#  EvoK: Connecting loved ones through Heart Rate sharing

Esha Shandilya<EMAIL_ADDRESS>Rochester Institute of TechnologyUSA ,  Yiwen
Wang<EMAIL_ADDRESS>Rochester Institute of TechnologyUSA ,  Xuan Zhao
<EMAIL_ADDRESS>Rochester Institute of TechnologyUSA and  Mingming Fan
<EMAIL_ADDRESS>Rochester Institute of TechnologyUSA

(2021)

###### Abstract.

In this work, we present EvoK, a new way of sharing one’s heart rate with
feedback from their close contacts to alleviate social isolation and
loneliness. EvoK consists of a pair of wearable prototype devices (i.e.,
sender and receiver). The sender is designed as a headband enabling continuous
sensing of heart rate with aesthetic designs to maximize social acceptance.
The receiver is designed as a wristwatch enabling unobtrusive receiving of the
loved one’s continuous heart rate with multi-modal notification systems.

Emotion sharing, heart rate, social isolation, mental health, wearable device

††copyright: acmcopyright††copyright: none††journalyear: 2021††doi:
10.1145/1122445.1122456††conference: CHI EA ’21: Extended Abstracts of the
2021 CHI Conference on Human Factors in Computing Systems; May 08–13, 2021;
Yokohama, Japan††booktitle: CHI EA ’21: Extended Abstracts of the 2021 CHI
Conference on Human Factors in Computing Systems, May 08–13, 2021, Yokohama,
Japan††price: 15.00††isbn: 978-1-4503-XXXX-X/18/06††ccs: Human-centered
computing Human computer interaction (HCI)

##  1\. Introduction

According to WHO (World Health Organization), more than 264 million people
worldwide have suffered from depression (WHO, 2020). Without any intervention,
depression could lead to suicide and cause mortality in a hazardous condition.
One factor that seriously affects people’s mental health is social isolation
and loneliness because of the lack of family ties, and communication (Amzat
and Jayawardena, 2016). Moreover, because of the COVID-19, the depression even
doubled due to the implementation of new social rules such as social
distancing and quarantine policy to protect everyone from the viruses
(Marroquín et al., 2020). The lack of interaction further intensifies their
loneliness and adversely affects their mental health. In serious conditions,
the isolated environment could induce physical illness and mental diseases
(Hawkley and Cacioppo, 2010).

Researchers have investigated ways to alleviate the social loneliness of
individuals, such as increasing one’s interaction with their families and
designing education programs and virtual companions (Pettigrew and Roberts,
2008; Tsiourti et al., 2014; Waycott et al., 2015). One way to improve one’s
social interaction and induce empathy is to sense and share their biosignals,
such as breath patterns and heart rates (Frey, 2014; Frey et al., 2018; Liu et
al., 2019; Min and Nam, 2014). However, due to the limitation in comfort
levels and elusive vibration feedback, it is necessary to investigate new
wearable form factors to comfortably and effectively sense and share people’s
biosignals to increase their emotional connections with their loved ones. In
this work, we design a pair of wearable devices for people to communicate
their heart rate and for their loved ones to receive the heart rate
notification with visual and audio feedback. The pair of devices is designed
to strengthen the relationship between users and their loved ones through
ambient feedback, comfortable and socially-acceptable design.

Reproducibility: The source code for EvoK is available at
https://github.com/EshaShandilya/evok.

##  2\. Background and Related Work

Biosignals, such as pulse sensing (PPG signal), brain electrical activity (EEG
signal), and respiratory rate, are usually measured to understand the
physiological process and activity of human beings (Frey et al., 2018; Ramirez
and Vamvakousis, 2012; Temko, 2017). One such biosignal is heart rate, which
is helpful in expressing distinct aspects of a person’s emotional state
(Slovák et al., 2012). Moreover, exchanging heart rate can affect users’
social interaction and enhance their engagement (Frey, 2014; Slovák et al.,
2012).

This has motivated researchers to design different form factors to sense and
share heart rates. For example, Werner et al. (Werner et al., 2008) designed a
ring that can detect the wearer’s heart rate and send it to the partner’s ring
via vibration feedback. However, participants felt the vibration feedback as a
feeling of ”electric shock” and was elusive to infer the corresponding heart
rate. Croft and Lotan (Lotan and Croft, 2007) created a device named imPulse
with a curved surface so that users could put it on their laps and palms on
the surface, providing synchronizing light and vibration feedback. However,
imPulse is nonwearable, which makes it immobile and unusable when a user is
performing other activities. Min and Nam designed WearBEAT to share body sound
including the sounds of heartbeat (Min and Nam, 2014). In their design, one
user wore the sound input part on the chest mount to sense the heart rate, and
the other user received vibration feedback on their wrist as output. However,
the chest-mounted prototype violates the parameters of Zeagler’s (Zeagler,
2017) body map locations for wearable; since the position near breast could be
uncomfortable for wearers especially for non-male users, which might affect
its social-acceptability.

Inspired by these designs, in this work, we explore a different form factor to
sense and share one’s heart rate with the aim of increasing its comfort level
and social-acceptability. We adopt PPG sensing to detect heart rate as it has
been demonstrated to be a promising wearable heart rate sensing approach
(Frey, 2014). Through the combination of headband and wristwatch, we strive to
provide a comfortable wearing experience and an intuitive interaction.

