34 research outputs found

### Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle

We show that the Wannier obstruction and the fragile topology of the nearly
flat bands in twisted bilayer graphene at magic angle are manifestations of the
nontrivial topology of two-dimensional real wave functions characterized by the
Euler class. To prove this, we examine the generic band topology of two
dimensional real fermions in systems with space-time inversion $I_{ST}$
symmetry. The Euler class is an integer topological invariant classifying real
two band systems. We show that a two-band system with a nonzero Euler class
cannot have an $I_{ST}$-symmetric Wannier representation. Moreover, a two-band
system with the Euler class $e_{2}$ has band crossing points whose total
winding number is equal to $-2e_2$. Thus the conventional Nielsen-Ninomiya
theorem fails in systems with a nonzero Euler class. We propose that the
topological phase transition between two insulators carrying distinct Euler
classes can be described in terms of the pair creation and annihilation of
vortices accompanied by winding number changes across Dirac strings. When the
number of bands is bigger than two, there is a $Z_{2}$ topological invariant
classifying the band topology, that is, the second Stiefel Whitney class
($w_2$). Two bands with an even (odd) Euler class turn into a system with
$w_2=0$ ($w_2=1$) when additional trivial bands are added. Although the
nontrivial second Stiefel-Whitney class remains robust against adding trivial
bands, it does not impose a Wannier obstruction when the number of bands is
bigger than two. However, when the resulting multi-band system with the
nontrivial second Stiefel-Whitney class is supplemented by additional chiral
symmetry, a nontrivial second-order topology and the associated corner charges
are guaranteed.Comment: 23 pages, 13 figure

### Topological Circular Dichroism in Chiral Multifold Semimetals

Uncovering the physical contents of the nontrivial topology of quantum states
is a critical problem in condensed matter physics. Here, we study the
topological circular dichroism in chiral semimetals using linear response
theory and first-principles calculations. We show that, when the low-energy
spectrum respects emergent SO(3) rotational symmetry, topological circular
dichroism is forbidden for Weyl fermions, and thus is unique to chiral
multifold fermions. This is a result of the selection rule that is imposed by
the emergent symmetry under the combination of particle-hole conjugation and
spatial inversion. Using first-principles calculations, we predict that
topological circular dichroism occurs in CoSi for photon energy below about 0.2
eV. Our work demonstrates the existence of a response property of
unconventional fermions that is fundamentally different from the response of
Dirac and Weyl fermions, motivating further study to uncover other unique
responses.Comment: 6+7 pages, 4+4 figure

### Superconductivity-Induced Spectral Weight Transfer due to Quantum Geometry

Optical spectral weight transfer associated with the onset of
superconductivity at high energy scales compared with the superconducting gap
has been observed in several systems such as high-$T_c$ cuprates. While there
are still debates on the origin of this phenomenon, a consensus is that it is
due to strong correlation effects beyond the BCS theory. Here we show that
there is another route to a nonzero spectral weight transfer based on the
quantum geometry of the conduction band in multiband systems. We discuss
applying this idea to twisted multilayer graphene.Comment: 5 pages, 2 figure

### Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges

We study the band topology and the associated linking structure of
topological semimetals with nodal lines carrying $Z_{2}$ monopole charges,
which can be realized in three-dimensional systems invariant under the
combination of inversion $P$ and time reversal $T$ when spin-orbit coupling is
negligible. In contrast to the well-known $PT$-symmetric nodal lines protected
only by $\pi$ Berry phase in which a single nodal line can exist, the nodal
lines with $Z_{2}$ monopole charges should always exist in pairs. We show that
a pair of nodal lines with $Z_{2}$ monopole charges is created by a {\it double
band inversion} (DBI) process, and that the resulting nodal lines are always
{\it linked by another nodal line} formed between the two topmost occupied
bands. It is shown that both the linking structure and the $Z_{2}$ monopole
charge are the manifestation of the nontrivial band topology characterized by
the {\it second Stiefel-Whitney class}, which can be read off from the Wilson
loop spectrum. We show that the second Stiefel-Whitney class can serve as a
well-defined topological invariant of a $PT$-invariant two-dimensional (2D)
insulator in the absence of Berry phase. Based on this, we propose that pair
creation and annihilation of nodal lines with $Z_{2}$ monopole charges can
mediate a topological phase transition between a normal insulator and a
three-dimensional weak Stiefel-Whitney insulator (3D weak SWI). Moreover, using
first-principles calculations, we predict ABC-stacked graphdiyne as a nodal
line semimetal (NLSM) with $Z_{2}$ monopole charges having the linking
structure. Finally, we develop a formula for computing the second
Stiefel-Whitney class based on parity eigenvalues at inversion invariant
momenta, which is used to prove the quantized bulk magnetoelectric response of
NLSMs with $Z_2$ monopole charges under a $T$-breaking perturbation.Comment: 4+28 pages, 3+17 figure

