Flat band localization due to self-localized orbital

doi:10.1007/s11467-023-1306-2

Front. Phys.

2023, Vol. 18

Issue (6) : 63302 https://doi.org/10.1007/s11467-023-1306-2

RESEARCH ARTICLE

Flat band localization due to self-localized orbital

Zhen Ma¹, Wei-Jin Chen², Yuntian Chen²(

), Jin-Hua Gao¹(

), X. C. Xie^3,^4,⁵

¹. School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
². School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China
³. International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
⁴. Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
⁵. CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China

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Abstract

We discover a new wave localization mechanism in a periodic wave system, which can produce a novel type of flat band and is distinct from the known localization mechanisms, i.e., Anderson localization and flat band lattices. The first example we give is a designed electron waveguide (EWG) on 2DEG with special periodic confinement potential. Numerical calculations show that, with proper confinement geometry, electrons can be completely localized in an open waveguide. We interpret this flat band localization (FBL) phenomenon by introducing the concept of self-localized orbitals. Essentially, each unit cell of the waveguide is equivalent to an artificial atom, where the self-localized orbital is a special eigenstate with unique spatial distribution. These self-localized orbitals form the flat bands in the waveguide. Such self-localized orbital induced FBL is a general phenomenon of wave motion, which can arise in any wave systems with carefully engineered boundary conditions. We then design a metallic waveguide (MWG) array to illustrate that similar FBL can be readily realized and observed with electromagnetic waves.

Keywords flat band localization self-localized orbital electron waveguide

Corresponding Author(s): Yuntian Chen,Jin-Hua Gao

About author:

* Both are co-first authors.

Issue Date: 16 June 2023

Cite this article:

Zhen Ma,Wei-Jin Chen,Yuntian Chen, et al. Flat band localization due to self-localized orbital[J]. Front. Phys. , 2023, 18(6): 63302.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1306-2
https://academic.hep.com.cn/fop/EN/Y2023/V18/I6/63302

Fig.1 (a) Schematic of the electron waveguide (EWG) on 2DEG. The electrons are confined in a dark-colored region, and the dashed box indicates a unit cell of the waveguide. (b) One example of

U (r)

in one unit cell.

U (r)

is zero inside the waveguide (the gray region) and infinite outside. Here,

d

= 52 nm,

h

= 14 nm,

l

= 26 nm. The corresponding band structure is given in (d). (c) is the

| ? k (r) | 2

of the flat band (upper one) at the

Γ

(k = 0) point, marked as black dot in (d). (e) and (g) are two other EWGs, where

U (r)

are of different shapes, and the corresponding band structures are given in (f) and (h), respectively.

| ? k (r) | 2

of the flat band at the marked k point (black dot) are also plotted in (e) and (f). The geometry parameters for (e) and (f) are given in the Electronic Supplementary Materials.

Fig.2 (a)

U (r)

of an isolated artificial atom (or quantum dot). The geometry parameters are the same as Fig.1(b).

U (r)

is zero inside the atom (gray region) and infinite outside. (b) and (c) are the wave functions

| ? (r) | 2

of the fourth and sixth orbitals (eigenstates) in the isolated atom, respectively. (d) is the wave function

| ? k (r) | 2

of the sixth band (upper flat band) at

Γ

point (

k = 0

) for the EWG in Fig.1(d), while (e) is that of the fourth band (dispersive). We plot one unit cell in (d) but two unit cells in (e) in order to show the bond between two adjacent orbitals.

Fig.3 (a) Schematic of the metallic waveguide array, where the shape of the cross section of one unit cell in x?y plane is given in (b). In (b), the geometry of each unit cell is determined by d, l, h, where d is the lattice constant, h is the height between the bottom and the lowest upper surface, l is the hight of the bump of the upper surface. The electromagnetic wave propagate along z-axis, and can leak from one waveguide to the neighbouring waveguide in the x?y plane; three different waveguide arrays, i.e., labelled as w1, w2, w3, are examined, see the mode profiles (

E z

) in (c, e, g) and the band diagram in (d, f, h) for w1, w2, w3. The geomentric parameters for w1, w2, w3 are given by as follows,

d / l / h

= 16/8/5 cm for w1,

d / l / h

=16/8/9.2 cm for w2,

d / l / h

= 16/8/11.2 cm for w3.

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