Tight-binding reduction and topological equivalence in strong magnetic fields
نویسندگان
چکیده
Topological insulators (TIs) are a class of materials which insulating in their bulk form yet, upon introduction an boundary or edge, e.g. by abruptly terminating the material, may exhibit spontaneous current along boundary. This property is quantified topological indices associated with either edge system. In field condensed matter physics, tight binding (discrete) approximate models, parametrized hopping coefficients, have been used successfully to capture behavior TIs many settings. However, whether such models same features as underlying continuum quantum physics has open question. We resolve this question context archetypal example materials, integer Hall effect. study Hamiltonians, Hλ, govern electron motion two-dimensional crystal under influence perpendicular magnetic field. No assumption made on translation invariance crystal. prove, regime where both strength and depth potential sufficiently large, λ≫1, that low-lying energy spectrum eigenstates (and corresponding large time dynamics) Hλ well-described scale-free discrete Hamiltonian, HTB; we show norm resolvent convergence. The relevant index conductivity, expressible Fredholm index. prove for λ HTB agree. proved separately geometries. Our results justify principle using matter.
منابع مشابه
Neutrinos in Strong Magnetic Fields
We compute the dispersion relations for neutrinos propagating in an electroweak plasma, in the presence of very strong magnetic fields. The neutrino self-energy is calculated in the one-loop approximation. We consider only contributions of the first Landau level to the propagator of the W -bosons, and distinguish between motion parallel or perpendicular to the external magnetic field. We find t...
متن کاملTopological Quantum Field Theory and Strong Shift Equivalence
Given a TQFT in dimension d + 1, and an infinite cyclic covering of a closed (d + 1)-dimensional manifold M , we define an invariant taking values in a strong shift equivalence class of matrices. The notion of strong shift equivalence originated in R. Williams’ work in symbolic dynamics. The Turaev-Viro module associated to a TQFT and an infinite cyclic covering is then given by the Jordan form...
متن کاملPlasma dynamics in pulsed strong magnetic fields
Recent investigations of the interaction of fast-rising magnetic fields with multi-species plasmas at densities of 10– 10 cm are described. The configurations studied are planar or coaxial interelectrode gaps pre-filled with plasmas, known as plasma opening switches. The diagnostics are based on time-dependent, spatially resolved spectroscopic observations. Three-dimensional spatial resolution ...
متن کاملElectromagnetic Shocks in Strong Magnetic Fields
The nonlinear properties of electromagnetic waves traveling through a magnetized vacuum is of particular interest in the study of neutron stars. Heisenberg and Euler [1] and Weisskopf [2] first derived nonlinear corrections to the Maxwell equations of the electromagnetic field. Lutzky and Toll [3] and Zheleznyakov and Fabrikant [4] applied the weak-field expansion to show that shock waves can d...
متن کاملPhysics in Ultra-strong Magnetic Fields
In magnetic fields stronger than BQ ≡ m 2 ec /h̄e = 4.4 × 10 Gauss, an electron’s Landau excitation energy exceeds its rest energy. I review the physics of this strange regime and some of its implications for the crusts and magnetospheres of neutron stars. In particular, I describe how ultra-strong fields • render the vacuum birefringent and capable of distorting and magnifying images (“magnetic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2022
ISSN: ['1857-8365', '1857-8438']
DOI: https://doi.org/10.1016/j.aim.2022.108343