##  3\. EvoK

###  3.1. Design Considerations

We followed an iterative design process to finalize the key design
considerations for our wearable devices. The design considerations were based
on - i) trade-offs between the comfort level and the detection accuracy of the
heart rate sensor, ii) ambient notification, iii) socially-acceptable designs.
Trade-offs between the Comfort Level and the Detection Accuracy of the Heart
Rate Sensor: Before concluding the sensor’s placement, we tested various
feasible locations, specifically the finger-tip and the ear-lobe, to wear the
heart rate sensor to get accurate heart rate. We observed that the finger-tip
position added noise to the heart rate due to hand-movements, whereas the
sensor’s placement on the ear-lobe reduced noise in the recorded heart rate.
Consequently, we decided to use the ear-lobe for the sensor’s placement.
However, the batteries’ weight pulls the sensor down when placed on the
earlobe, impacting the wearer’s comfort and the sensor’s accuracy. To overcome
this challenge, we brainstormed a solution that could support the batteries’
weight to keep the heart rate sensor’s position intact on the ear lobe,
providing a seamless experience to the wearer. We deliberated the feasibility
of multiple design alternatives such as earrings, neckwear, hair clips, and
headbands. The headband prototype, Figures 2, offers the best weight
distribution of the batteries than the competing alternatives; the encased
batteries are attached to the headband, which rests on the head, providing
stable heart rate sensor positioning.
Ambient Notification: The next design consideration was to design an
unobtrusive notification, which the wearer can easily follow without getting
overwhelmed with the constant influx of the sender’s heart rate. According to
Hansson and Ljungstrand (Hansson and Ljungstrand, 2000) colored LED lights are
less intrusive methods of notification systems than other forms such as sound.
Therefore, we devised three different LED lights to indicate the heart rate
range; considering that the normal heart rate range is between 60 to 100 for
an adult, according to Mayo Clinic (Laskowski, 2020). In the Figures 4, we see
the blue light for heart rate less than 60, the green light for the heart rate
between 60 and 100, and red to highlight the heart rate beyond 100. In case
there is a constant high heart rate of the sender (beyond 100), the receiver
(wearer) will be alerted by a high pitched sound. Moreover, we also provide an
option for the user to control the sender’s heart rate transmission by
pressing a button on the receiver’s prototype. We abandoned the idea of
incorporating haptic feedback to the prototypes, as it may be intrusive and
dysfunctional for users to interact with the prototype.
Socially-acceptable Designs: Social acceptability of a wearable device
directly depends on its placement on the user’s body (Zeagler, 2017). Our
wearable designs are conceptualized according to the socially-acceptable body
locations suggested by Zeagler (Zeagler, 2017) that provide comfort and
confidence to the wearer in public. Therefore, after referring to the body map
(Zeagler, 2017), we chose the two areas – the head and the wrist that offer
comparatively better affordance for the device placement, and thus we select
the form-factors of a headband for the sender and a wrist-watch for a
receiver. Such form-factors, (headband and wrist-watch), Figures 2 and 3, are
intuitive, user-friendly and easy to interact with as these are familiar form-
factors to the users. We carefully determined these designs as these are
gender-neutral and to the most extent used by many. However, we did not
conduct user research to assess the designs’ social acceptance.

Figure 1. This is the final stage, where we work to consolidate all the
sensors in a usable and functional wearable design. Here the heart rate sensor
is a headband design for the sender and when heart rate will be sensed from a
specific range then, the data will be shared in the form of visuals with music
to the receiver which is in the form of a wrist watch. For different heart
ranges, there are specific notifications, please refer Figure 4 for full
explanation on design notifications.

The headband and other components.

###  3.2. Implementation

Our system consists of two parts, the sender and the receiver. The sender’s
heart rate will be detected and sent to the receiver, and the receiver will
get different visual and audio notifications according to the received heart
rate value.

To conceptualize the sender part, we used a pulse rate sensor to detect the
heart rate. The pulse rate sensor was connected to the micro: bit and the code
for calculating the heart rate was downloaded to the micro: bit. The pulse
rate sensor could be placed on the fingertip or earlobe. We tested both these
two placements and found that placing the sensor on the earlobe gave us more
stable signals. Also, considering the convenience of a user wearing the
wearable device, the sensor should be intact while working out, performing
some activity, and resting state. Thus, we decided to put the sensor on the
earlobe. We tried to put the sensor on the earlobe and connected it to the
micro: bit. We found that the gravity of the micro: bit would exert a great
downward force on the earlobe, which could cause ear discomfort. We needed to
put the micro: bit in a supportive position. Our initial idea was to put it in
the cloth pocket; however, not all tops had pockets. Then we turned to body
parts and found the head would be a good choice to put the micro: bit on. We
wanted to make our device portable and could be used by anyone. The idea of
the hairpin was abandoned because it did not apply to people with short hair.
Our idea was to attach the micro: bit to a headband Figure 2. To compact the
battery and connector, we used the 3D printer to print a small box so that all
components can get packed in one Figure 2. When the sender uses this device,
they need to put the headband on and place the pulse rate sensor on the
earlobe, as shown in the Figure 1. After wearing the device, it needs to
collect one or two minutes of data before getting the wearer’s normal heart
rate.

Figure 2. The final design for the sender - Sender’s headband: a wearable
headband banded with a 3D printing compact box, includes battery, Micobits,
connector and linked with pulse sensor.

The headband and other components.

For the receiver part, we designed some feedback and interactions for the
receiver. The receiver also needed to wear the micro: bit to receive the data
from the sender. To make it easier to see the heart rate value and feedback,
we made the device in the form of a wristwatch. We purchased a somatosensory
control development board with a wrist band, an RGB led light, a buzzer, and a
speaker, Figure 3. The micro: bit was connected to the board Figure 3. We
tried to utilize the buzzer to provide haptic feedback; however, the micro:
bit was not powerful enough to implement real-time haptic feedback and caused
long delays. In our design, we only used the led light and speaker to provide
visual and audible feedback, the description can be seen in Figure 4. When the
sender’s heart rate was below the normal range (Laskowski, 2020), which was
less than 60 per minute, the light would be blue. When the heart rate value
was in the normal range between 60 and 100, the light would be green. When the
heart rate was beyond the normal range, which meant over 100 per minute, the
light would turn red, accompanied by a beep sound. The normal range of 60 to
100 was only used for our test. Users could set their own heart rate normal
range. Additionally, to provide more flexibility, the receiver could control
whether to receive the data or not. They could press the left button on the
micro: bit to stop receiving the data and feedback and press the left button
again to resume receiving the data and feedback.

Figure 3. Receiver’s wristwatch: contains a somatosensory control development
board which enables a user to interact with the prototype through audio,
visual and haptic feedback.

Receiver’s wristwatch components.

Figure 4. Three ranges of heart rate with corresponding feedback: Blue LED
represents less than 60. Green LED represents the normal range between 60 and
100. Red LED and alarming sound represents over 100. According to Mayo Clinic
(Laskowski, 2020) , the normal resting heart rate of an individual ranges
between 60 and 100; other factors such as, age, fitness level, emotions could
also influence the heart rate. The heartbeat value of the sender is displayed
on the Microbit’s screen. Note: The heart rates displayed are two and three
digit numbers. One single digit is shown at a time, and the digits are moving
from right to left. The first value on the receiver’s device is the first
digit 3 of 30 with a blue LED light, second value is 5, the last digit of
value 65 with green LED light, and the last value is 1, the first digit of 130
with red LED light.

