# Symmetry-breaking normal state response and surface superconductivity in
topological semimetal YPtBi

Hyunsoo Kim  Maryland Quantum Materials Center, Department of Physics,
University of Maryland, College Park, Maryland 20742, USA  Department of
Physics, Missouri University of Science and Technology, Rolla, Missouri 65409,
USA  Tristin Metz  Maryland Quantum Materials Center, Department of Physics,
University of Maryland, College Park, Maryland 20742, USA  Halyna Hodovanets
Maryland Quantum Materials Center, Department of Physics, University of
Maryland, College Park, Maryland 20742, USA  Department of Physics, Missouri
University of Science and Technology, Rolla, Missouri 65409, USA  Daniel Kraft
Maryland Quantum Materials Center, Department of Physics, University of
Maryland, College Park, Maryland 20742, USA  Kefeng Wang  Maryland Quantum
Materials Center, Department of Physics, University of Maryland, College Park,
Maryland 20742, USA  Yun Suk Eo  Maryland Quantum Materials Center, Department
of Physics, University of Maryland, College Park, Maryland 20742, USA
Department of Physics & Astronomy, Texas Tech University, Lubbock, Texas
79410, USA  Johnpierre Paglione  Maryland Quantum Materials Center, Department
of Physics, University of Maryland, College Park, Maryland 20742, USA
Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada

###### Abstract

Most of the half-Heusler RPtBi compounds (R=rare earth) host various surface
states due to spin-orbit coupling driven topological band structure. While
recent ARPES measurements ubiquitously reported the existence of surface
states in RPtBi, their evidence by other experimental techniques remains
elusive. Here we report the angle-dependent magnetic field response of
electrical transport properties of YPtBi in both the normal and
superconducting states. The angle dependence of both magnetoresistance and the
superconducting upper critical field breaks the rotational symmetry of the
cubic crystal structure, and the angle between the applied magnetic field and
the measurement plane of a plate-like sample prevails. Furthermore, the
measured upper critical field is notably higher than the bulk response for an
in-plane magnetic field configuration, suggesting the presence of quasi-2D
superconductivity. Our work suggests the transport properties cannot be
explained solely by the bulk carrier response, requiring robust normal and
superconducting surface states to flourish in YPtBi.

##  I Introduction

It has long been known that the boundary between two solid-state systems can
host fascinating electronic states that can fundamentally differ from those of
the host materials [1]. Traditionally, such boundary states are best
demonstrated at the interface of different semiconductors, and the systematic
control of the semiconductor heterostructure led to the discovery of
topological edge states in the Quantum Hall (QH) phase [2]. Over the past
decades, the experimental realization of the Quantum Spin Hall (QSH) effect
[3, 4], topological insulator (TI) phases [5] and more recently the fractional
quantum anomalous Hall effect (FQAHE) [6, 7, 8, 9, 10] have launched intense
research activities investigating of various surface states in compounds with
finite topological invariants [11, 12, 13]. Such topological surface states
provide a unique transport mechanism immune to back-scattering due to its
time-reversal invariant nature, making it a promising candidate for various
technological applications. Superconducting topological surface states are of
particular interest because of the possibility of harboring an exotic Majorana
surface fluid [14, 15, 16, 17, 18], hosting novel phenomena such as the Klein
paradox [19, 20], and harboring intrinsic surface superconductivity mediated
by electron-phonon interaction as predicted for a TI [13]. Due to the low-
dimensional nature of a surface superconducting state, it is protected from
orbital pair-breaking in the case of a parallel applied field [21], and can
withstand a high in-plane magnetic field. While surface nucleation of the
classic superconducting “$H_{c3}$” phase is well known to manifest a higher
critical field $H_{c3}(0)\approx 1.7H_{c2}(0)$ [22, 21, 23], topological
surface superconductivity with strong spin-orbit coupling can also lead to
extremely high upper critical fields exceeding the Pauli paramagnetic limiting
field [24, 25, 26].

The half-Heusler RPtBi (R=rare earth) compounds have attracted a great deal of
attention because of possible topological surface states [27, 28, 29]. The
theoretical band structure is consistent with a topological semimetal driven
by the strong spin-orbit coupling which inverts the $s$-orbital derived
$\Gamma_{6}$ band and $p$-orbital derived $\Gamma_{8}$ band. The theoretical
chemical potential lies on a quadratically touching point of the $\Gamma_{8}$
band, which makes YPtBi a zero-gap semiconductor or semimetal [27, 28, 30,
31]. On the other hand, the experimentally determined chemical potential sits
about 35 meV below the touching point [32, 31, 33]. The quasiparticles are
best described by the $j=3/2$ Luttinger-Kohn Hamiltonian [30, 34, 31, 33],
which was experimentally verified by recent quantum oscillations experiments
[33]. These $j=3/2$ quasiparticles can form Cooper pairs with total effective
spin angular momentum $J$ beyond spin triplet states $J=1$ [30, 35, 36], and a
$J=3$ septet pairing state was proposed to reconcile evidence for
unconventional line-nodal superconductivity [30, 31, 37]. This so-called
“high-spin” superconductivity offers the potential to realize various
topological superconducting states [30, 36], and can harbor a Majorana surface
fluid [14, 15, 16, 17, 18] which can be utilized for fault-tolerant
topological quantum information technology.

