or (iii) pinched non-crossing loops [3 (c)-dashed
line]. Based on symmetry, loops can be categorized as (i) even-symmetric loops
(c), (ii) odd-symmetric loops (a,b), or (iii) asymmetric loops (d). Loops can
also be classified according to the number of crossings: zero [1(a)], one
[1(c) and 1(d)], two [1(b)], and more. Furthermore, the direction of the loop
provides another classification criterion: (i) clockwise or (ii) counter-
clockwise loops. This detailed classification framework helps in understanding
the diverse types of hysteresis behaviors and the underlying physical
mechanisms, providing insights into the internal dynamics of the systems
exhibiting these loops. Specific cases will be discussed subsequently.

Another aspect to be explored in the behavior of Mem-emitters is the contrast
between population-driven and transition-rate-driven Mem-emitters. Population-
driven Mem-emitters are characterized by their modulation through fluctuations
in population density, $N$. In these devices, the primary mechanism
influencing light emission is the variation in the number of charge carriers
or emitters. This can be achieved through charge injection or extraction by
adjusting the external electric field, which directly affects the population
of excited states capable of emitting photons. This type of Mem-emitter is
particularly suitable for applications where the control of the number of
active emitters and the emission intensity, $Q$, is crucial, such as in
optoelectronic switches or variable light sources. The response time of these
devices is typically governed by the rates of charge carrier injection and
recombination 9.

On the other hand, transition rate-driven Mem-emitters are primarily modulated
through the tuning of the optical transition rate ($1/\tau$) with
electromagnetic fields. In these devices, the focus is on altering the
probability of radiative transitions between energy levels rather than the
population density. The intensity of the emission is controlled by tuning the
wavefunctions involved in the transition rate between states, which can be
influenced by external electromagnetic fields and internal variables. This
approach is ideal for applications requiring precise control over emission
timing and intensity, such as in advanced communication systems and high-
precision sensors. The response time in transition rate-driven Mem-emitters is
influenced by the dynamics of the transition rates, which can be fine-tuned
for specific applications. It is important to note that population and
transition rate-driven mechanisms can coexist and might interfere in many
systems and devices during the measurements.

Mem-emitters built on functional TMD heterostructures and two-dimensional (2D)
semiconductors, in general, present a highly promising platform for exploring
Mem-emitter functionalities due to several unique and advantageous properties
10. Their atomic-scale thickness allows for extreme miniaturization of devices
and results in a high surface-to-volume ratio, which enhances the interaction
of the material with external fields and surrounding environments. 11, 12 The
reduced dimensionality also facilitates better control over the material’s
electronic and optical properties, making them highly sensitive to external
stimuli such as proximity effects (of electrochemical nature) 13, 14, 15 and
high local electric fields. 16, 17 We should note that memory traces have
already been observed in the optical response of of TMDs-based devices, 18,
19, 20 but they have not yet been explored or characterized as the significant
feature they evidently are.

Many TMDs, such as MoS2, WS2, and WSe2, exhibit a direct bandgap in their
monolayer form, which is crucial for efficient light emission 21, 22. The
bandgap of these materials can be tuned by applying strain, electric fields,
or by stacking different layers, enabling precise control over their optical
properties 21, 23. This tunability is essential for developing transition
rate-driven Mem-emitters where controlling the emission wavelength and
intensity is key. They also exhibit exceptionally strong light-matter
interaction due to their reduced dimensionality and high exciton binding
energy 24, 21. This results in enhanced optical absorption and emission
efficiencies, making them ideal for optoelectronic applications 25.
Additionally, 2D TMDs possess well-resolved excitonic complex emission lines,
such as neutral excitons and trions. 26, 27, 28 These distinct emission lines
offer a precise platform for probing mem-emitting abilities, as they provide
clear, identifiable markers for studying the dynamics of light emission and
its modulation under various external stimuli. The ability to resolve and
manipulate these excitonic features enhances the potential for developing
sophisticated and highly controllable Mem-emitter devices. Additionally, 2D
semiconductors can be easily integrated with other materials, including
traditional semiconductors, insulators, and metals, to form heterostructures
and hybrid devices. 29, 30 This compatibility facilitates the design of
complex devices with tailored properties, combining the advantages of
different material systems to optimize performance for specific applications.