Different LED light colors and audio for different heart beat value.

##  4\. Conclusion

We present novel prototype designs with feedback for sharing heart rates to
alleviate people’s social isolation from their loved ones. This work presents
a demonstration with a pair of wearable devices that mainly use micro:bit
processor and a heart rate sensor. We exclusively made our designs wearable to
ensure continuous connectivity through heart rate sharing and indicating the
user’s physical and mental well-being.

Future work should investigate users’ attitudes and perception towards the
proposed way of sensing and sharing heart rates and elicit feedback to further
improve its comfort level and social acceptability. Moreover, it is worth
conducting a long-term in-the-wild study to reveal both technical issues, such
as battery life, and practical issues emerging from a wide range of daily
scenarios. Lastly, as heart rate patterns may vary from person to person and
can carry important health- or emotion- related information, it is worth
exploring the characteristics of such patterns and designing prototypes to
capture and communicate them among loved ones.

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††thanks: Authors contributed equally, correspondence email:
<EMAIL_ADDRESS>Authors contributed equally, correspondence email:
<EMAIL_ADDRESS>
# Anatomy of nanomagnetic switching at a 3D Topological Insulator PN junction

Hamed Vakili  Yunkun Xie  Samiran Ganguly  Avik W. Ghosh  Department of
Physics,University of Virginia, Charlottesville, VA 22903 USA  School of
Electrical and Computer Engineering, University of Virginia, Charlottesville,
VA 22903 USA

###### Abstract

A P-N junction engineered within a Dirac cone system acts as a gate tunable
angular filter based on Klein tunneling. For a 3D topological insulator with a
substantial bandgap, such a filter can produce a charge-to-spin conversion due
to the dual effects of spin-momentum locking and momentum filtering. We
analyze how spins filtered at an in-plane topological insulator PN junction
(TIPNJ) interact with a nanomagnet, and argue that the intrinsic charge-to-
spin conversion does not translate to an external gain if the nanomagnet also
acts as the source contact. Regardless of the nanomagnet’s position, the spin
torque generated on the TIPNJ is limited by its surface current density, which
in turn is limited by the bulk bandgap. Using quantum kinetic models, we
calculated the spatially varying spin potential and quantified the
localization of the current versus the applied bias. Additionally, with the
magnetodynamic simulation of a soft magnet, we show that the PN junction can
offer a critical gate tunability in the switching probability of the
nanomagnet, with potential applications in probabilistic neuromorphic
computing.

###### pacs:

Valid PACS appear here

††preprint: APS/123-QED

Three-dimensional topological insulator surfaces enjoy gapless topological
surface states (TSS) protected by spatial inversion and time-reversal
symmetry. In many ways, they are similar to low-energy graphene bands, except
the Dirac cones are labeled by spins rather than pseudospins, with a similar
Chern number chen2009experimental ; xia2009observation ; zhang2009topological
. Numerous novel physical phenomena have been explored with TSS across
graphene PN junctions. In particular, we can draw inspiration from graphene PN
junctions that have served as a convenient laboratory for Klein tunnel
devices, with potentially important contributions to low-power digital as well
as high-speed analog switches beenakker2008colloquium ; stander2009evidence ;
sajjad2013manipulating ; reza_modeling_2016 ; chiba_magnetic-proximity-
induced_2017 ; fert_efficiency ; SOT3dTI .

The intrinsic spin-momentum locking of TSS in a TI material allows conversion
of a charge current into a spin current at a higher efficiency than heavy
metal underlayers in common spin-orbit torque devices Fan2014 ; PRLSOT ;
SOTfert . In fact, the spin-momentum locking feature of TSS imposes spin
conservation rules across a PN junction, suggesting a charge-to-spin
conversion ratio (scaled dimensionally like the Spin Hall Angle except between
longitudinal current densities) can exceed unity and be as high as 20
habib2015chiral . This number is much higher than the Spin Hall Angle measured
in heavy metals such as Pt ($0.07$)liu2011spin , $\beta$-Ta
($0.12-0.15$)liu2012spin , and in Pt-doped Au ($0.12$)gu2010surface . However,
besides an idealized assumption about the presence of a large non-leaky
bandgap (perhaps more suitable to TIs like SmB6 than Bi2Se3), it is also worth
emphasizing that the spin ‘amplification’ effect was studied on a homogeneous
TIPNJ, where the source/drain contacts are assumed to be extensions of the TI
surface as well. While it is easy to over-generalize the high charge-to-spin
conversion efficiency to the TI-ferromagnet interface, it is not a
straightforward equivalence to the homogeneous TI surface and deserves proper
analysis.

In this paper, we argue that the aforementioned large spin amplification is an
intrinsic effect that does not automatically induce a large spin current
across the TI/nanomagnetic contact interface. Fig. 1 shows some possible
setups for a nanomagnet on TIPNJ. Our focus is on configuration (a) and we
will use Non-Equilibrium Green’s Function (NEGF) simulations on the TSS to
help clarify the difference between intrinsic versus extrinsic charge-to-spin
gain in TIPNJ. We also show a NEGF treatment of a full 3D slab that allows us
to compare the surface versus bulk shunt resistances. In practice, it can be a
challenge to isolate the surface contribution from the bulk in common binary
TI compounds such as $\mathrm{Bi_{2}Se_{3}}$,
$\mathrm{Bi_{2}Te_{3}}$taskin2009quantum ; butch2010strong . One possible
solution is to alloy the binary TIs into ternary compounds like
$\mathrm{Bi_{2}Te_{2}Se}$ tuned to have a low carrier density in the bulk
jia2011low . Another way to improve the TSS portion of the total current is by
inserting a ferromagnetic layer with a perpendicular anisotropy to one surface
(Fig 5.b,c), which we will cover later.

A PN junction provides a gate tunable filter on the spins. For sufficient
current densities it can flip a low barrier in-plane magnet unidirectionally.
The latter can be flipped back with an oppositely directed current in a
symmetric set-up. The low barrier magnet is useful for three-terminal
stochastic computing ASN ; BSN , where the PN junction provides a gate
tunability of the average magnetization that follows a neuron-like nonlinear
activation function.