Figure 1:  Resistivity and Hall measurements in YPtBi. (a) Normalized
temperature-dependent resistivity $\rho_{xx}(T)/\rho_{xx}(300\textmd{K})$.
Inset: low-temperature part. (b) Field-dependent Hall resistivity
$\rho_{xy}(H)$ in sample S4 at various temperatures with $H\parallel$[100].
(c) Comparison of temperature-dependent $R_{H}(T)$ to $\rho_{xx}(T)$.

In YPtBi, multiple ARPES experiments found metallic surface states [38, 39,
31, 40], but the topological nature of the surface states is not transparent.
Furthermore, the detailed structure of the bulk $\Gamma_{8}$ band near the
touching point needs to be experimentally verified, which depends on the
choice of many-body potential energy term in first-principle calculations
[29]. Understanding the band structure and superconducting properties in YPtBi
would shed light on the current unresolved issues. Moreover, observations of
an enhanced onset of the superconducting transition temperature $T_{c}$ [41]
and indications of an unconventional surface superconducting state [42] in
YPtBi suggest a possible topological chiral state to thrive on the surface of
this material [43]. In this work, we investigate the angle-dependent
electrical transport properties in normal and superconducting states in
topological semimetal YPtBi to understand the symmetry constraints on these
novel phases.

##  II Experiment

Single crystals of the half-Heusler YPtBi were synthesized by utilizing a
high-temperature flux technique in molten Bi with a starting ratio of 1:1:20
for Y, Pt, and Bi, respectively. YPtBi single crystals were grown out of
molten Bi with starting composition Y:Pt:Bi = 1:1:20 (atomic ratio) [32, 31].
The starting materials Y ingot (99.9%), Pt powder (99.95%), and Bi chunk
(99.999%) were put into an alumina crucible, and the crucible was sealed
inside an evacuated quartz ampule. The ampule was heated slowly to 1150°C,
kept for 10 hours, and then cooled down to 500°C at a 3°C/hour rate, where the
excess of molten Bi was decanted by centrifugation. The MgAgAs-type half-
Heusler phase ($F\bar{4}3m$) of the single crystal samples was confirmed by
powder x-ray diffraction pattern. A single-crystal x-ray technique was
utilized to determine the crystallographic directions [31].

For transport measurements, samples were mechanically polished into bar- or
plate-like shapes with typical dimensions 1.0$\times$0.3$\times$0.035 mm3.
Electrical contacts to high-purity silver wire leads were attached by using
silver paste. Typical contact resistances were of order $\sim 1~{}\Omega$ or
less. Magneto-transport measurements were performed using a Quantum Design
Physical Property Measurement System equipped with a 14 T superconducting
magnet and a single-axis rotator. Electrical resistance and Hall voltage were
determined by using an ac resistance bridge. For measurements of the angle-
dependent superconducting upper critical field, we utilized an Oxford
instruments dilution refrigerator and a 5 T two-axis vector magnet.

##  III Results

Figure 1(a) presents the temperature-dependent resistivity $\rho_{xx}(T)$ of
four different YPtBi samples in the absence of magnetic fields. All
$\rho_{xx}(T)$ curves are normalized to the resistivity values determined at
300 K, and exhibit a nearly identical temperature dependence, with a negative
slope at high temperatures, an inflection point near 150 K, and a slight
variation of the residual resistivity values $\rho_{xx}(0)$. All samples
consistently show a broad maximum of around 80 K. The low-temperature part of
$\rho_{xx}(T)$ below $T=150$ K is shown in the inset which clearly displays
the positive slope of $\rho_{xx}(T)$ at low temperatures with much weaker
temperature variation.

Figure 1(b) shows the field-dependent Hall resistivity $\rho_{xy}(H)$ in
sample S4 at various temperatures with $H\parallel$[001]. For temperatures up
to 75 K, $\rho_{xy}(H)$ exhibits nearly linear field variation, but a
noticeable curvature in $\rho_{xy}(H)$ appears with temperatures above 100 K.
Overall temperature dependence becomes weaker with increasing temperature. The
temperature-dependent Hall coefficient $R_{H}(T)=V_{xy}t/I\mu_{0}H$ for sample
S4 is shown in Figure 1(c). Here $V_{xy}$ is the measured voltage with applied
$I$ and $H$, and $t$ is the thickness of the sample. The measured $V_{xy}(H)$
is not linear in $H$ at higher temperatures, and $R_{H}$ was determined by
fitting a linear line to the data up to 9 T. The error bars represent fitting
errors. $R_{H}(T)$ strongly depends on temperature with a negative slope
between 100 K and 350 K, but it is nearly constant below 100 K. This behavior
is reminiscent of $\rho_{xx}(T)$. For comparison $\rho_{xx}(T)$ is shown,
which was determined in the same sample, and they exhibit qualitatively the
same temperature variation [32]. Therefore, the non-metallic behavior of
$\rho_{xx}(T)$ is partially explained by the temperature variation of the
carrier density. As shown in the Hall effect (see Fig. 1(b)), $\rho_{xy}(H)$
is consistent with a hole-like single band for temperatures below 75 K. The
hole mobility can be estimated by using the relation, $R_{H}(T)/\rho_{xx}(T)$.
The inset of Fig. 1(c) shows the calculated $\mu_{h}$ which is about
$6.5\times 10^{3}$ cm2V-1s-1 up to 20 K.