To exemplify our Mem-emitter concept, we will use a device consisting of a 2D
TMD monolayer placed on a dielectric substrate and connected to two
electrodes, as depicted in Figure 1 (e). Note that this heterostructure also
serves as the gate setup for a single-layer TMD transistor 31, 6, 32. In this
capacitor configuration, under an applied bias, the electric field within the
TMD monolayer, $F_{TMD}$, is related to the applied voltage, $V$, and the
built-in polarization in the substrate, $P$, by the following expression

$F_{TMD}=\frac{V+\frac{P(V)}{\epsilon_{0}}d_{D}}{d_{D}\left(1+\chi_{TMD}\right)+d_{TMD}},$
(4)

where $\epsilon_{0}$ is the vacuum permittivity, $d_{TMD}$ and $d_{D}$ are the
thicknesses of the TMD monolayer and the dielectric layer, respectively;
$\chi_{TMD}$ is the dielectric susceptibility of the monolayer. Let’s assume
that the polarization of the substrate can be segmented into two
contributions: one that varies instantaneously with the local field in the
substrate region, $F_{D}$, as $P^{(0)}=\chi_{D}\epsilon_{0}F_{D}$, being
$\chi_{D}$ the dielectric susceptibility of the substrate, and a fluctuation,
$\delta P$, due to the leakeage or generation of non-equilibrium dipoles.
Thus, the total polarization can be expressed as

$P=P^{(0)}+\delta P.$ (5)

In that case, the local field at the TMD monolayer transforms to

$F_{TMD}=\left[V+\frac{\delta
P(V)}{\epsilon_{0}}d_{D}\right]\frac{\left(1+\chi_{D}\right)}{d_{D}\left(1+\chi_{TMD}\right)+d_{TMD}\left(1+\chi_{D}\right)},$
(6)

which, under the condition $d_{TMD}<<d_{D}$, simplifies to

$F_{TMD}=\left[\frac{V}{d_{D}}+\frac{\delta
P(V)}{\epsilon_{0}}\right]\frac{\left(1+\chi_{D}\right)}{\left(1+\chi_{TMD}\right)},$
(7)

Various concomitant processes of carrier trapping can contribute to the
polarization fluctuation, $\delta P=\sum_{j}\delta P_{j}$. We will consider
these processes to be independent, each with its own relaxation time and each
component $\delta P_{j}$ will define an internal state variable, as described
in Eq. 3 for our Mem-emitter definition. Under this approximation, the
fluctuation for each process j can be described by

$\frac{d\delta P_{j}}{dt}=-\frac{\delta P_{j}}{\tau_{j}}+g_{j}^{(p)}(V),$ (8)

where $\tau_{j}$ is the relaxation time and $g_{j}^{(p)}(V)$ is the
polarization transfer function dependent on the applied voltage $V$ described
in detail in Ref. 33. The sign of the transfer function determines whether the
process is of a generative or depletive nature. Additionally, the trapping and
release of carriers lead to fluctuations in the available extra charges,
$\delta n=\sum_{i}\delta n_{i}$, resulting from the independent generation of
nonequilibrium channels. Each of these channels leads to charge fluctuations,
$\delta n_{i}$, adding new components to our internal state variable vector
(Eq. 3), which, in anaology to Eq. 8, can be described using the relaxation
time approximation

$\frac{d\delta n_{i}}{dt}=-\frac{\delta n_{i}}{\tau_{i}}+g_{i}^{(n)}(V),$ (9)

where $g_{j}^{(n)}(V)$ is the non-equilibrium carrier transfer function for
each independent channel i that can be found defined in Ref. 3 in terms of
microscopic elements. The most strighforward way to prove the coexistence of
non-equilibrium processes with contrasting relaxation times is the analysis of
the time resolved transientes of the observables under constant bias, $V_{0}$.
In such conditions, using the charge fluctuation as reference, the solution is