### Two-dimensional higher-order topology in monolayer graphdiyne

Based on first-principles calculations and tight-binding model analysis, we
propose monolayer graphdiyne as a candidate material for a two-dimensional
higher-order topological insulator protected by inversion symmetry. Despite the
absence of chiral symmetry, the higher-order topology of monolayer graphdiyne
is manifested in the filling anomaly and charge accumulation at two corners.
Although its low energy band structure can be properly described by the
tight-binding Hamiltonian constructed by using only the $p_z$ orbital of each
atom, the corresponding bulk band topology is trivial. The nontrivial bulk
topology can be correctly captured only when the contribution from the core
levels derived from $p_{x,y}$ and $s$ orbitals are included, which is further
confirmed by the Wilson loop calculations. We also show that the higher-order
band topology of a monolayer graphdyine gives rise to the nontrivial band
topology of the corresponding three-dimensional material, ABC-stacked
graphdiyne, which hosts monopole nodal lines and hinge states.Comment: 19 pages, 4 figures, new titl

### Unconventional Topological Phase Transition in Two-Dimensional Systems with Space-Time Inversion Symmetry

We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z2 topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe/CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe/CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry. Â© 2017 American Physical Society1651sciescopu

### Unconventional Majorana fermions on the surface of topological superconductors protected by rotational symmetry

Topological superconductors are exotic gapped phases of matter hosting
Majorana mid-gap states on their boundary. In conventional topological
superconductors, Majorana in-gap states appear in the form of either localized
zero-dimensional modes or propagating spin-1/2 fermions with a
quasi-relativistic dispersion relation. Here we show that unconventional
propagating Majorana states can emerge on the surface of three-dimensional
topological superconductors protected by rotational symmetry. The
unconventional Majorana surface states fall into three different categories: a
spin-$S$ Majorana fermion with $(2S+1)$-fold degeneracy $(S\geq3/2)$, a
Majorana Fermi line carrying two distinct topological charges, and a quartet of
spin-1/2 Majorana fermions related by fourfold rotational symmetry. The
spectral properties of the first two kinds, which go beyond the conventional
spin-1/2 fermions, are unique to topological superconductors and have no
counterpart in topological insulators. We show that the unconventional Majorana
surface states can be obtained in the superconducting phase of doped $Z_2$
topological insulators or Dirac semimetals with rotational symmetry.Comment: 15+10 pages, 5 figures, Supplementary Note adde

### Higher-Order Topological Superconductivity of Spin-Polarized Fermions

We study the superconductivity of spin-polarized electrons in centrosymmetric
ferromagnetic metals. Due to the spin-polarization and the Fermi statistics of
electrons, the superconducting pairing function naturally has odd parity.
According to the parity formula proposed by Fu, Berg, and Sato, odd-parity
pairing leads to conventional first-order topological superconductivity when a
normal metal has an odd number of Fermi surfaces. Here, we derive generalized
parity formulae for the topological invariants characterizing higher-order
topology of centrosymmetric superconductors. Based on the formulae, we
systematically classify all possible band structures of ferromagnetic metals
that can induce inversion-protected higher-order topological superconductivity.
Among them, doped ferromagnetic nodal semimetals are identified as the most
promising normal state platform for higher-order topological superconductivity.
In two dimensions, we show that odd-parity pairing of doped Dirac semimetals
induces a second-order topological superconductor. In three dimensions,
odd-parity pairing of doped nodal line semimetals generates a nodal line
topological superconductor with monopole charges. On the other hand, odd-parity
pairing of doped monopole nodal line semimetals induces a three-dimensional
third-order topological superconductor. Our theory shows that the combination
of superconductivity and ferromagnetic nodal semimetals opens up a new avenue
for future topological quantum computations using Majorana zero modes.Comment: 6+13 pages, 2+1 figures; accepted versio