Figure 1: Top view of different configurations of nanomagnet on a TIPNJ. (a)
Nanomagnet as the source contact. (b) Floating nanomagnet located between
source and drain contacts. (c) Floating nanomagnet outside the source-drain
path. (d) A variation of the out-of-location floating nanomagnet. The gate (PN
junction interface) is at $45^{\circ}$ degree from the source-drain direction.
The angled PN junction can reflect electrons from the source to the
nanomagnet.

Computational Method. Near the Dirac point, the 3DTI Hamiltonian can be
described as zhang2009topological :

$\epsilon_{0}(k)+\begin{pmatrix}\mathcal{M}(k)&A_{1}k_{z}&0&A_{2}k_{-}\\\
A_{1}k_{z}&-\mathcal{M}(k)&A_{2}k_{-}&0\\\
0&A_{2}k_{+}&\mathcal{M}(k)&-A_{1}k_{z}\\\
A_{2}k_{+}&0&-A_{1}k_{z}&-\mathcal{M}(k)\end{pmatrix}$ (1)

with $k_{\pm}={k_{x}\pm ik_{y}}$,
$\epsilon_{0}(k)=C+D_{1}k_{z}^{2}+D_{2}(k_{x}^{2}+k_{y}^{2})$ and
$\mathcal{M}(k)=M-B_{1}k_{z}^{2}-B_{2}(k_{x}^{2}+k_{y}^{2})$. For
$\mathrm{Bi_{2}Se_{3}}$, the parameters used are:
$M=0.28~{}\mathrm{eV},A_{1}=2.3~{}\mathrm{eV\mathring{A}},A_{2}=3.3~{}\mathrm{eV\mathring{A}},B_{1}=6.8~{}\mathrm{eV\mathring{A}^{2}},B_{2}=44.5~{}\mathrm{eV\mathring{A}^{2}},C=-0.0068~{}\mathrm{eV},D_{1}=5.74~{}\mathrm{eV\mathring{A}^{2}},D_{2}=30~{}\mathrm{eV\mathring{A}^{2}}$.
These parameters yield a bulk bandgap of $\approx 300~{}\mathrm{meV}$. We used
the 3D Hamiltonian to study the surface versus bulk current. By discretizing
the 3DTI Hamiltonian we get the lattice Hamiltonian:

$\displaystyle
H_{\mathrm{3DTI}}=\sum_{i}c^{\dagger}_{i}\varepsilon_{\mathrm{3DTI}}c_{i}+\sum_{i}\bigg{(}c^{\dagger}_{i,i,i}\frac{T_{x}}{2}c_{i+1,i,i}+$
$\displaystyle
c^{\dagger}_{i,i,i}\frac{T_{y}}{2}c_{i,i+1,i}+c^{\dagger}_{i,i,i}\frac{T_{z}}{2}c_{i,i,i+1}+\mathrm{H.C.}\bigg{)}$
(2)

Where $\varepsilon_{\mathrm{3DTI}}=(C-2D_{1}/a^{2}-4D_{2}/a^{2})I_{4\times
4}+(M-2B_{1}/a^{2}-4B_{2}/a^{2})I_{2\times 2}\otimes\tau_{z}$,
$T_{x,y}=B_{2}/a^{2}\;I_{2\times 2}\otimes\tau_{z}+D_{2}/a^{2}\;I_{4\times
4}-iA_{2}/2a\;\sigma_{x,y}\otimes\tau_{x}$, $T_{z}=B_{1}/a^{2}\;I_{2\times
2}\otimes\tau_{z}+D_{1}/a^{2}\;I_{4\times
4}-iA_{1}/2a\;\sigma_{z}\otimes\tau_{x}$, and H.C. is the Hermitian conjugate.
The z-direction is set perpendicular to the quantum layers. While the 3DTI
Hamiltonian was used to study the bulk-surface current distributions and
current shunting, we need to adopt a simpler TSS model for simulating the
charge/spin transport in the combined system of a TIPNJ and a nanomagnet (Fig.
2):
$H_{\mathrm{TSS}}=v_{F}\mathbf{\hat{z}}\cdot\left(\bm{\sigma}\times\mathbf{p}\right)$.
To discretize this Hamiltonian, a Wilson mass term needs to be added to avoid
the fermion doubling problem hong2012modeling :

$\begin{split}H_{\mathrm{TSS}}&=v_{F}\mathbf{\hat{z}}\cdot\left(\bm{\sigma}\times\mathbf{p}\right)+\gamma\hbar
v_{F}\sigma_{z}(k_{x}^{2}+k_{y}^{2})\\\
&=\sum_{i}c^{\dagger}_{i}\varepsilon_{\mathrm{TI}}c_{i}+\sum_{i}\left(c_{i,i}^{\dagger}t_{x}c_{i,i+1}+\mathrm{H.C.}\right)\\\
&\qquad\qquad\quad+\sum_{j}\left(c^{\dagger}_{j,j}t_{y}c_{j,j+1}+\mathrm{H.C.}\right)\end{split}$
(3)

where $\varepsilon_{\mathrm{TI}}=-4\hbar v_{F}{\alpha}\sigma^{z}/a$,
$t_{x}=\hbar v_{F}[{i}\sigma^{y}/2+{\alpha}\sigma^{z}]/a$, $t_{y}=\hbar
v_{F}[-{i}\sigma^{x}/2+{\alpha}\sigma^{z}]/a$. $a=5\,\mathrm{\AA}$ is the grid
spacing, $v_{F}=0.5\times 10^{6}\,\mathrm{m/s}$, and $\alpha=\gamma/a$ is a
fitting parameter set to $\alpha=1$ to generate a bandstructure that
reproduces the ideal linear bands within a energy window of $0.5\,\mathrm{eV}$
habib2015chiral . $\mathbf{\hat{z}}$ is the normal vector to the surface and
$v_{F}$ is the speed of electrons near the Dirac point.
$\bm{\sigma}=(\sigma_{x},\sigma_{y},\sigma_{z})$ are the Pauli matrices.