$\delta
n(V_{0})=\sum_{i}\left[g_{i}^{(n)}(V_{0})\tau_{i}+A_{i}\exp\left(-\frac{t}{\tau_{i}}\right)\right],$
(10)

with $A_{i}=\delta n_{i}(0)-g_{i}^{(n)}(V_{0})\tau_{i}$, where $\delta
n_{i}(0)$ is the initial condition when the pulse $V_{0}$ is applied. The
solution for the polarization fluctuation would be analogous. This equation
highlights how different relaxation times manifest in the transient response
of the system. Some results are illustrated in Figures 1 (f) and 1 (g). Figure
1 (f) shows monotonic trends, while Figure 1 (g) displays non-monotonic trends
for two concurrent processes with contrasting relaxation times differing by
two orders of magnitude. The monotonicity is determined by the parameters
$A_{i}$, whose sign depends on the initial condition. Thus, no direct
conclusion on the character (sign) of the transfer functions,
$g_{i}^{(n)}(V_{0})$ or $g_{j}^{(p)}(V_{0})$, can be extracted from these
trends in case the observables are related to either $\delta n$ or $\delta P$,
respectively.

Let us now discuss some particular cases of interest under periodic triangular
voltage bias, $V$, with period T, as represented in Figure 2 (a). In this
scenario, according to Eqs. 8 and 9, the system response will evolve towards a
periodic behavior once any transient effects, which depend on the initial
conditions, have faded. Note also that any dynamic process, $k$, for which
$\tau_{k}<<T$, will manifest itself as instantaneous and its contribution to
the fluctuation of either polarization or charge will be reduced to $\delta
P_{k}(V)=\tau_{k}g_{k}^{(p)}(V)$ or $\delta n_{k}(V)=\tau_{k}g_{k}^{(n)}(V)$,
respectively. This reflects the nature of the transfer functions (or their
superpositions) under very slow driving conditions. In turn, under adequate
voltage drives, the stable cyclic response can reveal signatures of memory
effects through hysteresis in the observable versus voltage characteristics.
According to Eq. 7, any hysteresis observed in the polarization versus $V$
will be reflected in any observable that depends on the local electric field
at the TMD monolayer. For instance, reminiscent of ferroelectric apparent
responses, 34 would manifest as counterclockwise loops.

Two polarization transfer functions are illustrated in Figures 2(b) and 2 (c).
The first function results in an absolute increase in polarization for both
positive and negative bias [Fig. 2(b)], whereas the second function
characterizes a potential dipole leakage with an opposite sign relative to the
bias [Fig. 2(c)]. Assuming the same relaxation times for each of these
processes, $\tau_{1}=\tau_{2}$, and a voltage sweeping period of
$T=2\pi\tau_{1}$, the resulting local electric field hysteresis, according to
Eqs.7 and 8, is shown in Figures 2(d) and 2 (e), respectively. Note that the
nature of generation or leakage determines the direction of the hysteresis
loop: counterclockwise loops for delayed increased polarization and clockwise
loops if prevailing leaking polarization mechanisms 33. In cases where these
processes interfere, the loop’s shape transforms into a multicrossing pattern,
as depicted in Figure 2(f). Due to the reactive nature of the delayed
polarization response, the field hysteresis will consistently appear as open
loops around $V=0$. These loops collapse during very slow or very fast voltage
sweeps using $\tau_{1}$ as reference as depicted in Figure 2(g) by the
calculated loop area. Discussions on the conditions for maximal memory
response can be found in Refs. 35, 3. The voltage amplitude also influences
the shape of the loops, as shown in Figure 2(g), where a change in the sign of
the loop area indicates an inversion of the loop direction.

