关注：

1) 绝缘体、导体、半导体的能带理论解释、费米能级

2) 绝缘体的种类：Mott-Hubbard insulator and charge-transfer insulator，Topological insulator

3) 超导体的种类

对于金属，绝对零度下，电子占据的最高能级就是费米能级。

对于绝缘体和半导体，Fermi能级则处于禁带中间。特别是本征半导体和绝缘体，因为它们的价带是填满了价电子（占据几率为100%）、导带是完全空着的（占据几率为0%），则它们的Fermi能级正好位于禁带中央（占据几率为50%）。即使温度升高时，本征激发而产生出了电子-空穴对，但由于导带中增加的电子数等于价带中减少的电子数，则禁带中央的能级仍然是占据几率为50%，所以本征半导体的Fermi能级的位置不随温度而变化，始终位于禁带中央。

②ermi能级实际上起到了衡量能级被电子占据的几率大小的一个标准的作用。在E<EF时，f(E) >1/2；在E>EF时，f(E) <1/2；在E=EF时，f(E)=1/2。譬如，当(E–EF) >5kT时，f(E) < 0.007，即比EF高5kT的能级被电子占据的几率只有0.7%。因此，EF的高低（位置）就反映了能带中的某个能级是否被电子所占据的情况。Fermi能级上电子占据的几率刚好为50%。

• Mott insulator, a type of electrical insulator

• Topological insulator, a material that behaves as an insulator in its interior while permitting the movement of charges on its boundary

Mott insulator ·Semiconductor ·Semimetal ·Conductor ·Superconductor

摘录学习：

http://baike.baidu.com/link?url=okrGFdVk2vgaaRi_JImPU9MvUE11L1NbpenHoW3k7UgFQpfPIxfhSvyzO57MZdNgETe4gvFoX-zlo4qcvv7wezCxd3Ic6UjtJYrv8RE7d1VuvBhpo5KC6y_naSyDrsWI

绝缘材料中通常只有微量的自由电子，在未被击穿前参加导电的带电粒子主要是由热运动而离解出来的本征离子和杂质粒子。绝缘体的电学性质反映在电导、极化、损耗和击穿等过程中。

导电

     绝缘体是不存在电导的物质。电子能带理论指出，固体中的电子仅允许存在于一定的能量状态，这些能量状态形成彼此分离的能带。电子趋向于先占据能量最低的能带，在绝对零度能够被填满的能量最高的能带叫做价带，价带之上的能带叫做导带，价带和导带之间的空隙叫做能隙。

    在绝对零度以上，价带电子部分被激发而跃迁至导带，成为导带电子，并在价带留下空穴。根据能带理论，被电子填满的能带或空的能带对电导没有贡献，电导仅来源于半满的能带，导带电子和价带空穴合称载流子。金属的导带被部分填充，因而有好的电导。对于半导体和绝缘体，在绝度零度下价带被填满，而导带没有电子。在常温下，半导体由于能隙较小，可以通过热激发而形成电子空穴对，因而具有一定的电导。相反，绝大多数绝缘体通常具有非常大的带隙宽度，价带电子很难被激发至导带，因此绝缘体的载流子浓度极低，相应地电导也极低，或者说这种材料绝缘。
　　对于绝缘体，总存在一个击穿电压，这个电压能给予价带电子足够的能量，将其激发到导带。一旦超过了击穿电压，这种材料就不再绝缘了。然而，击穿通常伴随着破坏材料绝缘性的物理或化学变化。
　　以上讨论仅涉及电子导电。除了不存在电子导电，绝缘体中也不能有其他移动电荷带来的电导。例如，如果液体或气体中有离子存在，离子可以定向移动形成电流，因而这种材料是导体。电解液或等离子体都是导体，不管有没有电子的流动存在。

击穿

莫特绝缘体是像NiO、CoO、MnO等过渡金属简单氧化物，一个晶胞中具有奇数个价电子，按照能带理论应当有良好的导电性，而实验表明却是透明的绝缘体

Peierls与Mott认为问题在于电子之间相互作用引起的关联效应。这些氧化物后来被称为Mott绝缘体。以CoO为例，当电流通过时依赖于形成可以移动的组态Co3+与Co+，而在位关联能则可以阻止其形成。^[1]