A generic ferromagnetic (FM) nanomagnet is modeled by a tight-binding
Hamiltonian in a cubic lattice with a single orbital per site:

$\begin{split}H_{\mathrm{FM}}=&\sum_{i,\sigma,\sigma^{\prime}}c^{\dagger}_{i\sigma}\left(\varepsilon_{\mathrm{FM}}\delta_{\sigma\sigma^{\prime}}-\frac{\bm{\Delta}}{2}\cdot\bm{\sigma}\right)c_{i\sigma^{\prime}}\\\
&\qquad-t\sum_{i,i^{\prime},\sigma}\left(c_{i\sigma}^{\dagger}c_{i^{\prime}\sigma}+\mathrm{H.C.}\right)\end{split}$
(4)

where $\varepsilon_{\mathrm{FM}}$ is the onsite energy.
$\bm{\Delta}=\Delta\mathbf{m}$ is the exchange energy split along the
direction of the magnetization $\mathbf{m}$. $i^{\prime}$ goes through all
neighbors of site $i$. $t=\hbar^{2}/{2m^{*}a^{2}}$ is the electron hopping
energy with effective electron mass $m^{*}$. The hopping term between the FM
and TI surface is tuned to $t_{\mathrm{FM-TI}}=2.3t$ to minimize the contact
resistance. The FM parameters
$m^{*}=0.5m_{e},\,\varepsilon_{\mathrm{FM}}=1.3\,\mathrm{eV},\Delta=0.8\,\mathrm{eV}$
result in a spin polarization
$\eta=(D_{\uparrow}-D_{\downarrow})/(D_{\uparrow}+D_{\downarrow})\approx 0.57$
around the Fermi energy with density of states $D_{\uparrow}=1.34\times
10^{46}\,\mathrm{J^{-1}m^{-3}},D_{\downarrow}=0.357\times
10^{46}\,\mathrm{J^{-1}m^{-3}}$ for the spin up ($-y$)/down ($+y$) channels.
These numbers are a bit lower than the nanomagnet modeled in
roy2015magnetization , mostly due to the reduced size of our simulated magnet.
Fig. 2 shows the discretization of the coupled system including the
ferromagnetic contact and the TI surface. The TI surface is assumed to be
doped N-type with a single gate controlling the drain side. The periodic
boundary condition is adopted in the $y$ direction and characterized by the
transverse quasi-momentum $\mathbf{k}_{\perp}$.

Figure 2: Schematics of the discretization of a TIPNJ with a nanomagnet as the
source contact. The ferromagnetic contact has dimension $20\,\mathrm{nm}$
along the x-direction. The TI surface is $150\,\mathrm{nm}$ long with
$40\,\mathrm{nm}$ on the P and N side and $70\,\mathrm{nm}$ transitioning from
N to P side. The gate on the drain side can swing the local TI surface to
P-type. The red line represents the electrostatic potential of the TIPNJ.

Part of the FM contact is included in the channel Hamiltonian while the rest
is assumed to be infinite in the +z direction and modeled by a self-energy
$\Sigma_{S}$ using recursive Green’s functions. For simplicity, the drain is
just an extended part of the TI surface and included as a surface self-energy
term $\Sigma_{D}$ that can be obtained with an iterative approach
sancho1985highly . The retarded Green’s function $G^{r}$ and electron
correlation matrix $G^{n}$ can be calculated through the Non-Equilibrium
Green’s function method datta1997electronic

$\displaystyle G^{r}(E,\mathbf{k_{\perp}})$ $\displaystyle=$
$\displaystyle[EI-H(\mathbf{k_{\perp}})-\Sigma_{S}(E,\mathbf{k_{\perp}})-\Sigma_{D}(E,\mathbf{k_{\perp}})]^{-1}$
$\displaystyle G^{n}(E,\mathbf{k_{\perp}})$ $\displaystyle=$ $\displaystyle
G^{r}\left(f_{S}\Gamma_{S}+f_{D}\Gamma_{D}\right)G^{r\dagger}$ (5)
$\displaystyle\Gamma_{S,D}$ $\displaystyle=$ $\displaystyle
i\left(\Sigma_{S,D}-\Sigma_{S,D}^{\dagger}\right)$ (6)

with $f_{S,D}$ the Fermi-Dirac distribution function on the source/drain
sides, and $I$ the identity matrix. The charge current is conserved throughout
the structure and can be evaluated as:

$I_{q}(E)=\frac{q}{h}\sum_{\mathbf{k_{\perp}}}\mathrm{Tr}\left[\Gamma_{S}G^{r}\Gamma_{D}G^{r\dagger}\right](f_{S}-f_{D})$
(7)

while the charge and spin current from site $i$ to $j$ are calculated as:

$\displaystyle\mathbf{J}^{i\rightarrow j}_{s}(E)$ $\displaystyle=$
$\displaystyle\frac{q}{ih}\sum_{\mathbf{k_{\perp}}}\mathrm{Tr}\left[\bm{\sigma}\left(H_{ij}G^{n}_{ji}-G^{n}_{ji}H_{ij}\right]\right)$
$\displaystyle\mathbf{J}^{i\rightarrow j}_{q}(E)$ $\displaystyle=$
$\displaystyle\frac{q}{ih}\sum_{\mathbf{k_{\perp}}}\mathrm{Tr}\left[\left(H_{ij}G^{n}_{ji}-G^{n}_{ji}H_{ij}\right]\right)$
(8)

The bias induced carrier density $n=n_{\mathrm{neq}}-n_{\mathrm{eq}}$ where
$n_{\mathrm{neq}},n_{\mathrm{eq}}$ are obtained from:

$\displaystyle n_{\mathrm{eq}}$ $\displaystyle=$
$\displaystyle-\frac{1}{\pi}\mathbf{Tr}\left(\sum_{\mathbf{k_{\perp}}}\int
dE\mathbf{Im}(G^{r}(E,k_{\perp}))\right)f_{0}(E)$ $\displaystyle
n_{\mathrm{neq}}$ $\displaystyle=$ $\displaystyle\frac{1}{2\pi
i}\mathbf{Tr}\left(\sum_{\mathbf{k_{\perp}}}\int dEG^{n}(E,k_{\perp})\right)$
(9)

where $f_{0}$ is the equilibrium Fermi-Dirac distribution.