Figure 2:  Temperature-dependent carrier density and mobility. (a) Carrier
densities $n_{h}$ and $n_{e}$ in YPtBi at various temperatures, which are
determined by fitting the two-carrier model (Eq. 1) to the experimental Hall
data shown in Fig. 1. (b) Mobilities $\mu_{h}$ and $\mu_{e}$ are similarly
determined at various temperatures.

In a single-band approximation, the carrier density can be determined by the
relation, $R_{H}=1/en_{h}$, which is $n_{h}=2.1\times 10^{18}$ cm-3 at $T=2$
K. However, we cannot employ this approximation at higher temperatures above
100 K because of the pronounced curvature. The observed behavior of
$\rho_{xy}(H)$ in Fig. 1(b) is consistent with the appearance of the electron-
like carrier with increasing temperature. Temperature dependence of the
carrier density $n$ and mobility $\mu$ of electron-and hole-like carriers are
determined by fitting the two-band model to the experimental $\rho_{xy}(H)$ by
using the relation [44]:

$\rho_{yx}(B)=\frac{B}{e}\frac{(n_{h}\mu_{h}^{2}-n_{e}\mu_{e}^{2})+(n_{h}-n_{e})\mu_{h}^{2}\mu_{e}^{2}B^{2}}{(n_{h}\mu_{h}+n_{e}\mu_{e})^{2}+(n_{h}-n_{e})^{2}\mu_{h}^{2}\mu_{e}^{2}B^{2}}$
(1)

The determined $n_{e}$ and $n_{h}$ are displayed in Fig. 2(a). Below $T\approx
100$ K, only the hole-like carriers are active, but the electron-like carriers
start populating above 100 K. $n_{e}$ is comparable to $n_{h}$ at high
temperatures above 200 K. Our results indicate that YPtBi is a nearly
compensated semimetal at room temperature, which explains the larger non-
saturating magnetoresistance [45, 46, 47, 48].

The temperature-dependent mobility of the electron-like carrier $\mu_{e}$ and
the hole-like carrier $\mu_{h}$ are displayed in Fig. 2(b). Whereas $n_{h}$
increases monotonically with temperature, $\mu_{e}$ exhibits only weak
variation over the entire temperature range.

Figure 3(a) shows field-dependent $\rho_{xx}(H)$ in S1 at $T=2$ K with various
angles. The sample is cut out of the (001) plane. The rotation of $H$ is
indicated in the inset. The angle represents a polar angle measured from
[001], normal to the sample plane, to [010] direction which is the electric
current direction. In this configuration, the angle-dependent $\rho_{xx}$ is
dominated by the Lorentz force, and magnetoresistance (MR) is zero in
principle when $\theta=90\degree$. In our experiment with $\theta=90\degree$,
$\rho_{xx}$ moderately increases with $H$, yielding $\rho_{xx}(14\textmd{
T})\approx 1.14\rho_{xx}(0\textmd{ T})$. We define
$\Delta\rho_{xx}(\theta)=[\rho_{xx}(14\textmd{ T})-\rho_{xx}(0\textmd{
T})]/\rho_{xx}(0\textmd{ T})$ at a given angle $\theta$. At $T=2$ K,
$\Delta\rho_{xx}(0\degree)/\Delta\rho_{xx}(90\degree)\approx 5.6$, which can
be accounted for by the angle-dependent Lorentz force. The Shubnikov-de Haas
(SdH) effect is visible in the high field region, and the angle-dependent SdH
effect is consistent with the presence of a $j=3/2$ quasiparticle Fermi
surface in YPtBi [33].

Figure 3(b) shows the field-variation of $\rho_{xx}(H)$ in the same sample S1
at $T=2$ K with a rotating field from [001] to [100] as depicted in the inset.
In this experiment, however, the orientation of $H$ remains perpendicular to
the direction of the electric current, and the nominal contribution of the
Lorentz force remains uniform upon rotation. Since the angular variation of
intrinsic $\rho_{xx}$ will be governed by the microscopic parameters such as
effective mass $m^{*}$, Fermi velocity $v_{F}$, etc, the rotational symmetry
in $\rho_{xx}$ should follow the crystallographic symmetry. In this case, it
would exhibit a four-fold symmetry with
$\rho_{xx}^{\textmd{\tiny[001]}}=\rho_{xx}^{\textmd{\tiny[100]}}$. However, we
observed
$\rho_{xx}^{\textmd{\tiny[100]}}(H)=1.27\rho_{xx}^{\textmd{\tiny[100]}}(H)$
with $\mu_{0}H=14$ T, and therefore $\Delta\rho_{xx}(\theta)$ breaks
rotational symmetry.