Figure 2:  (a) Periodic voltage input. Electric polarization transfer function
for: (b) $g_{1}^{(p)}$, that increases nonequilibrium polarization with
voltage and (c), the corresponding transfer function, $g_{2}^{(p)}$, for a
leaking channel. Stable cycles of the electric field at the TMD layer in the
presence of the process activated by: (d) $g_{1}^{(p)}$, (e) $g_{2}^{(p)}$,
and (f) the combined effect of $g_{1}^{(p)}+g_{2}^{(p)}$ assuming equal
relaxation times for both mechanisms and voltage sweeps with period
$T=2\pi\tau_{1}$. The arrows in (d)-(f) indicate the direction of the $V$
sweep. (g) Voltage loop area as a function of the voltage period and (h) as a
function of the voltage amplitude. Figure 3: (a) Symmetric transffer functions
for nonequilibrium charges of generation (positive) and trapping character
(negative). (b) The corresponding loops for each of these three processes with
$\tau_{1}=\tau_{3}>>\tau_{2}$ for voltage sweeps with period $T=2\pi\tau_{1}$.
(c) Combined effect of the $\delta n_{1}+\delta n_{2}$ dynamics. (d) Combining
$\delta n_{1}+\delta n_{2}+\delta n_{3}$. (e) Two asymmetric transfer
functions with contrasting characters and efficiencies and the combineed
effect of them displayed in panel (f). Panels (g) and (h) unveil the
combination of opposite characters analogous to (e) and (f), respectively. The
arrows indicate the orientation of the $V$ sweep.

The charge fluctuations can exhibit a wide variety of responses, as
illustrated in Fig. 3. Panel 3 (a) presents three symmetric yet contrasting
transfer functions that drive the charge fluctuations shown in panel 3 (b)
under voltage cycles with $T=2\pi\tau_{1}$, with
$\tau_{3}=\tau_{1}>>\tau_{2}$. In these conditions, $\delta n_{1}$ and $\delta
n_{3}$ exhibit pinched hysteresis at $V=0$ with opposite directions, while
$\delta n_{2}\simeq\tau_{2}g^{(n)}_{2}$, following a quasi-stationary
(instantaneous) response, with no open hysteresis. As stated previously, it is
possible to encounter concomitant processes with contrasting transfer
functions and relaxation times. To illustrate this, we show the combined
effects of adding $\delta n_{1}+\delta n_{2}$, in panel 3 (c) and $\delta
n_{1}+\delta n_{2}+\delta n_{3}$ in panel 3 (d).

The histeresis crossing at $V=0$ is disrupted when inversion symmetry is
broken. In Figure 3, we illustrate the combined effect of two transfer
functions with contrasting characteristics. In this scenario, the asymmetry is
controlled by a single parameter in the transfer function, as detailed in
Ref.3. The symmetry break alters the loop’s shape, as shown in Figure 3(f),
with the emergence of multiple loop intersections. These crossings can be
attributed to the multiple sign changes of the function
$g^{(n)}_{4}+g^{(n)}_{5}$ in panel 3 (e), although the positions of the
intersections and the character change of the transfer functions (sign
inversion with applied bias) are not correlated.

By modifying the character and symmetry constraints of the transfer function,
as displayed in panel 3 (g), the topology of the charge fluctuation changes,
as represented in panel 3 (h), resulting in a complete inversion of the loop
direction. Thus, the hysteresis shape and direction encapsulate crucial
information about the nature of the internal microscopic mechanisms that lead
to charge or polarization fluctuation.

Note that in our proposed Mem-emitter architecture, all internal variables are
contained within the substrate material, while all observables emerge from the
TMD monolayer. We must now correlate these internal variables with the memory
traces of the observables of our Mem-emitter: the emission intensity Q and the
position of the emission line at $\hbar\omega=\Delta E_{f,i}$ according to the
approximations introduced in Eqs. 1 and 2.