Figure 3: I-V characteristic of TIPNJ with a ferromagnetic source contact. (a)
TIPNJ setup with a nanomagnet as the source. The magnetization of the FM
contact is oriented to the $-y$ direction. The gate contact is present but not
visualized in the schematic. (b) Charge and spin current densities calculated
at different locations. $J_{q}$ is the charge current density (conserved
throughout the system). $J_{sy}^{\mathrm{TI}}$ is the spin current (polarized
along $-y$ direction) calculated on the TI surface on the source side (N
side). $J_{sy}^{\mathrm{FM-TI}}$ is the spin current density at the FM-TI
interface. The source-drain bias $V_{sd}$ is fixed at $0.1\,\mathrm{V}$ and
the magnetization of the nanomagnet is aligned in the $-y$ direction. (c) Spin
density shows almost no change with gate voltage and is the same in the source
and drain side of TI. This indicates that the spin current amplification in
the source region of TI can not be used for magnet switching.

Results: charge-to-spin conversion in TIPNJ. Our previous workhabib2015chiral
showed that the TIPNJ acts like a spin collimator that increases the non-
equilibrium spin current while reducing the charge current at the same time.
The corresponding spin-to-charge ratio (the longitudinal equivalent of the
Spin Hall Angle $\theta_{\mathrm{SH}}$) at the source contact can go up to as
high as $20$ habib2015chiral . While it is easy to assume that this conversion
would dramatically improve the switching efficiency if we replace the ‘TI
source contact’ with a ferromagnetic contact, we show here that the impressive
gain is limited to the TI surface (we refer to this as the ‘intrinsic’ gain).
To see the difference between the intrinsic and the external gain, we
calculated the spin current at two locations along the transport direction:
one between the FM contact and the TI surface, the other one on the N-type TI
surface, as indicated in Fig. 3(a). Fig. 3(b) compares the charge current with
the spin currents at the above-mentioned locations as a function of the gate
voltage. As the gate voltage sweeps from $-0.3\,\mathrm{V}$ to
$0\,\mathrm{V}$, the TI surface transitions from a PN junction to a
homogeneous N-type surface. The behavior of the charge current (independent of
where it is being calculated) and TI surface spin current
$J_{sy}^{\mathrm{TI}}$, with a maximum ratio of
$J_{sy}^{\mathrm{TI}}/J_{q}>20$ resembles the results from habib2015chiral ,
where the PN junction effectively suppresses the charge current while
amplifying the nonequilibrium spin current. However, the spin current across
the nanomagnetic contact $J_{sy}^{\mathrm{FM-TI}}$ does not follow the in-
plane surface spin current but instead follows the charge current. While the
ratio $J_{sy}^{\mathrm{FM-TI}}/J_{q}$ is very close to $100\%$,
$J_{sy}^{\mathrm{FM-TI}}$ never exceeds the charge current regardless of which
regime the TI surface is in. Looking at the bias-induced charge and spin
carrier density, we can see the picture more clearly (Fig. 3.c). The spin
density shows no change on the source and drain sides of TI. However, the
charge densities show significant variations in the source and drain regions
(opposite of currents’ behavior). This further solidifies the above
explanation, as the charge densities from the incoming and reflected currents
add up in the source region but are subtracted for spin density.

Figure 4: Fermi levels $f_{\mu}$ for different spin channels on the TI surface
in different regimes (TIPNJ versus homogeneous TI surface). $\mu_{s}(\mu_{d})$
is the Fermi level of the source (drain) contact. As can be seen from the
comparison, PN junction raises the Fermi level of all spin channels on the
source side due to the reflection of the junction potential barrier. The
biggest potential drop happens near the junction interface. In the case of
homogeneous TI, the Fermi level remains uniform throughout the TI surface from
the source to the drain.

To better understand this discrepancy, we look at the individual Fermi levels
$f_{\mu}$ in each spin channel (where spin-up corresponds to $-y$ while spin-
down corresponds to $+y$) on the TI surface (Fig. 4). The Fermi levels are
calculated by simulating a magnetic probe at each lattice point which draws
net zero currents from the channel with negligible deformation of the channel
Hamiltonian. The calculated quantity is
$f_{\mu}=\frac{Tr(\Gamma_{\mathrm{FM}}G^{n})}{Tr(\Gamma_{\mathrm{FM}}A)}$
hong2012modeling  where $\Gamma_{\mathrm{FM}}(\pm
y)=\gamma_{m}(I\pm\sigma_{y})$ is the coupling between FM probe and the TI
surface with $\gamma_{m}\ll\hbar v_{f}/a$ being the coupling strength. Due to
the spin-momentum locking of the TI surface states, electrons in the spin-up
channel can only move in the $+x$ direction while electrons in the spin-down
channel move in the opposite direction, roughly along two one-way streets (for
3D TSS, the angular transition is continuous)yunkunklein . This behavior
results in the ‘intrinsic’ spin amplification observed on the TI surface: non-
equilibrium electrons moving in opposite directions due to electron reflection
at the PN junction reduce the net charge current while increasing the net
nonequilibrium spin current. However, when the nanomagnet contact exchanges
electrons with the TI surface, the electrons flow bidirectionally regardless
of their spin orientations. Ultimately, the rate of influx and outflow of
spins from the nanomagnet is controlled by the difference in the
electrochemical potentials between the magnet and the TI surface. Being the
source contact, the magnet has the highest electrochemical potential in both
spin channels. Therefore one expects a net outflow of electrons from the
magnet to the TI surface in both spin channels. The net spin current is just
the difference between the charge currents in different spin channels, which
is always lower than the sum of them. The extrinsic spin amplification in this
configuration, with the magnet doubling as the current source, cannot exceed
unity.

The limit on external charge-to-spin gain is imposed by having the nanomaget
as the source contact. A more common setup is to have a floating nanomagnet on
top of a TI (see fig. 1(b)). There are several research papers that discuss
this configuration (without a PN junction) in detail, such as the proximity
effect induced by the magnetic field from the magnet duan2015nonlinear , and
the shunting of the charge current from the TI surface to a conductive
magnetic layer roy2015magnetization . With this configuration, the
electrochemical potential of the nanomagnet is free to adjust in order to draw
a net zero charge current.

The charge-to-spin conversion rate depends on the splitting of the
electrochemical potentials of the opposite spin channels. With TIPNJ, Fig. 4
shows that the splitting narrows compared to the homogeneous TI surface, which
means the PN junction effectively turns off the spin torque from the TI
surface.