Figure 3:  Angle-dependent magnetoresistance in YPtBi. (a) Field-dependent
$\rho_{xx}(H)$ with various angles determined at $T=2$ K. Field was rotated
from [001] to [010] as indicated in inset. (b) Similar $\rho_{xx}(H)$ data
with field rotation transverse to the electric current from [001] to [100].
(c) $\Delta\rho_{xx}(\theta)=[\rho_{xx}(14\textmd{ T})-\rho_{xx}(0\textmd{
T})]/\rho_{xx}(0\textmd{ T})$ as a function of the angle at various
temperatures with a magnetic field rotating around the current direction. (d)
Temperature variation of the magnetoresistance ratio
$\Delta\rho_{xx}(0\degree)/\Delta\rho_{xx}(90\degree)$ determined at 14 T.

We investigated the anomalous rotational symmetry of MR at various
temperatures. Figure 3(c) is a polar plot of the angle-dependent
$\Delta\rho_{xx}(\theta)$ at various temperatures with a magnetic field
rotating around the current direction. The angular variation exhibits a two-
fold symmetry at all measured temperatures, but it is much more pronounced at
low temperatures. Between 2 K and 150 K, $\Delta\rho_{xx}(\theta)$ exhibits a
butterfly-like shape, most notably below 50 K where the anisotropy remains
nearly temperature-independent to the lowest temperatures. At high
temperatures, $\Delta\rho_{xx}(\theta)$ exhibits a nearly four-fold symmetry
and is notably smaller when a field is applied along the [110] equivalent
orientations. The temperature variation of the ratio
$\Delta\rho_{xx}(0\degree)/\Delta\rho_{xx}(90\degree)$, which reflects the
two-fold symmetry breaking anisotropy, is shown in Figure 3(d). Starting close
to unity at room temperature, the anisotropy rapidly increases upon cooling,
reaching nearly a factor of two at low temperatures. This observation suggests
that additional factors need to be considered to explain the measured angular
variation of magnetoresistance.

To investigate the effect of the anomalous rotational symmetry on the
superconducting state, we determined the angle-dependence of the
superconducting upper critical field $H_{c2}$ by electrical transport
measurements. Figure 4 shows the angular variation of $H_{c2}(T)$ in the
samples with (001) and (111) planes. At each angle, $H_{c2}$ was determined at
the 50% of superconducting-to-normal state transition while ramping up $H$ at
a fixed temperature of $T=100$ mK. Figure 4(a) displays the results in the
(001)-sample. The black square symbols represent $H_{c2}$ with a magnetic
field rotating in the sample plane as indicated in the inset. The angle-
dependent $H_{c2}$ exhibits a nearly four-fold symmetry with a weak variation
around $\mu_{0}H_{c2}(0)=2.2$ T that is significantly higher than the reported
1.5 T [32]. The blue triangle symbols represent $H_{c2}$ with a magnetic field
rotating around the electric current, starting from the direction parallel to
the sample plane as indicated in the inset. With increasing angle, $H_{c2}$
rapidly decreases. The angle-dependence clearly exhibits a two-fold symmetry
with about 30% reduction in $H_{c2}$ when the magnetic field is applied
perpendicular to the sample plane.

Figure 4(b) shows the results from similar experiments with a sample prepared
from the (111) plane. The black square symbols represent $H_{c2}$ from the in-
plane rotation experiments while the blue triangle symbols represent that from
the rotation around the electrical current. The rotation is depicted in the
inset for both rotation experiments. $H_{c2}$ in the experiment with in-plane
rotation shows overall higher values similar to the results from the
(001)-sample. In both (001)-and (111)-samples, angle-dependent $H_{c2}$ is
dominated by the angle between the applied $H$ and the sample plane,
irrespective to the crystallographic direction similar to the angle-dependence
of magnetoresistance in the normal state.

Figure 4:  Anisotropy of superconducting upper critical field $H_{c2}$ at
$T=100$ mK in YPtBi. The symbols represent $\mu_{0}H$ determined with a
magnetic field rotation as depicted in the inset for (a) the (001)-sample and
(b) the (111)-sample.

##  IV discussion

The observed breaking of the rotational symmetry of cubic crystal in both
normal and superconducting states by our transport measurements indicates the
presence of a 2D state. Several recent ARPES studies consistently showed a
large chemical potential shift of about 300 meV at the surface [38, 39, 31,
40] which is in stark contrast to the bulk chemical potential determined by
Hall effect and quantum oscillation experiments [32, 31, 33]. This leads to
the possibility of different electronic phases near the surface and points out
that the measured resistivity might not be solely from the bulk. The
longitudinal transport is likely carried by both bulk and surface, i.e., two-
channel parallel transport, and the contribution of a surface component is
rather significant at low temperatures (see Fig. 3). The local maximum around
80 K is probably associated with the crossover of a dominant component from
non-metallic bulk at high temperatures to metallic surface at low
temperatures, similarly with the onset of a low-temperature plateau in the
topological Kondo insulator due to the surface state [49, 50, 51]. However,
the significant charge imbalance at the surface due to band bending in YPtBi
[31] implies a continuous change of carrier concentration near the surface,
and therefore a simple two-channel model may not be sufficient, calling for a
sophisticated model based on realistic surface states.

