Related Experiment Video
Updated: May 11, 2026
10:28
Probing the Structure and Dynamics of Interfacial Water with Scanning Tunneling Microscopy and Spectroscopy
Published on: May 27, 2018
Tamm-Hubbard surface states in the continuum
1Dipartimento di Fisica, Politecnico di Milano and Istituto di Fotonica e Nanotecnologie del Consiglio Nazionale delle Ricerche, Milano, Italy. longhi@fisi.polimi.it
Summary
Two-particle surface bound states, or Tamm-Hubbard bound states embedded in the continuum (BIC), emerge at lattice edges. These thresholdless states require specific attractive/repulsive impurity and Hubbard interactions (UV < 0).
Area of Science:
- Condensed matter physics
- Quantum mechanics
Background:
- The Bose-Hubbard model describes interacting bosons on a lattice.
- Bound states embedded in the continuum (BIC) are exotic quantum states.
- Surface states at lattice edges are crucial for material properties.
Purpose of the Study:
- To investigate the existence of two-particle surface bound states embedded in the continuum (BIC) in a 1D lattice.
- To analyze the conditions for sustaining these Tamm-Hubbard BIC states.
- To explore the role of impurity potential and Hubbard interaction.
Main Methods:
- Utilizing the Bose-Hubbard model framework.
- Analyzing a semi-infinite one-dimensional tight-binding lattice.
- Investigating surface phenomena at the lattice boundary with impurity potential.
Main Results:
- Demonstrated the possibility of sustaining two-particle surface bound states (BIC) at the lattice edge.
- Showed that these Tamm-Hubbard BIC states exist for any infinitesimally-small impurity potential V.
- Identified the condition UV < 0 for the existence of these states, where U is the Hubbard interaction and V is the impurity potential.
Conclusions:
- Thresholdless Tamm-Hubbard BIC states can be realized at the edge of a 1D lattice.
- The interplay between impurity potential and Hubbard interaction governs the formation of these surface states.
- This finding opens avenues for controlling quantum states at material surfaces.
Related Concept Videos
01:12Fermi Level Dynamics
The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
01:16Equipotential Surfaces and Conductors
For a conductor in which all charges are at rest, the conductor's surface is equipotential. The electric field is always perpendicular to equipotential surfaces. Therefore, in a conductor with static charges, the electric field just outside the conductor is always perpendicular to the conductor's surface. Any tangential component of the electric field will cause charges to move inside the conductor, which will violate the electrostatic nature of the system. In an electrostatic situation, if a...
01:29Equipotential Surfaces and Field Lines
Electric potential can be pictorially represented as a three-dimensional surface. On such a surface, the electric potential is constant everywhere. The equipotential surface is always perpendicular to the electric field lines, and while it is three-dimensional, it can be treated as an equipotential line in a two-dimensional case. These equipotential lines are also always perpendicular to electric field lines. The term equipotential is often used as a noun, referring to an equipotential line or...
01:20Region of Convergence of Laplace Tarnsform
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This substitution...
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This substitution...
02:42Valence Bond Theory
Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
01:18Fermi Level
The Fermi-Dirac function is represented by an S-shaped curve indicating the probability of an energy state being occupied by an electron at a given temperature. The Fermi level is the energy level at which there is a fifty percent chance of finding an electron, and it is positioned between the lower-energy valence band and the higher-energy conduction band.
At absolute zero temperature, electrons fill all energy states up to the Fermi level, leaving upper states empty. As the temperature rises,...
At absolute zero temperature, electrons fill all energy states up to the Fermi level, leaving upper states empty. As the temperature rises,...