In devices with inversion symetry break such as the one proposed in Figure 1
(e), the modulation of the optical transition rate in the 2D TMD monolayer can
be proportional to the local electric field 36, 37

$\delta K_{f,i}\propto F_{TMD}(V).$ (11)

This is also the case for the renormalization of the effective energy gap in
excitonic complexes under inversion asymmetry conditions 16, 36

$\delta\Delta E_{f,i}\propto F_{TMD}(V).$ (12)

We should also note that a perpendicular electric field can result in
different slopes for the renormalizations of the exciton and trion energies,
as outlined in Ref. 38.

Considering the optical transition rate (Eq. 2) $1/\tau=K_{f,i}(F_{TMD})\cdot
D\left[\Delta E_{f,i}(F_{TMD})-\hbar\omega\right]$ , we expect the electric
field memory modulation with the internal variables to be translated into a
transition-rate-driven Mem-emitter, following the trends reported in Figure 2,
which could tune any excitonic complex emission. However, in the presence of
electron fluctuation, $\delta n$, the trion emission intensity, $Q_{trion}$,
has been proven to decouple from the exciton emission, $Q_{exc}$, given the
expected ratio 39, 40

$\frac{Q_{trion}}{Q_{exc}}\propto\left[n_{0}+\delta n\left(V\right)\right].$
(13)

If the effect of electron fluctuation prevails over electric field modulation,
we can anticipate excitons to be prone to exhibit transition rate-driven
character in response to the local field, $F_{TMD}(V)$ as shown in Figure 2.
Conversely, trions may demonstrate a mixed response, acting as population-
driven Mem-emitters, in line with the behavior of $\delta n(V)$ depicted in
Figure 3, while also showing transition rate-driven characteristics, similar
to excitons. We believe that this control of stable light intensity and photon
energy patterns can encode diverse information beyond the internal state
characterization, with potential impact on communication and information
processing.

In summary, the concept of Mem-emitters introduces an approach to enhancing
and diversifying optoelectronic device functionalities. In this perspective,
understanding the differences between population-driven and transition-rate-
driven Mem-emitters opens up a wide array of applications. Population-driven
Mem-emitters offer the advantage of straightforward modulation of emitter
density, making them suitable for optoelectronic switches, variable light
sources, and applications where the control of active emitters is essential.
In contrast, transition-rate-driven Mem-emitters provide refined control over
emission properties, making them ideal for high-precision and advanced
optoelectronic applications, such as communication systems and sensors
requiring precise emission control. By exploring these contrasting mechanisms,
and the information encoded in the light emission patterns, it is possible to
develop more versatile and efficient light-emitting devices tailored to
specific needs in various technological fields. Based on this analysis, two
conditions are sufficient for Mem-emitter abilities to emerge (or be
resolved): (i) the proper tuning of external drives to match the internal time
scale appropriate for a given internal state variable [see Fig. 2 (g)] and
(ii) the comparable strength of fluctuations of these variables with respect
to their equilibrium or instantaneous reference values, according to Eqs. 5
and 13. In particular, we anticipate that these unique properties could pave
the way for the development of innovative technologies for memory and
computation. TMDs and other 2D semiconductor monolayers offer a versatile and
powerful platform for developing Mem-emitter functionalities when coupled to
adequate substrates due to their unique properties, including atomic-scale
thickness, tunable electronic properties, and strong light-matter interaction.
Their ability to be modulated by external fields and integrated with other
materials enhances their potential for advanced optoelectronic applications
and in particular those related to memory effects. This underscores the
critical importance of selecting appropriate substrates that would provide the
ingredients for memory-related dynamics. Given the ubiquitous nature of the
memory effects described, we can foresee that mem-emitting properties can also
serve as a versatile tool for characterizing the intrinsic dynamics of complex
systems beyond the functionalities of the Mem-emitter itself. This study was
financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível
Superior - Brazil (CAPES) and the Conselho Nacional de Desenvolvimento
Científico e Tecnológico - Brazil (CNPq) Projs. 311536/2022-0, 309920/2021-3,
and 306170/2023-0.

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