The Hall effect is not affected by the thin surface layer and is dominated by
the bulk carriers. The temperature-dependent Hall effect can shed light on the
detailed structure of electronic bands near the chemical potential, which is
still under debate as the local density approximation [38, 52] predicts a
significant overlapping of the hole-like and electron-like bands (compensated
semimetal) whereas quadratically point-touching bands are predicted by other
calculations [28, 27, 53]. While the result of our Hall effect measurement
cannot precisely predict the band structure, it rules out the compensated
semimetal since we do not see any electron-like band at low temperatures.

The surface states affect the superconductivity in YPtBi, and exotic surface
superconductivity may coexist with the bulk superconductivity [42, 43]. Due to
the dimensional and potentially unconventional properties, the surface
superconductivity may exhibit distinct characteristics in the upper critical
fields. Strong magnetic fields can generally suppress the superconducting
states by two well-known mechanisms. First, superconductivity will be
destabilized when free energy reduction due to Pauli spin paramagnetism in a
finite magnetic field favors over the superconducting condensation energy[54].
The Pauli paramagnetic limiting field $H_{P}$ for spin-1/2 spin-singlet
pairing is given by $\Delta_{0}/\sqrt{2}\mu_{B}$ for a parabolic band where
$\Delta_{0}$ is the magnitude of the superconducting energy gap at zero
temperature and $\mu_{B}$ is the Bohr magneton. For a weak-coupling BCS
superconductor, $\Delta_{0}\approx 1.764k_{B}T_{c}$. Therefore,
$\mu_{0}H_{P}=aT_{c}$ where $a\approx 1.86$ T/K. In this approximation, the
expected $H_{P}$ in YPtBi is $\mu_{0}H_{P}\approx 1.53$ T.

Secondly, the Cooper pair can be de-paired when the increased kinetic energy
due to the additional orbital motion from the presence of a magnetic field
exceeds the pairing potential energy. For a weak-coupling BCS superconductor
with a spherical Fermi surface, the orbital pair-breaking effect is best
described by $H_{c2}(0)\approx 0.727|H^{\prime}_{c2}(T_{c})|T_{c}$ [55], which
corresponds to $\mu_{0}H=1.11$ T for YPtBi. Here, we used
$\mu_{0}H^{\prime}_{c2}(T_{c})=-1.98$ T/K. Generally, $H_{P}$ is greater than
the orbital $H_{c2}(0)$, and therefore $H_{p}$ is observed only when the
orbital pair-breaking mechanism is significantly weakened.

While a large effective mass naturally leads to a higher orbital-limiting
$H_{c2}$ value expectation, quasi-2D systems can exhibit exceptionally high
$H_{c2}$ when $H$ is parallel to the plane, limiting the orbital motion. In
this case, the Pauli limiting field will determine the upper critical field.
However, the Pauli mechanism can be avoided by accommodating the Cooper pairs
with a finite momentum [56, 57]. Alternatively, Ising superconductivity due to
strong spin-orbit coupling can lead to critical fields far exceeding the Pauli
limit [24].

The presence of strong spin-orbit coupling [58] or anisotropic superconducting
gap structure [59] would lead to significant magnetic anisotropic energy which
results in the sizable angular variation of $H_{c2}$ in a 3D system. In such
cases, the angle variation of $H_{c2}$ would depend on the orientation of
applied $H$ with respect to the crystallographic direction. In YPtBi, we
observed a large anisotropy in $H_{c2}$ which is irrespective of the bulk
crystal symmetry. When $H$ is parallel to the plane of the plate-like sample,
$H_{c2}$ is consistently higher in various samples, which is reminiscent of
angular variation of $H_{c2}$ in a quasi-2D system, and the anomalous
electronic phase could exist at the boundary of the sample considering the
topological nature of the bulk band structure.

The anomalous transport properties of both normal and superconducting states
in YPtBi, possibly arising from topological surface states, would suggest an
exotic superconducting state is responsible for the observed high upper
critical field. The twofold symmetry observed in YPtBi is strikingly similar
to evidence for nematic superconductivity reported in experiments on the doped
topological insulator Bi2Se3 [60], twisted bilayer graphene [61], and most
recently the kagome superconductor CsV3Sb5 [62]. While this seems to be a
common feature, isolating the surface and bulk contributions will require more
sophisticated experiments such as the double Corbino disc technique [51].