Figure 5: a) The ratio of TSS-to-Bulk current contributions as a function of
the bulk band gap for various carrier energies. We simulate different bulk
bandgaps by varying M 0.28, 0.38 and 0.55 $eV$ . For electron energies inside
the bulk bandgap, the TSS dominate. We see that for energies above the band
gap the TSS is weakly localized. b) Current distribution and a corresponding
simple resistance model for $\mathrm{Bi_{3}Se_{2}}$ (with a bulk gap of 0.3
eV) at 0.2 V applied bias. The magnetic layer with perpendicular anisotropy
(PMA) inserted between the bottom TI surface and the substrate (not shown)
shows a possible way to lower the shunting effect. c) The surface current is
defined as the current in the top layers; from the top layer to the layer with
peaked current density. d) Two ways to improve the surface-to-bulk current
ratio: with a larger bulk band gap, the surface current increases while the
total current decreases. Alternatively, by inserting a magnetic layer with
perpendicular anisotropy at the bottom surface, the total current is reduced
while the current at the opposite surface is almost unaffected, translating to
a higher contribution for the top surface. $V_{s}$ and $V_{d}$ are $\pm
V_{b}/2$

.

Because of the current shunting to the bulk of the 3DTI, the surface spin
current calculated from TSS Hamiltonian Eq. 3 is overestimated. To study the
surface-bulk current distribution, the 3DTI Hamiltonian as described in Eq. 2
is employed. With equation 8, the current density for each layer is calculated
and separated into bulk and surface currents. To get a simple resistance
model, we use two parallel resistances for bulk $R_{b}$ and surface $R_{s}$.
Based on the current distributions, the ratio of resistances is calculated.
Here we define the surface current as the current in the top (bottom) layers:
starting from the top (bottom) surface layer to the layer where the current
density is peaked as shown in Fig. 5.c. TSS has a practical limitation on how
much current increases with applied bias. For electrons with higher energies
that are only accessible with a higher bias, the conductive state will no
longer be strongly localized at the surface and will shunt into the bulk (Fig.
5(a)). Such a shunting 3dTIacoustic  implies that a significant portion of the
current will be diverted away from the surface, reducing the carrier exchange
between the FM and TI and degrading the switching efficiency. Increasing the
bias above the bulk bandgap will therefore have diminishing returns. For
example, for $\mathrm{Bi_{2}Se_{3}}$ the localized current at the surface
(about $2\mathrm{nm}$ thick, Fig. 5.b) carries only $30\%$ of the total
current. One way to alleviate this is by finding a 3DTI material with a larger
bulk bandgap, as can be seen in Fig 5(a-b). Alternatively, inserting or doping
the TI surface in contact with the substrate (Fig. 5b,d) the 3DTI grown on
with a PMA magnet can also increase $\theta_{\mathrm{SH}}$. This is due to the
fact that out-of-plane Zeeman energy kane ; nikolic3dti ; chiba_magnetic-
proximity-induced_2017 ; tokura_magnetic_2019  (Added as
$m_{z}\sigma_{z}\otimes I_{2\times 2}$ to TI onsite energy for the bottom
surface) opens up a gap. Since this effect is localized only at one surface,
the opposite surface is nearly unaffected. However, the total current is now
smaller as the total resistance of the channel is increased.

TIPNJ as a RAM. For the nanomagnet-as-source-contact configuration sans
external gain, the gate controls the TIPNJ resistance and thus can be used to
tune the total spin current and the spin torque applied on the nanomagnet. The
structure of such a device is shown in Fig. 6, where the TIPNJ would have a
transistor-like behavior. However, the maximum bias window is limited by the
bandgap of the bulk TI. While we have discussed ways to alleviate the shunting
issue, they might be challenging to achieve experimentally. Having said that,
we looked at a possible 1 transistor-1 magnetic tunnel junction (1T1MTJ)
1T1MTJ  device based on TIPNJ. The switching of a magnet parallel or anti-
parallel to the injected spin current polarization is known as the anti-
damping switching. The required critical spin current is given by (ignoring
the effects of the rotation of spins from interfacial Zeeman field) sun :

$I_{s}\approx\frac{4q\alpha k_{B}T\Delta}{\hbar}$ (10)

where $\Delta$ is the dimensionless energy barrier and $\alpha$ is the Gilbert
damping. From NEGF calculations, we can see that at low biases, spin currents
of $100~{}\mathrm{\mu A}$ at a width of 40 $\mathrm{nm}$ is achievable. This
would be enough to switch a magnet with $\Delta=40,\;$ (needed for a reliable
memory at room temperature liu2012spin ), $\alpha=0.1$ at a write error rate
(WER) of $10^{-9}$ and a switching time of $5\mathrm{ns}$. The switching
roughly translates to an energy consumption of $\approx 600\;\mathrm{fj/bit}$.
It has been reported that 3DTI can be more energy efficient than heavy metals
PRLSOT ; Liu_ti . However, by improving the interfacial quality of FM and
heavy metal, a significant increase in efficiency of heavy metal has also been
reported fert_efficiency ; improvedHM . This suggests that although 3DTI might
not provide higher energy efficiency compared to heavy metals, TIPNJ can
operate at low voltages suitable for more energy efficient applications such
as RAM. For instance, the tuning of the TI surface state can be achieved by
small applied voltages ($V_{d}\leq 0.1-0.5V$ as compared to $0.9V$ for CMOS
transistors).

Figure 6: Figure shows the structure of a 1T-1MTJ memory based on TIPNJ. The
TIPNJ acts as the transistor element of the memory. $V_{g}$ is the gate
voltage which controls the type of TI (P or N), which then can tune the TSS
accordingly. The $V_{\mathrm{out}}$ is the output voltage which depends on the
magnetization direction.

From a practical perspective, the required on/off current ratio $\beta$ from
reliable spin torque switching can be deducted from the error rate butler ;
fokker :

$\beta={\log\Bigl{[}\frac{\pi^{2}\Delta}{4P_{e}}\Bigr{]}}/{\log\Bigl{[}\frac{\pi^{2}\Delta}{4(1-P_{e})}}\Bigr{]}$
(11)

For a typical write error rate $P_{e}=10^{-9}$, the minimum $\beta$ is about
5.5. In comparison, the $\beta\approx 8$ calculated from NEGF simulations
shows that the gating mechanism works well enough for a TI based 1T-1MTJ RAM.

