Related papers: Tensor Berry connections and their topological inv…
The picture of how a gap closes in a semiconductor has been radically transformed by topological concepts. Instead of the gap closing and immediately re-opening, topological arguments predict that, in the absence of inversion symmetry, a…
We show that topological transitions in electronic spin transport are feasible by a controlled manipulation of spin-guiding fields. The transitions are determined by the topology of the fields texture through an effective Berry phase…
The linear positive magnetoresistance (LPMR) is a widely observed phenomenon in topological materials, which is promising for potential applications on topological spintronics. However, its mechanism remains ambiguous yet and the effect is…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
In these notes, we review the role of Berry phases and topology in noninteracting electron systems. Topics including the adiabatic theorem, parallel transport, and Wannier functions are reviewed, with a focus on the connection to…
We study the response of quantum many-body systems to coupling some of their degrees of freedom to external gauge fields. This serves to understand the current Green functions and transport properties of interacting many-body systems. Our…
Topological effects arising from the Berry curvature lead to intriguing transport signatures in quantum materials. Two such phenomena are the chiral anomaly and nonlinear Hall effect (NLHE). A unified description of these transport regimes…
We introduce a quantum geometric tensor in a curved space with a parameter-dependent metric, which contains the quantum metric tensor as the symmetric part and the Berry curvature corresponding to the antisymmetric part. This…
We present an in-depth analysis of the orbital magnetism by means of the so-called modern theory based on the Berry phase across distinct classes of materials-d transition metals, sp metals, and transition metal dichalcogenides-highlighting…
The phase diagram of the Bose-Fermi Kondo model contains an SU(2)-invariant Kondo-screened phase separated by a continuous quantum phase transition from a Kondo-destroyed local moment phase. We analyze the effect of the Berry phase term of…
Thermoelectric transport coefficients up to linear order in the applied magnetic field are microscopically studied using Kubo-Luttinger linear response theory and thermal Green's functions. We derive exact formulas for the thermoelectric…
The rigid rotor is a classic problem in quantum mechanics, describing the dynamics of a rigid body with its centre of mass held fixed. The configuration space of this problem is $SO(3)$, the space of all rotations in three dimensions. This…
In this paper, we extend the quantum geometric tensor for parameter-dependent curved spaces to higher dimensions, and introduce an equivalent definition that generalizes the Zanardi, et al, formulation of the tensor. The parameter-dependent…
Berry phase plays an important role in determining many physical properties of quantum systems. However, a Berry phase altering energy spectrum of a quantum system is comparatively rare. Here, we report an unusual tunable valley polarized…
We study the phases of the SU(N1)X SU(N2) gauge theory with a bi-fundamental fermion in 3+1 dimensions. We show that the discrete anomalies and Berry phases associated to the one-form symmetry of the theory allow for several topologically…
Bose gas on a two-leg ladder exhibits an interesting topological phase. We show the presence of a bosonic symmetry-protected-topological (SPT) phase protected by $Z_2\times Z_2$ symmetry. This symmetry leads to $Z_4$ fractional quantization…
The semiclassical quantization of cyclotron orbits for two-dimensional Bloch electrons in a coupled two band model with a particle-hole symmetric spectrum is considered. As concrete examples, we study graphene (both mono and bilayer) and…
We investigate the bulk-boundary correspondence for massless Dirac fermion in $\alpha$-${T}_3$ lattice where the Berry phase can be continuously tuned from $\pi $ (graphene) to $0$ ($T_3$ or dice lattice) without modifying the energy…
We present an extension of Landau's theory of phase transitions by incorporating the topology of the order parameter. When the order parameter comprises several components arising from multiplicity in the same irreducible representation of…
We study the quantum nonlinear Hall effect in two-dimensional materials with time-reversal symmetry. When only one mirror line exists, a transverse charge current occurs in second-order response to an external electric field, as a result of…