##  V summary

We investigated the anisotropy of transport properties in the normal and
superconducting states of the topological semimetal YPtBi. The non-metallic
electrical resistivity of YPtBi, which rises on cooling along with the Hall
coefficient, entails an inherent anisotropy in its response to applied
magnetic fields that follows a symmetry reduced from that of the four-fold
cubic symmetry of the crystallographic structure. The longitudinal resistivity
exhibits an anomalous two-fold rotational symmetry up rotation of an applied
field perpendicular to the applied electrical current at all temperatures but
becomes more pronounced at low temperatures. In the superconducting state,
this reduced symmetry is also apparent in the measured anisotropy of the upper
critical field, which also does not follow the rotational symmetry of crystal
structure when a magnetic field is rotated out of the sample plane. Our
results imply the anomalous rotational symmetry-breaking apparent in both the
normal and superconducting states of YPtBi cannot be explained by bulk carrier
contributions, but must arise from contributions of topological surface
states, laying a cornerstone for the realization of time-reversal symmetry-
breaking topological surface superconductivity.

##  VI acknowledgement

This work was supported by the U.S. Department of Energy (DOE) Award No. DE-
SC-0019154 (experimental investigations), and the Gordon and Betty Moore
Foundation’s EPiQS Initiative through Grant No. GBMF4419 (materials
synthesis). Undergraduate research (D.K.) was generously supported by the
Maryland Quantum Materials Center.

