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Topological symmetries, invertible and otherwise, play a fundamental role in the investigation of quantum field theories. Despite their ubiquitous importance across a multitude of disciplines ranging from string theory to condensed matter…
Topological matter is a trending topic in condensed matter: From a fundamental point of view it has introduced new phenomena and tools, and for technological applications, it holds the promise of basic stable quantum computing. Similarly,…
Quantum anomalies arise when symmetries of a classical theory cannot be preserved upon quantization, leading to unconventional topological responses. A prominent example is the parity anomaly of a single two-dimensional Dirac fermion, which…
Two quintessential ingredients governing the topological invariant of a system are the dimensionality and the symmetry of the system. Due to the recent development of thin film and artificial superstructure growth technique, it is possible…
Quantum simulation is making a significant impact on scientific research. The prevailing tendency of the field is to build quantum simulators that get closer to real-world systems of interest, in particular electronic materials. However,…
Realizing the topological bands of helical states poses a challenge in studying ultracold atomic gases. Motivated by the recent experimental success in realizing chiral optical ladders, here we present a scheme for synthesizing topological…
Atomically thin topological materials are attracting growing attention for their potential to radically transform classical and quantum electronic device concepts. Amongst them is the quantum spin Hall (QSH) insulator - a two-dimensional…
High-dimensional quantum information processing has become a mature field of research with several different approaches being adopted for the encoding of $D$-dimensional quantum systems. Such progress has fueled the search of reliable…
This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have recently been explored in a range of different…
One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems,…
Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here we discuss possible extensions of this concept to density matrices describing statistical…
The properties of topological systems are inherently tied to their dimensionality. Higher-dimensional physical systems exhibit topological properties not shared by their lower dimensional counterparts and, in general, offer richer physics.…
A concrete strategy is presented for generating strong topological insulators in $d+d'$ dimensions which have quantized physics in $d$ dimensions. Here, $d$ counts the physical and $d'$ the virtual dimensions. It consists of seeking…
The discovery of the quantum Hall effect in 2D systems opens the door to topological phases of matter. A quantum Hall effect in 3D is a long-sought phase of matter and has inspired many efforts and claims. In the perspective, we review our…
In recent years, various classes of systems were proposed to realize topological states of matter. One of them are multiterminal Josephson junctions where topological Andreev bound states are constructed in the synthetic space of…
The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past thirty years, has generated many groundbreaking new ideas and concepts. Very early on it was realized that the zoo of…
Identifying novel topological properties of topological quantum states of matter, such as exemplified by the quantized Hall conductance, is a valuable step towards realizing materials with attractive topological attributes that guarantee…
The quantum Hall effect in a 2D electron system expresses a topological invariant, leading to a quantized conductivity. The thermal Hall and thermoelectric Nernst conductances in two dimensions are also reported to be quantized in specific…
We investigate topology-changing processes in 4-dimensional quantum gravity with a negative cosmological constant. By playing the ``gluing-polytope game" in hyperbolic geometry, we explicitly construct an instanton-like solution without…
Quantum spin Hall insulators, or synonymously known as 2D topological insulators, are crucial 2D systems hosting topologically protected edge states. The working temperature of this topological quantum phase is dictated by the inverted…