费米能级

http://baike.baidu.com/item/%E8%B4%B9%E7%B1%B3%E8%83%BD%E7%BA%A7

现在假想 把所有的费米子 从这些量子态上移开。之后再把这些费米子按照一定的规则（例如泡利原理等）填充在各个可供占据的量子能态上，并且这种填充过程中每个费米子都占据 最低的可供占据的量子态。最后一个费米子占据着的量子态 即可粗略理解为费米能级。 虽然严格来说，费米能级等于费米子系统在趋于绝对零度时的化学势；但是在半导体物理和电子学领域中，费米能级则经常被当做电子或空穴化学势的代名词。

一般来说，“费米能级"这个术语所代表的含义可以从上下语境中判断。

对于金属，绝对零度下，电子占据的最高能级就是费米能级。

对于绝缘体和半导体，Fermi能级则处于禁带中间。特别是本征半导体和绝缘体，因为它们的价带是填满了价电子（占据几率为100%）、导带是完全空着的（占据几率为0%），则它们的Fermi能级正好位于禁带中央（占据几率为50%）。即使温度升高时，本征激发而产生出了电子-空穴对，但由于导带中增加的电子数等于价带中减少的电子数，则禁带中央的能级仍然是占据几率为50%，所以本征半导体的Fermi能级的位置不随温度而变化，始终位于禁带中央。

https://en.wikipedia.org/wiki/Mott_insulator

Mott insulators are a class of materials that should conductelectricity under conventional band theories, but are insulators when measured (particularly at low temperatures). This effect is due to electron–electron interactions, which are not considered in conventional band theory.

The bandgap in a Mott insulator exists between bands of like character, such as 3d character, whereas the bandgap in charge transfer insulators exists between anion and cation states,^[1] such as between O 2p and Ni 3d bands in NiO. ^[2]

Although the band theory of solids had been very successful in describing various electrical properties of materials, in 1937 Jan Hendrik de Boer and Evert Johannes Willem Verwey pointed out that a variety of transition metal oxides predicted to be conductors by band theory (because they have an odd number of electrons per unit cell) are insulators.^[3]Nevill Mott and Rudolf Peierls then (also in 1937) predicted that this anomaly can be explained by including interactions between electrons.^[4]

In 1949, in particular, Mott proposed a model for NiO as an insulator, where conduction is based on the formula^[5]

In this situation, the formation of an energy gap preventing conduction can be understood as the competition between the Coulomb potentialU between 3d electrons and the transfer integral t of 3d electrons between neighboring atoms (the transfer integral is a part of the tight-binding approximation). The total energy gap is then

where z is the number of nearest-neighbor atoms.

In general, Mott insulators occur when the repulsive Coulomb potential U is large enough to create an energy gap. One of the simplest theories of Mott insulators is the 1963 Hubbard model. The crossover from a metal to a Mott insulator as U is increased can be predicted within the so-called dynamical mean field theory.

Mottism denotes the additional ingredient, aside from antiferromagnetic ordering, which is necessary to fully describe a Mott Insulator. In other words, we might write

Thus, mottism accounts for all of the properties of Mott insulators that cannot be attributed simply to antiferromagnetism.

There are a number of properties of Mott insulators, derived from both experimental and theoretical observations, which cannot be attributed to antiferromagnetic ordering and thus constitute mottism. These properties include

• Spectral weight transfer on the Mott scale ^[6][7]

• Vanishing of the single particle Green function along a connected surface in momentum space in the first Brillouin zone^[8]

• Two sign changes of the Hall coefficient as electron doping goes from n=0{displaystyle n=0} to n=2{displaystyle n=2} (band insulators have only one sign change at n=1{displaystyle n=1})

• The presence of a charge 2e{displaystyle 2e} (with e<0{displaystyle e<0} the charge of an electron) boson at low energies ^[9][10]

• A pseudogap away from half-filling (n=1{displaystyle n=1}) ^[11]

Mott insulators are of growing interest in advanced physics research, and are not yet fully understood. They have applications in thin-filmmagneticheterostructures and high-temperature superconductivity, for example.^[12]

This kind of insulator can become a conductor by changing some parameters, which may be composition, pressure, strain, voltage, or magnetic field. The effect is known as a Mott transition and can be used to build smaller field-effect transistors, switches and memory devices than possible with conventional materials.^[13][14][15]