## References

  * Shockley [1939] W. Shockley, Phys. Rev. 56, 317 (1939).
  * Klitzing  _et al._ [1980] K. v. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
  * Bernevig  _et al._ [2006] B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314, 1757 (2006).
  * König  _et al._ [2007] M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Science 318, 766 (2007).
  * Hasan and Kane [2010] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
  * Cai  _et al._ [2023] J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtzmann, Y. Zhang, F. Fan, T. Taniguchi, K. Watanabe, Y. Ran, T. Cao, L. Fu, D. Xiao, W. Yao, and X. Xu, Nature 622, 63 (2023).
  * Park  _et al._ [2023] H. Park, J. Cai, E. Anderson, Y. Zhang, J. Zhu, X. Liu, C. Wang, W. Holtzmann, C. Hu, Z. Liu, T. Taniguchi, K. Watanabe, J.-H. Chu, T. Cao, L. Fu, W. Yao, C.-Z. Chang, D. Cobden, D. Xiao, and X. Xu, Nature 622, 74 (2023).
  * Zeng  _et al._ [2023] Y. Zeng, Z. Xia, K. Kang, J. Zhu, P. Knüppel, C. Vaswani, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Nature 622, 69 (2023).
  * Xu  _et al._ [2023] F. Xu, Z. Sun, T. Jia, C. Liu, C. Xu, C. Li, Y. Gu, K. Watanabe, T. Taniguchi, B. Tong, J. Jia, Z. Shi, S. Jiang, Y. Zhang, X. Liu, and T. Li, Phys. Rev. X 13, 031037 (2023).
  * Lu  _et al._ [2024] Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seo, K. Watanabe, T. Taniguchi, L. Fu, and L. Ju, Nature 626, 759 (2024).
  * Kim  _et al._ [2012a] D. Kim, Q. Li, P. Syers, N. P. Butch, J. Paglione, S. D. Sarma, and M. S. Fuhrer, Phys. Rev. Lett. 109, 166801 (2012a).
  * Kim  _et al._ [2012b] D. Kim, S. Cho, N. P. Butch, P. Syers, K. Kirshenbaum, S. Adam, J. Paglione, and M. S. Fuhrer, Nature Physics 8, 459 (2012b).
  * Das Sarma and Li [2013] S. Das Sarma and Q. Li, Phys. Rev. B 88, 081404 (2013).
  * Timm  _et al._ [2017] C. Timm, A. P. Schnyder, D. F. Agterberg, and P. M. R. Brydon, Phys. Rev. B 96, 094526 (2017).
  * Yang  _et al._ [2017] W. Yang, T. Xiang, and C. Wu, Phys. Rev. B 96, 144514 (2017).
  * Ghorashi  _et al._ [2017] S. A. A. Ghorashi, S. Davis, and M. S. Foster, Phys. Rev. B 95, 144503 (2017).
  * Wu  _et al._ [2020] T. C. Wu, H. K. Pal, P. Hosur, and M. S. Foster, Phys. Rev. Lett. 124, 067001 (2020).
  * Zhang and Das Sarma [2021] R.-X. Zhang and S. Das Sarma, Phys. Rev. Lett. 126, 137001 (2021).
  * Young and Kim [2009] A. F. Young and P. Kim, Nature Physics 5, 222 (2009).
  * Lee  _et al._ [2019] S. Lee, V. Stanev, X. Zhang, D. Stasak, J. Flowers, J. S. Higgins, S. Dai, T. Blum, X. Pan, V. M. Yakovenko, J. Paglione, R. L. Greene, V. Galitski, and I. Takeuchi, Nature 570, 344 (2019).
  * Tinkham [2004] M. Tinkham,  _Introduction to Superconductivity: Second Edition_, 2nd ed. (Dover Publications, 2004).
  * Saint-James and Gennes [1963] D. Saint-James and P. Gennes, Physics Letters 7, 306 (1963).
  * Kim  _et al._ [2013] H. Kim, N. H. Sung, B. K. Cho, M. A. Tanatar, and R. Prozorov, Phys. Rev. B 87, 094515 (2013).
  * Lu  _et al._ [2015] J. M. Lu, O. Zheliuk, I. Leermakers, N. F. Q. Yuan, U. Zeitler, K. T. Law, and J. T. Ye, Science 350, 1353 (2015).
  * Xi  _et al._ [2016] X. Xi, Z. Wang, W. Zhao, J.-H. Park, K. T. Law, H. Berger, L. Forró, J. Shan, and K. F. Mak, Nature Physics 12, 139 (2016).
  * Saito  _et al._ [2016] Y. Saito, Y. Nakamura, M. S. Bahramy, Y. Kohama, J. Ye, Y. Kasahara, Y. Nakagawa, M. Onga, M. Tokunaga, T. Nojima, Y. Yanase, and Y. Iwasa, Nature Physics 12, 144 (2016).
  * Chadov  _et al._ [2010] S. Chadov, X. Qi, J. Kübler, G. H. Fecher, C. Felser, and S. C. Zhang, Nat Mater 9, 541 (2010).
  * Lin  _et al._ [2010] H. Lin, L. A. Wray, Y. Xia, S. Xu, S. Jia, R. J. Cava, A. Bansil, and M. Z. Hasan, Nat Mater 9, 546 (2010).
  * Feng  _et al._ [2010] W. Feng, D. Xiao, Y. Zhang, and Y. Yao, Phys. Rev. B 82, 235121 (2010).
  * Brydon  _et al._ [2016] P. M. R. Brydon, L. Wang, M. Weinert, and D. F. Agterberg, Phys. Rev. Lett. 116, 177001 (2016).
  * Kim  _et al._ [2018] H. Kim, K. Wang, Y. Nakajima, R. Hu, S. Ziemak, P. Syers, L. Wang, H. Hodovanets, J. D. Denlinger, P. M. R. Brydon, D. F. Agterberg, M. A. Tanatar, R. Prozorov, and J. Paglione, Science Advances 4, 10.1126/sciadv.aao4513 (2018).
  * Butch  _et al._ [2011] N. P. Butch, P. Syers, K. Kirshenbaum, A. P. Hope, and J. Paglione, Phys. Rev. B 84, 220504 (2011).
  * Kim  _et al._ [2022] H. Kim, J. Lee, H. Hodovanets, K. Wang, J. D. Sau, and J. Paglione, Phys. Rev. Res. 4, 033169 (2022).
  * Cano  _et al._ [2017] J. Cano, B. Bradlyn, Z. Wang, M. Hirschberger, N. P. Ong, and B. A. Bernevig, Phys. Rev. B 95, 161306 (2017).