Figure 7:  (a) Proposed experimental set-up to test gate tunable up to down (1
to 0) switching and vice-versa. Dual TIPNJ setup for switching the nanomagnet
back and forth. (b) Voltage pulse profile. (c) Stochastic Landau Lifshitz
Gilbert (LLG) simulation of magnetodynamics of an in-plane nanomagnet
($40\times 20\times 4\,\mathrm{nm}$) with
$M_{s}=400\,\mathrm{emu/cc},\;\alpha=0.1$ with thermal stability
$\Delta\approx 5$ at 300K. When the drain $V_{d1}$ is activated with a
positive bias relative to the source, the spin torque flips the magnet’s in-
plane magnetization ($m_{y}:+1\rightarrow-1$), at which point further spin
injection is blocked by spin-momentum coupling and the magnetization stays
pinned. Subsequently activating the other TIPNJ with $V_{d2}$ flips the magnet
back to the $-y$ orientation.

Volatile Memory. Although it is possible to enhance the TIPNJ current through
material engineering to achieve the required current to drive traditional RAM
applications, we also explored what is possible under conditions where leakage
current and interfacial imperfections lower the spin current generated on a
TIPNJ. To quantify the driveability of the TIPNJ, we have simulated the
magnetodynamics of a nanomagnet under the TIPNJ current with the
phenomenological Landau-Lifshitz-Gilbert (LLG) equation with a stochastic
Langevin correction:

$\begin{split}\frac{d\mathbf{m}}{dt}=&-\frac{\mu_{0}\gamma}{1+\alpha^{2}}\mathbf{m}\times\mathbf{h}-\frac{\alpha\mu_{0}\gamma}{(1+\alpha^{2})}\mathbf{m}\times\left(\mathbf{m}\times\mathbf{h}\right)\\\
&-\frac{\mu_{B}}{q\Omega
M_{s}(1+\alpha^{2})}\mathbf{m}\times\left(\mathbf{m}\times\mathbf{I}_{s}\right)\\\
\mathbf{h}=&\mathbf{H}_{\mathrm{eff}}+\bm{\tau}_{s},~{}~{}\bm{\tau}_{s}=\sqrt{\frac{2\alpha
k_{B}T}{\mu_{0}\gamma\Omega M_{s}}}\mathbf{G}\end{split}$ (12)

where $\mathbf{m}$ is the normalized magnetic moment;
$\mathbf{H}_{\mathrm{eff}}$ is the effective field from the intrinsic
anisotropy of the magnet; $M_{s}$ is the saturation magnetization; $\Omega$ is
the volume of nanomagnet; $\mathbf{I}_{s}$ is the spin current with the vector
pointing at the spin direction. $\bm{\tau}_{s}$ is a stochastic thermal torque
term representing the thermal noise. $\mathbf{G}$ a three dimensional Gaussian
white noise with mean $\langle G(t)\rangle=0$ and standard deviation of
$\langle G^{2}(t)\rangle=1$. First, we propose a configuration (Fig. 7(a)) for
an experimental verification of the switching of a nanomagnet from a TIPNJ. A
symmetric structure is needed for flipping the magnetization back-and-forth,
generating a periodic signal that can be read out by stacking an MTJ or spin
valve structure on top of the switching magnet. Our simulation shows that the
TIPNJ can reliably drive a small magnet with an adequate anisotropy energy
barrier ($5k_{B}T$) to reliably switch back and forth with a current
(proportional to the longitudinal dimension of the magnet) as low as
$I_{s}=10\,\mathrm{\mu A}$. When we further lower the anisotropy barrier, we
entered a regime where the tunability of the TIPNJ is favored over its
driveability. A nanomagnet with very small energy barrier ($\sim 1k_{B}T$) can
operate in the stochastic switching regime. At room temperature, those magnets
flip their magnetic moments frequently and stochastically under the influence
of thermal noise. A small current can tip the balance of the two energy
minimum orientations along the easy axis and affect the probability of the
magnetic moment pointing at the direction decided by the current direction,
with a binary stochastic neuron like tanh behavior on average. Fig. 8 shows
the tuning of switching probability under a small spin current
$I_{s}=5\,\mathrm{\mu A}$ generated from the TIPNJ. The state (probability) of
the nanomagnet can be extracted through a time-average measurement on the
magnetic moment. This kind of setup can be used in generating random numbers
fukushima2014spin , or stochastic signal processing ganguly2018analog . The
energy cost for this is calculated to be $\approx 20\;\mathrm{fj/bit}$.

Figure 8: Programming a magnet based binary stochastic neuron using gate
tunable PN junction barrier. Low-energy barrier magnet operating in the
stochastic regime. A nanomaget of dimension $20\,\mathrm{nm}\times
18\,\mathrm{nm}\times 5\,\mathrm{nm}$ with approximately $\sim 1k_{B}T$ energy
barrier. The current is applied as a linear ramp from $+5\,\mathrm{\mu A}$ to
$-5\,\mathrm{\mu A}$ where negative current means the current is flowing
through the other PN junction, which can be achieved by tuning the drain or
gate bias.

Conclusion. In this paper, we have taken a closer look at the tuning of the
TSS spin current in a TIPNJ as was originally proposed in habib2015chiral . We
have analyzed the intricate nature of the charge-to-spin conversion on the TI
surface with a nanomagnetic source contact. More importantly, we have
clarified an important difference between the intrinsic charge-to-spin gain
observed on a homogeneous TI surface, and the external gain useful for
switching a nanomagnet. Additionally, we have looked at the limitations on the
magnitude of the surface current, which is mostly determined by the bulk
bandgap, and discussed two ways to improve it. While those issues seem to
suggest the TIPNJ might not be able to offer a superior solution for common
memory/logic applications, it can still work well as a RAM because of its gate
tunability and low bias operation. Furthermore, the spatial programmability
introduced by the PN junction may find use in novel applications such as
probabilistic or neuromorphic applications.

Acknowledgments. This work is supported by the Army Research Lab (ARL) and in
part by the NSF I/UCRC on Multi-functional Integrated System Technology (MIST)
Center; IIP-1439644, IIP-1439680, IIP-1738752, IIP-1939009, IIP-1939050, and
IIP-1939012. We acknowledge helpful discussions with Mahesh Neupane and George
De Coster at ARL.

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