Solid State Physics-1 by Branislav K. Nikolic book free download

PHYS 624: Introduction to Solid State Physics

COURSE CONTENTS:

Condensed Matter Systems

v Hard Matter

· Crystalline Solids (Metals, Insulators, Semiconductors)

· Non-Crystalline Solids

· Quasicrystals

· Amorphous Solids (Glass)

· Polymer Solids (Glass and Rubber)

· Crystalline Solids +Defects

· (point, dislocations, surfaces, and interfaces)

· Soft Matter

· Colloidal Dispersions

· Polymer Melts and Solutions

· Liquid Crystals

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· Biomatter (proteins, membranes, nucleic acids)

Basic Notions of Condensed Matter:

vQuasiparticles excitations which look nearly as individual particles as possible - modern

condensed matter theory asserts that a solid crystal is actually a gas of weakly interacting quasiparticles.

broken symmetry, long-range order, and order parameters

Phases of the matter are characterized by the symmetry of their ground (lowest energy) state (Landau, 1937).

Experimental Probes of Condensed Matter Phases and Quasiparticle Dynamics:

· Scattering: Send neutrons or X-rays into the system with prescribed energy and momentum; measure the energy and momentum of the outgoing neutrons or X-rays.

· NMR: Apply static magnetic field B and measure absorption and emission of magnetic radiation at frequencies of the order of wc= geB/m.

· Thermodynamics: Measure the response of macroscopic variables (energy, volume, etc.) to variations of the temperature, pressure, etc.

· Transport: Set up a potential Ñj or thermal gradient ÑT and measure the electrical or heat current. The gradients can be held constant or made to oscillate at finite frequency.

Quantum Hamiltonian of Condensed Matter Physics:

“The general theory of quantum mechanics is now almost complete. The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.”

Complexity in Solid State Hamiltonian:

Even for chemists, the task of solving the Schrödinger equation for modest multielectron atoms proves insurmountable without bold approximations.

Exchange-Correlation Hole:

Surrounding every electron in a solid there's an exclusion zone, called the exchange-correlation hole, into which other electrons rarely venture. This is the hole around an electron near the Centre of a bond in silicon.

Breaking the Symmetry:

QUESTION: In QM we learn that the ground state must have the symmetry of the Hamiltonian - so there can't be a dipole moment (interactions between ions and electrons have no preferred direction in space). On the other hand, the ammonia molecule obviously has a dipole moment?

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RESOLUTION: The ammonia molecule the ground state is a superposition of states, to recover the symmetry of the Hamiltonian. However, at short time-scale molecule can be trapped in one of the states (due to large the potential barrier for tunneling between the states), and we measure non-zero dipole moment.

QUESTION: What about larger molecules (> 10 atoms) that have definite three-dimensional structures that break the symmetry of the Hamiltonian?

RESOLUTION: We cannot understand the structure of molecules

starting from Quantum Mechanics of elementary particles - we need

additional theoretical ideas (emergent phenomena)!

Broken Symmetries and Phases of Matter:

· Phases of the matter often exhibit much less symmetry than underlying microscopic equations.

· Example: Water exhibits full translational and rotational symmetry of Newton’s or Schrödinger’s equations; Ice, however, is only invariant under the discrete translational and rotational group of its crystal lattice the translational and rotational symmetry of the microscopic equations have been spontaneously broken!

· Order Parameter Paradigm (L. D. Landau, 1940s): Development of phases in a material can be described by the emergence of an "order the parameter “(which fluctuates strongly at the critical point):

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