  * Savary  _et al._ [2017] L. Savary, J. Ruhman, J. W. F. Venderbos, L. Fu, and P. A. Lee, Phys. Rev. B 96, 214514 (2017).
  * Venderbos  _et al._ [2018] J. W. F. Venderbos, L. Savary, J. Ruhman, P. A. Lee, and L. Fu, Phys. Rev. X 8, 011029 (2018).
  * Ishihara  _et al._ [2021] K. Ishihara, T. Takenaka, Y. Miao, Y. Mizukami, K. Hashimoto, M. Yamashita, M. Konczykowski, R. Masuki, M. Hirayama, T. Nomoto, R. Arita, O. Pavlosiuk, P. Wiśniewski, D. Kaczorowski, and T. Shibauchi, Phys. Rev. X 11, 041048 (2021).
  * Liu  _et al._ [2011] C. Liu, Y. Lee, T. Kondo, E. D. Mun, M. Caudle, B. N. Harmon, S. L. Bud’ko, P. C. Canfield, and A. Kaminski, Phys. Rev. B 83, 205133 (2011).
  * Liu  _et al._ [2016] Z. K. Liu, L. X. Yang, S.-C. Wu, C. Shekhar, J. Jiang, H. F. Yang, Y. Zhang, S.-K. Mo, Z. Hussain, B. Yan, C. Felser, and Y. L. Chen, Nature Communications 7, 12924 (2016).
  * Hosen  _et al._ [2020] M. M. Hosen, G. Dhakal, K. Dimitri, H. Choi, F. Kabir, C. Sims, O. Pavlosiuk, P. Wiśniewski, T. Durakiewicz, J.-X. Zhu, D. Kaczorowski, and M. Neupane, Scientific Reports 10, 12343 (2020).
  * Baek  _et al._ [2015] H. Baek, J. Ha, D. Zhang, B. Natarajan, J. P. Winterstein, R. Sharma, R. Hu, K. Wang, S. Ziemak, J. Paglione, Y. Kuk, N. B. Zhitenev, and J. A. Stroscio, Phys. Rev. B 92, 094510 (2015).
  * Persky  _et al._ [2023] E. Persky, A. Fang, X. Zhang, C. Adamo, E. Levenson-Falk, C. Shekhar, C. Felser, B. Yan, and A. Kapitulnik, Possible unconventional surface superconductivity in the half-heusler yptbi (2023), arXiv:2312.17213 [cond-mat.supr-con] .
  * Schwemmer  _et al._ [2022] T. Schwemmer, D. D. Sante, J. Schmalian, and R. Thomale, Chiral surface superconductivity in half-heusler semimetals (2022), arXiv:2212.09786 [cond-mat.supr-con] .
  * Luo  _et al._ [2016] Y. Luo, R. D. McDonald, P. F. S. Rosa, B. Scott, N. Wakeham, N. J. Ghimire, E. D. Bauer, J. D. Thompson, and F. Ronning, Scientific Reports 6, 27294 (2016).
  * Shekhar  _et al._ [2012a] C. Shekhar, S. Ouardi, G. H. Fecher, A. Kumar Nayak, C. Felser, and E. Ikenaga, Applied Physics Letters 100, 252109 (2012a).
  * Shekhar  _et al._ [2012b] C. Shekhar, S. Ouardi, A. K. Nayak, G. H. Fecher, W. Schnelle, and C. Felser, Phys. Rev. B 86, 155314 (2012b).
  * Shekhar  _et al._ [2013] C. Shekhar, M. Nicklas, A. K. Nayak, S. Ouardi, W. Schnelle, G. H. Fecher, C. Felser, and K. Kobayashi, Journal of Applied Physics 113, 17E142 (2013).
  * Shekhar  _et al._ [2018] C. Shekhar, N. Kumar, V. Grinenko, S. Singh, R. Sarkar, H. Luetkens, S.-C. Wu, Y. Zhang, A. C. Komarek, E. Kampert, Y. Skourski, J. Wosnitza, W. Schnelle, A. McCollam, U. Zeitler, J. Kübler, B. Yan, H.-H. Klauss, S. S. P. Parkin, and C. Felser, Proceedings of the National Academy of Sciences 115, 9140 (2018), https://www.pnas.org/doi/pdf/10.1073/pnas.1810842115 .
  * Wolgast  _et al._ [2013] S. Wolgast, i. m. c. b. u. i. e. i. f. Kurdak, K. Sun, J. W. Allen, D.-J. Kim, and Z. Fisk, Phys. Rev. B 88, 180405 (2013).
  * Syers  _et al._ [2015] P. Syers, D. Kim, M. S. Fuhrer, and J. Paglione, Phys. Rev. Lett. 114, 096601 (2015).
  * Eo  _et al._ [2019] Y. S. Eo, A. Rakoski, J. Lucien, D. Mihaliov, Ç. Kurdak, P. F. S. Rosa, and Z. Fisk, Proceedings of the National Academy of Sciences 116, 12638 (2019), https://www.pnas.org/doi/pdf/10.1073/pnas.1901245116 .
  * Meinert [2016] M. Meinert, Phys. Rev. Lett. 116, 137001 (2016).
  * Xiao  _et al._ [2010] D. Xiao, Y. Yao, W. Feng, J. Wen, W. Zhu, X.-Q. Chen, G. M. Stocks, and Z. Zhang, Phys. Rev. Lett. 105, 096404 (2010).
  * Clogston [1962] A. M. Clogston, Phys. Rev. Lett. 9, 266 (1962).
  * Helfand and Werthamer [1966] E. Helfand and N. R. Werthamer, Phys. Rev. 147, 288 (1966).
  * Fulde and Ferrell [1964] P. Fulde and R. A. Ferrell, Phys. Rev. 135, A550 (1964).
  * Larkin and Ovchinnikov [1964] A. I. Larkin and Y. N. Ovchinnikov, Zh. Eksperim. i Teor. Fiz. 47, 1136 (1964).
  * Werthamer  _et al._ [1966] N. R. Werthamer, E. Helfand, and P. C. Hohenberg, Phys. Rev. 147, 295 (1966).
  * Kogan and Prozorov [2012] V. G. Kogan and R. Prozorov, Reports on Progress in Physics 75, 114502 (2012).
  * Yonezawa  _et al._ [2017] S. Yonezawa, K. Tajiri, S. Nakata, Y. Nagai, Z. Wang, K. Segawa, Y. Ando, and Y. Maeno, Nature Physics 13, 123 (2017).
  * Cao  _et al._ [2021] Y. Cao, D. Rodan-Legrain, J. M. Park, N. F. Q. Yuan, K. Watanabe, T. Taniguchi, R. M. Fernandes, L. Fu, and P. Jarillo-Herrero, Science 372, 264 (2021), https://www.science.org/doi/pdf/10.1126/science.abc2836 .
  * Xiang  _et al._ [2021] Y. Xiang, Q. Li, Y. Li, W. Xie, H. Yang, Z. Wang, Y. Yao, and H.-H. Wen, Nature Communications 12, 6727 (2021).