  The emergence of superconductivity with doping from correlated insulators in
magic-angle twisted bilayer graphene (MATBG) has raised the intriguing
possibility that its pairing mechanism is distinct from that of conventional
superconductors, as described by the Bardeen-Cooper-Schrieffer (BCS) theory.
While there is now ample evidence for strong electronic correlations in MATBG,
recent studies have claimed that unlike correlated insulators,
superconductivity persists even when these interactions are partially screened.
This suggests that the pairing in MATBG might be conventional in nature, a
consequence of the large density of states of its nearly flat bands, perhaps
phonon-mediated as in BCS superconductors. Here we combine tunneling and
Andreev reflection spectroscopy with the scanning tunneling microscope (STM) to
observe several key experimental signatures for unconventional
superconductivity in MATBG. We show that the tunneling spectra below the
transition temperature $T_c$ are inconsistent with that of a conventional
s-wave superconductor, but rather resemble that of a nodal superconductor with
an anisotropic pairing mechanism. We observe a large discrepancy between the
tunneling energy gap $\Delta_T$, which far exceeds the mean-field BCS ratio
(with $2\Delta_T/k_BT_c \sim 25$) and the energy gap $\Delta_{AR}$ extracted
from Andreev reflection spectroscopy ($2\Delta_{AR}/k_BT_c \sim 6$). The
tunneling gap persists even when superconductivity is suppressed, indicating
its emergence from a pseudogap phase, with a suppressed density of states at
the Fermi level. Moreover, the pseudogap state and superconductivity are both
absent when MATBG is aligned with the hexagonal boron nitride (hBN) underneath.
These findings and other observations reported here provide a preponderance of
evidence for a non-BCS mechanism for superconductivity in MATBG.
